Finite Group Databasebeta

← #17197696

Subgroups — #17197696

Order 4352.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763370C211yesmaximal, characteristic
2#14531939C211yesmaximal, characteristic, complemented
3#14531939C211yesmaximal, characteristic, complemented
4#14531928C211yesmaximal, characteristic, complemented
5#14531924C211yesmaximal, characteristic, complemented
6#14531915C211yesmaximal, characteristic, complemented
7#14531824C211yesmaximal, characteristic, complemented
8#14531821C211yesmaximal, characteristic, complemented
9#14531783C211yesmaximal, characteristic, complemented
10#14531781C211yesmaximal, characteristic, complemented
11#14531771C211yesmaximal, characteristic, complemented
12#14531769C211yesmaximal, characteristic, complemented
13#14531762C211yesmaximal, characteristic, complemented
14#14531632C211yesmaximal, characteristic, complemented
15#14531632C211yesmaximal, characteristic, complemented
16C22⋊C4×D68C211yesmaximal, characteristic, complemented
17#14531604C211yesmaximal, characteristic, complemented
18#14531578C211yesmaximal, characteristic, complemented
19#14531547C211yesmaximal, characteristic, complemented
20#14531544C211yesmaximal, characteristic, complemented
21#14531476C211yesmaximal, characteristic, complemented
22#14531472C211yesmaximal, characteristic, complemented
23#14531446C211yesmaximal, characteristic, complemented
24#14531443C211yesmaximal, characteristic, complemented
25#14531440C211yesmaximal, characteristic, complemented
26#14531437C211yesmaximal, characteristic, complemented
27#14531363C211yesmaximal, characteristic, complemented
28C4×#10587568C211yesmaximal, characteristic, complemented
29#14531285C211yesmaximal, characteristic, complemented
30D17×#386C211yesmaximal, characteristic, complemented
31C17×#2335C211yesmaximal, characteristic, complemented
32C23×D68C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic, complemented
35#11763370C4116yescomplemented
36C2×#10587580C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587581C2211yescharacteristic
40C2×#10587581C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587568C2211yescharacteristic
45C2×#10587568C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×C4×D68C2211yescharacteristic
48C2×C4×D68C2211yescharacteristic
49C2×C4×D68C2211yescharacteristic, complemented
50C2×#10587579C2211yescharacteristic
51C2×#10587579C2211yescharacteristic
52C2×#10587579C2211yescharacteristic, complemented
53C2×C4×C22⋊D17C2211yescharacteristic, complemented
54C2×#10587567C2211yescharacteristic, complemented
55C2×#10587578C2211yescharacteristic, complemented
56C2×#10587578C2211yescharacteristic, complemented
57C2×#10587578C2211yescharacteristic, complemented
58C2×#10587558C2211yescharacteristic, complemented
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C2×C22⋊C4×D17C2211yescharacteristic, complemented
63C2×C22⋊C4×D17C2211yescharacteristic, complemented
64C2×C22⋊C4×D17C2211yescharacteristic, complemented
65#11762712C2211yescharacteristic
66#11762711C2211yescharacteristic, complemented
67#11762711C2211yescharacteristic, complemented
68#11762711C2211yescharacteristic, complemented
69#11762711C2211yescharacteristic, complemented
70#11762710C2211yescharacteristic, complemented
71#11762710C2211yescharacteristic, complemented
72#11762710C2211yescharacteristic, complemented
73#11762710C2211yescharacteristic, complemented
74#11762709C2211yescharacteristic
75#11762709C2211yescharacteristic
76#11762709C2211yescharacteristic, complemented
77#11762709C2211yescharacteristic, complemented
78#11762709C2211yescharacteristic, complemented
79#11762709C2211yescharacteristic, complemented
80#11762708C2211yescharacteristic, complemented
81#11762706C2211yescharacteristic, complemented
82#11762704C2211yescharacteristic, complemented
83#11762703C2211yescharacteristic, complemented
84#11762703C2211yescharacteristic, complemented
85#11762702C2211yescharacteristic, complemented
86#11762702C2211yescharacteristic, complemented
87#11762702C2211yescharacteristic, complemented
88#11762702C2211yescharacteristic, complemented
89#11762701C2211yescharacteristic, complemented
90#11762701C2211yescharacteristic, complemented
91#11762701C2211yescharacteristic, complemented
92#11762700C2211yescharacteristic, complemented
93#11762700C2211yescharacteristic, complemented
94#11762700C2211yescharacteristic, complemented
95#11762699C2211yescharacteristic, complemented
96#11762699C2211yescharacteristic, complemented
97#11762699C2211yescharacteristic, complemented
98#11762698C2211yescharacteristic, complemented
99#11762698C2211yescharacteristic, complemented
100#11762698C2211yescharacteristic, complemented
101#11762697C2211yescharacteristic, complemented
102#11762697C2211yescharacteristic, complemented
103#11762696C2211yescharacteristic, complemented
104#11762695C2211yescharacteristic, complemented
105#11762695C2211yescharacteristic, complemented
106#11762693C2211yescharacteristic, complemented
107#11762691C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762689C2211yescharacteristic
110#11762688C2211yescharacteristic, complemented
111#11762688C2211yescharacteristic, complemented
112#11762687C2211yescharacteristic
113#11762687C2211yescharacteristic
114#11762687C2211yescharacteristic
115#11762687C2211yescharacteristic
116#11762687C2211yescharacteristic, complemented
117#11762687C2211yescharacteristic, complemented
118#11762687C2211yescharacteristic, complemented
119#11762687C2211yescharacteristic, complemented
120#11762687C2211yescharacteristic, complemented
121#11762687C2211yescharacteristic, complemented
122#11762687C2211yescharacteristic, complemented
123#11762687C2211yescharacteristic, complemented
124#11762687C2211yescharacteristic, complemented
125#11762687C2211yescharacteristic, complemented
126#11762686C2211yescharacteristic, complemented
127#11762686C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic, complemented
131#11762685C2211yescharacteristic, complemented
132#11762684C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762683C2211yescharacteristic, complemented
135#11762683C2211yescharacteristic, complemented
136#11762683C2211yescharacteristic, complemented
137#11762683C2211yescharacteristic, complemented
138#11762680C2211yescharacteristic, complemented
139#11762680C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic, complemented
141#11762680C2211yescharacteristic, complemented
142#11762680C2211yescharacteristic, complemented
143#11762671C2211yescharacteristic, complemented
144#11762671C2211yescharacteristic, complemented
145#11762669C2211yescharacteristic, complemented
146#11762668C2211yescharacteristic, complemented
147#11762668C2211yescharacteristic, complemented
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150#11762664C2211yescharacteristic, complemented
151#11762664C2211yescharacteristic, complemented
152#11762664C2211yescharacteristic, complemented
153#11762664C2211yescharacteristic, complemented
154C4⋊C4×Dic17C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C4×#63227C2211yescharacteristic, complemented
159C4×#63227C2211yescharacteristic, complemented
160C4×#63227C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×#63227C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#389C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#387C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C17×#380C2211yescharacteristic, complemented
185C4×C4⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C2×D4×D17—42no—
200C2×D4×D17—42no—
201C2×D4×D17C2×C418yescomplemented
202C22×D68—42no—
203C22×D68—42no—
204C22×D68C2×C418yescomplemented
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×D68C2311yescharacteristic
212C22×C4×D17—42no—
213C22×C4×D17—42no—
214C22×C4×D17—42no—
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C17×#123C2×C418yescomplemented
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248C2×C42×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259#10587623C2×C418yescomplemented
260#10587615C2×C418yescomplemented
261C4×C22⋊D17—42no—
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324#10587581C2×C418yescomplemented
325#10587581C2×C418yescomplemented
326#10587580C2×C418yescomplemented
327#10587580C2×C418yescomplemented
328#10587579—42no—
329#10587579—42no—
330#10587579—42no—
331#10587578—42no—
332#10587578—42no—
333#10587578—42no—
334#10587570C2×C418yescomplemented
335#10587570C2×C418yescomplemented
336#10587568C2×C418yescomplemented
337#10587568C2×C418yescomplemented
338#10587568C2×C418yescomplemented
339#10587567—42no—
340C22⋊C4×D17—42no—
341C22⋊C4×D17—42no—
342C22⋊C4×D17—42no—
343C22⋊C4×D17—42no—
344C22⋊C4×D17—42no—
345C22⋊C4×D17C2×C418yescomplemented
346C4×D68—42no—
347C4×D68—42no—
348C4×D68—42no—
349#10587558—42no—
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382C24×C17C2411yescharacteristic
383C24×C17C2411yescharacteristic
384C23×D17—22no—
385C23×D17—22no—
386C23×D17—22no—
387C23×D17—22no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17—41no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17—41no—
394C23×D17—41no—
395C23×D17—41no—
396C23×D17—41no—
397C23×D17—41no—
398C23×D17—41no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17—41no—
402C23×D17C22×C414yes—
403C23×D17C22×C414yes—
404C23×D17C22×C414yescomplemented
405C23×D17C2411yescharacteristic
406C23×D17C2411yescharacteristic
407C23×D17C2411yescharacteristic
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C2×D4×C17—41no—
411C2×D4×C17—41no—
412C2×D4×C17C22×C414yes—
413C22×C4×C17—22no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17C22×C414yescomplemented
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17C22×C414yes—
441C2×C22⋊D17C22×C414yes—
442C2×C22⋊D17C22×C414yes—
443C2×C22⋊D17C22×C414yes—
444C22×Dic17—22no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458D4×D17—416no—
459C2×D68—22no—
460C2×D68—22no—
461C2×D68—22no—
462C2×D68—22no—
463C2×D68—416no—
464C2×D68—41no—
465C2×D68—41no—
466C2×D68—41no—
467C2×D68—41no—
468C2×D68—41no—
469C2×D68—41no—
470C2×D68—41no—
471C2×D68—41no—
472C2×D68—41no—
473C2×D68—41no—
474C2×D68C22×C414yes—
475C2×D68C22×C414yes—
476C2×D68C22×C414yes—
477C2×D68C22×C414yes—
478C2×D68C22×C414yes—
479C2×D68C22×C414yescomplemented
480C2×D68C22×C414yescomplemented
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
485C2×C4×D17—22no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—41no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C2×C4×D17—41no—
498C2×C4×D17—41no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—416no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17—41no—
515C2×C4×D17—41no—
516C2×C4×D17—41no—
517C2×C4×D17—41no—
518C2×C4×D17C22×C414yes—
519C2×C4×D17C22×C414yescomplemented
520C2×C4×D17C22×C414yescomplemented
521C4⋊C4×C17—22no—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17—41no—
525C4⋊C4×C17—41no—
526C4⋊C4×C17C22×C414yescomplemented
527C4⋊C4×C17C22×C414yescomplemented
528C22⋊C4×C17—22no—
529C22⋊C4×C17—41no—
530C22⋊C4×C17—41no—
531C22⋊C4×C17—41no—
532C22⋊C4×C17—41no—
533C22⋊C4×C17—41no—
534C22⋊C4×C17—41no—
535C22⋊C4×C17C22×C414yes—
536C22⋊C4×C17C22×C414yes—
537C22⋊C4×C17C22×C414yescomplemented
538C42×C17—41no—
539C42×C17—41no—
540C42×C17—41no—
541C42×C17—41no—
542C42×C17—41no—
543C22⋊Dic17—22no—
544C22⋊Dic17—41no—
545C22⋊Dic17—41no—
546C22⋊Dic17—41no—
547C22⋊Dic17—41no—
548C22⋊Dic17—41no—
549C22⋊Dic17—41no—
550C22⋊Dic17C22×C414yescomplemented
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563#63227—41no—
564#63227—41no—
565#63227—41no—
566#63227—41no—
567#63227—41no—
568#63227—41no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572#63227—41no—
573#63227—41no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580#63227—41no—
581#63227C22×C414yes—
582#63227C22×C414yes—
583#63227C22×C414yes—
584#63227C22×C414yes—
585#63227C22×C414yescomplemented
586#63227C22×C414yescomplemented
587#63227C22×C414yescomplemented
588#63227C22×C414yescomplemented
589C4⋊Dic17—22no—
590C4⋊Dic17—41no—
591C4⋊Dic17—41no—
592C4⋊Dic17—41no—
593C4⋊Dic17—41no—
594#63225—41no—
595#63225—41no—
596#63225—41no—
597#63225—41no—
598#63225—41no—
599#63225—41no—
600#63225C22×C414yescomplemented
601#63225C22×C414yescomplemented
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—41no—
605C4×Dic17—41no—
606C4×Dic17—41no—
607C4×Dic17—41no—
608C4×Dic17—41no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17—41no—
612C4×Dic17—41no—
613#34407—171nomaximal, Sylow
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17C23×C412yes—
627C23×C17C23×C412yes—
628C23×C17C2511yescharacteristic
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—28no—
658C22×D17—28no—
659C22×D17—44no—
660C22×D17—44no—
661C22×D17—44no—
662C22×D17—44no—
663C22×D17—44no—
664C22×D17—44no—
665C22×D17—44no—
666C22×D17—44no—
667C22×D17—44no—
668C22×D17—44no—
669C22×D17—44no—
670C22×D17—82no—
671C22×D17—82no—
672C22×D17—82no—
673C22×D17—82no—
674C22×D17—82no—
675C22×D17—82no—
676C22×D17—82no—
677C22×D17—82no—
678C22×D17C23×C412yes—
679C22×D17C23×C412yes—
680C22×D17C23×C412yes—
681C22×D17C23×C412yes—
682C22×D17C23×C412yes—
683C22×D17H(5,𝔽2)12yes—
684C22×D17H(5,𝔽2)12yes—
685D4×C17—44no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—21no—
705C2×C4×C17—21no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—21no—
712C2×C4×C17—21no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—44no—
720C2×C4×C17—44no—
721C2×C4×C17C23×C412yes—
722C2×C4×C17C23×C412yes—
723C2×C4×C17C23×C412yes—
724C2×C4×C17C23×C412yes—
725C2×C4×C17C23×C412yes—
726C2×C4×C17H(5,𝔽2)12yes—
727C22⋊D17—44no—
728C22⋊D17—44no—
729C22⋊D17—44no—
730C22⋊D17—44no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—44no—
761C2×Dic17C23×C412yes—
762C2×Dic17C23×C412yes—
763C2×Dic17C23×C412yes—
764C2×Dic17H(5,𝔽2)12yes—
765D68—28no—
766D68—28no—
767D68—44no—
768D68—44no—
769D68—44no—
770D68—44no—
771D68—44no—
772C4×D17—28no—
773C4×D17—44no—
774C4×D17—44no—
775C4×D17—44no—
776C4×D17—44no—
777C4×D17—44no—
778C4×D17—44no—
779C4×D17—82no—
780C4×D17—82no—
781C4×D17—82no—
782C4×D17—82no—
783C4×D17—82no—
784C4×D17—82no—
785C2×#534—171no—
786#2377—171no—
787#2377—171no—
788#2376—171no—
789#2375—171no—
790#2374—171no—
791#2363—171no—
792#2363—171no—
793#2359—171no—
794#2359—171no—
795#2359—171no—
796#2359—171no—
797#2358—171no—
798#2342—171no—
799#2342—171no—
800D4×C22⋊C4—171no—
801D4×C22⋊C4—171no—
802#2335—171no—
803#2335D1711yescharacteristic, complemented
804#2333—171no—
805#2333—171no—
806#2324—171no—
807#2324—171no—
808#2321—171no—
809#2321—171no—
810#2321—171no—
811#2321—171no—
812#2309—171no—
813C4×#120—171no—
814C4×#120—171no—
815C2×#386—171no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—22no—
820C22×C17—22no—
821C22×C17—22no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17—41no—
826C22×C17—41no—
827C22×C17—41no—
828C22×C17—41no—
829C22×C17—41no—
830C22×C17C24×C411yescharacteristic
831C22×C17C2×H(5,𝔽2)11yescharacteristic
832C22×C17C2×H(5,𝔽2)11yescharacteristic
833C22×C17C2×H(5,𝔽2)11yescharacteristic
834C22×C17C2×H(5,𝔽2)11yescharacteristic
835C22×C17#58511yescharacteristic
836C22×C17#58511yescharacteristic
837C2×D17—22no—
838C2×D17—22no—
839C2×D17—22no—
840C2×D17—22no—
841C2×D17—22no—
842C2×D17—22no—
843C2×D17—22no—
844C2×D17—22no—
845C2×D17—22no—
846C2×D17—22no—
847C2×D17—22no—
848C2×D17—22no—
849C2×D17—22no—
850C2×D17—22no—
851C2×D17—22no—
852C2×D17—22no—
853C2×D17—22no—
854C2×D17—22no—
855C2×D17—416no—
856C2×D17—41no—
857C2×D17—41no—
858C2×D17—41no—
859C2×D17—41no—
860C2×D17—41no—
861C2×D17—41no—
862C2×D17—41no—
863C2×D17—41no—
864C2×D17—41no—
865C2×D17—41no—
866C2×D17—41no—
867C2×D17—41no—
868C2×D17—41no—
869C2×D17—41no—
870C2×D17—41no—
871C2×D17—41no—
872C2×D17—88no—
873C2×D17—88no—
874C2×D17#51814yes—
875C4×C17—22no—
876C4×C17—22no—
877C4×C17—22no—
878C4×C17—22no—
879C4×C17—22no—
880C4×C17—22no—
881C4×C17—41no—
882C4×C17—41no—
883C4×C17—41no—
884C4×C17—41no—
885C4×C17—41no—
886C4×C17—41no—
887C4×C17—41no—
888Dic17—22no—
889Dic17—22no—
890Dic17—22no—
891Dic17—22no—
892Dic17—41no—
893Dic17—41no—
894Dic17—41no—
895Dic17—41no—
896Dic17—41no—
897Dic17—41no—
898Dic17—41no—
899C23×D4—171no—
900C23×D4—171no—
901C24×C4—171no—
902#534—1716no—
903C2×#123—171no—
904C2×#123—171no—
905C2×#123—171no—
906C2×#123C2×D1711yescharacteristic
907C2×#121—171no—
908C2×#121—171no—
909C2×#121—171no—
910C2×#121—171no—
911C2×#120—171no—
912C2×#120—171no—
913C2×#120—171no—
914C2×#120—171no—
915C2×C4×D4—171no—
916C2×C4×D4—171no—
917C2×C4×D4—171no—
918C2×C4×D4—171no—
919C2×C4×D4—171no—
920C2×C4×D4—171no—
921C2×C4×D4—171no—
922C2×C4×D4—171no—
923C2×#117—171no—
924C2×#117—171no—
925C2×#117—171no—
926C2×#117—171no—
927C22×C22⋊C4—171no—
928C22×C22⋊C4—171no—
929C22×C22⋊C4—171no—
930C22×C22⋊C4—171no—
931C22×C22⋊C4—171no—
932C22×C22⋊C4—171no—
933#390—171no—
934#390—171no—
935#390—171no—
936#390—171no—
937#390—171no—
938#390—171no—
939#390—171no—
940#390—171no—
941#390—171no—
942#390—171no—
943#390—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#390C2×D1711yescharacteristic
949#389—171no—
950#389—171no—
951#389—171no—
952#389C2×D1711yescharacteristic, complemented
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388—171no—
971#388—171no—
972#388—171no—
973#388C2×D1711yescharacteristic, complemented
974#388C2×D1711yescharacteristic, complemented
975#388C2×D1711yescharacteristic, complemented
976#388C2×D1711yescharacteristic, complemented
977#387—171no—
978#387—171no—
979#387—171no—
980#387—171no—
981#387—171no—
982#387—171no—
983#387C2×D1711yescharacteristic, complemented
984#387C2×D1711yescharacteristic, complemented
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386—171no—
990#386—171no—
991#386—171no—
992#386—171no—
993#386—171no—
994#386—171no—
995#386—171no—
996#386—171no—
997#386—171no—
998#386—171no—
999#386—171no—
1000#386—171no—
1001#386—171no—
1002#386—171no—
1003#386—171no—
1004#386—171no—
1005#386—171no—
1006#386—171no—
1007#386—171no—
1008#386C2×D1711yescharacteristic
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385—171no—
1016#385—171no—
1017#385—171no—
1018#385—171no—
1019#385—171no—
1020#385C2×D1711yescharacteristic, complemented
1021#381—171no—
1022#381—171no—
1023#380—171no—
1024#380—171no—
1025#380—171no—
1026#380C2×D1711yescharacteristic, complemented
1027#379—171no—
1028#379—171no—
1029#379—171no—
1030#379—171no—
1031#379—171no—
1032#379—171no—
1033C4×C4⋊C4—171no—
1034C4×C4⋊C4—171no—
1035C4×C4⋊C4—171no—
1036C4×C4⋊C4C2×D1711yescharacteristic, complemented
1037C4×C22⋊C4—171no—
1038C4×C22⋊C4—171no—
1039C4×C22⋊C4—171no—
1040C4×C22⋊C4—171no—
1041C4×C22⋊C4—171no—
1042C4×C22⋊C4—171no—
1043C4×C22⋊C4—171no—
1044C4×C22⋊C4—171no—
1045C4×C22⋊C4—171no—
1046C4×C22⋊C4—171no—
1047C4×C22⋊C4—171no—
1048C4×C22⋊C4—171no—
1049C4×C22⋊C4—171no—
1050C4×C22⋊C4—171no—
1051C4×C22⋊C4C2×D1711yescharacteristic, complemented
1052C4×C22⋊C4C2×D1711yescharacteristic, complemented
1053C2×#95—171no—
1054C2×#95—171no—
1055C2×C17—42no—
1056C2×C17—42no—
1057C2×C17C2×#51811yescharacteristic
1058C2×C17C4×H(5,𝔽2)11yescharacteristic
1059C2×C17C4×H(5,𝔽2)11yescharacteristic
1060C2×C17#353211yescharacteristic
1061C2×C17#353311yescharacteristic
1062C2×C17#354211yescharacteristic
1063C2×C17#354211yescharacteristic
1064D17—24no—
1065D17—42no—
1066D17—42no—
1067D17—42no—
1068D17—42no—
1069C25—171no—
1070C25—171no—
1071C25—171no—
1072C22×D4—171no—
1073C22×D4—171no—
1074C22×D4—171no—
1075C22×D4—171no—
1076C22×D4—178no—
1077C22×D4—178no—
1078C22×D4—171no—
1079C22×D4—171no—
1080C22×D4—171no—
1081C22×D4—171no—
1082C22×D4—171no—
1083C22×D4—171no—
1084C22×D4—171no—
1085C22×D4—682no—
1086C22×D4—682no—
1087C22×D4—682no—
1088C22×D4—682no—
1089C22×D4C22×D1711yescharacteristic
1090C23×C4—171no—
1091C23×C4—171no—
1092C23×C4—171no—
1093C23×C4—171no—
1094C23×C4—171no—
1095C23×C4—171no—
1096C23×C4—171no—
1097C23×C4—171no—
1098C23×C4—171no—
1099C23×C4—171no—
1100C23×C4—171no—
1101C23×C4—171no—
1102C23×C4—171no—
1103C23×C4—171no—
1104C23×C4—682no—
1105C23×C4—682no—
1106C23×C4—682no—
1107C23×C4C22×D1711yescharacteristic
1108C23×C4C22×D1711yescharacteristic
1109#123—178no—
1110#123—178no—
1111#123—178no—
1112#123C4×D1718yescomplemented
1113#121—178no—
1114#121—178no—
1115#121—178no—
1116#121—178no—
1117#120—178no—
1118#120—178no—
1119#120—178no—
1120#120—178no—
1121C4×D4—682no—
1122C4×D4—682no—
1123C4×D4—682no—
1124C4×D4—682no—
1125C4×D4—682no—
1126C4×D4—682no—
1127C4×D4—682no—
1128C4×D4—682no—
1129#117—682no—
1130#117—682no—
1131#117—682no—
1132#117—682no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—171no—
1146C2×C4⋊C4C22×D1711yescharacteristic
1147C2×C4⋊C4C22×D1711yescharacteristic
1148C2×C4⋊C4C22×D1711yescharacteristic
1149C2×C4⋊C4C22×D1711yescharacteristic
1150C2×C4⋊C4C22×D1711yescharacteristic
1151C2×C4⋊C4C22×D1711yescharacteristic
1152C2×C4⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—178no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—171no—
1189C2×C22⋊C4—171no—
1190C2×C22⋊C4—171no—
1191C2×C22⋊C4—171no—
1192C2×C22⋊C4—171no—
1193C2×C22⋊C4—171no—
1194C2×C22⋊C4—171no—
1195C2×C22⋊C4—171no—
1196C2×C22⋊C4—171no—
1197C2×C22⋊C4—171no—
1198C2×C22⋊C4—171no—
1199C2×C22⋊C4—171no—
1200C2×C22⋊C4—682no—
1201C2×C22⋊C4—682no—
1202C2×C22⋊C4—682no—
1203C2×C22⋊C4—682no—
1204C2×C22⋊C4—682no—
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C22⋊C4C22×D1711yescharacteristic
1208C2×C22⋊C4C22×D1711yescharacteristic
1209C2×C22⋊C4C22×D1711yescharacteristic
1210C2×C22⋊C4C22×D1711yescharacteristic
1211C2×C22⋊C4C22×D1711yescharacteristic
1212C2×C22⋊C4C22×D1711yescharacteristic
1213C2×C22⋊C4C22×D1711yescharacteristic
1214C2×C22⋊C4C22×D1711yescharacteristic
1215C2×C42—171no—
1216C2×C42—171no—
1217C2×C42—171no—
1218C2×C42—171no—
1219C2×C42—171no—
1220C2×C42—171no—
1221C2×C42—171no—
1222C2×C42—171no—
1223C2×C42—171no—
1224C2×C42—171no—
1225C2×C42—171no—
1226C2×C42C22×D1711yescharacteristic
1227C2×C42C22×D1711yescharacteristic
1228C2×C42C22×D1711yescharacteristic
1229C2×C42C22×D1711yescharacteristic
1230C2×C42C22×D1711yescharacteristic
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95—171no—
1243#95—171no—
1244#95—171no—
1245#95—171no—
1246#95—171no—
1247#95—171no—
1248#95—171no—
1249#95—171no—
1250#95—171no—
1251#95—171no—
1252#95—171no—
1253#95C22×D1711yescharacteristic
1254#95C22×D1711yescharacteristic
1255#95C22×D1711yescharacteristic
1256#95C22×D1711yescharacteristic
1257#95C22×D1711yescharacteristic
1258#95C22×D1711yescharacteristic
1259#95C22×D1711yescharacteristic
1260#95C22×D1711yescharacteristic
1261#95C22×D1711yescharacteristic
1262#95C22×D1711yescharacteristic
1263C17#3440711yescharacteristic, complemented, Sylow
1264C24—171no—
1265C24—171no—
1266C24—171no—
1267C24—171no—
1268C24—171no—
1269C24—174no—
1270C24—174no—
1271C24—174no—
1272C24—342no—
1273C24—342no—
1274C24—342no—
1275C24—342no—
1276C24—681no—
1277C24—681no—
1278C24—681no—
1279C24—681no—
1280C24—681no—
1281C24—681no—
1282C24—681no—
1283C24—681no—
1284C24—681no—
1285C24—681no—
1286C24—681no—
1287C24—681no—
1288C24—681no—
1289C24—681no—
1290C24C23×D1711yescharacteristic
1291C24C23×D1711yescharacteristic
1292C2×D4—41no—
1293C2×D4—41no—
1294C2×D4—174no—
1295C2×D4—174no—
1296C2×D4—174no—
1297C2×D4—174no—
1298C2×D4—174no—
1299C2×D4—174no—
1300C2×D4—174no—
1301C2×D4—174no—
1302C2×D4—174no—
1303C2×D4—174no—
1304C2×D4—174no—
1305C2×D4—342no—
1306C2×D4—342no—
1307C2×D4—342no—
1308C2×D4—342no—
1309C2×D4—681no—
1310C2×D4—681no—
1311C2×D4—681no—
1312C2×D4—681no—
1313C2×D4—681no—
1314C2×D4—681no—
1315C2×D4—681no—
1316C2×D4—681no—
1317C2×D4—681no—
1318C2×D4—681no—
1319C2×D4—6816no—
1320C2×D4—6816no—
1321C2×D4—681no—
1322C2×D4—681no—
1323C2×D4—681no—
1324C2×D4—681no—
1325C2×D4—681no—
1326C2×D4—681no—
1327C2×D4—681no—
1328C2×D4—681no—
1329C2×D4C2×C4×D1714yes—
1330C22×C4—22no—
1331C22×C4—41no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—41no—
1335C22×C4—171no—
1336C22×C4—171no—
1337C22×C4—171no—
1338C22×C4—171no—
1339C22×C4—174no—
1340C22×C4—174no—
1341C22×C4—174no—
1342C22×C4—171no—
1343C22×C4—171no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—171no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—681no—
1363C22×C4—681no—
1364C22×C4—681no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4—681no—
1372C22×C4—681no—
1373C22×C4—681no—
1374C22×C4—681no—
1375C22×C4—681no—
1376C22×C4—681no—
1377C22×C4—681no—
1378C22×C4—681no—
1379C22×C4—681no—
1380C22×C4—681no—
1381C22×C4—681no—
1382C22×C4—681no—
1383C22×C4—681no—
1384C22×C4—681no—
1385C22×C4—681no—
1386C22×C4—6816no—
1387C22×C4—681no—
1388C22×C4—681no—
1389C22×C4C2×C4×D1714yescomplemented
1390C22×C4C23×D1711yescharacteristic
1391C22×C4C23×D1711yescharacteristic
1392C22×C4C23×D1711yescharacteristic
1393C22×C4C23×D1711yescharacteristic
1394C22×C4C23×D1711yescharacteristic
1395C22×C4C23×D1711yescharacteristic
1396C22×C4C23×D1711yescharacteristic
1397C22×C4C23×D1711yescharacteristic
1398C22×C4C23×D1711yescharacteristic
1399C22×C4C23×D1711yescharacteristic
1400C22×C4C23×D1711yescharacteristic
1401C22×C4C23×D1711yescharacteristic
1402C22×C4C23×D1711yescharacteristic
1403C4⋊C4—22no—
1404C4⋊C4—41no—
1405C4⋊C4—41no—
1406C4⋊C4—41no—
1407C4⋊C4—41no—
1408C4⋊C4—174no—
1409C4⋊C4—174no—
1410C4⋊C4—342no—
1411C4⋊C4—681no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4—681no—
1416C4⋊C4—681no—
1417C4⋊C4—681no—
1418C4⋊C4—681no—
1419C4⋊C4—681no—
1420C4⋊C4—681no—
1421C4⋊C4C2×C4×D1714yescomplemented
1422C4⋊C4C2×C4×D1714yescomplemented
1423C22⋊C4—22no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—41no—
1430C22⋊C4—174no—
1431C22⋊C4—174no—
1432C22⋊C4—174no—
1433C22⋊C4—174no—
1434C22⋊C4—174no—
1435C22⋊C4—174no—
1436C22⋊C4—174no—
1437C22⋊C4—174no—
1438C22⋊C4—174no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—342no—
1444C22⋊C4—342no—
1445C22⋊C4—342no—
1446C22⋊C4—342no—
1447C22⋊C4—342no—
1448C22⋊C4—681no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C22⋊C4—681no—
1453C22⋊C4—681no—
1454C22⋊C4—681no—
1455C22⋊C4—681no—
1456C22⋊C4—681no—
1457C22⋊C4—681no—
1458C22⋊C4—681no—
1459C22⋊C4—681no—
1460C22⋊C4—681no—
1461C22⋊C4—681no—
1462C22⋊C4—681no—
1463C22⋊C4—681no—
1464C22⋊C4—681no—
1465C22⋊C4—681no—
1466C22⋊C4—681no—
1467C22⋊C4—681no—
1468C22⋊C4—681no—
1469C22⋊C4—681no—
1470C22⋊C4—681no—
1471C22⋊C4—681no—
1472C22⋊C4—681no—
1473C22⋊C4—681no—
1474C22⋊C4—681no—
1475C22⋊C4—681no—
1476C22⋊C4C2×C4×D1714yes—
1477C22⋊C4C2×C4×D1714yes—
1478C22⋊C4C2×C4×D1714yescomplemented
1479C42—41no—
1480C42—41no—
1481C42—41no—
1482C42—41no—
1483C42—41no—
1484C42—342no—
1485C42—342no—
1486C42—681no—
1487C42—681no—
1488C42—681no—
1489C42—681no—
1490C42—681no—
1491C42—681no—
1492C42—681no—
1493C42—681no—
1494C42—681no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—172no—
1508C23—172no—
1509C23—172no—
1510C23—172no—
1511C23—172no—
1512C23—172no—
1513C23—172no—
1514C23—348no—
1515C23—348no—
1516C23—341no—
1517C23—341no—
1518C23—341no—
1519C23—341no—
1520C23—341no—
1521C23—341no—
1522C23—341no—
1523C23—341no—
1524C23—341no—
1525C23—341no—
1526C23—341no—
1527C23—341no—
1528C23—341no—
1529C23—341no—
1530C23—341no—
1531C23—341no—
1532C23—341no—
1533C23—341no—
1534C23—341no—
1535C23—341no—
1536C23—341no—
1537C23—341no—
1538C23—341no—
1539C23—341no—
1540C23—341no—
1541C23—341no—
1542C23—341no—
1543C23—341no—
1544C23—684no—
1545C23—684no—
1546C23—684no—
1547C23—684no—
1548C23—684no—
1549C23—684no—
1550C23—684no—
1551C23—684no—
1552C23—684no—
1553C23—684no—
1554C23—684no—
1555C23—1362no—
1556C23—1362no—
1557C23—1362no—
1558C23—1362no—
1559C23—1362no—
1560C23—1362no—
1561C23—1362no—
1562C23—1362no—
1563C23C22×C4×D1712yes—
1564C23C22×C4×D1712yes—
1565C23C24×D1711yescharacteristic
1566D4—44no—
1567D4—348no—
1568D4—348no—
1569D4—684no—
1570D4—684no—
1571D4—684no—
1572D4—684no—
1573D4—684no—
1574D4—684no—
1575D4—684no—
1576D4—684no—
1577D4—684no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—44no—
1612C2×C4—44no—
1613C2×C4—172no—
1614C2×C4—172no—
1615C2×C4—172no—
1616C2×C4—172no—
1617C2×C4—348no—
1618C2×C4—341no—
1619C2×C4—341no—
1620C2×C4—341no—
1621C2×C4—341no—
1622C2×C4—341no—
1623C2×C4—341no—
1624C2×C4—341no—
1625C2×C4—341no—
1626C2×C4—341no—
1627C2×C4—341no—
1628C2×C4—341no—
1629C2×C4—341no—
1630C2×C4—341no—
1631C2×C4—341no—
1632C2×C4—341no—
1633C2×C4—341no—
1634C2×C4—341no—
1635C2×C4—341no—
1636C2×C4—341no—
1637C2×C4—341no—
1638C2×C4—341no—
1639C2×C4—341no—
1640C2×C4—341no—
1641C2×C4—341no—
1642C2×C4—341no—
1643C2×C4—341no—
1644C2×C4—341no—
1645C2×C4—341no—
1646C2×C4—341no—
1647C2×C4—684no—
1648C2×C4—684no—
1649C2×C4—684no—
1650C2×C4—684no—
1651C2×C4—684no—
1652C2×C4—684no—
1653C2×C4—684no—
1654C2×C4—1362no—
1655C2×C4—1362no—
1656C2×C4—1362no—
1657C2×C4—1362no—
1658C2×C4—1362no—
1659C2×C4—1362no—
1660C2×C4C22×C4×D1712yes—
1661C2×C4C22×C4×D1712yes—
1662C2×C4C22×C4×D1712yes—
1663C2×C4C22×C4×D1712yes—
1664C2×C4C22×C4×D1712yes—
1665C2×C4#1058769612yes—
1666C22—22no—
1667C22—22no—
1668C22—22no—
1669C22—22no—
1670C22—22no—
1671C22—22no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—174no—
1681C22—342no—
1682C22—342no—
1683C22—342no—
1684C22—342no—
1685C22—342no—
1686C22—342no—
1687C22—342no—
1688C22—342no—
1689C22—342no—
1690C22—342no—
1691C22—342no—
1692C22—342no—
1693C22—342no—
1694C22—342no—
1695C22—342no—
1696C22—342no—
1697C22—342no—
1698C22—342no—
1699C22—6816no—
1700C22—681no—
1701C22—681no—
1702C22—681no—
1703C22—681no—
1704C22—681no—
1705C22—681no—
1706C22—681no—
1707C22—681no—
1708C22—681no—
1709C22—681no—
1710C22—681no—
1711C22—681no—
1712C22—681no—
1713C22—681no—
1714C22—681no—
1715C22—681no—
1716C22—1368no—
1717C22—1368no—
1718C22C23×C4×D1711yescharacteristic
1719C22H(5,𝔽2)×D1711yescharacteristic
1720C22H(5,𝔽2)×D1711yescharacteristic
1721C22H(5,𝔽2)×D1711yescharacteristic
1722C22C2×#1058769611yescharacteristic
1723C22#1176364511yescharacteristic
1724C22#1176364611yescharacteristic
1725C4—22no—
1726C4—22no—
1727C4—22no—
1728C4—22no—
1729C4—22no—
1730C4—22no—
1731C4—41no—
1732C4—41no—
1733C4—41no—
1734C4—41no—
1735C4—41no—
1736C4—41no—
1737C4—41no—
1738C4—342no—
1739C4—342no—
1740C4—342no—
1741C4—342no—
1742C4—681no—
1743C4—681no—
1744C4—681no—
1745C4—681no—
1746C4—681no—
1747C4—681no—
1748C4—681no—
1749C2—42no—
1750C2—42no—
1751C2—344no—
1752C2—682no—
1753C2—682no—
1754C2—682no—
1755C2—682no—
1756C2D17×#51811yescharacteristic
1757C2#1454199011yescharacteristic
1758C2C4×#1058769611yescharacteristic
1759C2#1454293511yescharacteristic
1760C2#1454295911yescharacteristic
1761C2#1454309111yescharacteristic
1762C2#1454309611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2335C2
socle, cosocleC23×C17C25
prime radicalC2×#11763370C2
hypercenter#2335D17
hypocenterC17#34407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531939C2semidirect
3. #14531939C2semidirect
4. #14531928C2semidirect
5. #14531924C2semidirect
6. #14531915C2semidirect
7. #14531824C2semidirect
8. #14531821C2semidirect
9. #14531783C2semidirect
10. #14531781C2semidirect
11. #14531771C2semidirect
12. #14531769C2semidirect
13. #14531762C2semidirect
14. #14531632C2semidirect
15. #14531632C2semidirect
16. C22⋊C4×D68C2semidirect
17. #14531604C2semidirect
18. #14531578C2semidirect
19. #14531547C2semidirect
20. #14531544C2semidirect
21. #14531476C2semidirect
22. #14531472C2semidirect
23. #14531446C2semidirect
24. #14531443C2semidirect
25. #14531440C2semidirect
26. #14531437C2semidirect
27. #14531363C2semidirect
28. C4×#10587568C2semidirect
29. #14531285C2semidirect
30. D17×#386C2semidirect
31. C17×#2335C2semidirect
34. C23×C4×D17C22semidirect
35. #11763370C4semidirect
49. C2×C4×D68C22semidirect
52. C2×#10587579C22semidirect
53. C2×C4×C22⋊D17C22semidirect
54. C2×#10587567C22semidirect
55. C2×#10587578C22semidirect
56. C2×#10587578C22semidirect
57. C2×#10587578C22semidirect
58. C2×#10587558C22semidirect
62. C2×C22⋊C4×D17C22semidirect
63. C2×C22⋊C4×D17C22semidirect
64. C2×C22⋊C4×D17C22semidirect
66. #11762711C22semidirect
67. #11762711C22semidirect
68. #11762711C22semidirect
69. #11762711C22semidirect
70. #11762710C22semidirect
71. #11762710C22semidirect
72. #11762710C22semidirect
73. #11762710C22semidirect
76. #11762709C22semidirect
77. #11762709C22semidirect
78. #11762709C22semidirect
79. #11762709C22semidirect
80. #11762708C22semidirect
81. #11762706C22semidirect
82. #11762704C22semidirect
83. #11762703C22semidirect
84. #11762703C22semidirect
85. #11762702C22semidirect
86. #11762702C22semidirect
87. #11762702C22semidirect
88. #11762702C22semidirect
89. #11762701C22semidirect
90. #11762701C22semidirect
91. #11762701C22semidirect
92. #11762700C22semidirect
93. #11762700C22semidirect
94. #11762700C22semidirect
95. #11762699C22semidirect
96. #11762699C22semidirect
97. #11762699C22semidirect
98. #11762698C22semidirect
99. #11762698C22semidirect
100. #11762698C22semidirect
101. #11762697C22semidirect
102. #11762697C22semidirect
103. #11762696C22semidirect
104. #11762695C22semidirect
105. #11762695C22semidirect
106. #11762693C22semidirect
107. #11762691C22semidirect
108. #11762690C22semidirect
110. #11762688C22semidirect
111. #11762688C22semidirect
116. #11762687C22semidirect
117. #11762687C22semidirect
118. #11762687C22semidirect
119. #11762687C22semidirect
120. #11762687C22semidirect
121. #11762687C22semidirect
122. #11762687C22semidirect
123. #11762687C22semidirect
124. #11762687C22semidirect
125. #11762687C22semidirect
126. #11762686C22semidirect
127. #11762686C22semidirect
130. #11762685C22semidirect
131. #11762685C22semidirect
132. #11762684C22semidirect
133. #11762683C22semidirect
134. #11762683C22semidirect
135. #11762683C22semidirect
136. #11762683C22semidirect
137. #11762683C22semidirect
138. #11762680C22semidirect
139. #11762680C22semidirect
140. #11762680C22semidirect
141. #11762680C22semidirect
142. #11762680C22semidirect
143. #11762671C22semidirect
144. #11762671C22semidirect
145. #11762669C22semidirect
146. #11762668C22semidirect
147. #11762668C22semidirect
150. #11762664C22semidirect
151. #11762664C22semidirect
152. #11762664C22semidirect
153. #11762664C22semidirect
154. C4⋊C4×Dic17C22semidirect
155. C4×#63225C22semidirect
156. #11762660C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C4×#63227C22semidirect
159. C4×#63227C22semidirect
160. C4×#63227C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×#63227C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
175. C17×#389C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#388C22semidirect
180. C17×#387C22semidirect
181. C17×#387C22semidirect
183. C17×#385C22semidirect
184. C17×#380C22semidirect
185. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
201. C2×D4×D17C2×C4semidirect
204. C22×D68C2×C4semidirect
228. C17×#123C2×C4semidirect
259. #10587623C2×C4semidirect
260. #10587615C2×C4semidirect
324. #10587581C2×C4semidirect
325. #10587581C2×C4semidirect
326. #10587580C2×C4semidirect
327. #10587580C2×C4semidirect
334. #10587570C2×C4semidirect
335. #10587570C2×C4semidirect
336. #10587568C2×C4semidirect
337. #10587568C2×C4semidirect
338. #10587568C2×C4semidirect
345. C22⋊C4×D17C2×C4semidirect
404. C23×D17C22×C4semidirect
418. C22×C4×C17C22×C4semidirect
479. C2×D68C22×C4semidirect
480. C2×D68C22×C4semidirect
519. C2×C4×D17C22×C4semidirect
520. C2×C4×D17C22×C4semidirect
526. C4⋊C4×C17C22×C4semidirect
527. C4⋊C4×C17C22×C4semidirect
537. C22⋊C4×C17C22×C4semidirect
550. C22⋊Dic17C22×C4semidirect
585. #63227C22×C4semidirect
586. #63227C22×C4semidirect
587. #63227C22×C4semidirect
588. #63227C22×C4semidirect
600. #63225C22×C4semidirect
601. #63225C22×C4semidirect
803. #2335D17semidirect
952. #389C2×D17semidirect
973. #388C2×D17semidirect
974. #388C2×D17semidirect
975. #388C2×D17semidirect
976. #388C2×D17semidirect
983. #387C2×D17semidirect
984. #387C2×D17semidirect
1020. #385C2×D17semidirect
1026. #380C2×D17semidirect
1036. C4×C4⋊C4C2×D17semidirect
1051. C4×C22⋊C4C2×D17semidirect
1052. C4×C22⋊C4C2×D17semidirect
1112. #123C4×D17semidirect
1263. C17#34407semidirect
1389. C22×C4C2×C4×D17semidirect
1421. C4⋊C4C2×C4×D17semidirect
1422. C4⋊C4C2×C4×D17semidirect
1478. C22⋊C4C2×C4×D17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633702
#145319392
#145319282
#145319242
#145319152
#145318242
#145318212
#145317832
#145317812
#145317712
#145317692
#145317622
#145316322
C22⋊C4×D682
#145316042
#145315782
#145315472
#145315442
#145314762
#145314722
#145314462
#145314432
#145314402
#145314372
#145313632
C4×#105875682
#145312852
D17×#3862
C17×#23352
#3440717