Finite Group Databasebeta

← #17193388

Subgroups — #17193388

Order 4352.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763392C211yesmaximal, characteristic
2#14531595C211yesmaximal, characteristic, complemented
3#14531594C211yesmaximal, characteristic, complemented
4#14531580C211yesmaximal, characteristic, complemented
5#14531570C211yesmaximal, characteristic, complemented
6#14531565C211yesmaximal, characteristic, complemented
7#14531555C211yesmaximal, characteristic, complemented
8#14531547C211yesmaximal, characteristic, complemented
9#14531546C211yesmaximal, characteristic, complemented
10#14531515C211yesmaximal, characteristic, complemented
11#14531485C211yesmaximal, characteristic, complemented
12#14531447C211yesmaximal, characteristic, complemented
13#14531441C211yesmaximal, characteristic, complemented
14#14531418C211yesmaximal, characteristic, complemented
15#14531379C211yesmaximal, characteristic, complemented
16#14531334C211yesmaximal, characteristic, complemented
17#14531332C211yesmaximal, characteristic, complemented
18#14531325C211yesmaximal, characteristic, complemented
19#14531323C211yesmaximal, characteristic, complemented
20#14531316C211yesmaximal, characteristic, complemented
21#14531305C211yesmaximal, characteristic, complemented
22#14531301C211yesmaximal, characteristic, complemented
23#14531296C211yesmaximal, characteristic, complemented
24#14531294C211yesmaximal, characteristic, complemented
25#14531290C211yesmaximal, characteristic, complemented
26#14531289C211yesmaximal, characteristic, complemented
27#14531285C211yesmaximal, characteristic, complemented
28C4×D4×Dic17C211yesmaximal, characteristic, complemented
29C4×#10587567C211yesmaximal, characteristic, complemented
30C2×#11762656C211yesmaximal, characteristic, complemented
31C17×#2318C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33#11763392C4116yescomplemented
34C2×#10587584C2211yescharacteristic
35C2×#10587562C2211yescharacteristic
36C2×#10587561C2211yescharacteristic
37C2×#10587571C2211yescharacteristic
38C2×#10587580C2211yescharacteristic
39C2×#10587615C2211yescharacteristic
40C2×#10587564C2211yescharacteristic
41C2×#10587616C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587625C2211yescharacteristic
44C2×#10587568C2211yescharacteristic
45C2×#10587623C2211yescharacteristic
46C2×#10587573C2211yescharacteristic, complemented
47C2×D4×Dic17C2211yescharacteristic
48C2×D4×Dic17C2211yescharacteristic
49C2×#10587579C2211yescharacteristic
50C2×#10587579C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic, complemented
57C22×#63227C2211yescharacteristic
58C22×#63227C2211yescharacteristic
59C22×C4×Dic17C2211yescharacteristic
60C22×C4×Dic17C2211yescharacteristic
61C22×C4×Dic17C2211yescharacteristic, complemented
62C2×C42×D17C2211yescharacteristic, complemented
63#11762714C2211yescharacteristic, complemented
64#11762713C2211yescharacteristic, complemented
65#11762713C2211yescharacteristic, complemented
66#11762710C2211yescharacteristic
67#11762710C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762705C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic, complemented
76#11762701C2211yescharacteristic
77#11762701C2211yescharacteristic
78#11762701C2211yescharacteristic, complemented
79#11762700C2211yescharacteristic
80#11762700C2211yescharacteristic
81#11762700C2211yescharacteristic
82#11762700C2211yescharacteristic
83#11762699C2211yescharacteristic
84#11762699C2211yescharacteristic
85#11762698C2211yescharacteristic
86#11762698C2211yescharacteristic
87#11762698C2211yescharacteristic
88#11762698C2211yescharacteristic
89#11762698C2211yescharacteristic
90#11762698C2211yescharacteristic
91#11762698C2211yescharacteristic
92#11762698C2211yescharacteristic
93#11762698C2211yescharacteristic, complemented
94#11762698C2211yescharacteristic, complemented
95#11762698C2211yescharacteristic, complemented
96#11762697C2211yescharacteristic, complemented
97#11762696C2211yescharacteristic, complemented
98#11762694C2211yescharacteristic, complemented
99#11762694C2211yescharacteristic, complemented
100#11762691C2211yescharacteristic, complemented
101#11762691C2211yescharacteristic, complemented
102#11762691C2211yescharacteristic, complemented
103#11762691C2211yescharacteristic, complemented
104#11762691C2211yescharacteristic, complemented
105#11762690C2211yescharacteristic, complemented
106#11762690C2211yescharacteristic, complemented
107#11762688C2211yescharacteristic
108#11762688C2211yescharacteristic
109#11762687C2211yescharacteristic
110#11762687C2211yescharacteristic
111#11762687C2211yescharacteristic
112#11762687C2211yescharacteristic
113#11762686C2211yescharacteristic
114#11762686C2211yescharacteristic
115#11762686C2211yescharacteristic, complemented
116#11762685C2211yescharacteristic
117#11762685C2211yescharacteristic
118#11762685C2211yescharacteristic, complemented
119#11762683C2211yescharacteristic
120#11762683C2211yescharacteristic
121#11762683C2211yescharacteristic, complemented
122#11762682C2211yescharacteristic
123#11762682C2211yescharacteristic
124#11762681C2211yescharacteristic, complemented
125#11762680C2211yescharacteristic
126#11762680C2211yescharacteristic
127#11762676C2211yescharacteristic, complemented
128#11762673C2211yescharacteristic, complemented
129#11762671C2211yescharacteristic, complemented
130#11762668C2211yescharacteristic, complemented
131#11762667C2211yescharacteristic
132#11762667C2211yescharacteristic
133#11762664C2211yescharacteristic
134#11762664C2211yescharacteristic
135C4⋊C4×Dic17C2211yescharacteristic, complemented
136C4⋊C4×Dic17C2211yescharacteristic, complemented
137C4⋊C4×Dic17C2211yescharacteristic, complemented
138C4×#63225C2211yescharacteristic, complemented
139C4×C4⋊Dic17C2211yescharacteristic, complemented
140#11762660C2211yescharacteristic, complemented
141#11762660C2211yescharacteristic, complemented
142#11762660C2211yescharacteristic, complemented
143#11762660C2211yescharacteristic, complemented
144#11762660C2211yescharacteristic, complemented
145C22⋊C4×Dic17C2211yescharacteristic
146C22⋊C4×Dic17C2211yescharacteristic
147C22⋊C4×Dic17C2211yescharacteristic
148C22⋊C4×Dic17C2211yescharacteristic
149C22⋊C4×Dic17C2211yescharacteristic, complemented
150C22⋊C4×Dic17C2211yescharacteristic, complemented
151C22⋊C4×Dic17C2211yescharacteristic, complemented
152C4×#63227C2211yescharacteristic, complemented
153C4×C22⋊Dic17C2211yescharacteristic
154C4×C22⋊Dic17C2211yescharacteristic, complemented
155#11762656C2211yescharacteristic
156#11762656C2211yescharacteristic
157#11762656C2211yescharacteristic
158#11762656C2211yescharacteristic
159#11762656C2211yescharacteristic
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic
171C42×Dic17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C4×D4×C17C2211yescharacteristic
174C17×#388C2211yescharacteristic, complemented
175C17×#388C2211yescharacteristic, complemented
176C17×#387C2211yescharacteristic, complemented
177C17×#387C2211yescharacteristic, complemented
178C17×#386C2211yescharacteristic
179C17×#386C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#385C2211yescharacteristic
182C17×#383C2211yescharacteristic, complemented
183C17×#382C2211yescharacteristic, complemented
184C17×#381C2211yescharacteristic, complemented
185C17×#380C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic
187C2×C17×#95C2211yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×C4×D17—24no—
206C22×C4×D17—42no—
207C22×C4×D17—42no—
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×Dic34C2311yescharacteristic
216C4×D4×C17C2×C418yescomplemented
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C42×C17C2311yescharacteristic
231C2×C42×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239#10587625C2×C418yescomplemented
240#10587623C2×C418yescomplemented
241D4×Dic17—24no—
242D4×Dic17—24no—
243#10587616C2×C418yescomplemented
244#10587615C2×C418yescomplemented
245C4×C22⋊D17C2×C418yescomplemented
246C2×#63227—24no—
247C2×#63227C2×C418yescomplemented
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×#63225C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×C4×Dic17—42no—
294C2×C4×Dic17—42no—
295C2×C4×Dic17—42no—
296C2×C4×Dic17C2311yescharacteristic
297C2×C4×Dic17C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319#10587584C2×C418yescomplemented
320#10587580C2×C418yescomplemented
321#10587579—42no—
322#10587579—42no—
323#10587573—42no—
324#10587571C2×C418yescomplemented
325#10587570C2×C418yescomplemented
326#10587568C2×C418yescomplemented
327#10587567—24no—
328#10587567—24no—
329#10587567—42no—
330#10587567—42no—
331#10587567—42no—
332#10587564C2×C418yescomplemented
333#10587562C2×C418yescomplemented
334#10587561C2×C418yescomplemented
335C42×D17—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
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
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17C22×C414yes—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×D4×C17—22no—
389C2×D4×C17—22no—
390C2×D4×C17C22×C414yes—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17C22×C414yes—
402C22×C4×C17C22×C414yescomplemented
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C2×C22⋊D17—22no—
417C2×C22⋊D17—22no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17C22×C414yes—
425C2×C22⋊D17C22×C414yes—
426C2×C22⋊D17C22×C414yes—
427C2×C22⋊D17C22×C414yescomplemented
428C22×Dic17—22no—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—22no—
432C22×Dic17—22no—
433C22×Dic17—22no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17C22×C414yes—
441C22×Dic17#4114yes—
442C22×Dic17#4114yes—
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C2×D68—41no—
457C2×D68—41no—
458C2×D68—41no—
459C2×D68—41no—
460C2×D68C22×C414yes—
461C2×D68C22×C414yes—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—416no—
483C2×C4×D17C22×C414yescomplemented
484C2×Dic34—41no—
485C2×Dic34—41no—
486C2×Dic34C22×C414yescomplemented
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C4⋊C4×C17—41no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17C22×C414yescomplemented
492C22⋊C4×C17—22no—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17C22×C414yes—
499C22⋊C4×C17C22×C414yescomplemented
500C42×C17—41no—
501C42×C17—41no—
502C42×C17C22×C414yescomplemented
503C22⋊Dic17—22no—
504C22⋊Dic17—22no—
505C22⋊Dic17—22no—
506C22⋊Dic17—22no—
507C22⋊Dic17C22×C414yes—
508C22⋊Dic17C22×C414yescomplemented
509#63227—22no—
510#63227—22no—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227—41no—
519#63227—41no—
520#63227—41no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227C22×C414yes—
528#63227C22×C414yes—
529#63227C22×C414yes—
530#63227C22×C414yes—
531#63227C22×C414yes—
532#63227C22×C414yes—
533#63227C22×C414yes—
534#63227C22×C414yes—
535#63227C22×C414yescomplemented
536#63227C22×C414yescomplemented
537C4⋊Dic17—22no—
538C4⋊Dic17—22no—
539C4⋊Dic17C22×C414yescomplemented
540#63225—22no—
541#63225—22no—
542#63225—41no—
543#63225—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225C22×C414yescomplemented
551#63225C22×C414yescomplemented
552#63225C22×C414yescomplemented
553#63225C22×C414yescomplemented
554C4×Dic17—22no—
555C4×Dic17—22no—
556C4×Dic17—22no—
557C4×Dic17—22no—
558C4×Dic17—22no—
559C4×Dic17—22no—
560C4×Dic17—22no—
561C4×Dic17—22no—
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—22no—
565C4×Dic17—22no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17C22×C414yescomplemented
577C4×#538—171nomaximal, Sylow
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17C23×C412yes—
589C23×C17C23×C412yes—
590C23×C17C2×#4112yes—
591C23×C17C2×#4112yes—
592C23×C17C2511yescharacteristic
593C22×D17—28no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17C23×C412yes—
619C22×D17C23×C412yes—
620C22×D17C23×C412yes—
621D4×C17—28no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—44no—
657C2×C4×C17—44no—
658C2×C4×C17—44no—
659C2×C4×C17—44no—
660C2×C4×C17C23×C412yes—
661C2×C4×C17C23×C412yes—
662C2×C4×C17C23×C412yes—
663C2×C4×C17C23×C412yes—
664C2×C4×C17C23×C412yes—
665C22⋊D17—28no—
666C22⋊D17—44no—
667C22⋊D17—44no—
668C22⋊D17—44no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—28no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—44no—
699C2×Dic17—44no—
700C2×Dic17—44no—
701C2×Dic17—44no—
702C2×Dic17C23×C412yes—
703C2×Dic17C23×C412yes—
704C2×Dic17C23×C412yes—
705C2×Dic17C23×C412yes—
706C2×Dic17C23×C412yes—
707C2×Dic17C2×#4112yes—
708C2×Dic17C2×#4112yes—
709C2×Dic17C2×#4112yes—
710C2×Dic17C2×#4112yes—
711C2×Dic17H(5,𝔽2)12yes—
712C2×Dic17H(5,𝔽2)12yes—
713D68—44no—
714D68—44no—
715C4×D17—44no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—44no—
722Dic34—44no—
723C2×#538—171no—
724#2337—171no—
725#2337—171no—
726#2335—171no—
727#2335—171no—
728#2334—171no—
729#2334—171no—
730#2333—171no—
731#2333—171no—
732#2329—171no—
733#2325—171no—
734#2321—171no—
735#2321—171no—
736#2318—171no—
737#2318D1711yescharacteristic, complemented
738#2312—171no—
739C4×#126—171no—
740C4×#126—171no—
741C4×#124—171no—
742C4×#124—171no—
743C4×C22⋊Q8—171no—
744C4×#123—171no—
745C4×#123—171no—
746C4×#121—171no—
747C4×#121—171no—
748C4×#121—171no—
749C4×#120—171no—
750C4×#120—171no—
751C42×D4—171no—
752C42×D4—171no—
753C2×C4×C22⋊C4—171no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17C4×#4114yes—
768C22×C17C24×C411yescharacteristic
769C22×C17C22×#4111yescharacteristic
770C22×C17C22×#4111yescharacteristic
771C22×C17C2×H(5,𝔽2)11yescharacteristic
772C22×C17C2×H(5,𝔽2)11yescharacteristic
773C22×C17#58511yescharacteristic
774C22×C17#58511yescharacteristic
775C2×D17—22no—
776C2×D17—22no—
777C2×D17—22no—
778C2×D17—22no—
779C2×D17—22no—
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—416no—
785C2×D17—41no—
786C2×D17—41no—
787C2×D17—41no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—22no—
801C4×C17—22no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809C4×C17—41no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—22no—
816Dic17—22no—
817Dic17—22no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17#53814yescomplemented
823C24×C4—171no—
824#538—1716no—
825C2×#126—171no—
826C2×#126—171no—
827C2×#124—171no—
828C2×#124—171no—
829C2×#123—171no—
830C2×#123—171no—
831C2×C22⋊Q8—171no—
832C2×#121—171no—
833C2×#121—171no—
834C2×#121—171no—
835C2×#120—171no—
836C2×#120—171no—
837C2×C4×Q8—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4—171no—
846C2×C4×D4—171no—
847C2×C4×D4—171no—
848C2×C4×D4C2×D1711yescharacteristic
849C22×C22⋊C4—171no—
850C22×C22⋊C4—171no—
851C22×C42—171no—
852C22×C42—171no—
853C22×C42—171no—
854C22×C42—171no—
855#391—171no—
856#391—171no—
857#391—171no—
858#390—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390—171no—
863#389—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388C2×D1711yescharacteristic, complemented
890#388C2×D1711yescharacteristic, complemented
891#387—171no—
892#387—171no—
893#387—171no—
894#387—171no—
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387C2×D1711yescharacteristic, complemented
902#387C2×D1711yescharacteristic, complemented
903#386—171no—
904#386—171no—
905#386—171no—
906#386—171no—
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386—171no—
915#386C2×D1711yescharacteristic
916#386C2×D1711yescharacteristic
917#385—171no—
918#385—171no—
919#385—171no—
920#385—171no—
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385C2×D1711yescharacteristic
926#385C2×D1711yescharacteristic
927#383—171no—
928#383C2×D1711yescharacteristic, complemented
929#382—171no—
930#382C2×D1711yescharacteristic, complemented
931#381—171no—
932#381C2×D1711yescharacteristic, complemented
933#380—171no—
934#380—171no—
935#380—171no—
936#380C2×D1711yescharacteristic, complemented
937#379—171no—
938#379—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C4⋊C4—171no—
943C4×C4⋊C4—171no—
944C4×C4⋊C4—171no—
945C4×C4⋊C4—171no—
946C4×C4⋊C4—171no—
947C4×C4⋊C4—171no—
948C4×C4⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956C4×C22⋊C4—171no—
957C4×C22⋊C4—171no—
958C4×C22⋊C4—171no—
959C4×C22⋊C4—171no—
960C4×C22⋊C4—171no—
961C4×C22⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4C2×D1711yescharacteristic
975C2×#95—171no—
976C2×#95C2×D1711yescharacteristic
977C43—171no—
978C43—171no—
979C2×C17—24no—
980C2×C17—42no—
981C2×C17C2×C4×#4111yescharacteristic
982C2×C17C4×H(5,𝔽2)11yescharacteristic
983C2×C17C4×H(5,𝔽2)11yescharacteristic
984C2×C17C2×#53811yescharacteristic
985C2×C17#345511yescharacteristic
986C2×C17#345911yescharacteristic
987C2×C17#346011yescharacteristic
988D17—42no—
989D17—42no—
990D17—42no—
991C25—171no—
992C22×Q8—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—171no—
998C22×D4—171no—
999C22×D4C22×D1711yescharacteristic
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—344no—
1013C23×C4—682no—
1014C23×C4—682no—
1015C23×C4C22×D1711yescharacteristic
1016C23×C4C22×D1711yescharacteristic
1017C23×C4C22×D1711yescharacteristic
1018C23×C4C22×D1711yescharacteristic
1019#126—178no—
1020#126—178no—
1021#124—178no—
1022#124—178no—
1023#123—178no—
1024#123—178no—
1025C22⋊Q8—178no—
1026#121—178no—
1027#121—178no—
1028#121—178no—
1029#120—178no—
1030#120—178no—
1031C4×Q8—682no—
1032C4×D4—178no—
1033C4×D4—344no—
1034C4×D4—344no—
1035C4×D4—344no—
1036C4×D4—344no—
1037C4×D4—682no—
1038C4×D4—682no—
1039C4×D4—682no—
1040C4×D4—682no—
1041C4×D4—682no—
1042C4×D4C4×D1718yescomplemented
1043C2×C4⋊C4—171no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4C22×D1711yescharacteristic
1061C2×C4⋊C4C22×D1711yescharacteristic
1062C2×C4⋊C4C22×D1711yescharacteristic
1063C2×C4⋊C4C22×D1711yescharacteristic
1064C2×C4⋊C4C22×D1711yescharacteristic
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—178no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—344no—
1101C2×C22⋊C4C22×D1711yescharacteristic
1102C2×C22⋊C4C22×D1711yescharacteristic
1103C2×C22⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4C22×D1711yescharacteristic
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C42—171no—
1110C2×C42—171no—
1111C2×C42—171no—
1112C2×C42—171no—
1113C2×C42—171no—
1114C2×C42—171no—
1115C2×C42—171no—
1116C2×C42—171no—
1117C2×C42—171no—
1118C2×C42—171no—
1119C2×C42—171no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—682no—
1133C2×C42—682no—
1134C2×C42—682no—
1135C2×C42—682no—
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95C22×D1711yescharacteristic
1166#95C22×D1711yescharacteristic
1167#95C22×D1711yescharacteristic
1168#95C22×D1711yescharacteristic
1169#95C22×D1711yescharacteristic
1170#95C22×D1711yescharacteristic
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17C4×#53811yescharacteristic, complemented, Sylow
1180C24—171no—
1181C24—171no—
1182C24—171no—
1183C24—174no—
1184C24—342no—
1185C24—342no—
1186C24—681no—
1187C24—681no—
1188C24—681no—
1189C24—681no—
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C2×Q8—174no—
1193C2×Q8—681no—
1194C2×Q8—681no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—174no—
1198C2×D4—174no—
1199C2×D4—174no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—174no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—681no—
1206C2×D4—681no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4—681no—
1215C2×D4C2×C4×D1714yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—171no—
1227C22×C4—174no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—342no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—6816no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4C2×C4×D1714yes—
1277C22×C4C2×C4×D1714yescomplemented
1278C22×C4C23×D1711yescharacteristic
1279C22×C4C23×D1711yescharacteristic
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—174no—
1296C4⋊C4—174no—
1297C4⋊C4—174no—
1298C4⋊C4—174no—
1299C4⋊C4—174no—
1300C4⋊C4—342no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—681no—
1305C4⋊C4—681no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4C2×C4×D1714yescomplemented
1313C22⋊C4—22no—
1314C22⋊C4—22no—
1315C22⋊C4—41no—
1316C22⋊C4—41no—
1317C22⋊C4—41no—
1318C22⋊C4—41no—
1319C22⋊C4—174no—
1320C22⋊C4—174no—
1321C22⋊C4—174no—
1322C22⋊C4—174no—
1323C22⋊C4—174no—
1324C22⋊C4—174no—
1325C22⋊C4—174no—
1326C22⋊C4—174no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
1329C22⋊C4—174no—
1330C22⋊C4—174no—
1331C22⋊C4—342no—
1332C22⋊C4—342no—
1333C22⋊C4—342no—
1334C22⋊C4—342no—
1335C22⋊C4—342no—
1336C22⋊C4—342no—
1337C22⋊C4—342no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—681no—
1342C22⋊C4—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4C2×C4×D1714yes—
1354C22⋊C4C2×C4×D1714yescomplemented
1355C42—41no—
1356C42—41no—
1357C42—174no—
1358C42—342no—
1359C42—342no—
1360C42—342no—
1361C42—342no—
1362C42—342no—
1363C42—342no—
1364C42—342no—
1365C42—342no—
1366C42—342no—
1367C42—342no—
1368C42—342no—
1369C42—342no—
1370C42—681no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42C2×C4×D1714yescomplemented
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—172no—
1392C23—172no—
1393C23—172no—
1394C23—348no—
1395C23—341no—
1396C23—341no—
1397C23—341no—
1398C23—341no—
1399C23—341no—
1400C23—341no—
1401C23—341no—
1402C23—341no—
1403C23—341no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—684no—
1414C23—684no—
1415C23—684no—
1416C23—684no—
1417C23—684no—
1418C23—684no—
1419C23C22×C4×D1712yes—
1420C23C22×C4×D1712yes—
1421C23#41×D1712yes—
1422C23#41×D1712yes—
1423C23C24×D1711yescharacteristic
1424Q8—684no—
1425D4—28no—
1426D4—348no—
1427D4—684no—
1428D4—684no—
1429D4—684no—
1430D4—684no—
1431D4—684no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—44no—
1467C2×C4—44no—
1468C2×C4—44no—
1469C2×C4—44no—
1470C2×C4—172no—
1471C2×C4—172no—
1472C2×C4—172no—
1473C2×C4—172no—
1474C2×C4—172no—
1475C2×C4—172no—
1476C2×C4—172no—
1477C2×C4—172no—
1478C2×C4—172no—
1479C2×C4—172no—
1480C2×C4—172no—
1481C2×C4—348no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—684no—
1511C2×C4—684no—
1512C2×C4—684no—
1513C2×C4—684no—
1514C2×C4—684no—
1515C2×C4—684no—
1516C2×C4—684no—
1517C2×C4—684no—
1518C2×C4—684no—
1519C2×C4—684no—
1520C2×C4—684no—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4C22×C4×D1712yes—
1524C2×C4C22×C4×D1712yes—
1525C2×C4C22×C4×D1712yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—342no—
1540C22—342no—
1541C22—342no—
1542C22—342no—
1543C22—342no—
1544C22—342no—
1545C22—342no—
1546C22—342no—
1547C22—342no—
1548C22—6816no—
1549C22—681no—
1550C22—681no—
1551C22—681no—
1552C22—681no—
1553C22—681no—
1554C22—681no—
1555C22—681no—
1556C22—681no—
1557C22—681no—
1558C22—681no—
1559C22—681no—
1560C22—681no—
1561C22#1176327714yes—
1562C22C23×C4×D1711yescharacteristic
1563C22C2×#41×D1711yescharacteristic
1564C22C2×#41×D1711yescharacteristic
1565C22H(5,𝔽2)×D1711yescharacteristic
1566C22H(5,𝔽2)×D1711yescharacteristic
1567C22#1176364411yescharacteristic
1568C22#1176364611yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—41no—
1582C4—174no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—342no—
1587C4—342no—
1588C4—342no—
1589C4—342no—
1590C4—342no—
1591C4—681no—
1592C4—681no—
1593C4—681no—
1594C4—681no—
1595C2—24no—
1596C2—42no—
1597C2—682no—
1598C2—682no—
1599C2—682no—
1600C2C2×#1176327711yescharacteristic
1601C2#1454198811yescharacteristic
1602C2#1454199011yescharacteristic
1603C2D17×#53811yescharacteristic
1604C2#1454217011yescharacteristic
1605C2#1454219211yescharacteristic
1606C2#1454220311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2318C2
socle, cosocleC23×C17C25
prime radicalC2×#11763392C2
hypercenter#2318D17
hypocenterC17C4×#538
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #14531595C2semidirect
3. #14531594C2semidirect
4. #14531580C2semidirect
5. #14531570C2semidirect
6. #14531565C2semidirect
7. #14531555C2semidirect
8. #14531547C2semidirect
9. #14531546C2semidirect
10. #14531515C2semidirect
11. #14531485C2semidirect
12. #14531447C2semidirect
13. #14531441C2semidirect
14. #14531418C2semidirect
15. #14531379C2semidirect
16. #14531334C2semidirect
17. #14531332C2semidirect
18. #14531325C2semidirect
19. #14531323C2semidirect
20. #14531316C2semidirect
21. #14531305C2semidirect
22. #14531301C2semidirect
23. #14531296C2semidirect
24. #14531294C2semidirect
25. #14531290C2semidirect
26. #14531289C2semidirect
27. #14531285C2semidirect
28. C4×D4×Dic17C2semidirect
29. C4×#10587567C2semidirect
30. C2×#11762656C2semidirect
31. C17×#2318C2semidirect
33. #11763392C4semidirect
46. C2×#10587573C22semidirect
56. C2×#10587567C22semidirect
61. C22×C4×Dic17C22semidirect
62. C2×C42×D17C22semidirect
63. #11762714C22semidirect
64. #11762713C22semidirect
65. #11762713C22semidirect
70. #11762709C22semidirect
71. #11762706C22semidirect
72. #11762705C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
75. #11762703C22semidirect
78. #11762701C22semidirect
93. #11762698C22semidirect
94. #11762698C22semidirect
95. #11762698C22semidirect
96. #11762697C22semidirect
97. #11762696C22semidirect
98. #11762694C22semidirect
99. #11762694C22semidirect
100. #11762691C22semidirect
101. #11762691C22semidirect
102. #11762691C22semidirect
103. #11762691C22semidirect
104. #11762691C22semidirect
105. #11762690C22semidirect
106. #11762690C22semidirect
115. #11762686C22semidirect
118. #11762685C22semidirect
121. #11762683C22semidirect
124. #11762681C22semidirect
127. #11762676C22semidirect
128. #11762673C22semidirect
129. #11762671C22semidirect
130. #11762668C22semidirect
135. C4⋊C4×Dic17C22semidirect
136. C4⋊C4×Dic17C22semidirect
137. C4⋊C4×Dic17C22semidirect
138. C4×#63225C22semidirect
139. C4×C4⋊Dic17C22semidirect
140. #11762660C22semidirect
141. #11762660C22semidirect
142. #11762660C22semidirect
143. #11762660C22semidirect
144. #11762660C22semidirect
149. C22⋊C4×Dic17C22semidirect
150. C22⋊C4×Dic17C22semidirect
151. C22⋊C4×Dic17C22semidirect
152. C4×#63227C22semidirect
154. C4×C22⋊Dic17C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
171. C42×Dic17C22semidirect
172. C42×Dic17C22semidirect
174. C17×#388C22semidirect
175. C17×#388C22semidirect
176. C17×#387C22semidirect
177. C17×#387C22semidirect
182. C17×#383C22semidirect
183. C17×#382C22semidirect
184. C17×#381C22semidirect
185. C17×#380C22semidirect
216. C4×D4×C17C2×C4semidirect
239. #10587625C2×C4semidirect
240. #10587623C2×C4semidirect
243. #10587616C2×C4semidirect
244. #10587615C2×C4semidirect
245. C4×C22⋊D17C2×C4semidirect
247. C2×#63227C2×C4semidirect
319. #10587584C2×C4semidirect
320. #10587580C2×C4semidirect
324. #10587571C2×C4semidirect
325. #10587570C2×C4semidirect
326. #10587568C2×C4semidirect
332. #10587564C2×C4semidirect
333. #10587562C2×C4semidirect
334. #10587561C2×C4semidirect
402. C22×C4×C17C22×C4semidirect
427. C2×C22⋊D17C22×C4semidirect
483. C2×C4×D17C22×C4semidirect
486. C2×Dic34C22×C4semidirect
491. C4⋊C4×C17C22×C4semidirect
499. C22⋊C4×C17C22×C4semidirect
502. C42×C17C22×C4semidirect
508. C22⋊Dic17C22×C4semidirect
535. #63227C22×C4semidirect
536. #63227C22×C4semidirect
539. C4⋊Dic17C22×C4semidirect
550. #63225C22×C4semidirect
551. #63225C22×C4semidirect
552. #63225C22×C4semidirect
553. #63225C22×C4semidirect
576. C4×Dic17C22×C4semidirect
737. #2318D17semidirect
822. Dic17#538semidirect
889. #388C2×D17semidirect
890. #388C2×D17semidirect
901. #387C2×D17semidirect
902. #387C2×D17semidirect
928. #383C2×D17semidirect
930. #382C2×D17semidirect
932. #381C2×D17semidirect
936. #380C2×D17semidirect
1042. C4×D4C4×D17semidirect
1179. C17C4×#538semidirect
1277. C22×C4C2×C4×D17semidirect
1312. C4⋊C4C2×C4×D17semidirect
1354. C22⋊C4C2×C4×D17semidirect
1380. C42C2×C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117633922
#145315952
#145315942
#145315802
#145315702
#145315652
#145315552
#145315472
#145315462
#145315152
#145314852
#145314472
#145314412
#145314182
#145313792
#145313342
#145313322
#145313252
#145313232
#145313162
#145313052
#145313012
#145312962
#145312942
#145312902
#145312892
#145312852
C4×D4×Dic172
C4×#105875672
C2×#117626562
C17×#23182
C4×#53817