Finite Group Databasebeta

← #17198311

Subgroups — #17198311

Order 4352.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763375C211yesmaximal, characteristic
2#14531943C211yesmaximal, characteristic, complemented
3#14531936C211yesmaximal, characteristic, complemented
4#14531924C211yesmaximal, characteristic, complemented
5#14531921C211yesmaximal, characteristic, complemented
6#14531858C211yesmaximal, characteristic, complemented
7#14531856C211yesmaximal, characteristic, complemented
8#14531847C211yesmaximal, characteristic, complemented
9#14531845C211yesmaximal, characteristic, complemented
10#14531834C211yesmaximal, characteristic, complemented
11#14531833C211yesmaximal, characteristic, complemented
12#14531766C211yesmaximal, characteristic, complemented
13#14531764C211yesmaximal, characteristic, complemented
14#14531624C211yesmaximal, characteristic, complemented
15#14531608C211yesmaximal, characteristic, complemented
16#14531602C211yesmaximal, characteristic, complemented
17#14531602C211yesmaximal, characteristic, complemented
18#14531548C211yesmaximal, characteristic, complemented
19#14531505C211yesmaximal, characteristic, complemented
20#14531493C211yesmaximal, characteristic, complemented
21#14531489C211yesmaximal, characteristic, complemented
22#14531483C211yesmaximal, characteristic, complemented
23#14531447C211yesmaximal, characteristic, complemented
24#14531444C211yesmaximal, characteristic, complemented
25#14531443C211yesmaximal, characteristic, complemented
26#14531437C211yesmaximal, characteristic, complemented
27#14531390C211yesmaximal, characteristic, complemented
28#14531348C211yesmaximal, characteristic, complemented
29C4×#10587571C211yesmaximal, characteristic, complemented
30#14531276C211yesmaximal, characteristic, complemented
31C17×#2333C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34#11763375C4116yescomplemented
35C2×#10587626C2211yescharacteristic
36C2×#10587626C2211yescharacteristic
37C2×#10587571C2211yescharacteristic
38C2×#10587571C2211yescharacteristic
39C2×#10587581C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587624C2211yescharacteristic
42C2×#10587568C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587623C2211yescharacteristic
45C2×#10587623C2211yescharacteristic
46C2×C4×Dic34C2211yescharacteristic, complemented
47C2×C4×Dic34C2211yescharacteristic, complemented
48C2×C4×D68C2211yescharacteristic, complemented
49C2×D4×Dic17C2211yescharacteristic, complemented
50C2×D4×Dic17C2211yescharacteristic, complemented
51C2×#10587579C2211yescharacteristic, complemented
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic, complemented
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic, complemented
58C2×#10587567C2211yescharacteristic, complemented
59C2×#10587567C2211yescharacteristic, complemented
60C2×#10587567C2211yescharacteristic, complemented
61C2×#10587567C2211yescharacteristic, complemented
62C2×#10587578C2211yescharacteristic
63C22×#63227C2211yescharacteristic
64C22×#63227C2211yescharacteristic
65C2×C22⋊C4×D17C2211yescharacteristic
66C2×C22⋊C4×D17C2211yescharacteristic
67#11762713C2211yescharacteristic, complemented
68#11762713C2211yescharacteristic, complemented
69#11762711C2211yescharacteristic
70#11762711C2211yescharacteristic
71#11762711C2211yescharacteristic, complemented
72#11762710C2211yescharacteristic, complemented
73#11762709C2211yescharacteristic
74#11762709C2211yescharacteristic
75#11762709C2211yescharacteristic
76#11762709C2211yescharacteristic
77#11762709C2211yescharacteristic
78#11762709C2211yescharacteristic
79#11762709C2211yescharacteristic, complemented
80#11762709C2211yescharacteristic, complemented
81#11762709C2211yescharacteristic, complemented
82#11762709C2211yescharacteristic, complemented
83#11762709C2211yescharacteristic, complemented
84#11762709C2211yescharacteristic, complemented
85#11762703C2211yescharacteristic, complemented
86#11762703C2211yescharacteristic, complemented
87#11762702C2211yescharacteristic, complemented
88#11762702C2211yescharacteristic, complemented
89#11762701C2211yescharacteristic
90#11762701C2211yescharacteristic
91#11762701C2211yescharacteristic, complemented
92#11762701C2211yescharacteristic, complemented
93#11762701C2211yescharacteristic, complemented
94#11762700C2211yescharacteristic
95#11762700C2211yescharacteristic
96#11762700C2211yescharacteristic, complemented
97#11762700C2211yescharacteristic, complemented
98#11762700C2211yescharacteristic, complemented
99#11762699C2211yescharacteristic
100#11762699C2211yescharacteristic
101#11762699C2211yescharacteristic, complemented
102#11762698C2211yescharacteristic
103#11762698C2211yescharacteristic
104#11762698C2211yescharacteristic, complemented
105#11762697C2211yescharacteristic, complemented
106#11762697C2211yescharacteristic, complemented
107#11762695C2211yescharacteristic, complemented
108#11762695C2211yescharacteristic, complemented
109#11762694C2211yescharacteristic, complemented
110#11762694C2211yescharacteristic, complemented
111#11762692C2211yescharacteristic, complemented
112#11762692C2211yescharacteristic, complemented
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic
115#11762689C2211yescharacteristic, complemented
116#11762689C2211yescharacteristic, complemented
117#11762688C2211yescharacteristic, complemented
118#11762687C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762687C2211yescharacteristic
124#11762687C2211yescharacteristic, complemented
125#11762687C2211yescharacteristic, complemented
126#11762687C2211yescharacteristic, complemented
127#11762687C2211yescharacteristic, complemented
128#11762686C2211yescharacteristic
129#11762686C2211yescharacteristic
130#11762686C2211yescharacteristic, complemented
131#11762686C2211yescharacteristic, complemented
132#11762686C2211yescharacteristic, complemented
133#11762685C2211yescharacteristic, complemented
134#11762685C2211yescharacteristic, complemented
135#11762685C2211yescharacteristic, complemented
136#11762685C2211yescharacteristic, complemented
137#11762684C2211yescharacteristic, complemented
138#11762684C2211yescharacteristic, complemented
139#11762683C2211yescharacteristic, complemented
140#11762683C2211yescharacteristic, complemented
141#11762683C2211yescharacteristic, complemented
142#11762682C2211yescharacteristic, complemented
143#11762681C2211yescharacteristic, complemented
144#11762680C2211yescharacteristic, complemented
145#11762678C2211yescharacteristic, complemented
146#11762673C2211yescharacteristic, complemented
147#11762671C2211yescharacteristic, complemented
148#11762669C2211yescharacteristic, complemented
149#11762668C2211yescharacteristic
150#11762668C2211yescharacteristic
151#11762668C2211yescharacteristic, complemented
152#11762664C2211yescharacteristic
153#11762664C2211yescharacteristic
154#11762664C2211yescharacteristic
155#11762664C2211yescharacteristic
156C4⋊C4×Dic17C2211yescharacteristic, complemented
157C4×#63225C2211yescharacteristic, complemented
158#11762660C2211yescharacteristic, complemented
159#11762660C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C17×#390C2211yescharacteristic, complemented
175C17×#390C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic, complemented
184C17×#381C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C2×D4×D17—42no—
209C2×D4×D17—42no—
210C2×D4×D17C2×C418yescomplemented
211C2×#63252—42no—
212C2×#63252—42no—
213C2×#63252C2×C418yescomplemented
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×D68C2311yescharacteristic
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×Dic34C2311yescharacteristic
227C17×#121C2×C418yescomplemented
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊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×C42×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257#10587626C2×C418yescomplemented
258#10587626C2×C418yescomplemented
259#10587624C2×C418yescomplemented
260#10587623C2×C418yescomplemented
261#10587623C2×C418yescomplemented
262D4×Dic17—42no—
263D4×Dic17—42no—
264#10587616C2×C418yescomplemented
265C4×C22⋊D17—42no—
266C4×C22⋊D17—42no—
267C4×C22⋊D17—42no—
268C2×#63227—42no—
269C2×#63227—42no—
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×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331#10587581C2×C418yescomplemented
332#10587579—42no—
333#10587578C2×C418yescomplemented
334#10587571C2×C418yescomplemented
335#10587571C2×C418yescomplemented
336#10587568C2×C418yescomplemented
337#10587568C2×C418yescomplemented
338#10587567—42no—
339#10587567—42no—
340#10587567—42no—
341#10587567—42no—
342#10587567—42no—
343#10587567—42no—
344#10587567—42no—
345C22⋊C4×D17—42no—
346C22⋊C4×D17—42no—
347C4×D68—42no—
348C4×Dic34—42no—
349C4×Dic34—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
384C24×C17C2411yescharacteristic
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
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×D17C22×C414yes—
398C23×D17C22×C414yes—
399C23×D17C2411yescharacteristic
400C23×D17C2411yescharacteristic
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17C22×C414yes—
410C2×D4×C17C22×C414yes—
411C2×D4×C17C22×C414yes—
412C22×C4×C17—22no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17C22×C414yes—
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
432C22×C4×C17C2411yescharacteristic
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17C22×C414yes—
450C2×C22⋊D17C22×C414yes—
451C2×C22⋊D17C22×C414yes—
452C2×C22⋊D17C22×C414yes—
453C2×C22⋊D17C22×C414yes—
454C2×C22⋊D17C22×C414yes—
455C2×C22⋊D17C22×C414yes—
456C2×C22⋊D17C22×C414yes—
457C22×Dic17—22no—
458C22×Dic17—22no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481D4×D17—416no—
482#63252—416no—
483C2×D68—41no—
484C2×D68—41no—
485C2×D68—41no—
486C2×D68—41no—
487C2×D68—41no—
488C2×D68—41no—
489C2×D68—41no—
490C2×D68—41no—
491C2×D68C22×C414yes—
492C2×D68C22×C414yes—
493C2×D68C22×C414yes—
494C2×D68C22×C414yes—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
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×D17C22×C414yes—
518C2×C4×D17C22×C414yes—
519C2×Dic34—22no—
520C2×Dic34—22no—
521C2×Dic34C22×C414yes—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17C22×C414yes—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—41no—
528C22⋊C4×C17—41no—
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—
537C42×C17—41no—
538C42×C17—41no—
539C42×C17—41no—
540C42×C17—41no—
541C22⋊Dic17—22no—
542C22⋊Dic17—41no—
543C22⋊Dic17—41no—
544C22⋊Dic17—41no—
545C22⋊Dic17—41no—
546C22⋊Dic17—41no—
547C22⋊Dic17—41no—
548C22⋊Dic17—41no—
549C22⋊Dic17C22×C414yes—
550C22⋊Dic17C22×C414yes—
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
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#63227C22×C414yes—
578#63227C22×C414yes—
579#63227C22×C414yes—
580#63227C22×C414yes—
581#63227C22×C414yes—
582#63227C22×C414yes—
583C4⋊Dic17—22no—
584C4⋊Dic17—41no—
585C4⋊Dic17—41no—
586C4⋊Dic17—41no—
587C4⋊Dic17C22×C414yes—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—41no—
594#63225—41no—
595#63225—41no—
596#63225—41no—
597#63225—41no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
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×Dic17C22×C414yes—
611C4×Dic17C22×C414yes—
612#34438—171nomaximal, Sylow
613C23×C17—21no—
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×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17C23×C412yes—
632C23×C17C23×C412yes—
633C23×C17C23×C412yes—
634C23×C17C2511yescharacteristic
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—21no—
658C22×D17—21no—
659C22×D17—44no—
660C22×D17—44no—
661C22×D17—44no—
662C22×D17—44no—
663C22×D17—44no—
664C22×D17—44no—
665C22×D17—82no—
666C22×D17—82no—
667C22×D17—82no—
668C22×D17—82no—
669C22×D17—82no—
670C22×D17—82no—
671C22×D17—82no—
672C22×D17—82no—
673C22×D17C23×C412yes—
674C22×D17C23×C412yes—
675C22×D17C23×C412yes—
676C22×D17C23×C412yes—
677D4×C17—44no—
678D4×C17—44no—
679D4×C17—44no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
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—44no—
712C2×C4×C17—82no—
713C2×C4×C17—82no—
714C2×C4×C17C23×C412yes—
715C2×C4×C17C23×C412yes—
716C2×C4×C17C23×C412yes—
717C2×C4×C17C23×C412yes—
718C2×C4×C17H(5,𝔽2)12yes—
719C22⋊D17—28no—
720C22⋊D17—28no—
721C22⋊D17—28no—
722C22⋊D17—44no—
723C22⋊D17—44no—
724C22⋊D17—44no—
725C22⋊D17—44no—
726C22⋊D17—44no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
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—82no—
757C2×Dic17—82no—
758C2×Dic17—82no—
759C2×Dic17—82no—
760C2×Dic17C23×C412yes—
761C2×Dic17C23×C412yes—
762C2×Dic17C23×C412yes—
763C2×Dic17C23×C412yes—
764C2×Dic17H(5,𝔽2)12yes—
765C2×Dic17H(5,𝔽2)12yes—
766C2×Dic17H(5,𝔽2)12yes—
767D68—44no—
768D68—44no—
769D68—44no—
770D68—44no—
771C4×D17—28no—
772C4×D17—44no—
773C4×D17—82no—
774C4×D17—82no—
775C4×D17—82no—
776C4×D17—82no—
777C4×D17—82no—
778C4×D17—82no—
779Dic34—28no—
780C2×#535—171no—
781#2377—171no—
782#2377—171no—
783#2375—171no—
784#2375—171no—
785#2367—171no—
786#2367—171no—
787#2366—171no—
788#2366—171no—
789#2364—171no—
790#2364—171no—
791#2358—171no—
792#2358—171no—
793#2341—171no—
794#2339—171no—
795D4×C22⋊C4—171no—
796D4×C22⋊C4—171no—
797#2333—171no—
798#2333D1711yescharacteristic, complemented
799#2328—171no—
800#2326—171no—
801#2325—171no—
802#2325—171no—
803#2321—171no—
804#2321—171no—
805#2321—171no—
806#2321—171no—
807#2314—171no—
808C4×#127—171no—
809C4×#124—171no—
810#2298—171no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—22no—
814C22×C17—22no—
815C22×C17—22no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—22no—
820C22×C17—41no—
821C22×C17—41no—
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×C17—41no—
831C22×C17—41no—
832C22×C17C24×C411yescharacteristic
833C22×C17C2×H(5,𝔽2)11yescharacteristic
834C22×C17C2×H(5,𝔽2)11yescharacteristic
835C22×C17C2×H(5,𝔽2)11yescharacteristic
836C22×C17C2×H(5,𝔽2)11yescharacteristic
837C22×C17#58511yescharacteristic
838C22×C17#58511yescharacteristic
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—41no—
852C2×D17—41no—
853C2×D17—41no—
854C2×D17—41no—
855C2×D17—41no—
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—88no—
868C2×D17—88no—
869C4×C17—22no—
870C4×C17—22no—
871C4×C17—22no—
872C4×C17—22no—
873C4×C17—22no—
874C4×C17—41no—
875C4×C17—41no—
876C4×C17—41no—
877C4×C17—41no—
878C4×C17—41no—
879C4×C17—41no—
880C4×C17—41no—
881Dic17—22no—
882Dic17—22no—
883Dic17—22no—
884Dic17—22no—
885Dic17—41no—
886Dic17—41no—
887Dic17—41no—
888Dic17—41no—
889Dic17—41no—
890Dic17—41no—
891Dic17—41no—
892Dic17#51814yes—
893C22×#41—171no—
894C23×D4—171no—
895#535—1716no—
896C2×#127—171no—
897C2×#127—171no—
898C2×#124—171no—
899C2×#124—171no—
900C2×#121—171no—
901C2×#121—171no—
902C2×#121—171no—
903C2×#121C2×D1711yescharacteristic
904C2×#120—171no—
905C2×#120—171no—
906C2×#120—171no—
907C2×#120—171no—
908C2×C4×Q8—171no—
909C2×C4×Q8—171no—
910C2×C4×D4—171no—
911C2×C4×D4—171no—
912C2×C4×D4—171no—
913C2×C4×D4—171no—
914C2×C4×D4—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×C4×D4—171no—
924C2×#117—171no—
925C22×C22⋊C4—171no—
926C22×C22⋊C4—171no—
927C22×C22⋊C4—171no—
928C22×C22⋊C4—171no—
929#391—171no—
930#391—171no—
931#390—171no—
932#390—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#390C2×D1711yescharacteristic, complemented
948#390C2×D1711yescharacteristic, complemented
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
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#388C2×D1711yescharacteristic, complemented
972#388C2×D1711yescharacteristic, complemented
973#387—171no—
974#387—171no—
975#387—171no—
976#387—171no—
977#387—171no—
978#387—171no—
979#387C2×D1711yescharacteristic, complemented
980#387C2×D1711yescharacteristic, complemented
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
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#386C2×D1711yescharacteristic
1006#386C2×D1711yescharacteristic
1007#386C2×D1711yescharacteristic, complemented
1008#386C2×D1711yescharacteristic, complemented
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#384—171no—
1018#382—171no—
1019#381—171no—
1020#381C2×D1711yescharacteristic, complemented
1021#380—171no—
1022#380—171no—
1023#380—171no—
1024#380—171no—
1025#379—171no—
1026#379—171no—
1027#379—171no—
1028#379—171no—
1029C4×C4⋊C4—171no—
1030C4×C4⋊C4—171no—
1031C4×C4⋊C4—171no—
1032C4×C4⋊C4—171no—
1033C4×C22⋊C4—171no—
1034C4×C22⋊C4—171no—
1035C4×C22⋊C4—171no—
1036C4×C22⋊C4—171no—
1037C4×C22⋊C4—171no—
1038C4×C22⋊C4—171no—
1039C4×C22⋊C4—171no—
1040C4×C22⋊C4—171no—
1041C4×C22⋊C4—171no—
1042C4×C22⋊C4C2×D1711yescharacteristic, complemented
1043C4×C22⋊C4C2×D1711yescharacteristic, complemented
1044C4×C22⋊C4C2×D1711yescharacteristic, complemented
1045#376—171no—
1046C2×#95—171no—
1047C2×#95—171no—
1048C43—171no—
1049C2×C17—42no—
1050C2×C17—42no—
1051C2×C17—42no—
1052C2×C17C2×#51811yescharacteristic
1053C2×C17C4×H(5,𝔽2)11yescharacteristic
1054C2×C17C4×H(5,𝔽2)11yescharacteristic
1055C2×C17#354311yescharacteristic
1056C2×C17#354611yescharacteristic
1057C2×C17#355811yescharacteristic
1058C2×C17#356211yescharacteristic
1059D17—42no—
1060D17—42no—
1061D17—42no—
1062D17—42no—
1063C25—171no—
1064C25—171no—
1065C2×#41—178no—
1066C2×#41—682no—
1067C2×#41—682no—
1068C22×Q8—171no—
1069C22×D4—171no—
1070C22×D4—171no—
1071C22×D4—171no—
1072C22×D4—171no—
1073C22×D4—171no—
1074C22×D4—171no—
1075C22×D4—171no—
1076C22×D4—171no—
1077C22×D4—178no—
1078C22×D4—171no—
1079C22×D4—171no—
1080C22×D4—171no—
1081C22×D4—171no—
1082C22×D4—682no—
1083C22×D4—682no—
1084C22×D4C22×D1711yescharacteristic
1085C22×D4C22×D1711yescharacteristic
1086C22×D4C22×D1711yescharacteristic
1087C23×C4—171no—
1088C23×C4—171no—
1089C23×C4—171no—
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×C4C22×D1711yescharacteristic
1100C23×C4C22×D1711yescharacteristic
1101C23×C4C22×D1711yescharacteristic
1102#127—178no—
1103#127—178no—
1104#124—178no—
1105#124—178no—
1106#121—178no—
1107#121—178no—
1108#121—178no—
1109#121C4×D1718yescomplemented
1110#120—178no—
1111#120—178no—
1112#120—178no—
1113#120—178no—
1114C4×Q8—682no—
1115C4×Q8—682no—
1116C4×D4—682no—
1117C4×D4—682no—
1118C4×D4—682no—
1119C4×D4—682no—
1120C4×D4—682no—
1121C4×D4—682no—
1122C4×D4—682no—
1123C4×D4—682no—
1124C4×D4—682no—
1125C4×D4—682no—
1126C4×D4—682no—
1127C4×D4—682no—
1128C4×D4—682no—
1129C4×D4—682no—
1130#117—178no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
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×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
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—171no—
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—682no—
1192C2×C22⋊C4—682no—
1193C2×C22⋊C4—682no—
1194C2×C22⋊C4—682no—
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C22⋊C4C22×D1711yescharacteristic
1199C2×C22⋊C4C22×D1711yescharacteristic
1200C2×C22⋊C4C22×D1711yescharacteristic
1201C2×C22⋊C4C22×D1711yescharacteristic
1202C2×C22⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4C22×D1711yescharacteristic
1204C2×C22⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C42—171no—
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—171no—
1214C2×C42—171no—
1215C2×C42—171no—
1216C2×C42—171no—
1217C2×C42—171no—
1218C2×C42—171no—
1219C2×C42—171no—
1220C2×C42—171no—
1221C2×C42C22×D1711yescharacteristic
1222C2×C42C22×D1711yescharacteristic
1223C2×C42C22×D1711yescharacteristic
1224C2×C42C22×D1711yescharacteristic
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
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#95C22×D1711yescharacteristic
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252#95C22×D1711yescharacteristic
1253#95C22×D1711yescharacteristic
1254#95C22×D1711yescharacteristic
1255#95C22×D1711yescharacteristic
1256#95C22×D1711yescharacteristic
1257C17#3443811yescharacteristic, complemented, Sylow
1258C24—171no—
1259C24—171no—
1260C24—171no—
1261C24—171no—
1262C24—174no—
1263C24—174no—
1264C24—681no—
1265C24—681no—
1266C24—681no—
1267C24—681no—
1268C24—681no—
1269C24—681no—
1270C24—681no—
1271C24—681no—
1272C24—681no—
1273C24—681no—
1274C24—681no—
1275C24—681no—
1276C24C23×D1711yescharacteristic
1277C24C23×D1711yescharacteristic
1278C24C23×D1711yescharacteristic
1279#41—6816no—
1280C2×Q8—174no—
1281C2×Q8—342no—
1282C2×Q8—342no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—41no—
1286C2×D4—41no—
1287C2×D4—41no—
1288C2×D4—41no—
1289C2×D4—174no—
1290C2×D4—174no—
1291C2×D4—174no—
1292C2×D4—174no—
1293C2×D4—174no—
1294C2×D4—174no—
1295C2×D4—174no—
1296C2×D4—174no—
1297C2×D4—174no—
1298C2×D4—174no—
1299C2×D4—174no—
1300C2×D4—174no—
1301C2×D4—342no—
1302C2×D4—342no—
1303C2×D4—342no—
1304C2×D4—342no—
1305C2×D4—342no—
1306C2×D4—342no—
1307C2×D4—681no—
1308C2×D4—681no—
1309C2×D4—681no—
1310C2×D4—681no—
1311C2×D4—681no—
1312C2×D4—681no—
1313C2×D4—681no—
1314C2×D4—681no—
1315C2×D4—6816no—
1316C2×D4—681no—
1317C2×D4—681no—
1318C2×D4—681no—
1319C2×D4—681no—
1320C2×D4—681no—
1321C2×D4—681no—
1322C2×D4—681no—
1323C2×D4—681no—
1324C2×D4—681no—
1325C2×D4—681no—
1326C2×D4C2×C4×D1714yes—
1327C2×D4C2×C4×D1714yes—
1328C2×D4C2×C4×D1714yes—
1329C22×C4—22no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—41no—
1335C22×C4—41no—
1336C22×C4—41no—
1337C22×C4—171no—
1338C22×C4—171no—
1339C22×C4—171no—
1340C22×C4—171no—
1341C22×C4—171no—
1342C22×C4—174no—
1343C22×C4—174no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—171no—
1349C22×C4—171no—
1350C22×C4—171no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4—681no—
1361C22×C4—681no—
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×C4C2×C4×D1714yes—
1386C22×C4C23×D1711yescharacteristic
1387C22×C4C23×D1711yescharacteristic
1388C22×C4C23×D1711yescharacteristic
1389C22×C4C23×D1711yescharacteristic
1390C22×C4C23×D1711yescharacteristic
1391C22×C4C23×D1711yescharacteristic
1392C22×C4C23×D1711yescharacteristic
1393C22×C4C23×D1711yescharacteristic
1394C22×C4C23×D1711yescharacteristic
1395C22×C4C23×D1711yescharacteristic
1396C22×C4C23×D1711yescharacteristic
1397C22×C4C23×D1711yescharacteristic
1398C4⋊C4—41no—
1399C4⋊C4—41no—
1400C4⋊C4—174no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—681no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C4⋊C4—681no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4C2×C4×D1714yes—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—41no—
1419C22⋊C4—41no—
1420C22⋊C4—41no—
1421C22⋊C4—41no—
1422C22⋊C4—41no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—174no—
1427C22⋊C4—174no—
1428C22⋊C4—174no—
1429C22⋊C4—174no—
1430C22⋊C4—174no—
1431C22⋊C4—174no—
1432C22⋊C4—174no—
1433C22⋊C4—174no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—681no—
1441C22⋊C4—681no—
1442C22⋊C4—681no—
1443C22⋊C4—681no—
1444C22⋊C4—681no—
1445C22⋊C4—681no—
1446C22⋊C4—681no—
1447C22⋊C4—681no—
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⋊C4C2×C4×D1714yes—
1469C22⋊C4C2×C4×D1714yes—
1470C42—41no—
1471C42—41no—
1472C42—41no—
1473C42—41no—
1474C42—174no—
1475C42—174no—
1476C42—342no—
1477C42—342no—
1478C42—342no—
1479C42—342no—
1480C42—342no—
1481C42—342no—
1482C42—681no—
1483C42—681no—
1484C42—681no—
1485C42—681no—
1486C42—681no—
1487C42—681no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—172no—
1507C23—172no—
1508C23—172no—
1509C23—172no—
1510C23—341no—
1511C23—341no—
1512C23—341no—
1513C23—341no—
1514C23—341no—
1515C23—341no—
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—684no—
1535C23—684no—
1536C23—684no—
1537C23—684no—
1538C23—684no—
1539C23—684no—
1540C23—1362no—
1541C23—1362no—
1542C23—1362no—
1543C23—1362no—
1544C23—1362no—
1545C23—1362no—
1546C23—1362no—
1547C23—1362no—
1548C23C22×C4×D1712yes—
1549C23C22×C4×D1712yes—
1550C23C22×C4×D1712yes—
1551C23C24×D1711yescharacteristic
1552Q8—348no—
1553D4—44no—
1554D4—44no—
1555D4—44no—
1556D4—348no—
1557D4—348no—
1558D4—348no—
1559D4—684no—
1560D4—684no—
1561D4—684no—
1562D4—684no—
1563D4—684no—
1564D4—684no—
1565D4—684no—
1566D4—684no—
1567D4—684no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
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—44no—
1600C2×C4—82no—
1601C2×C4—82no—
1602C2×C4—172no—
1603C2×C4—172no—
1604C2×C4—172no—
1605C2×C4—172no—
1606C2×C4—172no—
1607C2×C4—172no—
1608C2×C4—172no—
1609C2×C4—348no—
1610C2×C4—341no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
1615C2×C4—341no—
1616C2×C4—341no—
1617C2×C4—341no—
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—684no—
1640C2×C4—1362no—
1641C2×C4—1362no—
1642C2×C4—1362no—
1643C2×C4—1362no—
1644C2×C4—1362no—
1645C2×C4—1362no—
1646C2×C4—1362no—
1647C2×C4—1362no—
1648C2×C4—1362no—
1649C2×C4—1362no—
1650C2×C4C22×C4×D1712yes—
1651C2×C4C22×C4×D1712yes—
1652C2×C4C22×C4×D1712yes—
1653C2×C4C22×C4×D1712yes—
1654C2×C4#1058769612yes—
1655C22—22no—
1656C22—22no—
1657C22—22no—
1658C22—22no—
1659C22—22no—
1660C22—22no—
1661C22—22no—
1662C22—22no—
1663C22—22no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—342no—
1677C22—342no—
1678C22—342no—
1679C22—342no—
1680C22—342no—
1681C22—342no—
1682C22—342no—
1683C22—342no—
1684C22—342no—
1685C22—342no—
1686C22—342no—
1687C22—342no—
1688C22—681no—
1689C22—681no—
1690C22—681no—
1691C22—681no—
1692C22—681no—
1693C22—681no—
1694C22—681no—
1695C22—681no—
1696C22—681no—
1697C22—681no—
1698C22—681no—
1699C22—681no—
1700C22—681no—
1701C22—681no—
1702C22—681no—
1703C22—681no—
1704C22—1368no—
1705C22—1368no—
1706C22C23×C4×D1711yescharacteristic
1707C22H(5,𝔽2)×D1711yescharacteristic
1708C22H(5,𝔽2)×D1711yescharacteristic
1709C22H(5,𝔽2)×D1711yescharacteristic
1710C22C2×#1058769611yescharacteristic
1711C22#1176364411yescharacteristic
1712C22#1176364511yescharacteristic
1713C4—22no—
1714C4—22no—
1715C4—22no—
1716C4—22no—
1717C4—22no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4—174no—
1726C4—342no—
1727C4—342no—
1728C4—342no—
1729C4—342no—
1730C4—681no—
1731C4—681no—
1732C4—681no—
1733C4—681no—
1734C4—681no—
1735C4—681no—
1736C4—681no—
1737C2—42no—
1738C2—42no—
1739C2—42no—
1740C2—682no—
1741C2—682no—
1742C2—682no—
1743C2—682no—
1744C2D17×#51811yescharacteristic
1745C2#1454198811yescharacteristic
1746C2C4×#1058769611yescharacteristic
1747C2#1454311311yescharacteristic
1748C2#1454314911yescharacteristic
1749C2#1454330511yescharacteristic
1750C2#1454336311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2333C2
socle, cosocleC23×C17C25
prime radicalC2×#11763375C2
hypercenter#2333D17
hypocenterC17#34438
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #14531943C2semidirect
3. #14531936C2semidirect
4. #14531924C2semidirect
5. #14531921C2semidirect
6. #14531858C2semidirect
7. #14531856C2semidirect
8. #14531847C2semidirect
9. #14531845C2semidirect
10. #14531834C2semidirect
11. #14531833C2semidirect
12. #14531766C2semidirect
13. #14531764C2semidirect
14. #14531624C2semidirect
15. #14531608C2semidirect
16. #14531602C2semidirect
17. #14531602C2semidirect
18. #14531548C2semidirect
19. #14531505C2semidirect
20. #14531493C2semidirect
21. #14531489C2semidirect
22. #14531483C2semidirect
23. #14531447C2semidirect
24. #14531444C2semidirect
25. #14531443C2semidirect
26. #14531437C2semidirect
27. #14531390C2semidirect
28. #14531348C2semidirect
29. C4×#10587571C2semidirect
30. #14531276C2semidirect
31. C17×#2333C2semidirect
34. #11763375C4semidirect
46. C2×C4×Dic34C22semidirect
47. C2×C4×Dic34C22semidirect
48. C2×C4×D68C22semidirect
49. C2×D4×Dic17C22semidirect
50. C2×D4×Dic17C22semidirect
51. C2×#10587579C22semidirect
54. C2×C4×C22⋊D17C22semidirect
57. C2×#10587567C22semidirect
58. C2×#10587567C22semidirect
59. C2×#10587567C22semidirect
60. C2×#10587567C22semidirect
61. C2×#10587567C22semidirect
67. #11762713C22semidirect
68. #11762713C22semidirect
71. #11762711C22semidirect
72. #11762710C22semidirect
79. #11762709C22semidirect
80. #11762709C22semidirect
81. #11762709C22semidirect
82. #11762709C22semidirect
83. #11762709C22semidirect
84. #11762709C22semidirect
85. #11762703C22semidirect
86. #11762703C22semidirect
87. #11762702C22semidirect
88. #11762702C22semidirect
91. #11762701C22semidirect
92. #11762701C22semidirect
93. #11762701C22semidirect
96. #11762700C22semidirect
97. #11762700C22semidirect
98. #11762700C22semidirect
101. #11762699C22semidirect
104. #11762698C22semidirect
105. #11762697C22semidirect
106. #11762697C22semidirect
107. #11762695C22semidirect
108. #11762695C22semidirect
109. #11762694C22semidirect
110. #11762694C22semidirect
111. #11762692C22semidirect
112. #11762692C22semidirect
115. #11762689C22semidirect
116. #11762689C22semidirect
117. #11762688C22semidirect
124. #11762687C22semidirect
125. #11762687C22semidirect
126. #11762687C22semidirect
127. #11762687C22semidirect
130. #11762686C22semidirect
131. #11762686C22semidirect
132. #11762686C22semidirect
133. #11762685C22semidirect
134. #11762685C22semidirect
135. #11762685C22semidirect
136. #11762685C22semidirect
137. #11762684C22semidirect
138. #11762684C22semidirect
139. #11762683C22semidirect
140. #11762683C22semidirect
141. #11762683C22semidirect
142. #11762682C22semidirect
143. #11762681C22semidirect
144. #11762680C22semidirect
145. #11762678C22semidirect
146. #11762673C22semidirect
147. #11762671C22semidirect
148. #11762669C22semidirect
151. #11762668C22semidirect
156. C4⋊C4×Dic17C22semidirect
157. C4×#63225C22semidirect
158. #11762660C22semidirect
159. #11762660C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×C22⋊Dic17C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762654C22semidirect
170. C2×#10587502C22semidirect
171. #95×D17C22semidirect
172. C42×Dic17C22semidirect
174. C17×#390C22semidirect
175. C17×#390C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
182. C17×#386C22semidirect
183. C17×#386C22semidirect
184. C17×#381C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
210. C2×D4×D17C2×C4semidirect
213. C2×#63252C2×C4semidirect
227. C17×#121C2×C4semidirect
257. #10587626C2×C4semidirect
258. #10587626C2×C4semidirect
259. #10587624C2×C4semidirect
260. #10587623C2×C4semidirect
261. #10587623C2×C4semidirect
264. #10587616C2×C4semidirect
331. #10587581C2×C4semidirect
333. #10587578C2×C4semidirect
334. #10587571C2×C4semidirect
335. #10587571C2×C4semidirect
336. #10587568C2×C4semidirect
337. #10587568C2×C4semidirect
798. #2333D17semidirect
947. #390C2×D17semidirect
948. #390C2×D17semidirect
971. #388C2×D17semidirect
972. #388C2×D17semidirect
979. #387C2×D17semidirect
980. #387C2×D17semidirect
1007. #386C2×D17semidirect
1008. #386C2×D17semidirect
1020. #381C2×D17semidirect
1042. C4×C22⋊C4C2×D17semidirect
1043. C4×C22⋊C4C2×D17semidirect
1044. C4×C22⋊C4C2×D17semidirect
1109. #121C4×D17semidirect
1257. C17#34438semidirect

Maximal subgroups

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

subgroupindex
C2×#117633752
#145319432
#145319362
#145319242
#145319212
#145318582
#145318562
#145318472
#145318452
#145318342
#145318332
#145317662
#145317642
#145316242
#145316082
#145316022
#145315482
#145315052
#145314932
#145314892
#145314832
#145314472
#145314442
#145314432
#145314372
#145313902
#145313482
C4×#105875712
#145312762
C17×#23332
#3443817