Finite Group Databasebeta

← #17941637

Subgroups — #17941637

Order 4352.

7346 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543100C214yesmaximal, complemented
2#14543077C214yesmaximal, complemented
3#14543059C212yesmaximal, complemented
4#14543044C212yesmaximal, complemented
5#14543033C211yesmaximal, characteristic, complemented
6#14543023C211yesmaximal, characteristic, complemented
7#14543011C212yesmaximal, complemented
8#14542993C214yesmaximal, complemented
9#14542974C214yesmaximal, complemented
10#14542955C214yesmaximal, complemented
11#14542939C214yesmaximal, complemented
12#14542922C214yesmaximal, complemented
13#14542386C214yesmaximal, complemented
14#14542342C214yesmaximal, complemented
15D4×#63252C214yesmaximal, complemented
16#14542202C214yesmaximal, complemented
17#14542191C214yesmaximal, complemented
18#14542174C212yesmaximal, complemented
19#14542113C212yesmaximal, complemented
20C2×#11763320C212yesmaximal, complemented
21C2×C17×#525C211yesmaximal, characteristic, complemented
22C22×#63252C2212yescomplemented
23C22×#63252C2212yescomplemented
24#11763562C2214yescomplemented
25#11763560C2218yescomplemented
26#11763556C2218yescomplemented
27#11763555C2218yescomplemented
28#11763554C2218yescomplemented
29#11763552C2214yescomplemented
30#11763549C2214yescomplemented
31#11763548C2218yescomplemented
32#11763548C2214yescomplemented
33#11763547C2218yescomplemented
34#11763543C2214yescomplemented
35#11763529C2214yescomplemented
36#11763524C2214yescomplemented
37#11763516C2214yescomplemented
38#11763513C2218yescomplemented
39#11763505C2214yescomplemented
40#11763505C2214yescomplemented
41#11763504C2218yescomplemented
42#11763502C2218yescomplemented
43#11763499C2214yescomplemented
44#11763499C2214yescomplemented
45#11763494C2218yescomplemented
46#11763490C2214yescomplemented
47#11763487C2214yescomplemented
48#11763486C2218yescomplemented
49#11763485C2218yescomplemented
50#11763485C2218yescomplemented
51#11763480C2214yescomplemented
52D4×Dic34C2214yescomplemented
53#11763468C2214yescomplemented
54#11763468C2214yescomplemented
55#11763464C2214yescomplemented
56#11763463C2214yescomplemented
57#11763460C2218yescomplemented
58#11763455C2214yescomplemented
59#11763455C2214yescomplemented
60#11763453C2218yescomplemented
61#11763449C2218yescomplemented
62#11763449C2218yescomplemented
63#11763448C2218yescomplemented
64#11763446C2218yescomplemented
65D4×D68C2214yescomplemented
66D4×C22⋊D17C2218yescomplemented
67#11763441C2214yescomplemented
68#11763438C2214yescomplemented
69#11763434C2214yescomplemented
70#11763430C2214yescomplemented
71#11763430C2214yescomplemented
72#11763429C2218yescomplemented
73#11763427C2218yescomplemented
74#11763421C2212yescomplemented
75#11763421C2212yescomplemented
76#11763414C2212yescomplemented
77#11763414C2212yescomplemented
78#11763411C2218yescomplemented
79#11763409C2218yescomplemented
80#11763408C2214yescomplemented
81#11763406C2218yescomplemented
82#11763405C2218yescomplemented
83#11763404C2214yescomplemented
84#11763402C2218yescomplemented
85#11763399C2214yescomplemented
86#11763397C2218yescomplemented
87#11763396C2214yescomplemented
88#11763395C2218yescomplemented
89#11763394C2218yescomplemented
90#11763394C2218yescomplemented
91#11763391C2218yescomplemented
92#11763387C2214yescomplemented
93#11763387C2214yescomplemented
94#11763386C2214yescomplemented
95#11763383C2214yescomplemented
96#11763380C2212yescomplemented
97#11763380C2212yescomplemented
98#11763376C2214yescomplemented
99#11763374C2218yescomplemented
100#11763373C2212yescomplemented
101#11763373C2212yescomplemented
102#11763369C2218yescomplemented
103#11763368C2214yescomplemented
104#11763368C2214yescomplemented
105#11763367C2214yescomplemented
106#11763366C2212yescomplemented
107#11763359C2212yescomplemented
108#11763356C2218yescomplemented
109#11763355C2214yescomplemented
110#11763355C2214yescomplemented
111#11763341C2218yescomplemented
112#11763339C2218yescomplemented
113#11763339C2218yescomplemented
114#11763337C2218yescomplemented
115#11763337C2218yescomplemented
116#11763320C2214yescomplemented
117#11763320C2214yescomplemented
118#11763320C2214yescomplemented
119#11763320C2214yescomplemented
120#11763320C2214yescomplemented
121#11763320C2214yescomplemented
122#11763320C2214yescomplemented
123#11763320C2214yescomplemented
124#11763320C2214yescomplemented
125#11763318C2218yescomplemented
126#11763318C2218yescomplemented
127#11763316C2214yescomplemented
128#11763316C2214yescomplemented
129C2×#10587615C2214yescomplemented
130C2×#10587610C2212yescomplemented
131C2×#10587610C2212yescomplemented
132C2×#10587616C2212yescomplemented
133C2×#10587616C2212yescomplemented
134C2×#10587639C2214yescomplemented
135C4×#63252C2214yescomplemented
136C4×#63254C2218yescomplemented
137C2×C4×C22⋊D17C2214yescomplemented
138C2×C4×C22⋊D17C2214yescomplemented
139C4×D4×D17C2218yescomplemented
140C2×#10587612C2212yescomplemented
141C2×#10587612C2212yescomplemented
142C22×#41×C17C2211yescharacteristic, complemented
143C24×C4×C17C2211yescharacteristic, complemented
144C17×#525C2211yescharacteristic
145C17×#525C2212yescomplemented
146C17×#525C2212yescomplemented
147C17×#525C2212yescomplemented
148C17×#525C2212yescomplemented
149C17×#525C2211yescharacteristic, complemented
150C17×#525C2211yescharacteristic, complemented
151C17×#525C2211yescharacteristic, complemented
152C17×#525C2214yescomplemented
153C2×C17×#123C2212yescomplemented
154C2×C17×C22⋊Q8C2212yescomplemented
155C2×C17×#121C2212yescomplemented
156C2×C17×#120C2212yescomplemented
157C2×C4×D4×C17C2214yescomplemented
158C2×C17×#117C2211yescharacteristic, complemented
159C25×C17C2311yescharacteristic
160C2×#41×C17—44no—
161C2×#41×C17C2311yescharacteristic
162C2×#41×C17C2311yescharacteristic
163C2×#41×C17C2312yes—
164C2×#41×C17C2311yescharacteristic
165C2×#41×C17C2312yes—
166C2×#41×C17C2311yescharacteristic
167C22×Q8×C17C2311yescharacteristic
168C22×D4×C17C2314yes—
169C22×D4×C17C2312yes—
170C22×D4×C17C2311yescharacteristic
171C23×C4×C17—44no—
172C23×C4×C17C2311yescharacteristic
173C23×C4×C17C2312yes—
174C23×C4×C17C2312yes—
175C23×C4×C17C2312yes—
176C23×C4×C17C2311yescharacteristic
177C23×C4×C17C2311yescharacteristic
178C23×C4×C17C2311yescharacteristic
179C23×C4×C17C2312yes—
180C23×C4×C17C2312yes—
181C23×C4×C17C2311yescharacteristic
182C23×C4×C17C2311yescharacteristic
183C22×C22⋊D17C2314yes—
184C22×C22⋊D17C2314yes—
185C22×C22⋊D17C2314yes—
186C22×C22⋊D17C2314yes—
187C2×#63254C2318yes—
188C2×D4×D17C2318yes—
189C2×#63252—48no—
190C2×#63252—48no—
191C2×#63252C2314yes—
192C2×#63252C2314yes—
193C2×#63252C2314yes—
194C2×#63252C2314yes—
195C2×#63252C2314yes—
196C2×#63252C2314yescomplemented
197C2×#63252C2314yescomplemented
198C22×D68C2312yes—
199C22×D68C2312yescomplemented
200C22×C4×D17C2314yes—
201C22×C4×D17C2314yescomplemented
202C22×Dic34C2312yes—
203C22×Dic34C2312yescomplemented
204C17×#123C2312yes—
205C17×#123C2312yes—
206C17×#123C2312yes—
207C17×#123C2312yes—
208C17×#123C2314yes—
209C17×#123C2314yes—
210C17×C22⋊Q8C2314yes—
211C17×C22⋊Q8C2312yes—
212C17×C22⋊Q8C2314yes—
213C17×C22⋊Q8C2312yes—
214C17×C22⋊Q8C2312yes—
215C17×C22⋊Q8C2312yes—
216C17×#121C2312yes—
217C17×#121C2314yes—
218C17×#121C2314yes—
219C17×#121C2312yes—
220C17×#121C2312yes—
221C17×#121C2312yes—
222C17×#120C2312yes—
223C17×#120C2312yes—
224C17×#120C2312yes—
225C17×#120C2314yes—
226C17×#120C2314yes—
227C17×#120C2312yes—
228C4×D4×C17C2314yes—
229C4×D4×C17C2314yes—
230C4×D4×C17C2314yes—
231C4×D4×C17C2314yes—
232C4×D4×C17C2314yes—
233C4×D4×C17C2314yes—
234C4×D4×C17C2314yes—
235C4×D4×C17C2314yes—
236C17×#117C2311yescharacteristic
237C17×#117C2312yes—
238C17×#117C2312yes—
239C17×#117C2312yes—
240C17×#117C2311yescharacteristic
241C2×C4⋊C4×C17C2314yes—
242C2×C4⋊C4×C17C2312yes—
243C2×C22⋊C4×C17C2312yes—
244C2×C22⋊C4×C17C2314yes—
245C2×C22⋊C4×C17C2314yes—
246C2×C42×C17C2312yes—
247#10587639C2318yes—
248#10587639C2318yes—
249#10587639C2318yes—
250#10587639C2318yes—
251#10587639C2318yes—
252C2×C22⋊Dic17C2314yes—
253C2×C22⋊Dic17C2314yes—
254C2×C22⋊Dic17C2314yes—
255C2×C22⋊Dic17C2314yes—
256#10587633C2314yescomplemented
257#10587633C2314yescomplemented
258#10587632C2318yescomplemented
259#10587632C2318yescomplemented
260#10587630C2314yescomplemented
261#10587630C2314yescomplemented
262#10587626C2318yes—
263#10587626C2314yes—
264#10587626C2314yes—
265#10587625C2318yes—
266#10587625C2318yes—
267#10587625C2318yes—
268#10587625C2318yes—
269#10587625C2318yes—
270#10587625C2318yes—
271#10587625C2318yescomplemented
272#10587625C2318yescomplemented
273#10587624C2318yes—
274#10587624C2318yes—
275#10587624C2318yes—
276#10587624C2318yes—
277#10587623C2314yes—
278#10587623C2318yes—
279#10587623C2314yes—
280#10587623C2318yes—
281#10587623C2314yescomplemented
282#10587623C2314yescomplemented
283#10587622C2314yes—
284#10587622C2318yes—
285#10587622C2314yes—
286#10587621C2318yes—
287#10587621C2314yes—
288#10587621C2318yes—
289#10587621C2314yes—
290#10587621C2314yescomplemented
291#10587621C2314yescomplemented
292D4×Dic17C2318yes—
293D4×Dic17C2318yes—
294#10587616C2318yes—
295#10587616C2314yes—
296#10587616C2314yes—
297#10587616C2314yes—
298#10587616C2314yes—
299#10587616C2314yes—
300#10587616C2314yes—
301#10587616C2314yes—
302#10587616C2314yes—
303#10587616C2314yescomplemented
304#10587616C2314yescomplemented
305#10587615C2318yes—
306#10587615C2318yes—
307#10587615C2318yes—
308#10587615C2318yes—
309#10587615C2318yes—
310C4×C22⋊D17C2318yes—
311C4×C22⋊D17C2318yes—
312C4×C22⋊D17C2318yes—
313C4×C22⋊D17C2318yes—
314C4×C22⋊D17C2318yes—
315C4×C22⋊D17C2318yes—
316C4×C22⋊D17C2318yes—
317C4×C22⋊D17C2318yes—
318C4×C22⋊D17C2318yes—
319C4×C22⋊D17C2318yes—
320C4×C22⋊D17C2318yescomplemented
321C4×C22⋊D17C2318yescomplemented
322C2×#63227C2314yes—
323C2×#63227C2314yes—
324#10587612C2314yes—
325#10587612C2314yes—
326#10587612C2314yes—
327#10587612C2314yes—
328#10587612C2314yes—
329#10587612C2312yescomplemented
330#10587612C2312yescomplemented
331#10587612C2314yescomplemented
332C2×C4⋊Dic17C2312yes—
333C2×C4⋊Dic17C2312yes—
334C2×C4⋊Dic17C2314yescomplemented
335#10587610C2314yes—
336#10587610C2314yes—
337#10587610C2318yes—
338#10587610C2314yes—
339#10587610C2314yes—
340#10587610C2314yes—
341#10587610C2314yes—
342#10587610C2314yes—
343#10587610C2314yes—
344#10587610C2314yescomplemented
345#10587610C2314yescomplemented
346C2×#63225C2314yes—
347C2×#63225C2314yes—
348C2×C4×Dic17C2314yes—
349C2×C4×Dic17C2314yescomplemented
350#10587584C2318yescomplemented
351#10587584C2318yescomplemented
352#10587584C2318yescomplemented
353#10587584C2318yescomplemented
354#10587583C2318yescomplemented
355#10587582C2318yescomplemented
356#10587582C2318yescomplemented
357#10587582C2318yescomplemented
358#10587582C2318yescomplemented
359#10587581C2318yescomplemented
360#10587580C2318yescomplemented
361#10587580C2318yescomplemented
362#10587580C2318yescomplemented
363#10587580C2318yescomplemented
364#10587579C2318yescomplemented
365#10587578C2318yescomplemented
366C4⋊C4×D17C2318yescomplemented
367#10587576C2318yescomplemented
368#10587575C2318yescomplemented
369#10587575C2318yescomplemented
370#10587575C2318yescomplemented
371#10587575C2318yescomplemented
372#10587574C2318yescomplemented
373#10587573C2318yescomplemented
374#10587572C2318yes—
375#10587572C2318yescomplemented
376#10587571C2318yes—
377#10587571C2318yes—
378#10587571C2318yes—
379#10587571C2318yes—
380#10587571C2318yescomplemented
381#10587571C2318yescomplemented
382#10587570C2318yes—
383#10587570C2318yes—
384#10587570C2318yes—
385#10587570C2318yes—
386#10587570C2318yescomplemented
387#10587570C2318yescomplemented
388#10587569C2318yes—
389#10587569C2318yes—
390#10587569C2318yes—
391#10587569C2318yes—
392#10587569C2318yescomplemented
393#10587569C2318yescomplemented
394#10587568C2318yes—
395#10587568C2318yescomplemented
396#10587567C2318yes—
397#10587567C2318yes—
398#10587567C2318yescomplemented
399#10587567C2318yescomplemented
400C22⋊C4×D17C2318yes—
401C22⋊C4×D17C2318yescomplemented
402#10587565C2318yes—
403#10587565C2318yes—
404#10587565C2318yes—
405#10587565C2318yes—
406#10587565C2318yescomplemented
407#10587565C2318yescomplemented
408#10587564C2318yes—
409#10587564C2318yes—
410#10587564C2318yescomplemented
411#10587564C2318yescomplemented
412#10587563C2318yes—
413#10587563C2318yescomplemented
414#10587561C2314yescomplemented
415#10587560C2312yescomplemented
416C4×D68C2314yescomplemented
417C4×D68C2314yescomplemented
418C4×D68C2318yescomplemented
419#10587558C2318yescomplemented
420C42×D17C2318yescomplemented
421#10587556C2312yescomplemented
422#10587556C2312yescomplemented
423#10587555C2314yescomplemented
424#10587555C2312yescomplemented
425C4×Dic34C2314yescomplemented
426C4×Dic34C2314yescomplemented
427C4×Dic34C2318yescomplemented
428C24×C17—42no—
429C24×C17—44no—
430C24×C17C2411yescharacteristic
431C24×C17C2412yes—
432C24×C17C2412yes—
433C24×C17C2412yes—
434C24×C17C2411yescharacteristic
435C24×C17C2411yescharacteristic
436C23×D17C2414yes—
437C23×D17C2414yes—
438#41×C17—42no—
439#41×C17—44no—
440#41×C17—42no—
441#41×C17—44no—
442#41×C17—42no—
443#41×C17—42no—
444C2×Q8×C17—42no—
445C2×Q8×C17C2411yescharacteristic
446C2×Q8×C17C2412yes—
447C2×Q8×C17C2411yescharacteristic
448C2×D4×C17—44no—
449C2×D4×C17—42no—
450C2×D4×C17—48no—
451C2×D4×C17C2414yes—
452C2×D4×C17C2414yes—
453C2×D4×C17C2412yes—
454C2×D4×C17C2412yes—
455C2×D4×C17C2412yes—
456C2×D4×C17C2412yes—
457C2×D4×C17C2411yescharacteristic
458C2×D4×C17C2412yes—
459C2×D4×C17C2411yescharacteristic
460C2×D4×C17C2414yes—
461C2×D4×C17C2414yes—
462C22×C4×C17—28no—
463C22×C4×C17—28no—
464C22×C4×C17—24no—
465C22×C4×C17—42no—
466C22×C4×C17—44no—
467C22×C4×C17—42no—
468C22×C4×C17—44no—
469C22×C4×C17—42no—
470C22×C4×C17—42no—
471C22×C4×C17—42no—
472C22×C4×C17—44no—
473C22×C4×C17C2412yes—
474C22×C4×C17C2412yes—
475C22×C4×C17C2412yes—
476C22×C4×C17C2412yes—
477C22×C4×C17C2412yes—
478C22×C4×C17C2412yes—
479C22×C4×C17C2412yes—
480C22×C4×C17C2412yes—
481C22×C4×C17C2412yes—
482C22×C4×C17C2412yes—
483C22×C4×C17C2411yescharacteristic
484C22×C4×C17C2411yescharacteristic
485C22×C4×C17C2411yescharacteristic
486C22×C4×C17C2411yescharacteristic
487C22×C4×C17C2411yescharacteristic
488C22×C4×C17C2412yes—
489C22×C4×C17C2412yes—
490C22×C4×C17C2412yes—
491C22×C4×C17C2412yes—
492C22×C4×C17C2411yescharacteristic
493C22×C4×C17C2412yes—
494C22×C4×C17C2411yescharacteristic
495C22×C4×C17C2414yes—
496C22×C4×C17C2411yescharacteristic
497C2×C22⋊D17—48no—
498C2×C22⋊D17—48no—
499C2×C22⋊D17—48no—
500C2×C22⋊D17—48no—
501C2×C22⋊D17C2418yes—
502C2×C22⋊D17C2418yes—
503C2×C22⋊D17C2418yes—
504C2×C22⋊D17C2418yes—
505C2×C22⋊D17C2418yes—
506C2×C22⋊D17C2418yes—
507C2×C22⋊D17C2418yes—
508C2×C22⋊D17C2418yes—
509C2×C22⋊D17C2418yes—
510C22×Dic17C2414yes—
511C22×Dic17C2414yes—
512C22×Dic17C2414yes—
513C22×Dic17C2418yes—
514C22×Dic17C2414yes—
515#63254—416no—
516D4×D17—416no—
517#63252—216no—
518#63252—48no—
519#63252—48no—
520#63252—48no—
521#63252—48no—
522#63252—48no—
523#63252—48no—
524C2×D68—44no—
525C2×D68—44no—
526C2×D68C2414yes—
527C2×D68C2414yes—
528C2×D68C2414yes—
529C2×D68C2418yes—
530C2×C4×D17—48no—
531C2×C4×D17—48no—
532C2×C4×D17C2418yes—
533C2×C4×D17C2418yes—
534C2×C4×D17C2418yes—
535C2×C4×D17C2418yes—
536C2×C4×D17C2418yes—
537C2×Dic34—44no—
538C2×Dic34—44no—
539C2×Dic34C2414yes—
540C2×Dic34C2414yes—
541C2×Dic34C2414yes—
542C2×Dic34C2418yes—
543C4⋊C4×C17C2414yes—
544C4⋊C4×C17C2414yes—
545C4⋊C4×C17C2414yes—
546C4⋊C4×C17C2414yes—
547C4⋊C4×C17C2412yes—
548C4⋊C4×C17C2414yes—
549C4⋊C4×C17C2412yes—
550C22⋊C4×C17C2414yes—
551C22⋊C4×C17C2414yes—
552C22⋊C4×C17C2414yes—
553C22⋊C4×C17C2414yes—
554C22⋊C4×C17C2414yes—
555C22⋊C4×C17C2414yes—
556C22⋊C4×C17C2414yes—
557C22⋊C4×C17C2412yes—
558C22⋊C4×C17C2414yes—
559C22⋊C4×C17C2414yes—
560C22⋊C4×C17C2412yes—
561C42×C17C2412yes—
562C42×C17C2412yes—
563C42×C17C2414yes—
564C22⋊Dic17C2418yes—
565C22⋊Dic17C2418yes—
566C22⋊Dic17C2418yes—
567C22⋊Dic17C2418yes—
568C22⋊Dic17C2418yes—
569C22⋊Dic17C2418yes—
570C22⋊Dic17C2418yes—
571C22⋊Dic17C2414yes—
572C22⋊Dic17C2414yes—
573C22⋊Dic17C2418yes—
574#63227C2418yes—
575#63227C2418yes—
576#63227C2418yes—
577#63227C2418yes—
578#63227C2418yes—
579#63227C2418yes—
580#63227C2418yes—
581#63227C2418yes—
582#63227C2418yes—
583#63227C2418yes—
584C4⋊Dic17C2414yes—
585C4⋊Dic17C2414yes—
586C4⋊Dic17C2418yes—
587C4⋊Dic17C2418yes—
588C4⋊Dic17C2418yes—
589C4⋊Dic17C2414yes—
590C4⋊Dic17C2414yes—
591#63225C2418yes—
592#63225C2418yes—
593#63225C2418yes—
594#63225C2418yes—
595#63225C2418yes—
596#63225C2418yes—
597#63225C2418yes—
598#63225C2418yes—
599#63225C2418yes—
600#63225C2418yes—
601C4×Dic17C2418yes—
602C4×Dic17C2418yes—
603C4×Dic17C2418yes—
604C4×Dic17C2414yes—
605C4×Dic17C2418yes—
606C4×Dic17C2414yes—
607#62729—171nomaximal, Sylow
608C23×C17—24no—
609C23×C17—22no—
610C23×C17—24no—
611C23×C17—24no—
612C23×C17—24no—
613C23×C17—24no—
614C23×C17—41no—
615C23×C17—42no—
616C23×C17—41no—
617C23×C17—42no—
618C23×C17—42no—
619C23×C17—42no—
620C23×C17—42no—
621C23×C17—44no—
622C23×C17—416no—
623C23×C17C2512yes—
624C23×C17C2512yes—
625C23×C17C2511yescharacteristic
626C23×C17C2511yescharacteristic
627C23×C17C2512yes—
628C23×C17C2511yescharacteristic
629C23×C17C2512yes—
630C22×D17—28no—
631C22×D17—44no—
632C22×D17—44no—
633C22×D17—48no—
634C22×D17—44no—
635C22×D17C2518yes—
636Q8×C17—41no—
637Q8×C17—42no—
638Q8×C17—41no—
639D4×C17—28no—
640D4×C17—28no—
641D4×C17—44no—
642D4×C17—44no—
643D4×C17—42no—
644D4×C17—42no—
645D4×C17—42no—
646D4×C17—42no—
647D4×C17—41no—
648D4×C17—42no—
649D4×C17—41no—
650C2×C4×C17—24no—
651C2×C4×C17—24no—
652C2×C4×C17—22no—
653C2×C4×C17—24no—
654C2×C4×C17—24no—
655C2×C4×C17—24no—
656C2×C4×C17—24no—
657C2×C4×C17—24no—
658C2×C4×C17—24no—
659C2×C4×C17—24no—
660C2×C4×C17—24no—
661C2×C4×C17—22no—
662C2×C4×C17—22no—
663C2×C4×C17—22no—
664C2×C4×C17—22no—
665C2×C4×C17—41no—
666C2×C4×C17—42no—
667C2×C4×C17—42no—
668C2×C4×C17—42no—
669C2×C4×C17—41no—
670C2×C4×C17—42no—
671C2×C4×C17—42no—
672C2×C4×C17—44no—
673C2×C4×C17H(5,𝔽2)14yes—
674C2×C4×C17C2514yes—
675C2×C4×C17C2514yes—
676C2×C4×C17C2512yes—
677C2×C4×C17C2512yes—
678C2×C4×C17C2512yes—
679C2×C4×C17C2512yes—
680C2×C4×C17C2511yescharacteristic
681C2×C4×C17C2511yescharacteristic
682C2×C4×C17C2511yescharacteristic
683C2×C4×C17C2511yescharacteristic
684C22⋊D17—216no—
685C22⋊D17—216no—
686C22⋊D17—48no—
687C22⋊D17—48no—
688C22⋊D17—48no—
689C22⋊D17—48no—
690C22⋊D17—48no—
691C22⋊D17—48no—
692C22⋊D17—48no—
693C2×Dic17—28no—
694C2×Dic17—44no—
695C2×Dic17—44no—
696C2×Dic17—48no—
697C2×Dic17—44no—
698C2×Dic17C2518yes—
699C2×Dic17C2518yes—
700C2×Dic17C2518yes—
701D68—28no—
702D68—44no—
703D68—44no—
704D68—48no—
705C4×D17—216no—
706C4×D17—48no—
707C4×D17—48no—
708C4×D17—48no—
709C4×D17—48no—
710Dic34—28no—
711Dic34—44no—
712Dic34—44no—
713Dic34—48no—
714#3542—174no—
715#3541—174no—
716#3540—172no—
717#3539—172no—
718#3538—171no—
719#3537—171no—
720#3536—172no—
721#3535—174no—
722#3534—174no—
723#3533—174no—
724#3532—174no—
725#3529—174no—
726#3481—174no—
727#3475—174no—
728D4×#41—174no—
729#3460—174no—
730#3459—174no—
731#3455—172no—
732#3449—172no—
733C2×#525—172no—
734C2×#525D1711yescharacteristic, complemented
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—21no—
742C22×C17—21no—
743C22×C17—24no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—24no—
748C22×C17—22no—
749C22×C17—44no—
750C22×C17—48no—
751C22×C17—48no—
752C22×C17—44no—
753C22×C17—44no—
754C22×C17—84no—
755C22×C17C2×H(5,𝔽2)12yes—
756C22×C17#58514yes—
757C22×C17C2611yescharacteristic
758C2×D17—28no—
759C2×D17—28no—
760C2×D17—28no—
761C2×D17—88no—
762C2×D17—88no—
763C4×C17—22no—
764C4×C17—22no—
765C4×C17—22no—
766C4×C17—22no—
767C4×C17—21no—
768C4×C17—21no—
769C4×C17—24no—
770C4×C17—24no—
771C4×C17C2×H(5,𝔽2)12yes—
772C4×C17C2×H(5,𝔽2)12yes—
773Dic17—28no—
774Dic17—28no—
775Dic17—28no—
776C22×#41—172no—
777C22×#41—172no—
778C22×#41C2×D1711yescharacteristic, complemented
779C24×C4C2×D1711yescharacteristic, complemented
780#563—174no—
781#563—178no—
782#562—178no—
783#562—178no—
784#562—178no—
785H(3,𝔽4)—174no—
786#560—174no—
787#560—178no—
788#560—178no—
789#560—174no—
790#559—174no—
791#556—174no—
792#555—174no—
793#554—178no—
794#554—174no—
795#553—178no—
796#553—178no—
797#553—174no—
798#553—174no—
799#552—174no—
800#552—174no—
801#552—178no—
802#551—174no—
803#551—178no—
804#551—174no—
805#551—178no—
806#551—178no—
807#550—174no—
808D4×Q8—174no—
809#548—174no—
810#548—174no—
811#547—174no—
812#547—174no—
813#547—178no—
814#546—178no—
815#546—178no—
816#546—178no—
817#546—174no—
818#546—174no—
819#546—178no—
820#546—178no—
821D42—178no—
822D42—174no—
823D42—174no—
824#544—174no—
825#543—174no—
826#542—178no—
827#542—178no—
828#542—174no—
829#542—174no—
830#541—172no—
831#541—172no—
832#540—178no—
833#540—178no—
834#540—172no—
835#540—172no—
836#539—178no—
837#539—178no—
838#539—174no—
839#539—174no—
840#539—178no—
841#538—178no—
842#538—174no—
843#538—178no—
844#538—174no—
845#538—178no—
846#538—178no—
847#538—178no—
848#537—174no—
849#537—174no—
850#537—174no—
851#536—172no—
852#536—172no—
853#536—174no—
854#535—172no—
855#535—172no—
856#535—174no—
857#535—178no—
858#534—174no—
859#534—174no—
860#534—174no—
861#534—178no—
862#533—172no—
863#532—174no—
864#532—174no—
865#532—178no—
866#532—172no—
867#529—178no—
868#529—178no—
869#529—178no—
870#529—178no—
871#529—178no—
872#525—174no—
873#525—174no—
874#525—174no—
875#525—174no—
876#525—174no—
877#525—174no—
878#525—174no—
879#525—174no—
880#525—174no—
881#525—174no—
882#525—174no—
883#525—178no—
884#525—178no—
885#525C2×D1711yescharacteristic
886#525C2×D1712yescomplemented
887#525C2×D1712yescomplemented
888#525C2×D1712yescomplemented
889#525C2×D1712yescomplemented
890#525C2×D1711yescharacteristic, complemented
891#525C2×D1711yescharacteristic, complemented
892#525C2×D1711yescharacteristic, complemented
893#525C2×D1714yescomplemented
894C2×#123—174no—
895C2×#123C2×D1712yescomplemented
896C2×C22⋊Q8—172no—
897C2×C22⋊Q8—172no—
898C2×C22⋊Q8C2×D1712yescomplemented
899C2×#121—172no—
900C2×#121—172no—
901C2×#121C2×D1712yescomplemented
902C2×#120—174no—
903C2×#120C2×D1712yescomplemented
904C4×#41—178no—
905C4×#41—174no—
906C2×C4×D4—174no—
907C2×C4×D4—174no—
908C2×C4×D4—178no—
909C2×C4×D4C2×D1714yescomplemented
910C2×#117—172no—
911C2×#117—172no—
912C2×#117C2×D1711yescharacteristic, complemented
913C2×C17—24no—
914C2×C17—22no—
915C2×C17—42no—
916C2×C17—42no—
917C2×C17—41no—
918C2×C17—41no—
919C2×C17—42no—
920C2×C17C22×H(5,𝔽2)11yescharacteristic
921C2×C17C2×#58512yes—
922D17—48no—
923C25C22×D1711yescharacteristic
924C2×#41—44no—
925C2×#41—178no—
926C2×#41—174no—
927C2×#41—174no—
928C2×#41—174no—
929C2×#41—174no—
930C2×#41—174no—
931C2×#41—174no—
932C2×#41—174no—
933C2×#41—688no—
934C2×#41—688no—
935C2×#41C22×D1711yescharacteristic
936C2×#41C22×D1712yes—
937C2×#41C22×D1711yescharacteristic
938C2×#41C22×D1711yescharacteristic
939C2×#41C22×D1712yes—
940C2×#41C22×D1711yescharacteristic
941C22×Q8—172no—
942C22×Q8—172no—
943C22×Q8C22×D1711yescharacteristic
944C22×D4—174no—
945C22×D4—174no—
946C22×D4—174no—
947C22×D4—174no—
948C22×D4—178no—
949C22×D4—172no—
950C22×D4—172no—
951C22×D4C22×D1714yes—
952C22×D4C22×D1712yes—
953C22×D4C22×D1711yescharacteristic
954C23×C4—44no—
955C23×C4—174no—
956C23×C4—174no—
957C23×C4C22×D1712yes—
958C23×C4C22×D1712yes—
959C23×C4C22×D1711yescharacteristic
960C23×C4C22×D1711yescharacteristic
961C23×C4C22×D1712yes—
962C23×C4C22×D1711yescharacteristic
963C23×C4C22×D1712yes—
964C23×C4C22×D1712yes—
965C23×C4C22×D1711yescharacteristic
966C23×C4C22×D1711yescharacteristic
967C23×C4C22×D1711yescharacteristic
968C4⋊Q8—174no—
969C4⋊Q8—174no—
970C4⋊Q8—178no—
971C4⋊Q8—172no—
972C4⋊Q8—174no—
973#127—174no—
974#127—174no—
975#127—178no—
976#127—172no—
977#126—178no—
978#126—178no—
979#126—178no—
980#126—178no—
981#126—178no—
982#126—178no—
983#126—178no—
984#126—178no—
985#126—178no—
986#126—178no—
987#125—178no—
988#125—178no—
989#125—178no—
990#125—178no—
991#125—178no—
992#125—172no—
993#125—172no—
994#124—174no—
995#124—174no—
996#124—178no—
997#124—174no—
998#124—174no—
999#124—178no—
1000#124—178no—
1001#124—178no—
1002#124—178no—
1003#124—178no—
1004#124—178no—
1005#124—174no—
1006#123—174no—
1007#123—174no—
1008#123—174no—
1009#123—174no—
1010#123—178no—
1011#123—178no—
1012#123—178no—
1013#123—178no—
1014#123—178no—
1015#123—178no—
1016#123—178no—
1017#123—178no—
1018#123—178no—
1019#123—178no—
1020#123—178no—
1021#123—178no—
1022#123—178no—
1023#123—178no—
1024#123—178no—
1025#123—178no—
1026#123—178no—
1027#123—178no—
1028#123—178no—
1029#123C22×D1712yes—
1030#123C22×D1714yes—
1031#123C22×D1714yes—
1032#123C22×D1712yes—
1033#123C22×D1712yes—
1034#123C22×D1712yes—
1035C22⋊Q8—178no—
1036C22⋊Q8—178no—
1037C22⋊Q8—174no—
1038C22⋊Q8—174no—
1039C22⋊Q8—174no—
1040C22⋊Q8—174no—
1041C22⋊Q8—174no—
1042C22⋊Q8—174no—
1043C22⋊Q8—174no—
1044C22⋊Q8—174no—
1045C22⋊Q8—174no—
1046C22⋊Q8—174no—
1047C22⋊Q8—178no—
1048C22⋊Q8—178no—
1049C22⋊Q8—178no—
1050C22⋊Q8—178no—
1051C22⋊Q8—178no—
1052C22⋊Q8—178no—
1053C22⋊Q8—178no—
1054C22⋊Q8—178no—
1055C22⋊Q8—178no—
1056C22⋊Q8—178no—
1057C22⋊Q8C22×D1712yes—
1058C22⋊Q8C22×D1712yes—
1059C22⋊Q8C22×D1712yes—
1060C22⋊Q8C22×D1712yes—
1061C22⋊Q8C22×D1714yes—
1062C22⋊Q8C22×D1714yes—
1063#121—178no—
1064#121—178no—
1065#121—178no—
1066#121—178no—
1067#121—178no—
1068#121—178no—
1069#121—178no—
1070#121—178no—
1071#121—178no—
1072#121—178no—
1073#121—178no—
1074#121—178no—
1075#121—174no—
1076#121—174no—
1077#121—174no—
1078#121—174no—
1079#121—174no—
1080#121—174no—
1081#121—174no—
1082#121—174no—
1083#121—174no—
1084#121—174no—
1085#121—178no—
1086#121—178no—
1087#121—178no—
1088#121—178no—
1089#121—178no—
1090#121—178no—
1091#121—178no—
1092#121—178no—
1093#121C22×D1712yes—
1094#121C22×D1712yes—
1095#121C22×D1712yes—
1096#121C22×D1712yes—
1097#121C22×D1714yes—
1098#121C22×D1714yes—
1099#120—178no—
1100#120—178no—
1101#120—178no—
1102#120—178no—
1103#120—178no—
1104#120—174no—
1105#120—174no—
1106#120—174no—
1107#120—174no—
1108#120—178no—
1109#120—178no—
1110#120—178no—
1111#120—178no—
1112#120C22×D1712yes—
1113#120C22×D1714yes—
1114#120C22×D1714yes—
1115#120C22×D1712yes—
1116#120C22×D1712yes—
1117#120C22×D1712yes—
1118C4×Q8—178no—
1119C4×Q8—178no—
1120C4×Q8—174no—
1121C4×Q8—174no—
1122C4×D4—178no—
1123C4×D4—178no—
1124C4×D4—178no—
1125C4×D4—178no—
1126C4×D4—178no—
1127C4×D4—178no—
1128C4×D4—178no—
1129C4×D4—178no—
1130C4×D4—178no—
1131C4×D4—178no—
1132C4×D4—178no—
1133C4×D4—178no—
1134C4×D4—178no—
1135C4×D4—178no—
1136C4×D4—178no—
1137C4×D4—178no—
1138C4×D4—178no—
1139C4×D4—178no—
1140C4×D4—178no—
1141C4×D4—178no—
1142C4×D4—174no—
1143C4×D4—174no—
1144C4×D4C22×D1714yes—
1145C4×D4C22×D1714yes—
1146C4×D4C22×D1714yes—
1147C4×D4C22×D1714yes—
1148C4×D4C22×D1714yes—
1149C4×D4C22×D1714yes—
1150C4×D4C22×D1714yes—
1151C4×D4C22×D1714yes—
1152#117—174no—
1153#117—174no—
1154#117—174no—
1155#117—174no—
1156#117—174no—
1157#117—174no—
1158#117—172no—
1159#117—172no—
1160#117—178no—
1161#117—178no—
1162#117—178no—
1163#117—178no—
1164#117C22×D1711yescharacteristic
1165#117C22×D1712yes—
1166#117C22×D1712yes—
1167#117C22×D1712yes—
1168#117C22×D1711yescharacteristic
1169C2×C4⋊C4—172no—
1170C2×C4⋊C4—172no—
1171C2×C4⋊C4—174no—
1172C2×C4⋊C4—174no—
1173C2×C4⋊C4—174no—
1174C2×C4⋊C4—178no—
1175C2×C4⋊C4C22×D1712yes—
1176C2×C4⋊C4C22×D1714yes—
1177C2×C22⋊C4—174no—
1178C2×C22⋊C4—174no—
1179C2×C22⋊C4—174no—
1180C2×C22⋊C4—174no—
1181C2×C22⋊C4—174no—
1182C2×C22⋊C4—174no—
1183C2×C22⋊C4—178no—
1184C2×C22⋊C4—178no—
1185C2×C22⋊C4C22×D1712yes—
1186C2×C22⋊C4C22×D1714yes—
1187C2×C22⋊C4C22×D1714yes—
1188C2×C42—174no—
1189C2×C42—174no—
1190C2×C42—178no—
1191C2×C42C22×D1712yes—
1192C17#6272911yescharacteristic, complemented, Sylow
1193C24—42no—
1194C24—44no—
1195C24—174no—
1196C24—174no—
1197C24C23×D1711yescharacteristic
1198C24C23×D1712yes—
1199C24C23×D1712yes—
1200C24C23×D1712yes—
1201C24C23×D1711yescharacteristic
1202C24C23×D1711yescharacteristic
1203#41—42no—
1204#41—44no—
1205#41—42no—
1206#41—44no—
1207#41—42no—
1208#41—42no—
1209#41—3416no—
1210#41—688no—
1211#41—688no—
1212#41—688no—
1213#41—688no—
1214#41—688no—
1215#41—688no—
1216#41—6816no—
1217C2×Q8—42no—
1218C2×Q8—174no—
1219C2×Q8—178no—
1220C2×Q8—174no—
1221C2×Q8—174no—
1222C2×Q8—684no—
1223C2×Q8—684no—
1224C2×Q8C23×D1711yescharacteristic
1225C2×Q8C23×D1712yes—
1226C2×Q8C23×D1711yescharacteristic
1227C2×D4—42no—
1228C2×D4—44no—
1229C2×D4—48no—
1230C2×D4—178no—
1231C2×D4—178no—
1232C2×D4—178no—
1233C2×D4—178no—
1234C2×D4—178no—
1235C2×D4—178no—
1236C2×D4—178no—
1237C2×D4—178no—
1238C2×D4—178no—
1239C2×D4—174no—
1240C2×D4—178no—
1241C2×D4—174no—
1242C2×D4—174no—
1243C2×D4—684no—
1244C2×D4—684no—
1245C2×D4—688no—
1246C2×D4—6816no—
1247C2×D4—688no—
1248C2×D4—688no—
1249C2×D4—688no—
1250C2×D4C23×D1714yes—
1251C2×D4C23×D1714yes—
1252C2×D4C23×D1714yes—
1253C2×D4C23×D1714yes—
1254C2×D4C23×D1711yescharacteristic
1255C2×D4C23×D1712yes—
1256C2×D4C23×D1712yes—
1257C2×D4C23×D1712yes—
1258C2×D4C23×D1712yes—
1259C2×D4C23×D1712yes—
1260C2×D4C23×D1711yescharacteristic
1261C22×C4—24no—
1262C22×C4—28no—
1263C22×C4—28no—
1264C22×C4—42no—
1265C22×C4—44no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—174no—
1273C22×C4—174no—
1274C22×C4—178no—
1275C22×C4—174no—
1276C22×C4—174no—
1277C22×C4—178no—
1278C22×C4—178no—
1279C22×C4—178no—
1280C22×C4—178no—
1281C22×C4—178no—
1282C22×C4—688no—
1283C22×C4—688no—
1284C22×C4C23×D1712yes—
1285C22×C4C23×D1712yes—
1286C22×C4C23×D1712yes—
1287C22×C4C23×D1712yes—
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1712yes—
1290C22×C4C23×D1712yes—
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1712yes—
1294C22×C4C23×D1712yes—
1295C22×C4C23×D1712yes—
1296C22×C4C23×D1712yes—
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1714yes—
1300C22×C4C23×D1712yes—
1301C22×C4C23×D1712yes—
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1712yes—
1304C22×C4C23×D1712yes—
1305C22×C4C23×D1711yescharacteristic
1306C22×C4C23×D1712yes—
1307C22×C4C23×D1711yescharacteristic
1308C4⋊C4—174no—
1309C4⋊C4—174no—
1310C4⋊C4—178no—
1311C4⋊C4—178no—
1312C4⋊C4—174no—
1313C4⋊C4—174no—
1314C4⋊C4—178no—
1315C4⋊C4—178no—
1316C4⋊C4—178no—
1317C4⋊C4—178no—
1318C4⋊C4—178no—
1319C4⋊C4—178no—
1320C4⋊C4—178no—
1321C4⋊C4—178no—
1322C4⋊C4—178no—
1323C4⋊C4—178no—
1324C4⋊C4—178no—
1325C4⋊C4C23×D1714yes—
1326C4⋊C4C23×D1714yes—
1327C4⋊C4C23×D1712yes—
1328C4⋊C4C23×D1714yes—
1329C4⋊C4C23×D1712yes—
1330C4⋊C4C23×D1714yes—
1331C4⋊C4C23×D1714yes—
1332C22⋊C4—178no—
1333C22⋊C4—178no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—178no—
1337C22⋊C4—178no—
1338C22⋊C4—178no—
1339C22⋊C4—178no—
1340C22⋊C4—178no—
1341C22⋊C4—178no—
1342C22⋊C4—178no—
1343C22⋊C4—178no—
1344C22⋊C4—178no—
1345C22⋊C4—178no—
1346C22⋊C4—178no—
1347C22⋊C4—178no—
1348C22⋊C4—178no—
1349C22⋊C4—178no—
1350C22⋊C4—178no—
1351C22⋊C4—178no—
1352C22⋊C4C23×D1714yes—
1353C22⋊C4C23×D1714yes—
1354C22⋊C4C23×D1714yes—
1355C22⋊C4C23×D1714yes—
1356C22⋊C4C23×D1712yes—
1357C22⋊C4C23×D1714yes—
1358C22⋊C4C23×D1712yes—
1359C22⋊C4C23×D1714yes—
1360C22⋊C4C23×D1714yes—
1361C22⋊C4C23×D1714yes—
1362C22⋊C4C23×D1714yes—
1363C42—174no—
1364C42—178no—
1365C42—178no—
1366C42—174no—
1367C42—178no—
1368C42—178no—
1369C42C23×D1712yes—
1370C42C23×D1712yes—
1371C42C23×D1714yes—
1372C23—22no—
1373C23—24no—
1374C23—24no—
1375C23—24no—
1376C23—24no—
1377C23—24no—
1378C23—41no—
1379C23—42no—
1380C23—41no—
1381C23—42no—
1382C23—42no—
1383C23—42no—
1384C23—42no—
1385C23—44no—
1386C23—416no—
1387C23—178no—
1388C23—348no—
1389C23—684no—
1390C23—684no—
1391C23—684no—
1392C23—688no—
1393C23C24×D1712yes—
1394C23C24×D1711yescharacteristic
1395C23C24×D1711yescharacteristic
1396C23C24×D1712yes—
1397C23C24×D1712yes—
1398C23C24×D1711yescharacteristic
1399C23C24×D1712yes—
1400Q8—41no—
1401Q8—42no—
1402Q8—41no—
1403Q8—348no—
1404Q8—684no—
1405Q8—684no—
1406Q8—688no—
1407D4—28no—
1408D4—28no—
1409D4—41no—
1410D4—42no—
1411D4—41no—
1412D4—42no—
1413D4—42no—
1414D4—42no—
1415D4—42no—
1416D4—44no—
1417D4—44no—
1418D4—3416no—
1419D4—3416no—
1420D4—348no—
1421D4—684no—
1422D4—684no—
1423D4—688no—
1424D4—688no—
1425D4—688no—
1426D4—688no—
1427D4—688no—
1428D4—688no—
1429D4—688no—
1430D4—688no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—41no—
1447C2×C4—42no—
1448C2×C4—42no—
1449C2×C4—42no—
1450C2×C4—42no—
1451C2×C4—42no—
1452C2×C4—41no—
1453C2×C4—44no—
1454C2×C4—178no—
1455C2×C4—178no—
1456C2×C4—178no—
1457C2×C4—348no—
1458C2×C4—3416no—
1459C2×C4—688no—
1460C2×C4—688no—
1461C2×C4—688no—
1462C2×C4—688no—
1463C2×C4—684no—
1464C2×C4—684no—
1465C2×C4—684no—
1466C2×C4—688no—
1467C2×C4#1058769114yes—
1468C2×C4C24×D1712yes—
1469C2×C4C24×D1712yes—
1470C2×C4C24×D1714yes—
1471C2×C4C24×D1714yes—
1472C2×C4C24×D1711yescharacteristic
1473C2×C4C24×D1711yescharacteristic
1474C2×C4C24×D1712yes—
1475C2×C4C24×D1712yes—
1476C2×C4C24×D1711yescharacteristic
1477C2×C4C24×D1711yescharacteristic
1478C22—22no—
1479C22—22no—
1480C22—22no—
1481C22—21no—
1482C22—21no—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—24no—
1487C22—24no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—48no—
1493C22—44no—
1494C22—44no—
1495C22—48no—
1496C22—44no—
1497C22—84no—
1498C22—348no—
1499C22—348no—
1500C22—348no—
1501C22—1368no—
1502C22—1368no—
1503C22C2×#1058769112yes—
1504C22#1176364514yes—
1505C22C25×D1711yescharacteristic
1506C4—22no—
1507C4—21no—
1508C4—21no—
1509C4—22no—
1510C4—22no—
1511C4—22no—
1512C4—24no—
1513C4—24no—
1514C4—348no—
1515C4—348no—
1516C4—348no—
1517C4C2×#1058769112yes—
1518C4C2×#1058769112yes—
1519C2—22no—
1520C2—24no—
1521C2—41no—
1522C2—41no—
1523C2—42no—
1524C2—42no—
1525C2—42no—
1526C2—688no—
1527C2C22×#1058769111yescharacteristic
1528C2C2×#1176364512yes—
subgroupG/H
centerC2×C4C24×D17
commutator, socle, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#525C2
hypercenterC2×#525D17
hypocenterC17#62729
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #14543100C2semidirect
2. #14543077C2semidirect
3. #14543059C2semidirect
4. #14543044C2semidirect
5. #14543033C2semidirect
6. #14543023C2semidirect
7. #14543011C2semidirect
8. #14542993C2semidirect
9. #14542974C2semidirect
10. #14542955C2semidirect
11. #14542939C2semidirect
12. #14542922C2semidirect
13. #14542386C2semidirect
14. #14542342C2semidirect
15. D4×#63252C2semidirect
16. #14542202C2semidirect
17. #14542191C2semidirect
18. #14542174C2semidirect
19. #14542113C2semidirect
20. C2×#11763320C2semidirect
21. C2×C17×#525C2semidirect
22. C22×#63252C22semidirect
23. C22×#63252C22semidirect
24. #11763562C22semidirect
25. #11763560C22semidirect
26. #11763556C22semidirect
27. #11763555C22semidirect
28. #11763554C22semidirect
29. #11763552C22semidirect
30. #11763549C22semidirect
31. #11763548C22semidirect
32. #11763548C22semidirect
33. #11763547C22semidirect
34. #11763543C22semidirect
35. #11763529C22semidirect
36. #11763524C22semidirect
37. #11763516C22semidirect
38. #11763513C22semidirect
39. #11763505C22semidirect
40. #11763505C22semidirect
41. #11763504C22semidirect
42. #11763502C22semidirect
43. #11763499C22semidirect
44. #11763499C22semidirect
45. #11763494C22semidirect
46. #11763490C22semidirect
47. #11763487C22semidirect
48. #11763486C22semidirect
49. #11763485C22semidirect
50. #11763485C22semidirect
51. #11763480C22semidirect
52. D4×Dic34C22semidirect
53. #11763468C22semidirect
54. #11763468C22semidirect
55. #11763464C22semidirect
56. #11763463C22semidirect
57. #11763460C22semidirect
58. #11763455C22semidirect
59. #11763455C22semidirect
60. #11763453C22semidirect
61. #11763449C22semidirect
62. #11763449C22semidirect
63. #11763448C22semidirect
64. #11763446C22semidirect
65. D4×D68C22semidirect
66. D4×C22⋊D17C22semidirect
67. #11763441C22semidirect
68. #11763438C22semidirect
69. #11763434C22semidirect
70. #11763430C22semidirect
71. #11763430C22semidirect
72. #11763429C22semidirect
73. #11763427C22semidirect
74. #11763421C22semidirect
75. #11763421C22semidirect
76. #11763414C22semidirect
77. #11763414C22semidirect
78. #11763411C22semidirect
79. #11763409C22semidirect
80. #11763408C22semidirect
81. #11763406C22semidirect
82. #11763405C22semidirect
83. #11763404C22semidirect
84. #11763402C22semidirect
85. #11763399C22semidirect
86. #11763397C22semidirect
87. #11763396C22semidirect
88. #11763395C22semidirect
89. #11763394C22semidirect
90. #11763394C22semidirect
91. #11763391C22semidirect
92. #11763387C22semidirect
93. #11763387C22semidirect
94. #11763386C22semidirect
95. #11763383C22semidirect
96. #11763380C22semidirect
97. #11763380C22semidirect
98. #11763376C22semidirect
99. #11763374C22semidirect
100. #11763373C22semidirect
101. #11763373C22semidirect
102. #11763369C22semidirect
103. #11763368C22semidirect
104. #11763368C22semidirect
105. #11763367C22semidirect
106. #11763366C22semidirect
107. #11763359C22semidirect
108. #11763356C22semidirect
109. #11763355C22semidirect
110. #11763355C22semidirect
111. #11763341C22semidirect
112. #11763339C22semidirect
113. #11763339C22semidirect
114. #11763337C22semidirect
115. #11763337C22semidirect
116. #11763320C22semidirect
117. #11763320C22semidirect
118. #11763320C22semidirect
119. #11763320C22semidirect
120. #11763320C22semidirect
121. #11763320C22semidirect
122. #11763320C22semidirect
123. #11763320C22semidirect
124. #11763320C22semidirect
125. #11763318C22semidirect
126. #11763318C22semidirect
127. #11763316C22semidirect
128. #11763316C22semidirect
129. C2×#10587615C22semidirect
130. C2×#10587610C22semidirect
131. C2×#10587610C22semidirect
132. C2×#10587616C22semidirect
133. C2×#10587616C22semidirect
134. C2×#10587639C22semidirect
135. C4×#63252C22semidirect
136. C4×#63254C22semidirect
137. C2×C4×C22⋊D17C22semidirect
138. C2×C4×C22⋊D17C22semidirect
139. C4×D4×D17C22semidirect
140. C2×#10587612C22semidirect
141. C2×#10587612C22semidirect
142. C22×#41×C17C22semidirect
143. C24×C4×C17C22semidirect
145. C17×#525C22semidirect
146. C17×#525C22semidirect
147. C17×#525C22semidirect
148. C17×#525C22semidirect
149. C17×#525C22semidirect
150. C17×#525C22semidirect
151. C17×#525C22semidirect
152. C17×#525C22semidirect
153. C2×C17×#123C22semidirect
154. C2×C17×C22⋊Q8C22semidirect
155. C2×C17×#121C22semidirect
156. C2×C17×#120C22semidirect
157. C2×C4×D4×C17C22semidirect
158. C2×C17×#117C22semidirect
196. C2×#63252C23semidirect
197. C2×#63252C23semidirect
199. C22×D68C23semidirect
201. C22×C4×D17C23semidirect
203. C22×Dic34C23semidirect
256. #10587633C23semidirect
257. #10587633C23semidirect
258. #10587632C23semidirect
259. #10587632C23semidirect
260. #10587630C23semidirect
261. #10587630C23semidirect
271. #10587625C23semidirect
272. #10587625C23semidirect
281. #10587623C23semidirect
282. #10587623C23semidirect
290. #10587621C23semidirect
291. #10587621C23semidirect
303. #10587616C23semidirect
304. #10587616C23semidirect
320. C4×C22⋊D17C23semidirect
321. C4×C22⋊D17C23semidirect
329. #10587612C23semidirect
330. #10587612C23semidirect
331. #10587612C23semidirect
334. C2×C4⋊Dic17C23semidirect
344. #10587610C23semidirect
345. #10587610C23semidirect
349. C2×C4×Dic17C23semidirect
350. #10587584C23semidirect
351. #10587584C23semidirect
352. #10587584C23semidirect
353. #10587584C23semidirect
354. #10587583C23semidirect
355. #10587582C23semidirect
356. #10587582C23semidirect
357. #10587582C23semidirect
358. #10587582C23semidirect
359. #10587581C23semidirect
360. #10587580C23semidirect
361. #10587580C23semidirect
362. #10587580C23semidirect
363. #10587580C23semidirect
364. #10587579C23semidirect
365. #10587578C23semidirect
366. C4⋊C4×D17C23semidirect
367. #10587576C23semidirect
368. #10587575C23semidirect
369. #10587575C23semidirect
370. #10587575C23semidirect
371. #10587575C23semidirect
372. #10587574C23semidirect
373. #10587573C23semidirect
375. #10587572C23semidirect
380. #10587571C23semidirect
381. #10587571C23semidirect
386. #10587570C23semidirect
387. #10587570C23semidirect
392. #10587569C23semidirect
393. #10587569C23semidirect
395. #10587568C23semidirect
398. #10587567C23semidirect
399. #10587567C23semidirect
401. C22⋊C4×D17C23semidirect
406. #10587565C23semidirect
407. #10587565C23semidirect
410. #10587564C23semidirect
411. #10587564C23semidirect
413. #10587563C23semidirect
414. #10587561C23semidirect
415. #10587560C23semidirect
416. C4×D68C23semidirect
417. C4×D68C23semidirect
418. C4×D68C23semidirect
419. #10587558C23semidirect
420. C42×D17C23semidirect
421. #10587556C23semidirect
422. #10587556C23semidirect
423. #10587555C23semidirect
424. #10587555C23semidirect
425. C4×Dic34C23semidirect
426. C4×Dic34C23semidirect
427. C4×Dic34C23semidirect
734. C2×#525D17semidirect
778. C22×#41C2×D17semidirect
779. C24×C4C2×D17semidirect
886. #525C2×D17semidirect
887. #525C2×D17semidirect
888. #525C2×D17semidirect
889. #525C2×D17semidirect
890. #525C2×D17semidirect
891. #525C2×D17semidirect
892. #525C2×D17semidirect
893. #525C2×D17semidirect
895. C2×#123C2×D17semidirect
898. C2×C22⋊Q8C2×D17semidirect
901. C2×#121C2×D17semidirect
903. C2×#120C2×D17semidirect
909. C2×C4×D4C2×D17semidirect
912. C2×#117C2×D17semidirect
1192. C17#62729semidirect

Maximal subgroups

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

subgroupindex
#145431002
#145430772
#145430592
#145430442
#145430332
#145430232
#145430112
#145429932
#145429742
#145429552
#145429392
#145429222
#145423862
#145423422
D4×#632522
#145422022
#145421912
#145421742
#145421132
C2×#117633202
C2×C17×#5252
#6272917