Finite Group Databasebeta

← #32906030

Subgroups — #32906030

Order 18176.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602255C214yesmaximal, complemented
2#22602252C212yesmaximal, complemented
3#22602241C212yesmaximal, complemented
4#22602229C214yesmaximal, complemented
5#22602219C212yesmaximal, complemented
6#22602209C212yesmaximal, complemented
7#22602196C214yesmaximal, complemented
8#22602183C214yesmaximal, complemented
9#22602175C214yesmaximal, complemented
10#22602168C214yesmaximal, complemented
11#22601938C214yesmaximal, complemented
12#22601931C214yesmaximal, complemented
13#22601902C214yesmaximal, complemented
14#22601896C214yesmaximal, complemented
15#22601728C212yesmaximal, complemented
16#22601725C212yesmaximal, complemented
17#22601670C212yesmaximal, complemented
18#22601637C211yesmaximal, characteristic, complemented
19#22601636C211yesmaximal, characteristic, complemented
20#22601635C211yesmaximal, characteristic, complemented
21#533×D71C211yesmaximal, characteristic, complemented
22#532×D71C211yesmaximal, characteristic, complemented
23#22601539C212yesmaximal, complemented
24C2×C4×#11765865C211yesmaximal, characteristic, complemented
25C71×#3444C211yesmaximal, characteristic, complemented
26C22×#11765865C2211yescharacteristic
27C2×#41×D71C2212yes—
28#17986733C2218yescomplemented
29#17986732C2218yescomplemented
30#17986732C2214yescomplemented
31#17986731C2214yescomplemented
32#17986726C2214yescomplemented
33#17986725C2214yescomplemented
34#17986721C2214yescomplemented
35#17986720C2214yescomplemented
36#17986718C2214yescomplemented
37#17986717C2214yescomplemented
38#17986717C2218yescomplemented
39#17986716C2218yescomplemented
40#17986713C2214yescomplemented
41#17986712C2214yescomplemented
42#17986708C2214yescomplemented
43#17986705C2214yescomplemented
44#17986702C2214yescomplemented
45#17986700C2218yescomplemented
46#17986699C2214yescomplemented
47#17986699C2218yescomplemented
48#17986698C2218yescomplemented
49#17986696C2214yescomplemented
50#17986694C2218yescomplemented
51#17986694C2218yescomplemented
52#17986693C2214yescomplemented
53#17986693C2218yescomplemented
54#17986690C2214yescomplemented
55#17986688C2214yescomplemented
56#17986687C2214yescomplemented
57#17986685C2218yescomplemented
58#17986683C2214yescomplemented
59#17986682C2218yescomplemented
60#17986678C2218yescomplemented
61#17986677C2218yescomplemented
62#17986674C2218yescomplemented
63#17986673C2218yescomplemented
64#17986668C2214yescomplemented
65#17986667C2214yescomplemented
66#17986661C2214yescomplemented
67#17986659C2214yescomplemented
68#17986657C2214yescomplemented
69#17986656C2214yescomplemented
70#17986651C2214yescomplemented
71#17986648C2214yescomplemented
72#17986646C2214yescomplemented
73#17986644C2214yescomplemented
74#17986642C2214yescomplemented
75#17986637C2214yescomplemented
76#17986622C2214yescomplemented
77#17986621C2214yescomplemented
78#17986616C2214yescomplemented
79#17986614C2214yescomplemented
80#17986609C2214yescomplemented
81#17986607C2214yescomplemented
82#17986602C2214yescomplemented
83#17986600C2214yescomplemented
84#17986593C2218yescomplemented
85#17986591C2218yescomplemented
86#17986584C2218yescomplemented
87#17986582C2218yescomplemented
88#17986579C2214yescomplemented
89#17986578C2214yescomplemented
90#17986572C2214yes—
91#17986571C2214yescomplemented
92#17986565C2214yes—
93#17986564C2214yescomplemented
94#17986560C2214yes—
95#17986559C2214yes—
96#17986556C2212yescomplemented
97#17986556C2211yescharacteristic, complemented
98#17986555C2212yescomplemented
99#17986554C2212yescomplemented
100#17986554C2212yescomplemented
101#17986554C2212yescomplemented
102#17986553C2214yescomplemented
103#17986552C2212yescomplemented
104#17986551C2214yescomplemented
105#17986550C2211yescharacteristic, complemented
106#17986550C2212yescomplemented
107#17986549C2211yescharacteristic
108#17986549C2212yescomplemented
109#17986548C2212yescomplemented
110#17986547C2211yescharacteristic, complemented
111#17986547C2212yescomplemented
112#17986546C2214yescomplemented
113#17986546C2218yescomplemented
114#17986545C2212yes—
115#17986544C2214yes—
116C4⋊Q8×D71C2212yescomplemented
117C4⋊Q8×D71C2211yescharacteristic, complemented
118#127×D71C2211yescharacteristic, complemented
119#17986536C2214yescomplemented
120#17986535C2214yescomplemented
121#17986534C2214yescomplemented
122#17986533C2214yescomplemented
123#17986533C2214yescomplemented
124#17986533C2214yescomplemented
125#17986533C2218yescomplemented
126#17986531C2218yescomplemented
127#17986531C2214yescomplemented
128#17986530C2214yescomplemented
129#17986529C2218yescomplemented
130#17986528C2214yescomplemented
131#17986527C2218yescomplemented
132#125×D71C2212yescomplemented
133#124×D71C2212yescomplemented
134#17986512C2214yescomplemented
135#17986511C2212yescomplemented
136#17986510C2212yescomplemented
137#17986510C2214yescomplemented
138#17986509C2214yescomplemented
139#17986508C2218yes—
140#17986506C2212yescomplemented
141C22⋊Q8×D71C2214yes—
142#121×D71C2214yes—
143#17986481C2214yescomplemented
144#17986478C2214yescomplemented
145#17986478C2218yescomplemented
146#17986475C2214yescomplemented
147#17986471C2218yes—
148#17986471C2214yescomplemented
149#41×Dic71C2212yescomplemented
150C4×#11765866C2214yescomplemented
151C4×#11765865C2212yes—
152C4×#11765865C2212yes—
153C4×#11765865C2212yes—
154C4×#11765865C2212yes—
155C4×#11765865C2212yescomplemented
156C4×#11765865C2212yescomplemented
157C4×#11765865C2212yescomplemented
158C4×#11765865C2212yescomplemented
159C4×#11765865C2212yescomplemented
160C4×#11765865C2214yescomplemented
161C4×#11765865C2214yescomplemented
162#17986467C2212yescomplemented
163#17986467C2214yescomplemented
164C4×#11765864C2214yescomplemented
165C2×C4×Dic142C2212yescomplemented
166C4×Q8×D71C2214yescomplemented
167C2×C4×D284C2212yes—
168C2×C4×C22⋊D71C2212yes—
169C2×C4×C22⋊D71C2212yescomplemented
170C4×D4×D71C2214yescomplemented
171C2×#14556087C2211yescharacteristic, complemented
172C2×#14556085C2211yescharacteristic
173C2×#14556085C2211yescharacteristic, complemented
174C2×#14556085C2214yescomplemented
175#117×D71C2212yes—
176#117×D71C2214yescomplemented
177C2×C42×D71C2211yescharacteristic
178C2×C42×D71C2211yescharacteristic, complemented
179#533×C71C2212yescomplemented
180#533×C71C2211yescharacteristic, complemented
181#532×C71C2211yescharacteristic
182#532×C71C2212yescomplemented
183#529×C71C2214yescomplemented
184#529×C71C2214yescomplemented
185#529×C71C2214yescomplemented
186#525×C71C2212yescomplemented
187#525×C71C2214yescomplemented
188C4×#41×C71C2212yescomplemented
189C4×#41×C71C2214yescomplemented
190C22×C42×C71C2211yescharacteristic, complemented
191C2×#11765866C2312yes—
192C2×#11765866C2314yes—
193C2×#11765865—28no—
194C2×#11765865C2312yes—
195C2×#11765865C2312yes—
196C2×#11765865C2314yes—
197C2×#11765865C2312yes—
198C2×#11765865C2312yes—
199C2×#11765865C2312yes—
200C2×#11765865C2314yes—
201C2×#11765864C2314yes—
202C2×#11765864C2312yes—
203C2×#11765864C2314yes—
204#41×D71—216no—
205C22×Dic142C2311yescharacteristic
206C2×Q8×D71C2312yes—
207C2×Q8×D71C2314yes—
208C22×D284C2311yescharacteristic
209C22×C22⋊D71C2311yescharacteristic
210C22×C22⋊D71C2311yescharacteristic
211C2×D4×D71C2314yes—
212C2×D4×D71C2312yes—
213C2×D4×D71C2314yes—
214C22×C4×D71C2314yes—
215C22×C4×D71C2311yescharacteristic
216C22×C4×D71C2312yes—
217C22×C4×D71C2312yes—
218C22×C4×D71C2311yescharacteristic
219#14556128C2311yescharacteristic
220#14556128C2312yes—
221#14556127C2318yes—
222#14556127C2314yes—
223#14556127C2314yes—
224#14556127C2314yes—
225#14556126C2312yes—
226#14556126C2314yes—
227#14556125C2311yescharacteristic
228#14556124C2318yes—
229#14556124C2312yes—
230#14556124C2314yes—
231#14556123C2318yes—
232#14556123C2318yes—
233#14556123C2318yes—
234#14556122C2318yes—
235#14556122C2318yes—
236#14556122C2318yes—
237#14556121C2318yes—
238#14556121C2318yes—
239#14556121C2318yes—
240#14556121C2318yes—
241#14556121C2318yes—
242#14556120C2318yes—
243#14556120C2314yes—
244#14556120C2312yes—
245#14556119C2318yes—
246#14556119C2314yes—
247#14556119C2314yes—
248#14556119C2314yes—
249#14556118C2318yes—
250#14556118C2318yes—
251#14556118C2318yes—
252#14556117C2312yes—
253#14556117C2314yes—
254#14556116C2318yes—
255#14556116C2314yes—
256#14556116C2312yes—
257#14556115C2318yes—
258#14556115C2312yes—
259#14556115C2314yes—
260#14556114C2318yes—
261#14556114C2318yes—
262#14556114C2318yes—
263#14556114C2318yes—
264#14556114C2318yes—
265#14556113C2318yes—
266#14556113C2318yes—
267#14556113C2318yes—
268#14556112C2314yes—
269#14556112C2318yes—
270#14556111C2314yes—
271#14556111C2318yes—
272#14556111C2318yes—
273#14556111C2318yes—
274#14556110C2318yes—
275#14556110C2318yes—
276#14556110C2318yes—
277#14556110C2318yes—
278#14556110C2318yes—
279#14556109C2314yes—
280#14556109C2318yes—
281#14556108C2314yes—
282#14556108C2318yes—
283#14556108C2314yes—
284#14556108C2314yes—
285#14556107C2314yes—
286#14556107C2318yes—
287#14556107C2314yes—
288#14556107C2314yes—
289#14556106C2318yes—
290#14556106C2318yes—
291#14556106C2318yes—
292#14556105C2318yes—
293#14556105C2318yes—
294#14556105C2318yes—
295#14556104C2314yes—
296#14556104C2314yes—
297#14556104C2314yes—
298#14556103C2318yes—
299#14556103C2314yes—
300#14556103C2314yes—
301#14556103C2314yes—
302#14556102C2314yes—
303#14556102C2318yes—
304#14556102C2314yes—
305#14556102C2314yes—
306#14556101C2318yes—
307#14556101C2318yes—
308#14556101C2318yes—
309#14556101C2318yes—
310#14556101C2318yes—
311#14556100C2318yes—
312#14556100C2318yes—
313#14556100C2318yes—
314#14556099C2314yes—
315#14556099C2318yes—
316#14556099C2318yes—
317#14556099C2314yes—
318#14556099C2314yes—
319#14556098C2314yes—
320#14556098C2318yes—
321#14556097C2314yes—
322#14556096C2314yes—
323#14556096C2318yes—
324Q8×Dic71C2314yes—
325Q8×Dic71C2314yes—
326Q8×Dic71C2314yes—
327C4×Dic142C2314yes—
328C4×Dic142C2314yes—
329C4×Dic142C2312yes—
330C4×Dic142C2312yes—
331C4×Dic142C2312yes—
332C4×Dic142C2312yes—
333C4×Dic142C2312yes—
334C4×Dic142C2312yes—
335C4×Dic142C2318yes—
336C4×Dic142C2314yes—
337C4×Dic142C2318yes—
338C4×Dic142C2312yes—
339C4×Dic142C2312yes—
340#14556093C2314yes—
341#14556093C2314yes—
342#14556093C2314yes—
343#14556093C2318yes—
344#14556093C2318yes—
345C4×D284C2314yes—
346C4×D284C2312yes—
347C4×D284C2314yes—
348C4×D284C2312yes—
349C4×D284C2312yes—
350C4×D284C2312yes—
351C4×D284C2318yes—
352C4×D284C2312yes—
353C4×D284C2312yes—
354C4×D284C2312yes—
355C4×D284C2312yes—
356C4×D284C2314yes—
357C4×D284C2318yes—
358D4×Dic71C2318yes—
359D4×Dic71C2314yes—
360D4×Dic71C2314yes—
361D4×Dic71C2314yes—
362#14556090C2314yes—
363#14556090C2314yes—
364#14556090C2314yes—
365#14556090C2318yes—
366#14556090C2318yes—
367C4×C22⋊D71C2318yes—
368C4×C22⋊D71C2312yes—
369C4×C22⋊D71C2312yes—
370C4×C22⋊D71C2312yes—
371C4×C22⋊D71C2312yes—
372C4×C22⋊D71C2312yes—
373C4×C22⋊D71C2318yes—
374C4×C22⋊D71C2312yes—
375C4×C22⋊D71C2312yes—
376C4×C22⋊D71C2312yes—
377C4×C22⋊D71C2318yes—
378C4×C22⋊D71C2312yes—
379C4×C22⋊D71C2318yes—
380C4×C22⋊D71C2312yes—
381C4×C22⋊D71C2312yes—
382C4×C22⋊D71C2312yes—
383C4×C22⋊D71C2312yes—
384C4×C22⋊D71C2312yes—
385C4×C22⋊D71C2318yes—
386C4×C22⋊D71C2312yes—
387C4×C22⋊D71C2312yes—
388C4×C22⋊D71C2318yes—
389C4×C22⋊D71C2318yes—
390(C22⋊D71)⋊C4C2318yes—
391(C22⋊D71)⋊C4C2318yes—
392(C22⋊D71)⋊C4C2318yes—
393(C22⋊D71)⋊C4C2318yes—
394(C22⋊D71)⋊C4C2318yes—
395#14556087C2312yes—
396#14556087C2312yes—
397#14556087C2314yes—
398#14556087C2312yes—
399#14556087C2314yes—
400#14556087C2312yes—
401#14556087C2312yes—
402#14556086C2314yes—
403#14556086C2318yes—
404#14556086C2318yes—
405#14556086C2314yes—
406#14556086C2314yes—
407#14556085C2312yes—
408#14556085C2312yes—
409#14556085C2318yes—
410#14556085C2318yes—
411#14556085C2318yes—
412#14556085C2314yes—
413#14556085C2311yescharacteristic
414#14556085C2311yescharacteristic
415#14556085C2311yescharacteristic
416#14556085C2312yes—
417#14556085C2311yescharacteristic
418#14556085C2312yes—
419#14556085C2314yes—
420#14556085C2312yes—
421#14556085C2312yes—
422#14556085C2314yes—
423#14556084C2314yes—
424#14556084C2318yes—
425#14556084C2318yes—
426C2×C4⋊Dic71C2312yes—
427C2×Dic71⋊C4C2312yes—
428C2×Dic71⋊C4C2318yes—
429C2×Dic71⋊C4C2312yes—
430C4⋊C4×D71C2314yes—
431C4⋊C4×D71C2318yes—
432C4⋊C4×D71C2314yes—
433C4⋊C4×D71C2318yes—
434C4⋊C4×D71C2314yes—
435C2×C22⋊Dic71C2312yes—
436C2×(C2×D71)⋊C4C2312yes—
437C2×(C2×D71)⋊C4C2318yes—
438C2×(C2×D71)⋊C4C2312yes—
439C22⋊C4×D71C2314yes—
440C22⋊C4×D71C2318yes—
441C22⋊C4×D71C2318yes—
442C2×C4×Dic71C2311yescharacteristic
443C2×C4×Dic71C2312yes—
444C2×C4×Dic71C2311yescharacteristic
445C2×C4×Dic71C2312yes—
446C2×C4×Dic71C2314yes—
447C42×D71C2312yes—
448C42×D71C2312yes—
449C42×D71C2311yescharacteristic
450C42×D71C2311yescharacteristic
451C42×D71C2311yescharacteristic
452C42×D71C2311yescharacteristic
453C42×D71C2312yes—
454C42×D71C2312yes—
455C42×D71C2312yes—
456C42×D71C2312yes—
457C42×D71C2314yes—
458C42×D71C2314yes—
459C42×D71C2314yes—
460C2×#41×C71C2312yes—
461C2×#41×C71C2314yes—
462C23×C4×C71C2311yescharacteristic
463C23×C4×C71C2312yes—
464C4⋊Q8×C71C2311yescharacteristic
465C4⋊Q8×C71C2312yes—
466#127×C71C2311yescharacteristic
467#126×C71C2318yes—
468#125×C71C2314yes—
469#125×C71C2312yes—
470#124×C71C2314yes—
471#124×C71C2312yes—
472#123×C71C2314yes—
473#123×C71C2318yes—
474C22⋊Q8×C71C2314yes—
475C22⋊Q8×C71C2314yes—
476C22⋊Q8×C71C2314yes—
477#121×C71C2314yes—
478#121×C71C2314yes—
479#121×C71C2314yes—
480#120×C71C2314yes—
481C4×Q8×C71C2314yes—
482C4×Q8×C71C2314yes—
483C4×Q8×C71C2314yes—
484C4×D4×C71C2318yes—
485C4×D4×C71C2314yes—
486C4×D4×C71C2314yes—
487C4×D4×C71C2318yes—
488C4×D4×C71C2318yes—
489C4×D4×C71C2314yes—
490#117×C71C2318yes—
491#117×C71C2314yes—
492#117×C71C2312yes—
493#117×C71C2314yes—
494C2×C42×C71C2311yescharacteristic
495C2×C42×C71C2312yes—
496C2×C42×C71C2312yes—
497C2×C42×C71C2312yes—
498C2×C42×C71C2312yes—
499C2×C42×C71C2311yescharacteristic
500C2×C42×C71C2312yes—
501C2×C42×C71C2314yes—
502C23×D71C2411yescharacteristic
503C23×D71C2414yes—
504C23×D71C2411yescharacteristic
505#11765866—28no—
506#11765866—48no—
507#11765865—28no—
508#11765865—216no—
509#11765865—28no—
510#11765865—28no—
511#11765865—28no—
512#11765865—28no—
513#11765865—48no—
514#11765864—216no—
515#11765864—28no—
516#11765864—48no—
517C2×Dic142—24no—
518C2×Dic142C2412yes—
519C2×Dic142C2414yes—
520C2×Dic142C2414yes—
521C2×Dic142C2412yes—
522C2×Dic142C2412yes—
523C2×Dic142C2418yes—
524Q8×D71—28no—
525Q8×D71—48no—
526C2×D284—24no—
527C2×D284C2414yes—
528C2×D284C2412yes—
529C2×D284C2414yes—
530C2×D284C2412yes—
531C2×D284C2412yes—
532C2×D284C2418yes—
533C2×C22⋊D71—24no—
534C2×C22⋊D71—24no—
535C2×C22⋊D71C2414yes—
536C2×C22⋊D71C2414yes—
537C2×C22⋊D71C2414yes—
538C2×C22⋊D71C2412yes—
539C2×C22⋊D71C2412yes—
540C2×C22⋊D71C2412yes—
541C2×C22⋊D71C2412yes—
542C2×C22⋊D71C2418yes—
543C2×C22⋊D71C2418yes—
544C2×C22⋊D71C2418yes—
545D4×D71—216no—
546D4×D71—28no—
547D4×D71—48no—
548C22×Dic71C2411yescharacteristic
549C22×Dic71C2414yes—
550C22×Dic71C2412yes—
551C22×Dic71C2412yes—
552C22×Dic71C2418yes—
553C22×Dic71C2411yescharacteristic
554C2×C4×D71—24no—
555C2×C4×D71—216no—
556C2×C4×D71—44no—
557C2×C4×D71—44no—
558C2×C4×D71#4118yescomplemented
559C2×C4×D71C2412yes—
560C2×C4×D71C2414yes—
561C2×C4×D71C2412yes—
562C2×C4×D71C2412yes—
563C2×C4×D71C2414yes—
564C2×C4×D71C2414yes—
565C2×C4×D71C2412yes—
566C2×C4×D71C2412yes—
567C2×C4×D71C2412yes—
568C2×C4×D71C2412yes—
569C2×C4×D71C2412yes—
570C2×C4×D71C2412yes—
571C2×C4×D71C2412yes—
572C2×C4×D71C2418yes—
573C2×C4×D71C2418yes—
574C2×C4×D71C2418yes—
575C2×C4×D71C2411yescharacteristic
576C2×C4×D71C2411yescharacteristic
577C2×C4×D71C2411yescharacteristic
578C2×C4×D71C2411yescharacteristic
579C4⋊Dic71C2414yes—
580C4⋊Dic71C2414yes—
581C4⋊Dic71C2414yes—
582C4⋊Dic71C2418yes—
583C4⋊Dic71C2418yes—
584C4⋊Dic71C2412yes—
585C4⋊Dic71C2412yes—
586C4⋊Dic71C2412yes—
587C4⋊Dic71C2412yes—
588C4⋊Dic71C2418yes—
589Dic71⋊C4C2412yes—
590Dic71⋊C4C2418yes—
591Dic71⋊C4C2418yes—
592Dic71⋊C4C2418yes—
593Dic71⋊C4C2418yes—
594Dic71⋊C4C2418yes—
595Dic71⋊C4C2412yes—
596Dic71⋊C4C2412yes—
597Dic71⋊C4C2418yes—
598Dic71⋊C4C2412yes—
599Dic71⋊C4C2412yes—
600Dic71⋊C4C2412yes—
601Dic71⋊C4C2418yes—
602Dic71⋊C4C2412yes—
603Dic71⋊C4C2412yes—
604Dic71⋊C4C2418yes—
605Dic71⋊C4C2418yes—
606C22⋊Dic71C2414yes—
607C22⋊Dic71C2418yes—
608C22⋊Dic71C2418yes—
609C22⋊Dic71C2412yes—
610C22⋊Dic71C2412yes—
611C22⋊Dic71C2412yes—
612C22⋊Dic71C2412yes—
613C22⋊Dic71C2418yes—
614C22⋊Dic71C2418yes—
615(C2×D71)⋊C4C2412yes—
616(C2×D71)⋊C4C2418yes—
617(C2×D71)⋊C4C2418yes—
618(C2×D71)⋊C4C2418yes—
619(C2×D71)⋊C4C2412yes—
620(C2×D71)⋊C4C2412yes—
621(C2×D71)⋊C4C2418yes—
622(C2×D71)⋊C4C2412yes—
623(C2×D71)⋊C4C2412yes—
624(C2×D71)⋊C4C2412yes—
625(C2×D71)⋊C4C2418yes—
626(C2×D71)⋊C4C2412yes—
627(C2×D71)⋊C4C2412yes—
628(C2×D71)⋊C4C2418yes—
629(C2×D71)⋊C4C2418yes—
630(C2×D71)⋊C4C2418yes—
631(C2×D71)⋊C4C2418yes—
632C4×Dic71C2411yescharacteristic
633C4×Dic71C2411yescharacteristic
634C4×Dic71C2412yes—
635C4×Dic71C2412yes—
636C4×Dic71C2414yes—
637C4×Dic71C2412yes—
638C4×Dic71C2411yescharacteristic
639C4×Dic71C2411yescharacteristic
640C4×Dic71C2412yes—
641C4×Dic71C2412yes—
642C4×Dic71C2412yes—
643C4×Dic71C2412yes—
644C4×Dic71C2412yes—
645C4×Dic71C2412yes—
646C4×Dic71C2412yes—
647C4×Dic71C2418yes—
648C4×Dic71C2418yes—
649C4×Dic71C2418yes—
650C4×Dic71C2418yes—
651C24×C71C2411yescharacteristic
652#41×C71—28no—
653#41×C71—48no—
654C2×Q8×C71C2412yes—
655C2×Q8×C71C2414yes—
656C2×D4×C71C2414yes—
657C2×D4×C71C2412yes—
658C2×D4×C71C2414yes—
659C2×D4×C71C2418yes—
660C22×C4×C71—24no—
661C22×C4×C71—44no—
662C22×C4×C71C2412yes—
663C22×C4×C71C2414yes—
664C22×C4×C71C2411yescharacteristic
665C22×C4×C71C2412yes—
666C22×C4×C71C2412yes—
667C22×C4×C71C2412yes—
668C22×C4×C71C2412yes—
669C22×C4×C71C2412yes—
670C22×C4×C71C2412yes—
671C22×C4×C71C2412yes—
672C22×C4×C71C2418yes—
673C22×C4×C71C2411yescharacteristic
674C4⋊C4×C71C2414yes—
675C4⋊C4×C71C2414yes—
676C4⋊C4×C71C2414yes—
677C4⋊C4×C71C2418yes—
678C4⋊C4×C71C2418yes—
679C4⋊C4×C71C2418yes—
680C22⋊C4×C71C2414yes—
681C22⋊C4×C71C2418yes—
682C22⋊C4×C71C2418yes—
683C22⋊C4×C71C2418yes—
684C22⋊C4×C71C2418yes—
685C42×C71C2411yescharacteristic
686C42×C71C2411yescharacteristic
687C42×C71C2412yes—
688C42×C71C2412yes—
689C42×C71C2412yes—
690C42×C71C2412yes—
691C42×C71C2411yescharacteristic
692C42×C71C2412yes—
693C42×C71C2412yes—
694C42×C71C2411yescharacteristic
695C42×C71C2414yes—
696C42×C71C2418yes—
697C23×C71—22no—
698C23×C71—42no—
699C23×C71C2514yes—
700C23×C71C2512yes—
701C23×C71C2511yescharacteristic
702C22×D71—22no—
703C22×D71—28no—
704C22×D71—42no—
705C22×D71—42no—
706C22×D71—48no—
707C22×D71C2×#4114yes—
708C22×D71C2512yes—
709C22×D71C2514yes—
710C22×D71C2511yescharacteristic
711C22×D71C2511yescharacteristic
712Q8×C71—24no—
713Q8×C71—28no—
714D4×C71—28no—
715D4×C71—24no—
716D4×C71—28no—
717D4×C71—48no—
718C2×C4×C71—22no—
719C2×C4×C71—24no—
720C2×C4×C71—24no—
721C2×C4×C71—28no—
722C2×C4×C71—24no—
723C2×C4×C71—24no—
724C2×C4×C71—24no—
725C2×C4×C71—42no—
726C2×C4×C71—42no—
727C2×C4×C71—42no—
728C2×C4×C71—48no—
729C2×C4×C71C2×#4114yes—
730C2×C4×C71C2512yes—
731C2×C4×C71C2512yes—
732C2×C4×C71C2512yes—
733C2×C4×C71C2512yes—
734C2×C4×C71C2514yes—
735C2×C4×C71C2518yes—
736C2×C4×C71C2511yescharacteristic
737C2×C4×C71C2512yes—
738C2×C4×C71C2511yescharacteristic
739C22⋊D71—28no—
740C22⋊D71—28no—
741C22⋊D71—24no—
742C22⋊D71—24no—
743C22⋊D71—28no—
744C22⋊D71—24no—
745C22⋊D71—24no—
746C22⋊D71—48no—
747C22⋊D71—48no—
748C22⋊D71—48no—
749C2×Dic71—22no—
750C2×Dic71—28no—
751C2×Dic71—42no—
752C2×Dic71—42no—
753C2×Dic71—48no—
754C2×Dic71C2×#4114yes—
755C2×Dic71C2512yes—
756C2×Dic71C2512yes—
757C2×Dic71C2512yes—
758C2×Dic71C2512yes—
759C2×Dic71C2514yes—
760C2×Dic71C2518yes—
761C2×Dic71C2512yes—
762C2×Dic71C2511yescharacteristic
763C2×Dic71C2511yescharacteristic
764D284—28no—
765D284—24no—
766D284—24no—
767D284—24no—
768D284—28no—
769D284—48no—
770C4×D71—28no—
771C4×D71—24no—
772C4×D71—24no—
773C4×D71—28no—
774C4×D71—24no—
775C4×D71—24no—
776C4×D71—24no—
777C4×D71—24no—
778C4×D71—28no—
779C4×D71—42no—
780C4×D71—42no—
781C4×D71—42no—
782C4×D71—42no—
783C4×D71—48no—
784C4×D71—48no—
785C4×D71—48no—
786C4×D71C2×#4114yes—
787C4×D71C2×#4114yes—
788C4×D71C2×#4114yes—
789C4×D71C2×#4114yes—
790Dic142—24no—
791Dic142—28no—
792Dic142—28no—
793Dic142—24no—
794Dic142—24no—
795Dic142—48no—
796C22×C71—22no—
797C22×C71—24no—
798C22×C71—22no—
799C22×C71—28no—
800C22×C71—22no—
801C22×C71—22no—
802C22×C71—44no—
803C22×C71C22×#4112yes—
804C22×C71C2611yescharacteristic
805C2×D71—22no—
806C2×D71—22no—
807C2×D71—22no—
808C2×D71—24no—
809C2×D71—22no—
810C2×D71—22no—
811C2×D71—28no—
812C2×D71—44no—
813C2×D71—44no—
814C2×D71—88no—
815C2×D71C22×#4112yes—
816C2×D71C22×#4112yes—
817C4×C71—22no—
818C4×C71—24no—
819C4×C71—28no—
820C4×C71—22no—
821C4×C71—22no—
822C4×C71—22no—
823C4×C71C22×#4112yes—
824C4×C71C22×#4112yes—
825C4×C71#58514yes—
826Dic71—24no—
827Dic71—22no—
828Dic71—28no—
829Dic71—22no—
830Dic71—22no—
831Dic71—22no—
832Dic71—22no—
833Dic71C22×#4112yes—
834Dic71C22×#4112yes—
835#62815—711nomaximal, Sylow
836C2×C71—22no—
837C2×C71—44no—
838C2×C71—42no—
839C2×C71C23×#4111yescharacteristic
840C2×C71C2×#58512yes—
841D71—22no—
842D71—22no—
843D71—42no—
844D71—44no—
845#3512—714no—
846#3511—712no—
847#3511—712no—
848#3510—714no—
849#3509—712no—
850#3508—712no—
851#3507—714no—
852#3506—714no—
853#3505—714no—
854#3505—714no—
855#3480—714no—
856#3480—714no—
857#3475—714no—
858#3475—714no—
859#3455—712no—
860#3455—712no—
861#3449—712no—
862#3444—711no—
863#3444—711no—
864#3444—711no—
865#3444D7111yescharacteristic, complemented
866C2×#533—711no—
867C2×#532—711no—
868#3428—712no—
869C2×C4×#41—711no—
870C71#6281511yescharacteristic, complemented, Sylow
871C22×#41—712no—
872C22×#41—711no—
873#559—714no—
874#559—718no—
875#559—718no—
876#559—714no—
877#557—714no—
878#557—714no—
879#556—718no—
880#556—714no—
881#556—714no—
882#556—714no—
883#556—714no—
884#556—718no—
885#555—714no—
886#555—714no—
887#554—714no—
888#554—714no—
889#553—718no—
890#553—714no—
891#553—718no—
892#553—718no—
893#553—714no—
894#553—718no—
895#553—714no—
896#553—718no—
897#553—714no—
898#553—718no—
899#552—718no—
900#552—714no—
901#552—714no—
902#552—714no—
903#552—718no—
904#552—714no—
905#551—718no—
906#551—718no—
907#551—718no—
908#551—718no—
909#550—714no—
910#550—714no—
911#548—714no—
912#548—714no—
913#548—714no—
914#548—714no—
915#547—714no—
916#547—714no—
917#546—714no—
918#546—714no—
919#546—714no—
920#546—714no—
921#542—714no—
922#542—714no—
923#542—714no—
924#542—714no—
925#541—714no—
926#541—714no—
927#540—714no—
928#540—714no—
929#539—718no—
930#539—718no—
931#538—718no—
932#538—718no—
933#537—714no—
934#537—714no—
935#536—714no—
936#536—714no—
937#535—714no—
938#535—714no—
939#534—714no—
940#534—714no—
941#533—712no—
942#533—712no—
943#533—712no—
944#533—712no—
945#533—714no—
946#533—714no—
947#533—712no—
948#533—711no—
949#533—712no—
950#533C2×D7111yescharacteristic, complemented
951#533C2×D7112yescomplemented
952#532—712no—
953#532—711no—
954#532—712no—
955#532—711no—
956#532—712no—
957#532—712no—
958#532—714no—
959#532—714no—
960#532—718no—
961#532—711no—
962#532—712no—
963#532C2×D7111yescharacteristic
964#532C2×D7112yescomplemented
965C2×C4⋊Q8—711no—
966C2×C4⋊Q8—712no—
967C2×#127—711no—
968#529—714no—
969#529—714no—
970#529—714no—
971#529—714no—
972#529—714no—
973#529—714no—
974#529—718no—
975#529—718no—
976#529—718no—
977#529—714no—
978#529—714no—
979#529—714no—
980#529—718no—
981#529C2×D7114yescomplemented
982#529C2×D7114yescomplemented
983#529C2×D7114yescomplemented
984C2×#125—712no—
985C2×#124—712no—
986#525—712no—
987#525—712no—
988#525—714no—
989#525—714no—
990#525—714no—
991#525—718no—
992#525—712no—
993#525C2×D7112yescomplemented
994#525C2×D7114yescomplemented
995C2×C22⋊Q8—714no—
996C2×#121—714no—
997#520—714no—
998#520—718no—
999#520—714no—
1000#519—714no—
1001#518—718no—
1002#518—714no—
1003C4×#41—712no—
1004C4×#41—714no—
1005C4×#41—714no—
1006C4×#41—712no—
1007C4×#41—714no—
1008C4×#41—712no—
1009C4×#41—712no—
1010C4×#41—712no—
1011C4×#41—712no—
1012C4×#41—712no—
1013C4×#41—712no—
1014C4×#41—712no—
1015C4×#41—712no—
1016C4×#41—712no—
1017C4×#41—714no—
1018C4×#41—714no—
1019C4×#41C2×D7112yescomplemented
1020C4×#41C2×D7114yescomplemented
1021C2×C4×Q8—714no—
1022C2×C4×Q8—712no—
1023C2×C4×D4—712no—
1024C2×C4×D4—712no—
1025C2×C4×D4—714no—
1026C2×C4×D4—712no—
1027C2×#117—711no—
1028C2×#117—712no—
1029C2×#117—714no—
1030C2×#117—711no—
1031C2×#117—711no—
1032C2×#117—714no—
1033C22×C42—711no—
1034C22×C42—711no—
1035C22×C42C2×D7111yescharacteristic, complemented
1036C2×#41—714no—
1037C2×#41—712no—
1038C2×#41—714no—
1039C2×#41—714no—
1040C2×#41—712no—
1041C2×#41—714no—
1042C2×#41—712no—
1043C2×#41—712no—
1044C2×#41—714no—
1045C2×#41—712no—
1046C2×#41—712no—
1047C2×#41—712no—
1048C2×#41—1428no—
1049C2×#41—14216no—
1050C2×#41C22×D7112yes—
1051C2×#41C22×D7114yes—
1052C22×Q8—714no—
1053C22×Q8—712no—
1054C22×Q8—711no—
1055C22×D4—714no—
1056C22×D4—711no—
1057C22×D4—711no—
1058C22×D4—714no—
1059C22×D4—712no—
1060C22×D4—711no—
1061C23×C4—712no—
1062C23×C4—712no—
1063C23×C4—711no—
1064C23×C4—714no—
1065C23×C4—711no—
1066C23×C4C22×D7111yescharacteristic
1067C23×C4C22×D7112yes—
1068C4⋊Q8—712no—
1069C4⋊Q8—714no—
1070C4⋊Q8—714no—
1071C4⋊Q8—714no—
1072C4⋊Q8—714no—
1073C4⋊Q8—718no—
1074C4⋊Q8—711no—
1075C4⋊Q8—712no—
1076C4⋊Q8C22×D7111yescharacteristic
1077C4⋊Q8C22×D7112yes—
1078#127—712no—
1079#127—714no—
1080#127—718no—
1081#127—711no—
1082#127C22×D7111yescharacteristic
1083#126—718no—
1084#126—718no—
1085#126—718no—
1086#126—718no—
1087#126—718no—
1088#126—718no—
1089#126—718no—
1090#126—718no—
1091#126—718no—
1092#126—718no—
1093#126—718no—
1094#126C22×D7118yes—
1095#125—714no—
1096#125—718no—
1097#125—714no—
1098#125—714no—
1099#125—718no—
1100#125—718no—
1101#125—718no—
1102#125—712no—
1103#125—714no—
1104#125—718no—
1105#125C22×D7112yes—
1106#125C22×D7114yes—
1107#124—712no—
1108#124—714no—
1109#124—712no—
1110#124—714no—
1111#124—718no—
1112#124—718no—
1113#124—718no—
1114#124—718no—
1115#124—718no—
1116#124—718no—
1117#124—712no—
1118#124—714no—
1119#124—718no—
1120#124C22×D7112yes—
1121#124C22×D7114yes—
1122#123—714no—
1123#123—718no—
1124#123—714no—
1125#123—718no—
1126#123—718no—
1127#123—718no—
1128#123—718no—
1129#123—718no—
1130#123—718no—
1131#123—714no—
1132#123—718no—
1133#123—718no—
1134#123—718no—
1135#123—718no—
1136#123—718no—
1137#123—718no—
1138#123C22×D7114yes—
1139#123C22×D7118yes—
1140C22⋊Q8—714no—
1141C22⋊Q8—714no—
1142C22⋊Q8—714no—
1143C22⋊Q8—714no—
1144C22⋊Q8—714no—
1145C22⋊Q8—714no—
1146C22⋊Q8—718no—
1147C22⋊Q8—714no—
1148C22⋊Q8—718no—
1149C22⋊Q8—714no—
1150C22⋊Q8—714no—
1151C22⋊Q8—718no—
1152C22⋊Q8—718no—
1153C22⋊Q8—718no—
1154C22⋊Q8—718no—
1155C22⋊Q8—718no—
1156C22⋊Q8—718no—
1157C22⋊Q8C22×D7114yes—
1158C22⋊Q8C22×D7114yes—
1159C22⋊Q8C22×D7114yes—
1160#121—718no—
1161#121—714no—
1162#121—714no—
1163#121—714no—
1164#121—718no—
1165#121—718no—
1166#121—718no—
1167#121—718no—
1168#121—714no—
1169#121—714no—
1170#121—714no—
1171#121—718no—
1172#121—714no—
1173#121—714no—
1174#121—714no—
1175#121—718no—
1176#121—718no—
1177#121—718no—
1178#121—718no—
1179#121—718no—
1180#121—718no—
1181#121C22×D7114yes—
1182#121C22×D7114yes—
1183#121C22×D7114yes—
1184#120—714no—
1185#120—714no—
1186#120—718no—
1187#120—714no—
1188#120—718no—
1189#120C22×D7114yes—
1190C4×Q8—714no—
1191C4×Q8—714no—
1192C4×Q8—714no—
1193C4×Q8—714no—
1194C4×Q8—718no—
1195C4×Q8—714no—
1196C4×Q8—718no—
1197C4×Q8—714no—
1198C4×Q8—714no—
1199C4×Q8—712no—
1200C4×Q8—712no—
1201C4×Q8—712no—
1202C4×Q8—712no—
1203C4×Q8—712no—
1204C4×Q8—712no—
1205C4×Q8—712no—
1206C4×Q8—712no—
1207C4×Q8—718no—
1208C4×Q8—714no—
1209C4×Q8—718no—
1210C4×Q8—714no—
1211C4×Q8C22×D7114yes—
1212C4×Q8C22×D7114yes—
1213C4×Q8C22×D7114yes—
1214C4×D4—714no—
1215C4×D4—718no—
1216C4×D4—714no—
1217C4×D4—714no—
1218C4×D4—712no—
1219C4×D4—712no—
1220C4×D4—712no—
1221C4×D4—712no—
1222C4×D4—712no—
1223C4×D4—712no—
1224C4×D4—712no—
1225C4×D4—712no—
1226C4×D4—712no—
1227C4×D4—712no—
1228C4×D4—712no—
1229C4×D4—712no—
1230C4×D4—712no—
1231C4×D4—712no—
1232C4×D4—712no—
1233C4×D4—712no—
1234C4×D4—718no—
1235C4×D4—718no—
1236C4×D4—718no—
1237C4×D4—718no—
1238C4×D4—718no—
1239C4×D4—718no—
1240C4×D4—718no—
1241C4×D4—714no—
1242C4×D4—714no—
1243C4×D4—718no—
1244C4×D4—718no—
1245C4×D4—714no—
1246C4×D4—718no—
1247C4×D4—718no—
1248C4×D4—718no—
1249C4×D4—718no—
1250C4×D4—718no—
1251C4×D4—714no—
1252C4×D4—712no—
1253C4×D4—712no—
1254C4×D4—712no—
1255C4×D4—712no—
1256C4×D4—712no—
1257C4×D4—712no—
1258C4×D4—712no—
1259C4×D4—712no—
1260C4×D4—714no—
1261C4×D4—718no—
1262C4×D4—718no—
1263C4×D4—714no—
1264C4×D4C22×D7114yes—
1265C4×D4C22×D7118yes—
1266C4×D4C22×D7114yes—
1267C4×D4C22×D7118yes—
1268C4×D4C22×D7118yes—
1269C4×D4C22×D7114yes—
1270#117—712no—
1271#117—712no—
1272#117—712no—
1273#117—714no—
1274#117—712no—
1275#117—712no—
1276#117—714no—
1277#117—714no—
1278#117—718no—
1279#117—714no—
1280#117—714no—
1281#117—718no—
1282#117—714no—
1283#117—718no—
1284#117—718no—
1285#117—711no—
1286#117—711no—
1287#117—714no—
1288#117—711no—
1289#117—711no—
1290#117—712no—
1291#117—712no—
1292#117—714no—
1293#117—712no—
1294#117—712no—
1295#117—714no—
1296#117—712no—
1297#117—712no—
1298#117—718no—
1299#117—718no—
1300#117—718no—
1301#117C22×D7112yes—
1302#117C22×D7114yes—
1303#117C22×D7114yes—
1304#117C22×D7118yes—
1305C2×C4⋊C4—712no—
1306C2×C4⋊C4—712no—
1307C2×C4⋊C4—712no—
1308C2×C4⋊C4—718no—
1309C2×C4⋊C4—714no—
1310C2×C4⋊C4—718no—
1311C2×C4⋊C4—714no—
1312C2×C4⋊C4—718no—
1313C2×C4⋊C4—714no—
1314C2×C22⋊C4—712no—
1315C2×C22⋊C4—712no—
1316C2×C22⋊C4—712no—
1317C2×C22⋊C4—718no—
1318C2×C22⋊C4—714no—
1319C2×C22⋊C4—718no—
1320C2×C22⋊C4—718no—
1321C2×C42—711no—
1322C2×C42—711no—
1323C2×C42—714no—
1324C2×C42—712no—
1325C2×C42—712no—
1326C2×C42—714no—
1327C2×C42—714no—
1328C2×C42—714no—
1329C2×C42—712no—
1330C2×C42—712no—
1331C2×C42—712no—
1332C2×C42—712no—
1333C2×C42—711no—
1334C2×C42—711no—
1335C2×C42—712no—
1336C2×C42—711no—
1337C2×C42—711no—
1338C2×C42—712no—
1339C2×C42C22×D7111yescharacteristic
1340C2×C42C22×D7114yes—
1341C2×C42C22×D7112yes—
1342C2×C42C22×D7112yes—
1343C2×C42C22×D7112yes—
1344C2×C42C22×D7112yes—
1345C2×C42C22×D7112yes—
1346C2×C42C22×D7111yescharacteristic
1347C24—711no—
1348C24—714no—
1349C24—711no—
1350C24C23×D7111yescharacteristic
1351#41—28no—
1352#41—48no—
1353#41—2848no—
1354#41—2848no—
1355#41—2848no—
1356#41—1428no—
1357#41—1428no—
1358#41—1428no—
1359#41—1428no—
1360#41—14216no—
1361#41—14216no—
1362#41—1428no—
1363#41—1428no—
1364#41—1428no—
1365C2×Q8—2848no—
1366C2×Q8—718no—
1367C2×Q8—712no—
1368C2×Q8—712no—
1369C2×Q8—714no—
1370C2×Q8—714no—
1371C2×Q8—712no—
1372C2×Q8—1424no—
1373C2×Q8—1428no—
1374C2×Q8C23×D7112yes—
1375C2×Q8C23×D7114yes—
1376C2×D4—2848no—
1377C2×D4—718no—
1378C2×D4—718no—
1379C2×D4—718no—
1380C2×D4—712no—
1381C2×D4—714no—
1382C2×D4—712no—
1383C2×D4—712no—
1384C2×D4—714no—
1385C2×D4—712no—
1386C2×D4—714no—
1387C2×D4—718no—
1388C2×D4—712no—
1389C2×D4—714no—
1390C2×D4—712no—
1391C2×D4—712no—
1392C2×D4—714no—
1393C2×D4—1424no—
1394C2×D4—1428no—
1395C2×D4—1424no—
1396C2×D4—14216no—
1397C2×D4—1424no—
1398C2×D4C23×D7114yes—
1399C2×D4C23×D7112yes—
1400C2×D4C23×D7114yes—
1401C2×D4C23×D7118yes—
1402C22×C4—24no—
1403C22×C4—44no—
1404C22×C4—2844no—
1405C22×C4—2844no—
1406C22×C4—712no—
1407C22×C4—712no—
1408C22×C4—718no—
1409C22×C4—712no—
1410C22×C4—712no—
1411C22×C4—712no—
1412C22×C4—712no—
1413C22×C4—718no—
1414C22×C4—718no—
1415C22×C4—718no—
1416C22×C4—711no—
1417C22×C4—718no—
1418C22×C4—711no—
1419C22×C4—711no—
1420C22×C4—711no—
1421C22×C4—711no—
1422C22×C4—711no—
1423C22×C4—714no—
1424C22×C4—712no—
1425C22×C4—712no—
1426C22×C4—712no—
1427C22×C4—712no—
1428C22×C4—712no—
1429C22×C4—714no—
1430C22×C4—714no—
1431C22×C4—714no—
1432C22×C4—712no—
1433C22×C4—14216no—
1434C22×C4—1424no—
1435C22×C4C23×D7112yes—
1436C22×C4C23×D7111yescharacteristic
1437C22×C4C23×D7112yes—
1438C22×C4C23×D7112yes—
1439C22×C4C23×D7112yes—
1440C22×C4C23×D7114yes—
1441C22×C4C23×D7112yes—
1442C22×C4C23×D7112yes—
1443C22×C4C23×D7112yes—
1444C22×C4C23×D7112yes—
1445C22×C4C23×D7118yes—
1446C22×C4C23×D7111yescharacteristic
1447C4⋊C4—712no—
1448C4⋊C4—712no—
1449C4⋊C4—718no—
1450C4⋊C4—712no—
1451C4⋊C4—712no—
1452C4⋊C4—712no—
1453C4⋊C4—712no—
1454C4⋊C4—718no—
1455C4⋊C4—718no—
1456C4⋊C4—718no—
1457C4⋊C4—712no—
1458C4⋊C4—712no—
1459C4⋊C4—718no—
1460C4⋊C4—718no—
1461C4⋊C4—718no—
1462C4⋊C4—718no—
1463C4⋊C4—718no—
1464C4⋊C4—714no—
1465C4⋊C4—714no—
1466C4⋊C4—714no—
1467C4⋊C4—712no—
1468C4⋊C4—712no—
1469C4⋊C4—718no—
1470C4⋊C4—712no—
1471C4⋊C4—712no—
1472C4⋊C4—718no—
1473C4⋊C4—718no—
1474C4⋊C4C23×D7114yes—
1475C4⋊C4C23×D7114yes—
1476C4⋊C4C23×D7114yes—
1477C4⋊C4C23×D7118yes—
1478C4⋊C4C23×D7118yes—
1479C4⋊C4C23×D7118yes—
1480C22⋊C4—714no—
1481C22⋊C4—712no—
1482C22⋊C4—712no—
1483C22⋊C4—718no—
1484C22⋊C4—712no—
1485C22⋊C4—712no—
1486C22⋊C4—718no—
1487C22⋊C4—718no—
1488C22⋊C4—718no—
1489C22⋊C4—712no—
1490C22⋊C4—712no—
1491C22⋊C4—718no—
1492C22⋊C4—712no—
1493C22⋊C4—712no—
1494C22⋊C4—712no—
1495C22⋊C4—712no—
1496C22⋊C4—718no—
1497C22⋊C4—718no—
1498C22⋊C4—718no—
1499C22⋊C4—712no—
1500C22⋊C4—712no—
1501C22⋊C4—718no—
1502C22⋊C4—718no—
1503C22⋊C4—718no—
1504C22⋊C4—718no—
1505C22⋊C4—718no—
1506C22⋊C4C23×D7114yes—
1507C22⋊C4C23×D7118yes—
1508C22⋊C4C23×D7118yes—
1509C22⋊C4C23×D7118yes—
1510C22⋊C4C23×D7118yes—
1511C42—712no—
1512C42—712no—
1513C42—712no—
1514C42—711no—
1515C42—711no—
1516C42—712no—
1517C42—712no—
1518C42—712no—
1519C42—712no—
1520C42—712no—
1521C42—712no—
1522C42—718no—
1523C42—718no—
1524C42—718no—
1525C42—718no—
1526C42—711no—
1527C42—711no—
1528C42—712no—
1529C42—714no—
1530C42C23×D7111yescharacteristic
1531C42C23×D7111yescharacteristic
1532C42C23×D7112yes—
1533C42C23×D7112yes—
1534C42C23×D7112yes—
1535C42C23×D7112yes—
1536C42C23×D7112yes—
1537C42C23×D7118yes—
1538C42C23×D7111yescharacteristic
1539C42C23×D7112yes—
1540C42C23×D7114yes—
1541C42C23×D7111yescharacteristic
1542C23—22no—
1543C23—42no—
1544C23—2842no—
1545C23—2842no—
1546C23—2848no—
1547C23—714no—
1548C23—711no—
1549C23—711no—
1550C23—714no—
1551C23—712no—
1552C23—1428no—
1553C23—1422no—
1554C23C24×D7112yes—
1555C23C24×D7114yes—
1556C23C24×D7111yescharacteristic
1557Q8—24no—
1558Q8—28no—
1559Q8—2848no—
1560Q8—1424no—
1561Q8—1424no—
1562Q8—1428no—
1563Q8—1424no—
1564Q8—1428no—
1565D4—28no—
1566D4—24no—
1567D4—28no—
1568D4—48no—
1569D4—2848no—
1570D4—2848no—
1571D4—2848no—
1572D4—2848no—
1573D4—1424no—
1574D4—1424no—
1575D4—1428no—
1576D4—1424no—
1577D4—1424no—
1578D4—1428no—
1579D4—1424no—
1580D4—1424no—
1581D4—1428no—
1582D4—1428no—
1583D4—1424no—
1584D4—1428no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—28no—
1589C2×C4—24no—
1590C2×C4—24no—
1591C2×C4—24no—
1592C2×C4—42no—
1593C2×C4—42no—
1594C2×C4—42no—
1595C2×C4—48no—
1596C2×C4—2842no—
1597C2×C4—2842no—
1598C2×C4—2842no—
1599C2×C4—2842no—
1600C2×C4—2848no—
1601C2×C4—2848no—
1602C2×C4—2848no—
1603C2×C4—2842no—
1604C2×C4—2842no—
1605C2×C4—2848no—
1606C2×C4—714no—
1607C2×C4—711no—
1608C2×C4—711no—
1609C2×C4—714no—
1610C2×C4—714no—
1611C2×C4—714no—
1612C2×C4—714no—
1613C2×C4—712no—
1614C2×C4—712no—
1615C2×C4—712no—
1616C2×C4—712no—
1617C2×C4—714no—
1618C2×C4—718no—
1619C2×C4—712no—
1620C2×C4—1428no—
1621C2×C4—1428no—
1622C2×C4—1428no—
1623C2×C4—1422no—
1624C2×C4—1428no—
1625C2×C4—1424no—
1626C2×C4—1424no—
1627C2×C4—1424no—
1628C2×C4—1424no—
1629C2×C4—1424no—
1630C2×C4—1424no—
1631C2×C4#41×D7114yes—
1632C2×C4C24×D7112yes—
1633C2×C4C24×D7112yes—
1634C2×C4C24×D7114yes—
1635C2×C4C24×D7118yes—
1636C2×C4C24×D7112yes—
1637C2×C4C24×D7112yes—
1638C2×C4C24×D7111yescharacteristic
1639C2×C4C24×D7112yes—
1640C2×C4C24×D7111yescharacteristic
1641C22—22no—
1642C22—22no—
1643C22—24no—
1644C22—22no—
1645C22—22no—
1646C22—28no—
1647C22—44no—
1648C22—2844no—
1649C22—2844no—
1650C22—5688no—
1651C22—712no—
1652C22—712no—
1653C22—1422no—
1654C22—1424no—
1655C22—1428no—
1656C22—1422no—
1657C22—1422no—
1658C22—1422no—
1659C22—1422no—
1660C22C2×#41×D7112yes—
1661C22C25×D7111yescharacteristic
1662C4—22no—
1663C4—24no—
1664C4—22no—
1665C4—22no—
1666C4—22no—
1667C4—28no—
1668C4—712no—
1669C4—712no—
1670C4—1424no—
1671C4—1422no—
1672C4—1422no—
1673C4—1422no—
1674C4—1428no—
1675C4—1422no—
1676C4—1422no—
1677C4C2×#41×D7112yes—
1678C4C2×#41×D7112yes—
1679C4#1798683514yes—
1680C2—22no—
1681C2—42no—
1682C2—44no—
1683C2—2842no—
1684C2—2844no—
1685C2—1422no—
1686C2—1422no—
1687C2C22×#41×D7111yescharacteristic
1688C2C2×#1798683512yes—
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3444C2
hypercenter#3444D71
hypocenterC71#62815
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #22602255C2semidirect
2. #22602252C2semidirect
3. #22602241C2semidirect
4. #22602229C2semidirect
5. #22602219C2semidirect
6. #22602209C2semidirect
7. #22602196C2semidirect
8. #22602183C2semidirect
9. #22602175C2semidirect
10. #22602168C2semidirect
11. #22601938C2semidirect
12. #22601931C2semidirect
13. #22601902C2semidirect
14. #22601896C2semidirect
15. #22601728C2semidirect
16. #22601725C2semidirect
17. #22601670C2semidirect
18. #22601637C2semidirect
19. #22601636C2semidirect
20. #22601635C2semidirect
21. #533×D71C2semidirect
22. #532×D71C2semidirect
23. #22601539C2semidirect
24. C2×C4×#11765865C2semidirect
25. C71×#3444C2semidirect
28. #17986733C22semidirect
29. #17986732C22semidirect
30. #17986732C22semidirect
31. #17986731C22semidirect
32. #17986726C22semidirect
33. #17986725C22semidirect
34. #17986721C22semidirect
35. #17986720C22semidirect
36. #17986718C22semidirect
37. #17986717C22semidirect
38. #17986717C22semidirect
39. #17986716C22semidirect
40. #17986713C22semidirect
41. #17986712C22semidirect
42. #17986708C22semidirect
43. #17986705C22semidirect
44. #17986702C22semidirect
45. #17986700C22semidirect
46. #17986699C22semidirect
47. #17986699C22semidirect
48. #17986698C22semidirect
49. #17986696C22semidirect
50. #17986694C22semidirect
51. #17986694C22semidirect
52. #17986693C22semidirect
53. #17986693C22semidirect
54. #17986690C22semidirect
55. #17986688C22semidirect
56. #17986687C22semidirect
57. #17986685C22semidirect
58. #17986683C22semidirect
59. #17986682C22semidirect
60. #17986678C22semidirect
61. #17986677C22semidirect
62. #17986674C22semidirect
63. #17986673C22semidirect
64. #17986668C22semidirect
65. #17986667C22semidirect
66. #17986661C22semidirect
67. #17986659C22semidirect
68. #17986657C22semidirect
69. #17986656C22semidirect
70. #17986651C22semidirect
71. #17986648C22semidirect
72. #17986646C22semidirect
73. #17986644C22semidirect
74. #17986642C22semidirect
75. #17986637C22semidirect
76. #17986622C22semidirect
77. #17986621C22semidirect
78. #17986616C22semidirect
79. #17986614C22semidirect
80. #17986609C22semidirect
81. #17986607C22semidirect
82. #17986602C22semidirect
83. #17986600C22semidirect
84. #17986593C22semidirect
85. #17986591C22semidirect
86. #17986584C22semidirect
87. #17986582C22semidirect
88. #17986579C22semidirect
89. #17986578C22semidirect
91. #17986571C22semidirect
93. #17986564C22semidirect
96. #17986556C22semidirect
97. #17986556C22semidirect
98. #17986555C22semidirect
99. #17986554C22semidirect
100. #17986554C22semidirect
101. #17986554C22semidirect
102. #17986553C22semidirect
103. #17986552C22semidirect
104. #17986551C22semidirect
105. #17986550C22semidirect
106. #17986550C22semidirect
108. #17986549C22semidirect
109. #17986548C22semidirect
110. #17986547C22semidirect
111. #17986547C22semidirect
112. #17986546C22semidirect
113. #17986546C22semidirect
116. C4⋊Q8×D71C22semidirect
117. C4⋊Q8×D71C22semidirect
118. #127×D71C22semidirect
119. #17986536C22semidirect
120. #17986535C22semidirect
121. #17986534C22semidirect
122. #17986533C22semidirect
123. #17986533C22semidirect
124. #17986533C22semidirect
125. #17986533C22semidirect
126. #17986531C22semidirect
127. #17986531C22semidirect
128. #17986530C22semidirect
129. #17986529C22semidirect
130. #17986528C22semidirect
131. #17986527C22semidirect
132. #125×D71C22semidirect
133. #124×D71C22semidirect
134. #17986512C22semidirect
135. #17986511C22semidirect
136. #17986510C22semidirect
137. #17986510C22semidirect
138. #17986509C22semidirect
140. #17986506C22semidirect
143. #17986481C22semidirect
144. #17986478C22semidirect
145. #17986478C22semidirect
146. #17986475C22semidirect
148. #17986471C22semidirect
149. #41×Dic71C22semidirect
150. C4×#11765866C22semidirect
155. C4×#11765865C22semidirect
156. C4×#11765865C22semidirect
157. C4×#11765865C22semidirect
158. C4×#11765865C22semidirect
159. C4×#11765865C22semidirect
160. C4×#11765865C22semidirect
161. C4×#11765865C22semidirect
162. #17986467C22semidirect
163. #17986467C22semidirect
164. C4×#11765864C22semidirect
165. C2×C4×Dic142C22semidirect
166. C4×Q8×D71C22semidirect
169. C2×C4×C22⋊D71C22semidirect
170. C4×D4×D71C22semidirect
171. C2×#14556087C22semidirect
173. C2×#14556085C22semidirect
174. C2×#14556085C22semidirect
176. #117×D71C22semidirect
178. C2×C42×D71C22semidirect
179. #533×C71C22semidirect
180. #533×C71C22semidirect
182. #532×C71C22semidirect
183. #529×C71C22semidirect
184. #529×C71C22semidirect
185. #529×C71C22semidirect
186. #525×C71C22semidirect
187. #525×C71C22semidirect
188. C4×#41×C71C22semidirect
189. C4×#41×C71C22semidirect
190. C22×C42×C71C22semidirect
558. C2×C4×D71#41semidirect
865. #3444D71semidirect
870. C71#62815semidirect
950. #533C2×D71semidirect
951. #533C2×D71semidirect
964. #532C2×D71semidirect
981. #529C2×D71semidirect
982. #529C2×D71semidirect
983. #529C2×D71semidirect
993. #525C2×D71semidirect
994. #525C2×D71semidirect
1019. C4×#41C2×D71semidirect
1020. C4×#41C2×D71semidirect
1035. C22×C42C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226022552
#226022522
#226022412
#226022292
#226022192
#226022092
#226021962
#226021832
#226021752
#226021682
#226019382
#226019312
#226019022
#226018962
#226017282
#226017252
#226016702
#226016372
#226016362
#226016352
#533×D712
#532×D712
#226015392
C2×C4×#117658652
C71×#34442
#6281571