Finite Group Databasebeta

← #32905685

Subgroups — #32905685

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 2028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602429C213yesmaximal, complemented
2#22602427C211yesmaximal, characteristic, complemented
3#22602418C213yesmaximal, complemented
4#22602416C211yesmaximal, characteristic, complemented
5#22602336C211yesmaximal, characteristic, complemented
6#22602332C213yesmaximal, complemented
7#22602328C213yesmaximal, complemented
8#22602326C211yesmaximal, characteristic, complemented
9#22602201C213yesmaximal, complemented
10#22602199C213yesmaximal, complemented
11#22602147C211yesmaximal, characteristic, complemented
12#22602108C211yesmaximal, characteristic, complemented
13#22602042C213yesmaximal, complemented
14#22602040C213yesmaximal, complemented
15#22601990C211yesmaximal, characteristic, complemented
16#22601986C211yesmaximal, characteristic, complemented
17#22601957C211yesmaximal, characteristic, complemented
18#22601955C213yesmaximal, complemented
19#22601953C213yesmaximal, complemented
20#22601938C211yesmaximal, characteristic, complemented
21#22601931C213yesmaximal, complemented
22Q8×#11765865C211yesmaximal, characteristic, complemented
23#22601918C213yesmaximal, complemented
24#22601771C213yesmaximal, complemented
25#22601765C213yesmaximal, complemented
26#22601634C213yesmaximal, complemented
27#22601633C213yesmaximal, complemented
28C4×#14556176C211yesmaximal, characteristic, complemented
29C4×#14556175C211yesmaximal, characteristic, complemented
30C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
31C71×#3482C211yesmaximal, characteristic, complemented
32C2×#14556176C2211yescharacteristic
33C2×#14556175C2211yescharacteristic
34C22×Q8×D71C2211yescharacteristic
35#17986733C2216yescomplemented
36#17986732C2213yescomplemented
37#17986731C2213yescomplemented
38Q8×Dic142C2211yescharacteristic, complemented
39#17986729C2213yescomplemented
40#17986727C2213yescomplemented
41#17986727C2213yescomplemented
42#17986726C2213yescomplemented
43#17986726C2213yescomplemented
44#17986726C2216yescomplemented
45#17986725C2211yescharacteristic, complemented
46#17986725C2211yescharacteristic, complemented
47#17986724C2213yescomplemented
48#17986722C2213yescomplemented
49#17986721C2213yescomplemented
50#17986720C2213yescomplemented
51#17986718C2213yescomplemented
52#17986717C2216yescomplemented
53#17986717C2213yescomplemented
54#17986716C2216yescomplemented
55#17986716C2216yescomplemented
56#17986710C2213yes—
57#17986709C2213yes—
58#17986707C2213yes—
59#17986707C2213yescomplemented
60#17986705C2216yes—
61#17986704C2213yes—
62#17986704C2213yescomplemented
63#17986703C2216yes—
64#17986703C2216yescomplemented
65#17986702C2213yes—
66#17986700C2216yes—
67#17986699C2213yes—
68#17986696C2213yes—
69#17986694C2216yes—
70#17986693C2213yes—
71#17986691C2213yes—
72#17986690C2213yescomplemented
73#17986689C2213yes—
74#17986689C2213yescomplemented
75#17986687C2213yescomplemented
76#17986686C2216yes—
77#17986685C2216yescomplemented
78#17986684C2213yes—
79#17986682C2216yes—
80#17986682C2216yescomplemented
81#17986668C2211yescharacteristic, complemented
82#17986667C2213yescomplemented
83Q8×D284C2211yescharacteristic
84D4×Dic142C2213yes—
85#17986664C2213yes—
86Q8×C22⋊D71C2211yescharacteristic
87Q8×C22⋊D71C2211yescharacteristic
88Q8×C22⋊D71C2211yescharacteristic, complemented
89#17986662C2213yes—
90#17986662C2213yes—
91#17986662C2213yescomplemented
92#17986661C2211yescharacteristic
93#17986661C2211yescharacteristic, complemented
94#17986660C2211yescharacteristic
95#17986659C2213yes—
96#17986658C2213yes—
97#17986658C2213yescomplemented
98#17986657C2213yes—
99#17986657C2213yescomplemented
100#17986656C2211yescharacteristic
101#17986655C2213yes—
102#17986653C2213yes—
103#17986650C2213yes—
104#17986649C2213yes—
105#17986648C2216yes—
106#17986647C2216yes—
107#17986629C2213yes—
108#17986626C2213yes—
109#17986623C2213yescomplemented
110#17986622C2213yescomplemented
111#17986619C2216yescomplemented
112#17986618C2213yescomplemented
113#17986617C2216yescomplemented
114#17986616C2213yescomplemented
115#17986612C2213yescomplemented
116#17986610C2213yescomplemented
117#17986609C2213yescomplemented
118#17986609C2213yescomplemented
119#17986608C2216yescomplemented
120#17986606C2216yescomplemented
121#17986597C2216yes—
122#17986595C2216yes—
123#17986592C2216yes—
124#17986590C2216yes—
125#17986579C2213yes—
126#17986578C2213yes—
127#17986574C2213yes—
128#17986572C2213yes—
129#17986572C2213yes—
130#17986569C2213yes—
131#17986556C2213yescomplemented
132#17986555C2213yes—
133#17986553C2213yes—
134#17986553C2213yes—
135#17986553C2213yes—
136#17986553C2213yescomplemented
137#17986553C2216yescomplemented
138#17986553C2213yescomplemented
139#17986552C2213yes—
140#17986552C2216yescomplemented
141#17986551C2213yes—
142#17986548C2213yes—
143#17986546C2213yes—
144#17986546C2213yes—
145#17986546C2213yes—
146#17986545C2213yes—
147#17986544C2213yes—
148#17986536C2213yes—
149#17986536C2213yes—
150#17986536C2213yescomplemented
151#17986534C2213yes—
152#17986533C2213yes—
153#17986533C2213yescomplemented
154#17986532C2216yes—
155#17986532C2216yes—
156#17986531C2213yes—
157#17986531C2213yes—
158#17986531C2213yescomplemented
159#17986529C2213yes—
160#17986529C2213yes—
161#17986529C2213yes—
162#17986529C2213yes—
163#17986529C2216yescomplemented
164#17986528C2213yes—
165#17986527C2216yes—
166#17986527C2213yes—
167#17986527C2213yes—
168#17986527C2213yes—
169#17986527C2213yes—
170#17986527C2216yescomplemented
171#17986526C2216yes—
172#17986512C2213yes—
173#17986511C2213yes—
174#17986509C2213yes—
175#17986508C2213yes—
176#17986508C2213yes—
177#17986508C2211yescharacteristic
178#17986508C2213yes—
179#17986507C2216yes—
180#17986506C2213yes—
181#17986482C2211yescharacteristic, complemented
182#17986481C2213yes—
183#17986481C2211yescharacteristic, complemented
184#17986480C2213yes—
185#17986480C2213yescomplemented
186#17986479C2213yes—
187#17986478C2213yes—
188#17986478C2213yescomplemented
189#17986477C2211yescharacteristic, complemented
190#17986476C2213yescomplemented
191#17986475C2211yescharacteristic
192#17986475C2211yescharacteristic
193#17986475C2211yescharacteristic, complemented
194#17986475C2213yescomplemented
195C4×#11765866C2213yes—
196C4×#11765866C2211yescharacteristic, complemented
197C4×#11765865C2213yes—
198C4×#11765865C2213yes—
199C4×#11765865C2213yes—
200C4×#11765865C2213yes—
201C4×#11765865C2213yes—
202C4×#11765865C2213yescomplemented
203#17986467C2216yes—
204C4×#11765864C2213yes—
205C4×#11765864C2216yes—
206C4×#11765864C2213yescomplemented
207C2×Q8×Dic71C2211yescharacteristic
208C2×C4×Dic142C2213yes—
209C2×C4×Dic142C2213yescomplemented
210C2×#14556093C2213yes—
211C4×Q8×D71C2213yes—
212C4×Q8×D71C2211yescharacteristic
213C4×Q8×D71C2211yescharacteristic
214C4×Q8×D71C2213yes—
215C4×Q8×D71C2211yescharacteristic
216C4×Q8×D71C2213yes—
217C4×Q8×D71C2211yescharacteristic
218C4×Q8×D71C2213yes—
219C4×Q8×D71C2211yescharacteristic, complemented
220C4×Q8×D71C2213yescomplemented
221C2×C4⋊C4×D71C2213yes—
222C2×C42×D71C2213yes—
223#557×C71C2211yescharacteristic, complemented
224#556×C71C2213yescomplemented
225#552×C71C2213yes—
226#552×C71C2213yescomplemented
227D4×Q8×C71C2211yescharacteristic
228#548×C71C2211yescharacteristic
229#548×C71C2211yescharacteristic, complemented
230#547×C71C2213yes—
231#533×C71C2213yescomplemented
232#529×C71C2213yes—
233#529×C71C2213yescomplemented
234C4×#41×C71C2213yes—
235C4×#41×C71C2211yescharacteristic, complemented
236C2×C4×Q8×C71C2211yescharacteristic
237C2×C4×Q8×C71C2211yescharacteristic, complemented
238#14556176—28no—
239#14556175—28no—
240C2×#11765866C2313yes—
241C2×#11765866C2311yescharacteristic
242C2×#11765865C2313yes—
243C2×#11765865C2313yes—
244C2×#11765865C2313yes—
245C2×#11765865C2313yes—
246C2×#11765865C2311yescharacteristic
247C2×#11765865C2313yes—
248C2×#11765864C2313yes—
249C2×#11765864C2313yes—
250C2×#11765864C2316yes—
251C22×Dic142C2313yes—
252C22×Dic142C2313yes—
253C2×Q8×D71—28no—
254C2×Q8×D71C2313yes—
255C2×Q8×D71C2311yescharacteristic
256C2×Q8×D71C2313yes—
257C2×Q8×D71C2311yescharacteristic
258C2×Q8×D71C2313yes—
259C2×Q8×D71C2311yescharacteristic
260C22×C4×D71C2313yes—
261C22×C4×D71C2311yescharacteristic
262C22×C4×D71C2313yes—
263#14556128C2313yes—
264#14556128C2313yes—
265#14556127C2316yes—
266#14556127C2316yes—
267#14556127C2313yes—
268#14556127C2316yes—
269#14556127C2313yes—
270#14556127C2313yes—
271#14556127C2313yes—
272#14556127C2313yes—
273#14556127C2313yes—
274#14556126C2313yes—
275#14556126C2313yes—
276#14556126C2316yes—
277#14556126C2313yes—
278#14556126C2313yes—
279#14556124C2313yes—
280#14556124C2313yes—
281#14556123C2316yes—
282#14556123C2316yes—
283#14556123C2316yes—
284#14556123C2313yes—
285#14556123C2316yes—
286#14556123C2313yes—
287#14556123C2313yes—
288#14556123C2313yes—
289#14556122C2316yes—
290#14556122C2316yes—
291#14556121C2316yes—
292#14556121C2316yes—
293#14556121C2316yes—
294#14556121C2313yes—
295#14556121C2316yes—
296#14556121C2313yes—
297#14556121C2313yes—
298#14556121C2313yes—
299#14556120C2316yes—
300#14556120C2313yes—
301#14556120C2313yes—
302#14556119C2316yes—
303#14556119C2316yes—
304#14556119C2313yes—
305#14556119C2313yes—
306#14556119C2313yes—
307#14556119C2313yes—
308#14556118C2316yes—
309#14556118C2316yes—
310#14556118C2316yes—
311#14556118C2316yes—
312#14556118C2316yes—
313#14556118C2316yes—
314#14556118C2316yes—
315#14556118C2313yes—
316#14556118C2313yes—
317#14556118C2313yes—
318#14556118C2316yes—
319#14556118C2313yes—
320#14556117C2313yes—
321#14556117C2313yes—
322#14556116C2313yes—
323#14556116C2313yes—
324#14556115C2313yes—
325#14556115C2313yes—
326#14556114C2316yes—
327#14556114C2316yes—
328#14556114C2316yes—
329#14556114C2313yes—
330#14556114C2313yes—
331#14556114C2313yes—
332#14556114C2316yes—
333#14556114C2313yes—
334#14556113C2313yes—
335#14556113C2316yes—
336#14556113C2313yes—
337#14556113C2316yes—
338#14556113C2316yes—
339#14556113C2311yescharacteristic
340#14556113C2313yes—
341#14556112C2316yes—
342#14556112C2313yes—
343#14556112C2313yes—
344#14556111C2316yes—
345#14556111C2316yes—
346#14556110C2313yes—
347#14556110C2316yes—
348#14556110C2313yes—
349#14556110C2316yes—
350#14556110C2316yes—
351#14556110C2311yescharacteristic
352#14556110C2313yes—
353#14556109C2316yes—
354#14556109C2313yes—
355#14556109C2313yes—
356#14556108C2313yes—
357#14556108C2313yes—
358#14556108C2313yes—
359#14556108C2313yes—
360#14556108C2316yes—
361#14556108C2313yes—
362#14556108C2313yes—
363#14556107C2313yes—
364#14556107C2313yes—
365#14556107C2313yes—
366#14556107C2316yes—
367#14556107C2313yes—
368#14556106C2316yes—
369#14556106C2316yes—
370#14556106C2316yes—
371#14556106C2316yes—
372#14556106C2316yes—
373#14556106C2316yes—
374#14556106C2313yes—
375#14556106C2313yes—
376#14556106C2316yes—
377#14556106C2311yescharacteristic
378#14556106C2313yes—
379#14556105C2316yes—
380#14556105C2316yes—
381#14556105C2316yes—
382#14556105C2316yes—
383#14556105C2316yes—
384#14556105C2313yes—
385#14556105C2313yes—
386#14556105C2313yes—
387#14556105C2311yescharacteristic
388#14556104C2313yes—
389#14556104C2313yes—
390#14556104C2313yes—
391#14556104C2313yes—
392#14556104C2316yes—
393#14556104C2313yes—
394#14556104C2313yes—
395#14556103C2313yes—
396#14556103C2313yes—
397#14556103C2313yes—
398#14556103C2313yes—
399#14556102C2313yes—
400#14556102C2313yes—
401#14556101C2316yes—
402#14556101C2316yes—
403#14556101C2313yes—
404#14556101C2313yes—
405#14556101C2316yes—
406#14556101C2311yescharacteristic
407#14556101C2313yes—
408#14556100C2316yes—
409#14556100C2313yes—
410#14556100C2313yes—
411#14556100C2313yes—
412#14556100C2311yescharacteristic
413#14556099C2313yes—
414#14556099C2313yes—
415#14556099C2313yes—
416#14556099C2313yes—
417#14556098C2313yes—
418#14556098C2311yescharacteristic
419#14556096C2311yescharacteristic
420#14556096C2313yes—
421Q8×Dic71C2313yes—
422Q8×Dic71C2313yes—
423Q8×Dic71C2311yescharacteristic
424Q8×Dic71C2311yescharacteristic
425Q8×Dic71C2311yescharacteristic
426Q8×Dic71C2313yes—
427Q8×Dic71C2313yes—
428Q8×Dic71C2311yescharacteristic
429C4×Dic142C2313yes—
430C4×Dic142C2313yes—
431C4×Dic142C2313yes—
432C4×Dic142C2313yes—
433C4×Dic142C2313yes—
434C4×Dic142C2316yes—
435C4×Dic142C2316yes—
436C4×Dic142C2313yes—
437C4×Dic142C2313yes—
438C4×Dic142C2313yes—
439C4×Dic142C2313yes—
440C4×Dic142C2313yes—
441C4×Dic142C2316yes—
442C4×Dic142C2313yes—
443C4×Dic142C2313yes—
444C4×Dic142C2313yes—
445C4×Dic142C2313yes—
446C4×Dic142C2313yes—
447C4×Dic142C2316yes—
448C4×Dic142C2313yes—
449C4×Dic142C2313yes—
450C4×Dic142C2313yes—
451#14556093C2316yes—
452#14556093C2313yes—
453#14556093C2313yes—
454#14556093C2313yes—
455#14556093C2313yes—
456#14556093C2313yes—
457#14556093C2313yes—
458#14556093C2316yes—
459#14556093C2316yes—
460#14556093C2313yes—
461#14556093C2316yes—
462#14556093C2316yes—
463#14556093C2313yes—
464#14556093C2316yes—
465C4×D284C2313yes—
466C4×D284C2313yes—
467C4×D284C2313yes—
468C4×D284C2313yes—
469C4×D284C2313yes—
470C4×D284C2313yes—
471C4×D284C2313yes—
472C4×D284C2313yes—
473C4×D284C2311yescharacteristic
474C4×D284C2313yes—
475C4×D284C2313yes—
476C4×D284C2313yes—
477D4×Dic71C2313yes—
478D4×Dic71C2316yes—
479D4×Dic71C2313yes—
480#14556090C2316yes—
481#14556090C2313yes—
482#14556090C2313yes—
483#14556090C2316yes—
484#14556090C2316yes—
485C4×C22⋊D71C2313yes—
486C4×C22⋊D71C2313yes—
487C4×C22⋊D71C2313yes—
488C4×C22⋊D71C2313yes—
489C4×C22⋊D71C2316yes—
490C4×C22⋊D71C2313yes—
491C4×C22⋊D71C2313yes—
492C4×C22⋊D71C2313yes—
493C4×C22⋊D71C2313yes—
494C4×C22⋊D71C2313yes—
495C4×C22⋊D71C2313yes—
496C4×C22⋊D71C2313yes—
497C4×C22⋊D71C2313yes—
498C4×C22⋊D71C2313yes—
499C4×C22⋊D71C2313yes—
500C4×C22⋊D71C2313yes—
501C4×C22⋊D71C2313yes—
502C4×C22⋊D71C2316yes—
503C4×C22⋊D71C2313yes—
504C4×C22⋊D71C2311yescharacteristic
505C4×C22⋊D71C2311yescharacteristic
506C4×C22⋊D71C2313yes—
507(C22⋊D71)⋊C4C2316yes—
508(C22⋊D71)⋊C4C2316yes—
509(C22⋊D71)⋊C4C2316yes—
510(C22⋊D71)⋊C4C2316yes—
511(C22⋊D71)⋊C4C2316yes—
512(C22⋊D71)⋊C4C2316yes—
513(C22⋊D71)⋊C4C2316yes—
514(C22⋊D71)⋊C4C2316yes—
515#14556087C2313yes—
516#14556087C2313yes—
517#14556087C2313yes—
518#14556087C2313yes—
519#14556087C2313yes—
520#14556087C2313yes—
521#14556086C2313yes—
522#14556086C2313yes—
523#14556086C2316yes—
524#14556086C2313yes—
525#14556086C2316yes—
526#14556086C2313yes—
527#14556085C2313yes—
528#14556085C2313yes—
529#14556085C2313yes—
530#14556085C2313yes—
531#14556085C2316yes—
532#14556085C2313yes—
533#14556085C2313yes—
534#14556085C2313yes—
535#14556085C2316yes—
536#14556085C2311yescharacteristic
537#14556085C2313yes—
538#14556085C2313yes—
539#14556084C2316yes—
540#14556084C2316yes—
541#14556084C2316yes—
542#14556084C2316yes—
543C2×C4⋊Dic71C2313yes—
544C2×C4⋊Dic71C2313yes—
545C2×Dic71⋊C4C2316yes—
546C2×Dic71⋊C4C2316yes—
547C4⋊C4×D71C2313yes—
548C4⋊C4×D71C2316yes—
549C4⋊C4×D71C2316yes—
550C4⋊C4×D71C2313yes—
551C4⋊C4×D71C2313yes—
552C4⋊C4×D71C2313yes—
553C4⋊C4×D71C2316yes—
554C4⋊C4×D71C2313yes—
555C4⋊C4×D71C2313yes—
556C2×C4×Dic71C2313yes—
557C2×C4×Dic71C2313yes—
558C2×C4×Dic71C2313yes—
559C2×C4×Dic71C2316yes—
560C42×D71C2313yes—
561C42×D71C2313yes—
562C42×D71C2313yes—
563C42×D71C2313yes—
564C42×D71C2313yes—
565C42×D71C2313yes—
566C42×D71C2313yes—
567C42×D71C2313yes—
568C42×D71C2316yes—
569C42×D71C2313yes—
570C42×D71C2313yes—
571C2×#41×C71C2311yescharacteristic
572C2×#41×C71C2313yes—
573C22×Q8×C71C2311yescharacteristic
574C22×Q8×C71C2311yescharacteristic
575C4⋊Q8×C71C2313yes—
576C4⋊Q8×C71C2313yes—
577#126×C71C2316yes—
578#126×C71C2316yes—
579#125×C71C2316yes—
580#125×C71C2313yes—
581#125×C71C2313yes—
582#124×C71C2313yes—
583#124×C71C2313yes—
584#123×C71C2316yes—
585#123×C71C2316yes—
586C22⋊Q8×C71C2313yes—
587C22⋊Q8×C71C2313yes—
588C22⋊Q8×C71C2313yes—
589C22⋊Q8×C71C2316yes—
590C22⋊Q8×C71C2313yes—
591#121×C71C2313yes—
592#121×C71C2313yes—
593C4×Q8×C71C2311yescharacteristic
594C4×Q8×C71C2311yescharacteristic
595C4×Q8×C71C2311yescharacteristic
596C4×Q8×C71C2311yescharacteristic
597C4×Q8×C71C2313yes—
598C4×Q8×C71C2313yes—
599C4×Q8×C71C2313yes—
600C4×Q8×C71C2313yes—
601C4×Q8×C71C2313yes—
602C4×Q8×C71C2313yes—
603C4×D4×C71C2313yes—
604C4×D4×C71C2313yes—
605C4×D4×C71C2313yes—
606C4×D4×C71C2311yescharacteristic
607C4×D4×C71C2313yes—
608C4×D4×C71C2313yes—
609C4×D4×C71C2313yes—
610C4×D4×C71C2313yes—
611#117×C71C2313yes—
612#117×C71C2313yes—
613#117×C71C2313yes—
614#117×C71C2313yes—
615#117×C71C2316yes—
616C2×C4⋊C4×C71C2313yes—
617C2×C4⋊C4×C71C2313yes—
618C2×C42×C71C2313yes—
619C2×C42×C71C2313yes—
620C2×C42×C71C2313yes—
621C23×D71C2411yescharacteristic
622#11765866—24no—
623#11765866—212no—
624#11765865—212no—
625#11765865—212no—
626#11765865—212no—
627#11765865—24no—
628#11765865—212no—
629#11765865—46no—
630#11765864—212no—
631#11765864—212no—
632#11765864—412no—
633C2×Dic142—212no—
634C2×Dic142—212no—
635C2×Dic142C2416yes—
636C2×Dic142C2413yes—
637C2×Dic142C2413yes—
638C2×Dic142C2413yes—
639C2×Dic142C2413yes—
640C2×Dic142C2413yes—
641C2×Dic142C2411yescharacteristic
642C2×Dic142C2416yes—
643C2×Dic142C2413yes—
644C2×Dic142C2413yes—
645Q8×D71—24no—
646Q8×D71—24no—
647Q8×D71—212no—
648Q8×D71—212no—
649Q8×D71—212no—
650Q8×D71#4118yescomplemented
651C2×D284C2411yescharacteristic
652C2×D284C2413yes—
653C2×D284C2413yes—
654C2×D284C2413yes—
655C2×D284C2411yescharacteristic
656C2×D284C2413yes—
657C2×C22⋊D71C2413yes—
658C2×C22⋊D71C2413yes—
659C2×C22⋊D71C2413yes—
660C2×C22⋊D71C2411yescharacteristic
661C2×C22⋊D71C2411yescharacteristic
662C2×C22⋊D71C2413yes—
663C2×C22⋊D71C2413yes—
664C2×C22⋊D71C2413yes—
665C2×C22⋊D71C2411yescharacteristic
666C2×C22⋊D71C2411yescharacteristic
667C2×C22⋊D71C2416yes—
668C22×Dic71C2413yes—
669C22×Dic71C2413yes—
670C22×Dic71C2411yescharacteristic
671C22×Dic71C2416yes—
672C22×Dic71C2416yes—
673C2×C4×D71—212no—
674C2×C4×D71—24no—
675C2×C4×D71—46no—
676C2×C4×D71C2413yes—
677C2×C4×D71C2413yes—
678C2×C4×D71C2413yes—
679C2×C4×D71C2411yescharacteristic
680C2×C4×D71C2411yescharacteristic
681C2×C4×D71C2411yescharacteristic
682C2×C4×D71C2413yes—
683C2×C4×D71C2416yes—
684C2×C4×D71C2413yes—
685C2×C4×D71C2413yes—
686C2×C4×D71C2411yescharacteristic
687C2×C4×D71C2413yes—
688C2×C4×D71C2413yes—
689C2×C4×D71C2413yes—
690C2×C4×D71C2413yes—
691C2×C4×D71C2416yes—
692C2×C4×D71C2413yes—
693C2×C4×D71C2413yes—
694C2×C4×D71C2413yes—
695C2×C4×D71C2411yescharacteristic
696C4⋊Dic71C2413yes—
697C4⋊Dic71C2413yes—
698C4⋊Dic71C2416yes—
699C4⋊Dic71C2413yes—
700C4⋊Dic71C2413yes—
701C4⋊Dic71C2413yes—
702C4⋊Dic71C2413yes—
703C4⋊Dic71C2413yes—
704C4⋊Dic71C2416yes—
705C4⋊Dic71C2411yescharacteristic
706C4⋊Dic71C2413yes—
707C4⋊Dic71C2413yes—
708C4⋊Dic71C2413yes—
709C4⋊Dic71C2413yes—
710C4⋊Dic71C2413yes—
711C4⋊Dic71C2413yes—
712Dic71⋊C4C2416yes—
713Dic71⋊C4C2416yes—
714Dic71⋊C4C2416yes—
715Dic71⋊C4C2416yes—
716Dic71⋊C4C2413yes—
717Dic71⋊C4C2413yes—
718Dic71⋊C4C2416yes—
719Dic71⋊C4C2413yes—
720Dic71⋊C4C2413yes—
721Dic71⋊C4C2413yes—
722Dic71⋊C4C2413yes—
723Dic71⋊C4C2413yes—
724Dic71⋊C4C2416yes—
725Dic71⋊C4C2416yes—
726Dic71⋊C4C2416yes—
727Dic71⋊C4C2413yes—
728Dic71⋊C4C2411yescharacteristic
729Dic71⋊C4C2411yescharacteristic
730Dic71⋊C4C2413yes—
731Dic71⋊C4C2413yes—
732Dic71⋊C4C2416yes—
733Dic71⋊C4C2416yes—
734Dic71⋊C4C2411yescharacteristic
735Dic71⋊C4C2411yescharacteristic
736Dic71⋊C4C2413yes—
737Dic71⋊C4C2413yes—
738Dic71⋊C4C2413yes—
739Dic71⋊C4C2413yes—
740Dic71⋊C4C2413yes—
741Dic71⋊C4C2413yes—
742C22⋊Dic71C2413yes—
743C22⋊Dic71C2413yes—
744C22⋊Dic71C2413yes—
745C22⋊Dic71C2416yes—
746C22⋊Dic71C2411yescharacteristic
747C22⋊Dic71C2413yes—
748C22⋊Dic71C2411yescharacteristic
749C22⋊Dic71C2413yes—
750C22⋊Dic71C2413yes—
751C22⋊Dic71C2413yes—
752C22⋊Dic71C2413yes—
753(C2×D71)⋊C4C2411yescharacteristic
754(C2×D71)⋊C4C2411yescharacteristic
755(C2×D71)⋊C4C2411yescharacteristic
756(C2×D71)⋊C4C2411yescharacteristic
757(C2×D71)⋊C4C2413yes—
758(C2×D71)⋊C4C2413yes—
759(C2×D71)⋊C4C2413yes—
760(C2×D71)⋊C4C2413yes—
761(C2×D71)⋊C4C2413yes—
762(C2×D71)⋊C4C2413yes—
763(C2×D71)⋊C4C2416yes—
764(C2×D71)⋊C4C2413yes—
765(C2×D71)⋊C4C2413yes—
766(C2×D71)⋊C4C2416yes—
767(C2×D71)⋊C4C2416yes—
768(C2×D71)⋊C4C2411yescharacteristic
769(C2×D71)⋊C4C2411yescharacteristic
770(C2×D71)⋊C4C2413yes—
771(C2×D71)⋊C4C2413yes—
772(C2×D71)⋊C4C2413yes—
773(C2×D71)⋊C4C2413yes—
774(C2×D71)⋊C4C2413yes—
775(C2×D71)⋊C4C2413yes—
776(C2×D71)⋊C4C2416yes—
777C4×Dic71C2413yes—
778C4×Dic71C2411yescharacteristic
779C4×Dic71C2413yes—
780C4×Dic71C2413yes—
781C4×Dic71C2413yes—
782C4×Dic71C2413yes—
783C4×Dic71C2413yes—
784C4×Dic71C2413yes—
785C4×Dic71C2413yes—
786C4×Dic71C2413yes—
787C4×Dic71C2413yes—
788C4×Dic71C2413yes—
789C4×Dic71C2413yes—
790C4×Dic71C2413yes—
791C4×Dic71C2416yes—
792C4×Dic71C2413yes—
793C4×Dic71C2413yes—
794C4×Dic71C2413yes—
795C4×Dic71C2413yes—
796C4×Dic71C2416yes—
797C4×Dic71C2416yes—
798C4×Dic71C2416yes—
799#41×C71—24no—
800#41×C71—46no—
801C2×Q8×C71—24no—
802C2×Q8×C71—24no—
803C2×Q8×C71C2413yes—
804C2×Q8×C71C2413yes—
805C2×Q8×C71C2413yes—
806C2×Q8×C71C2411yescharacteristic
807C2×D4×C71C2413yes—
808C2×D4×C71C2413yes—
809C2×D4×C71C2411yescharacteristic
810C2×D4×C71C2413yes—
811C22×C4×C71C2413yes—
812C22×C4×C71C2413yes—
813C22×C4×C71C2411yescharacteristic
814C22×C4×C71C2413yes—
815C22×C4×C71C2413yes—
816C22×C4×C71C2411yescharacteristic
817C22×C4×C71C2413yes—
818C22×C4×C71C2413yes—
819C22×C4×C71C2413yes—
820C4⋊C4×C71C2413yes—
821C4⋊C4×C71C2413yes—
822C4⋊C4×C71C2413yes—
823C4⋊C4×C71C2416yes—
824C4⋊C4×C71C2416yes—
825C4⋊C4×C71C2411yescharacteristic
826C4⋊C4×C71C2413yes—
827C4⋊C4×C71C2413yes—
828C4⋊C4×C71C2413yes—
829C4⋊C4×C71C2413yes—
830C4⋊C4×C71C2413yes—
831C4⋊C4×C71C2413yes—
832C4⋊C4×C71C2416yes—
833C4⋊C4×C71C2416yes—
834C22⋊C4×C71C2411yescharacteristic
835C22⋊C4×C71C2411yescharacteristic
836C22⋊C4×C71C2413yes—
837C22⋊C4×C71C2413yes—
838C22⋊C4×C71C2416yes—
839C22⋊C4×C71C2413yes—
840C22⋊C4×C71C2413yes—
841C22⋊C4×C71C2416yes—
842C22⋊C4×C71C2416yes—
843C42×C71C2413yes—
844C42×C71C2411yescharacteristic
845C42×C71C2413yes—
846C42×C71C2413yes—
847C42×C71C2413yes—
848C42×C71C2413yes—
849C42×C71C2413yes—
850C42×C71C2413yes—
851C42×C71C2413yes—
852C42×C71C2413yes—
853C23×C71C2513yes—
854C23×C71C2511yescharacteristic
855C23×C71C2511yescharacteristic
856C22×D71—22no—
857C22×D71—22no—
858C22×D71—22no—
859C22×D71C2513yes—
860C22×D71C2511yescharacteristic
861C22×D71C2511yescharacteristic
862C22×D71C2511yescharacteristic
863Q8×C71—26no—
864Q8×C71—26no—
865Q8×C71—43no—
866Q8×C71C2×#4114yes—
867D4×C71—22no—
868D4×C71—26no—
869D4×C71—26no—
870D4×C71—43no—
871C2×C4×C71—26no—
872C2×C4×C71—26no—
873C2×C4×C71—26no—
874C2×C4×C71—26no—
875C2×C4×C71—22no—
876C2×C4×C71—22no—
877C2×C4×C71—26no—
878C2×C4×C71—43no—
879C2×C4×C71—43no—
880C2×C4×C71C2511yescharacteristic
881C2×C4×C71C2511yescharacteristic
882C2×C4×C71C2513yes—
883C2×C4×C71C2511yescharacteristic
884C2×C4×C71C2511yescharacteristic
885C2×C4×C71C2513yes—
886C2×C4×C71C2513yes—
887C2×C4×C71C2513yes—
888C2×C4×C71C2513yes—
889C2×C4×C71C2513yes—
890C2×C4×C71C2513yes—
891C2×C4×C71C2511yescharacteristic
892C22⋊D71—26no—
893C22⋊D71—22no—
894C22⋊D71—26no—
895C22⋊D71—22no—
896C22⋊D71—26no—
897C22⋊D71—22no—
898C22⋊D71—26no—
899C22⋊D71—26no—
900C22⋊D71—26no—
901C22⋊D71—22no—
902C22⋊D71—46no—
903C2×Dic71—26no—
904C2×Dic71—26no—
905C2×Dic71—212no—
906C2×Dic71—22no—
907C2×Dic71—46no—
908C2×Dic71C2511yescharacteristic
909C2×Dic71C2513yes—
910C2×Dic71C2513yes—
911C2×Dic71C2511yescharacteristic
912C2×Dic71C2513yes—
913C2×Dic71C2513yes—
914C2×Dic71C2513yes—
915C2×Dic71C2511yescharacteristic
916C2×Dic71C2511yescharacteristic
917C2×Dic71C2513yes—
918C2×Dic71C2513yes—
919C2×Dic71C2511yescharacteristic
920D284—22no—
921D284—26no—
922D284—26no—
923D284—22no—
924D284—26no—
925D284—43no—
926C4×D71—26no—
927C4×D71—22no—
928C4×D71—26no—
929C4×D71—26no—
930C4×D71—26no—
931C4×D71—22no—
932C4×D71—26no—
933C4×D71—22no—
934C4×D71—26no—
935C4×D71—212no—
936C4×D71—22no—
937C4×D71—43no—
938C4×D71—43no—
939C4×D71—43no—
940C4×D71—43no—
941C4×D71—46no—
942C4×D71—43no—
943C4×D71—43no—
944C4×D71C2×#41112yes—
945C4×D712−1+414yescomplemented
946Dic142—26no—
947Dic142—26no—
948Dic142—212no—
949Dic142—26no—
950Dic142—26no—
951Dic142—26no—
952Dic142—22no—
953Dic142—46no—
954Dic142—43no—
955Dic142C2×#41112yes—
956C22×C71—21no—
957C22×C71—21no—
958C22×C71—23no—
959C22×C71—21no—
960C22×C71—23no—
961C22×C71—21no—
962C22×C71—23no—
963C22×C71—21no—
964C22×C71#58512yes—
965C22×C71C2611yescharacteristic
966C2×D71—28no—
967C2×D71—21no—
968C2×D71—21no—
969C2×D71—21no—
970C2×D71—21no—
971C2×D71—23no—
972C2×D71—21no—
973C2×D71—23no—
974C2×D71—21no—
975C2×D71—21no—
976C2×D71—23no—
977C2×D71C22×#4112yes—
978C2×D71C2×2−1+412yes—
979C4×C71—21no—
980C4×C71—23no—
981C4×C71—23no—
982C4×C71—21no—
983C4×C71—23no—
984C4×C71—21no—
985C4×C71—23no—
986C4×C71—23no—
987C4×C71—23no—
988C4×C71—21no—
989C4×C71C22×#4116yes—
990C4×C71C2×2−1+412yes—
991Dic71—23no—
992Dic71—21no—
993Dic71—23no—
994Dic71—23no—
995Dic71—21no—
996Dic71—21no—
997Dic71—21no—
998Dic71—23no—
999Dic71—23no—
1000Dic71—23no—
1001Dic71C22×#4116yes—
1002Dic71C2×2−1+412yes—
1003#62788—711nomaximal, Sylow
1004C2×C71—22no—
1005C2×C71—43no—
1006C2×C71—41no—
1007C2×C71C23×#4111yescharacteristic
1008C2×C71C22×2−1+411yescharacteristic
1009C2×C71C2×#58511yescharacteristic
1010D71—22no—
1011D71—22no—
1012D71—43no—
1013D71—41no—
1014#3523—713no—
1015#3523—711no—
1016#3522—711no—
1017#3522—713no—
1018#3516—711no—
1019#3516—713no—
1020#3516—713no—
1021#3516—711no—
1022#3507—713no—
1023#3507—713no—
1024#3502—711no—
1025#3497—711no—
1026#3492—713no—
1027#3492—713no—
1028#3486—711no—
1029#3486—711no—
1030#3482—713no—
1031#3482—713no—
1032#3482—711no—
1033#3482D7111yescharacteristic, complemented
1034#3480—713no—
1035#3480—711no—
1036Q8×#41—713no—
1037Q8×#41—711no—
1038#3461—713no—
1039#3461—713no—
1040#3444—713no—
1041#3444—713no—
1042C4×2−1+4—711no—
1043C4×2−1+4—711no—
1044C22×C4×Q8—711no—
1045C71#6278811yescharacteristic, complemented, Sylow
1046C2×2−1+4—711no—
1047C2×2−1+4—711no—
1048C23×Q8—711no—
1049#559—713no—
1050#559—716no—
1051#559—713no—
1052Q82—713no—
1053Q82—711no—
1054#557—713no—
1055#557—716no—
1056#557—713no—
1057#557—713no—
1058#557—713no—
1059#557—711no—
1060#557—711no—
1061#557—713no—
1062#557C2×D7111yescharacteristic, complemented
1063#556—716no—
1064#556—716no—
1065#556—713no—
1066#556—713no—
1067#556—713no—
1068#556—713no—
1069#556—713no—
1070#556—716no—
1071#556C2×D7113yescomplemented
1072#554—713no—
1073#554—716no—
1074#554—716no—
1075#554—716no—
1076#554—713no—
1077#554—713no—
1078#554—713no—
1079#554—713no—
1080#554—713no—
1081#553—716no—
1082#553—713no—
1083#553—716no—
1084#553—713no—
1085#553—713no—
1086#553—713no—
1087#552—716no—
1088#552—713no—
1089#552—716no—
1090#552—713no—
1091#552—713no—
1092#552—713no—
1093#552—713no—
1094#552—716no—
1095#552—716no—
1096#552—713no—
1097#552C2×D7113yes—
1098#552C2×D7113yescomplemented
1099#550—711no—
1100#550—713no—
1101D4×Q8—711no—
1102D4×Q8—711no—
1103D4×Q8—711no—
1104D4×Q8—713no—
1105D4×Q8—713no—
1106D4×Q8—713no—
1107D4×Q8—713no—
1108D4×Q8—711no—
1109D4×Q8—713no—
1110D4×Q8C2×D7111yescharacteristic
1111#548—711no—
1112#548—711no—
1113#548—713no—
1114#548—713no—
1115#548—713no—
1116#548—713no—
1117#548—711no—
1118#548—711no—
1119#548—713no—
1120#548—713no—
1121#548C2×D7111yescharacteristic
1122#548C2×D7111yescharacteristic, complemented
1123#547—716no—
1124#547—716no—
1125#547—713no—
1126#547—713no—
1127#547—713no—
1128#547C2×D7113yes—
1129#544—713no—
1130#544—713no—
1131#542—713no—
1132#542—713no—
1133#542—716no—
1134#542—716no—
1135#542—713no—
1136#542—713no—
1137#541—713no—
1138#541—716no—
1139#541—716no—
1140#541—713no—
1141#541—713no—
1142#541—713no—
1143#539—716no—
1144#539—716no—
1145#539—716no—
1146#539—716no—
1147#537—713no—
1148#537—713no—
1149#536—713no—
1150#536—713no—
1151#536—713no—
1152#536—713no—
1153#533—713no—
1154#533—713no—
1155#533—713no—
1156#533—713no—
1157#533—713no—
1158#533—716no—
1159#533—713no—
1160#533—713no—
1161#533—713no—
1162#533—716no—
1163#533—713no—
1164#533C2×D7113yescomplemented
1165#532—713no—
1166#532—713no—
1167#532—713no—
1168#532—713no—
1169#532—713no—
1170#532—713no—
1171#529—716no—
1172#529—716no—
1173#529—713no—
1174#529—713no—
1175#529—716no—
1176#529—713no—
1177#529—713no—
1178#529—713no—
1179#529—713no—
1180#529—713no—
1181#529—713no—
1182#529—713no—
1183#529—713no—
1184#529—713no—
1185#529—716no—
1186#529—713no—
1187#529—716no—
1188#529—713no—
1189#529—713no—
1190#529—713no—
1191#529—713no—
1192#529—716no—
1193#529—713no—
1194#529—713no—
1195#529C2×D7113yes—
1196#529C2×D7113yescomplemented
1197#525—713no—
1198#525—716no—
1199#525—713no—
1200#525—713no—
1201#525—713no—
1202#525—711no—
1203#525—713no—
1204#525—713no—
1205#525—713no—
1206#520—711no—
1207#520—713no—
1208#520—711no—
1209#520—713no—
1210#520—713no—
1211#520—713no—
1212#520—713no—
1213#520—713no—
1214#519—711no—
1215#519—711no—
1216#519—711no—
1217#519—713no—
1218#519—711no—
1219#519—713no—
1220C4×#41—713no—
1221C4×#41—711no—
1222C4×#41—713no—
1223C4×#41—713no—
1224C4×#41—716no—
1225C4×#41—716no—
1226C4×#41—713no—
1227C4×#41—713no—
1228C4×#41—713no—
1229C4×#41—713no—
1230C4×#41—713no—
1231C4×#41—713no—
1232C4×#41C2×D7113yes—
1233C4×#41C2×D7111yescharacteristic, complemented
1234C2×C4×Q8—711no—
1235C2×C4×Q8—711no—
1236C2×C4×Q8—713no—
1237C2×C4×Q8—711no—
1238C2×C4×Q8—713no—
1239C2×C4×Q8—711no—
1240C2×C4×Q8—713no—
1241C2×C4×Q8—711no—
1242C2×C4×Q8—713no—
1243C2×C4×Q8—711no—
1244C2×C4×Q8—713no—
1245C2×C4×Q8—713no—
1246C2×C4×Q8—713no—
1247C2×C4×Q8—713no—
1248C2×C4×Q8C2×D7111yescharacteristic
1249C2×C4×Q8C2×D7111yescharacteristic, complemented
1250C22×C4⋊C4—713no—
1251C22×C42—713no—
12522−1+4—1428no—
12532−1+4—1428no—
1254C2×#41—713no—
1255C2×#41—711no—
1256C2×#41—716no—
1257C2×#41—713no—
1258C2×#41—713no—
1259C2×#41—713no—
1260C2×#41—713no—
1261C2×#41—711no—
1262C2×#41—713no—
1263C2×#41—713no—
1264C2×#41—713no—
1265C2×#41C22×D7111yescharacteristic
1266C2×#41C22×D7113yes—
1267C22×Q8—711no—
1268C22×Q8—713no—
1269C22×Q8—713no—
1270C22×Q8—711no—
1271C22×Q8—713no—
1272C22×Q8—711no—
1273C22×Q8—713no—
1274C22×Q8—713no—
1275C22×Q8—1428no—
1276C22×Q8C22×D7111yescharacteristic
1277C22×Q8C22×D7111yescharacteristic
1278C23×C4—713no—
1279C23×C4—713no—
1280C23×C4—711no—
1281C4⋊Q8—713no—
1282C4⋊Q8—713no—
1283C4⋊Q8—713no—
1284C4⋊Q8—713no—
1285C4⋊Q8—716no—
1286C4⋊Q8—713no—
1287C4⋊Q8—713no—
1288C4⋊Q8—713no—
1289C4⋊Q8—713no—
1290C4⋊Q8—716no—
1291C4⋊Q8—716no—
1292C4⋊Q8—716no—
1293C4⋊Q8—713no—
1294C4⋊Q8—713no—
1295C4⋊Q8—713no—
1296C4⋊Q8—713no—
1297C4⋊Q8C22×D7113yes—
1298C4⋊Q8C22×D7113yes—
1299#127—713no—
1300#127—713no—
1301#126—716no—
1302#126—713no—
1303#126—713no—
1304#126—713no—
1305#126—713no—
1306#126—716no—
1307#126—716no—
1308#126—716no—
1309#126—713no—
1310#126—713no—
1311#126—716no—
1312#126—713no—
1313#126—713no—
1314#126—716no—
1315#126—716no—
1316#126—716no—
1317#126—716no—
1318#126—716no—
1319#126C22×D7116yes—
1320#126C22×D7116yes—
1321#125—716no—
1322#125—713no—
1323#125—713no—
1324#125—713no—
1325#125—713no—
1326#125—713no—
1327#125—713no—
1328#125—716no—
1329#125—716no—
1330#125—716no—
1331#125—713no—
1332#125—713no—
1333#125—716no—
1334#125—716no—
1335#125—716no—
1336#125—716no—
1337#125—716no—
1338#125—716no—
1339#125—713no—
1340#125—713no—
1341#125—716no—
1342#125C22×D7113yes—
1343#125C22×D7113yes—
1344#125C22×D7116yes—
1345#124—713no—
1346#124—713no—
1347#124—713no—
1348#124—713no—
1349#124—716no—
1350#124—713no—
1351#124—713no—
1352#124—713no—
1353#124—713no—
1354#124—716no—
1355#124—716no—
1356#124—716no—
1357#124—713no—
1358#124—713no—
1359#124C22×D7113yes—
1360#124C22×D7113yes—
1361#123—713no—
1362#123—713no—
1363#123—716no—
1364#123—716no—
1365#123—716no—
1366#123—713no—
1367#123—711no—
1368#123—716no—
1369#123—713no—
1370#123—713no—
1371#123—716no—
1372#123—716no—
1373#123—713no—
1374#123—711no—
1375#123—713no—
1376#123—713no—
1377#123—716no—
1378#123—713no—
1379#123—713no—
1380#123—716no—
1381#123—716no—
1382#123—716no—
1383#123C22×D7116yes—
1384#123C22×D7116yes—
1385C22⋊Q8—713no—
1386C22⋊Q8—713no—
1387C22⋊Q8—713no—
1388C22⋊Q8—713no—
1389C22⋊Q8—713no—
1390C22⋊Q8—713no—
1391C22⋊Q8—716no—
1392C22⋊Q8—713no—
1393C22⋊Q8—713no—
1394C22⋊Q8—713no—
1395C22⋊Q8—713no—
1396C22⋊Q8—716no—
1397C22⋊Q8—713no—
1398C22⋊Q8—711no—
1399C22⋊Q8—716no—
1400C22⋊Q8—713no—
1401C22⋊Q8—713no—
1402C22⋊Q8—713no—
1403C22⋊Q8—713no—
1404C22⋊Q8—716no—
1405C22⋊Q8—713no—
1406C22⋊Q8—716no—
1407C22⋊Q8—713no—
1408C22⋊Q8—716no—
1409C22⋊Q8—713no—
1410C22⋊Q8—716no—
1411C22⋊Q8—713no—
1412C22⋊Q8—716no—
1413C22⋊Q8—716no—
1414C22⋊Q8—716no—
1415C22⋊Q8—713no—
1416C22⋊Q8—711no—
1417C22⋊Q8—713no—
1418C22⋊Q8—713no—
1419C22⋊Q8—716no—
1420C22⋊Q8—716no—
1421C22⋊Q8—716no—
1422C22⋊Q8—716no—
1423C22⋊Q8—716no—
1424C22⋊Q8C22×D7113yes—
1425C22⋊Q8C22×D7113yes—
1426C22⋊Q8C22×D7113yes—
1427C22⋊Q8C22×D7113yes—
1428C22⋊Q8C22×D7116yes—
1429#121—713no—
1430#121—711no—
1431#121—713no—
1432#121—713no—
1433#121—713no—
1434#121—713no—
1435#121—713no—
1436#121—713no—
1437#121—716no—
1438#121—713no—
1439#121—713no—
1440#121—713no—
1441#121—713no—
1442#121—713no—
1443#121—713no—
1444#121—713no—
1445#121—711no—
1446#121—716no—
1447#121—713no—
1448#121—713no—
1449#121—716no—
1450#121—716no—
1451#121C22×D7113yes—
1452#121C22×D7113yes—
1453#120—713no—
1454#120—711no—
1455#120—713no—
1456#120—711no—
1457C4×Q8—711no—
1458C4×Q8—713no—
1459C4×Q8—711no—
1460C4×Q8—713no—
1461C4×Q8—711no—
1462C4×Q8—713no—
1463C4×Q8—713no—
1464C4×Q8—711no—
1465C4×Q8—713no—
1466C4×Q8—716no—
1467C4×Q8—713no—
1468C4×Q8—713no—
1469C4×Q8—716no—
1470C4×Q8—713no—
1471C4×Q8—713no—
1472C4×Q8—716no—
1473C4×Q8—713no—
1474C4×Q8—713no—
1475C4×Q8—713no—
1476C4×Q8—716no—
1477C4×Q8—716no—
1478C4×Q8—716no—
1479C4×Q8—713no—
1480C4×Q8—716no—
1481C4×Q8—713no—
1482C4×Q8—713no—
1483C4×Q8—713no—
1484C4×Q8—716no—
1485C4×Q8—713no—
1486C4×Q8—713no—
1487C4×Q8—713no—
1488C4×Q8—713no—
1489C4×Q8—713no—
1490C4×Q8—716no—
1491C4×Q8—713no—
1492C4×Q8—713no—
1493C4×Q8—713no—
1494C4×Q8—716no—
1495C4×Q8—713no—
1496C4×Q8—713no—
1497C4×Q8—713no—
1498C4×Q8—713no—
1499C4×Q8—713no—
1500C4×Q8—713no—
1501C4×Q8C22×D7111yescharacteristic
1502C4×Q8C22×D7113yes—
1503C4×Q8C22×D7111yescharacteristic
1504C4×Q8C22×D7113yes—
1505C4×Q8C22×D7113yes—
1506C4×Q8C22×D7111yescharacteristic
1507C4×Q8C22×D7113yes—
1508C4×Q8C22×D7113yes—
1509C4×Q8C22×D7113yes—
1510C4×Q8C22×D7111yescharacteristic
1511C4×D4—713no—
1512C4×D4—713no—
1513C4×D4—716no—
1514C4×D4—713no—
1515C4×D4—711no—
1516C4×D4—713no—
1517C4×D4—711no—
1518C4×D4—713no—
1519C4×D4—713no—
1520C4×D4—713no—
1521C4×D4—713no—
1522C4×D4—713no—
1523C4×D4—713no—
1524C4×D4—716no—
1525C4×D4—713no—
1526C4×D4—713no—
1527C4×D4—713no—
1528C4×D4—713no—
1529C4×D4—713no—
1530C4×D4—713no—
1531C4×D4—716no—
1532C4×D4—713no—
1533C4×D4—713no—
1534C4×D4—713no—
1535C4×D4—713no—
1536C4×D4—716no—
1537C4×D4—713no—
1538C4×D4—713no—
1539C4×D4—716no—
1540C4×D4—716no—
1541C4×D4—716no—
1542C4×D4—716no—
1543C4×D4—716no—
1544C4×D4—716no—
1545C4×D4—716no—
1546C4×D4—716no—
1547C4×D4—716no—
1548C4×D4—716no—
1549C4×D4—713no—
1550C4×D4—711no—
1551C4×D4—713no—
1552C4×D4—713no—
1553C4×D4—713no—
1554C4×D4—713no—
1555C4×D4—713no—
1556C4×D4—713no—
1557C4×D4—713no—
1558C4×D4—713no—
1559C4×D4—713no—
1560C4×D4—713no—
1561C4×D4C22×D7113yes—
1562C4×D4C22×D7113yes—
1563C4×D4C22×D7111yescharacteristic
1564C4×D4C22×D7113yes—
1565C4×D4C22×D7113yes—
1566C4×D4C22×D7113yes—
1567C4×D4C22×D7113yes—
1568C4×D4C22×D7113yes—
1569#117—713no—
1570#117—713no—
1571#117—713no—
1572#117—713no—
1573#117—713no—
1574#117—713no—
1575#117—713no—
1576#117—713no—
1577#117—716no—
1578#117—713no—
1579#117—713no—
1580#117—716no—
1581#117—716no—
1582#117—716no—
1583#117—716no—
1584#117—716no—
1585#117—713no—
1586#117—711no—
1587#117—713no—
1588#117—713no—
1589#117—713no—
1590#117—713no—
1591#117—716no—
1592#117—716no—
1593#117—713no—
1594#117—713no—
1595#117—713no—
1596#117—713no—
1597#117C22×D7116yes—
1598#117C22×D7113yes—
1599#117C22×D7113yes—
1600#117C22×D7113yes—
1601#117C22×D7113yes—
1602C2×C4⋊C4—716no—
1603C2×C4⋊C4—713no—
1604C2×C4⋊C4—716no—
1605C2×C4⋊C4—713no—
1606C2×C4⋊C4—713no—
1607C2×C4⋊C4—713no—
1608C2×C4⋊C4—716no—
1609C2×C4⋊C4—716no—
1610C2×C4⋊C4—713no—
1611C2×C4⋊C4—713no—
1612C2×C4⋊C4—716no—
1613C2×C4⋊C4—713no—
1614C2×C4⋊C4—713no—
1615C2×C4⋊C4C22×D7113yes—
1616C2×C4⋊C4C22×D7113yes—
1617C2×C42—713no—
1618C2×C42—713no—
1619C2×C42—713no—
1620C2×C42—716no—
1621C2×C42—713no—
1622C2×C42—713no—
1623C2×C42—713no—
1624C2×C42—713no—
1625C2×C42—713no—
1626C2×C42—713no—
1627C2×C42—713no—
1628C2×C42—713no—
1629C2×C42—716no—
1630C2×C42—713no—
1631C2×C42—713no—
1632C2×C42C22×D7113yes—
1633C2×C42C22×D7113yes—
1634C2×C42C22×D7113yes—
1635C24—711no—
1636#41—24no—
1637#41—46no—
1638#41—2846no—
1639#41—28412no—
1640#41—14212no—
1641#41—1424no—
1642#41—14212no—
1643#41—14212no—
1644#41—14212no—
1645#41—14212no—
1646#41—14212no—
1647#41—14212no—
1648#41—1424no—
1649C2×Q8—24no—
1650C2×Q8—24no—
1651C2×Q8—718no—
1652C2×Q8—713no—
1653C2×Q8—716no—
1654C2×Q8—713no—
1655C2×Q8—713no—
1656C2×Q8—711no—
1657C2×Q8—716no—
1658C2×Q8—713no—
1659C2×Q8—713no—
1660C2×Q8—713no—
1661C2×Q8—713no—
1662C2×Q8—14212no—
1663C2×Q8—14212no—
1664C2×Q8—14212no—
1665C2×Q8—14212no—
1666C2×Q8—14212no—
1667C2×Q8—1424no—
1668C2×Q8—1424no—
1669C2×Q8C23×D7113yes—
1670C2×Q8C23×D7113yes—
1671C2×Q8C23×D7113yes—
1672C2×Q8C23×D7111yescharacteristic
1673C2×D4—716no—
1674C2×D4—711no—
1675C2×D4—713no—
1676C2×D4—711no—
1677C2×D4—713no—
1678C2×D4—711no—
1679C2×D4—713no—
1680C2×D4—713no—
1681C2×D4—711no—
1682C2×D4—713no—
1683C2×D4—713no—
1684C2×D4—713no—
1685C2×D4—713no—
1686C2×D4—711no—
1687C2×D4—713no—
1688C2×D4—711no—
1689C2×D4—713no—
1690C2×D4C23×D7113yes—
1691C2×D4C23×D7113yes—
1692C2×D4C23×D7111yescharacteristic
1693C2×D4C23×D7113yes—
1694C22×C4—2846no—
1695C22×C4—716no—
1696C22×C4—713no—
1697C22×C4—713no—
1698C22×C4—713no—
1699C22×C4—713no—
1700C22×C4—716no—
1701C22×C4—713no—
1702C22×C4—713no—
1703C22×C4—713no—
1704C22×C4—711no—
1705C22×C4—711no—
1706C22×C4—713no—
1707C22×C4—713no—
1708C22×C4—716no—
1709C22×C4—711no—
1710C22×C4—711no—
1711C22×C4—713no—
1712C22×C4—713no—
1713C22×C4—713no—
1714C22×C4—716no—
1715C22×C4—713no—
1716C22×C4—713no—
1717C22×C4—711no—
1718C22×C4—711no—
1719C22×C4—713no—
1720C22×C4—1424no—
1721C22×C4—14212no—
1722C22×C4C23×D7113yes—
1723C22×C4C23×D7113yes—
1724C22×C4C23×D7113yes—
1725C22×C4C23×D7113yes—
1726C22×C4C23×D7111yescharacteristic
1727C22×C4C23×D7113yes—
1728C22×C4C23×D7111yescharacteristic
1729C22×C4C23×D7113yes—
1730C22×C4C23×D7113yes—
1731C4⋊C4—716no—
1732C4⋊C4—716no—
1733C4⋊C4—716no—
1734C4⋊C4—716no—
1735C4⋊C4—713no—
1736C4⋊C4—713no—
1737C4⋊C4—713no—
1738C4⋊C4—713no—
1739C4⋊C4—716no—
1740C4⋊C4—713no—
1741C4⋊C4—713no—
1742C4⋊C4—713no—
1743C4⋊C4—711no—
1744C4⋊C4—713no—
1745C4⋊C4—711no—
1746C4⋊C4—713no—
1747C4⋊C4—713no—
1748C4⋊C4—711no—
1749C4⋊C4—711no—
1750C4⋊C4—716no—
1751C4⋊C4—716no—
1752C4⋊C4—716no—
1753C4⋊C4—713no—
1754C4⋊C4—713no—
1755C4⋊C4—713no—
1756C4⋊C4—713no—
1757C4⋊C4—716no—
1758C4⋊C4—716no—
1759C4⋊C4—713no—
1760C4⋊C4—713no—
1761C4⋊C4—713no—
1762C4⋊C4—713no—
1763C4⋊C4—716no—
1764C4⋊C4—713no—
1765C4⋊C4—713no—
1766C4⋊C4—713no—
1767C4⋊C4—713no—
1768C4⋊C4—713no—
1769C4⋊C4—711no—
1770C4⋊C4—713no—
1771C4⋊C4—713no—
1772C4⋊C4—716no—
1773C4⋊C4—713no—
1774C4⋊C4—713no—
1775C4⋊C4—713no—
1776C4⋊C4—713no—
1777C4⋊C4C23×D7113yes—
1778C4⋊C4C23×D7113yes—
1779C4⋊C4C23×D7116yes—
1780C4⋊C4C23×D7113yes—
1781C4⋊C4C23×D7116yes—
1782C4⋊C4C23×D7113yes—
1783C4⋊C4C23×D7113yes—
1784C4⋊C4C23×D7111yescharacteristic
1785C4⋊C4C23×D7116yes—
1786C4⋊C4C23×D7116yes—
1787C4⋊C4C23×D7113yes—
1788C4⋊C4C23×D7113yes—
1789C4⋊C4C23×D7113yes—
1790C4⋊C4C23×D7113yes—
1791C22⋊C4—713no—
1792C22⋊C4—711no—
1793C22⋊C4—713no—
1794C22⋊C4—713no—
1795C22⋊C4—711no—
1796C22⋊C4—713no—
1797C22⋊C4—713no—
1798C22⋊C4—713no—
1799C22⋊C4—713no—
1800C22⋊C4—713no—
1801C22⋊C4—716no—
1802C22⋊C4—713no—
1803C22⋊C4—711no—
1804C22⋊C4—713no—
1805C22⋊C4—711no—
1806C22⋊C4—713no—
1807C22⋊C4—713no—
1808C22⋊C4—716no—
1809C22⋊C4—713no—
1810C22⋊C4—711no—
1811C22⋊C4—711no—
1812C22⋊C4—713no—
1813C22⋊C4—713no—
1814C22⋊C4—713no—
1815C22⋊C4—711no—
1816C22⋊C4—711no—
1817C22⋊C4—716no—
1818C22⋊C4—713no—
1819C22⋊C4—713no—
1820C22⋊C4—713no—
1821C22⋊C4—713no—
1822C22⋊C4—716no—
1823C22⋊C4—713no—
1824C22⋊C4—713no—
1825C22⋊C4—716no—
1826C22⋊C4C23×D7113yes—
1827C22⋊C4C23×D7116yes—
1828C22⋊C4C23×D7113yes—
1829C22⋊C4C23×D7111yescharacteristic
1830C22⋊C4C23×D7111yescharacteristic
1831C22⋊C4C23×D7116yes—
1832C22⋊C4C23×D7116yes—
1833C22⋊C4C23×D7113yes—
1834C22⋊C4C23×D7113yes—
1835C42—713no—
1836C42—713no—
1837C42—713no—
1838C42—713no—
1839C42—713no—
1840C42—713no—
1841C42—713no—
1842C42—713no—
1843C42—713no—
1844C42—713no—
1845C42—716no—
1846C42—716no—
1847C42—713no—
1848C42—713no—
1849C42—716no—
1850C42—716no—
1851C42—713no—
1852C42—713no—
1853C42—713no—
1854C42—713no—
1855C42—711no—
1856C42—713no—
1857C42C23×D7113yes—
1858C42C23×D7113yes—
1859C42C23×D7113yes—
1860C42C23×D7113yes—
1861C42C23×D7113yes—
1862C42C23×D7113yes—
1863C42C23×D7113yes—
1864C42C23×D7113yes—
1865C42C23×D7113yes—
1866C42C23×D7111yescharacteristic
1867C23—711no—
1868C23—711no—
1869C23—713no—
1870C23—711no—
1871C23—1422no—
1872C23—1422no—
1873C23—1422no—
1874C23C24×D7111yescharacteristic
1875C23C24×D7113yes—
1876C23C24×D7111yescharacteristic
1877Q8—26no—
1878Q8—26no—
1879Q8—43no—
1880Q8—2843no—
1881Q8—2846no—
1882Q8—7112no—
1883Q8—14212no—
1884Q8—1426no—
1885Q8—1426no—
1886Q8—1426no—
1887Q8—1422no—
1888Q8—1426no—
1889Q8—1426no—
1890Q8#41×D7114yes—
1891D4—22no—
1892D4—26no—
1893D4—26no—
1894D4—43no—
1895D4—2843no—
1896D4—2846no—
1897D4—1422no—
1898D4—1426no—
1899D4—1426no—
1900D4—1422no—
1901D4—1426no—
1902D4—1426no—
1903D4—1422no—
1904D4—1426no—
1905D4—1422no—
1906D4—1426no—
1907D4—1422no—
1908D4—1426no—
1909D4—1422no—
1910D4—1426no—
1911D4—1426no—
1912C2×C4—26no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—26no—
1916C2×C4—22no—
1917C2×C4—26no—
1918C2×C4—22no—
1919C2×C4—43no—
1920C2×C4—43no—
1921C2×C4—2843no—
1922C2×C4—2843no—
1923C2×C4—2843no—
1924C2×C4—2843no—
1925C2×C4—2843no—
1926C2×C4—2843no—
1927C2×C4—2846no—
1928C2×C4—2846no—
1929C2×C4—711no—
1930C2×C4—713no—
1931C2×C4—7112no—
1932C2×C4—714no—
1933C2×C4—711no—
1934C2×C4—713no—
1935C2×C4—711no—
1936C2×C4—713no—
1937C2×C4—713no—
1938C2×C4—711no—
1939C2×C4—713no—
1940C2×C4—711no—
1941C2×C4—713no—
1942C2×C4—713no—
1943C2×C4—1426no—
1944C2×C4—1422no—
1945C2×C4—14212no—
1946C2×C4—1426no—
1947C2×C4—1422no—
1948C2×C4—1426no—
1949C2×C4—1422no—
1950C2×C4—14212no—
1951C2×C4—1426no—
1952C2×C4—1426no—
1953C2×C4—1426no—
1954C2×C4—1426no—
1955C2×C4—1422no—
1956C2×C4—1422no—
1957C2×C4—1426no—
1958C2×C4C24×D7111yescharacteristic
1959C2×C4C24×D7113yes—
1960C2×C4C24×D7113yes—
1961C2×C4C24×D7113yes—
1962C2×C4C24×D7113yes—
1963C2×C4C24×D7113yes—
1964C2×C4C24×D7113yes—
1965C2×C4C24×D7111yescharacteristic
1966C2×C4C24×D7111yescharacteristic
1967C2×C4C24×D7111yescharacteristic
1968C2×C4C24×D7113yes—
1969C2×C4C24×D7111yescharacteristic
1970C22—21no—
1971C22—21no—
1972C22—21no—
1973C22—23no—
1974C22—21no—
1975C22—23no—
1976C22—21no—
1977C22—23no—
1978C22—712no—
1979C22—712no—
1980C22—1428no—
1981C22—1423no—
1982C22—1421no—
1983C22—1423no—
1984C22—1421no—
1985C22—1421no—
1986C22—1423no—
1987C22—1421no—
1988C22—1421no—
1989C22—1421no—
1990C22—1421no—
1991C22#1798683512yes—
1992C22C25×D7111yescharacteristic
1993C4—21no—
1994C4—23no—
1995C4—23no—
1996C4—21no—
1997C4—23no—
1998C4—21no—
1999C4—23no—
2000C4—23no—
2001C4—21no—
2002C4—23no—
2003C4—716no—
2004C4—712no—
2005C4—1423no—
2006C4—1421no—
2007C4—1423no—
2008C4—1421no—
2009C4—1421no—
2010C4—1423no—
2011C4—1423no—
2012C4—1421no—
2013C4—1423no—
2014C4—1423no—
2015C4C2×#41×D7116yes—
2016C42−1+4×D7112yes—
2017C2—22no—
2018C2—41no—
2019C2—43no—
2020C2—2843no—
2021C2—2841no—
2022C2—1422no—
2023C2—1422no—
2024C2C22×#41×D7111yescharacteristic
2025C2C2×2−1+4×D7111yescharacteristic
2026C2C2×#1798683511yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3482C2
hypercenter#3482D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #22602429C2semidirect
2. #22602427C2semidirect
3. #22602418C2semidirect
4. #22602416C2semidirect
5. #22602336C2semidirect
6. #22602332C2semidirect
7. #22602328C2semidirect
8. #22602326C2semidirect
9. #22602201C2semidirect
10. #22602199C2semidirect
11. #22602147C2semidirect
12. #22602108C2semidirect
13. #22602042C2semidirect
14. #22602040C2semidirect
15. #22601990C2semidirect
16. #22601986C2semidirect
17. #22601957C2semidirect
18. #22601955C2semidirect
19. #22601953C2semidirect
20. #22601938C2semidirect
21. #22601931C2semidirect
22. Q8×#11765865C2semidirect
23. #22601918C2semidirect
24. #22601771C2semidirect
25. #22601765C2semidirect
26. #22601634C2semidirect
27. #22601633C2semidirect
28. C4×#14556176C2semidirect
29. C4×#14556175C2semidirect
30. C2×C4×Q8×D71C2semidirect
31. C71×#3482C2semidirect
35. #17986733C22semidirect
36. #17986732C22semidirect
37. #17986731C22semidirect
38. Q8×Dic142C22semidirect
39. #17986729C22semidirect
40. #17986727C22semidirect
41. #17986727C22semidirect
42. #17986726C22semidirect
43. #17986726C22semidirect
44. #17986726C22semidirect
45. #17986725C22semidirect
46. #17986725C22semidirect
47. #17986724C22semidirect
48. #17986722C22semidirect
49. #17986721C22semidirect
50. #17986720C22semidirect
51. #17986718C22semidirect
52. #17986717C22semidirect
53. #17986717C22semidirect
54. #17986716C22semidirect
55. #17986716C22semidirect
59. #17986707C22semidirect
62. #17986704C22semidirect
64. #17986703C22semidirect
72. #17986690C22semidirect
74. #17986689C22semidirect
75. #17986687C22semidirect
77. #17986685C22semidirect
80. #17986682C22semidirect
81. #17986668C22semidirect
82. #17986667C22semidirect
88. Q8×C22⋊D71C22semidirect
91. #17986662C22semidirect
93. #17986661C22semidirect
97. #17986658C22semidirect
99. #17986657C22semidirect
109. #17986623C22semidirect
110. #17986622C22semidirect
111. #17986619C22semidirect
112. #17986618C22semidirect
113. #17986617C22semidirect
114. #17986616C22semidirect
115. #17986612C22semidirect
116. #17986610C22semidirect
117. #17986609C22semidirect
118. #17986609C22semidirect
119. #17986608C22semidirect
120. #17986606C22semidirect
131. #17986556C22semidirect
136. #17986553C22semidirect
137. #17986553C22semidirect
138. #17986553C22semidirect
140. #17986552C22semidirect
150. #17986536C22semidirect
153. #17986533C22semidirect
158. #17986531C22semidirect
163. #17986529C22semidirect
170. #17986527C22semidirect
181. #17986482C22semidirect
183. #17986481C22semidirect
185. #17986480C22semidirect
188. #17986478C22semidirect
189. #17986477C22semidirect
190. #17986476C22semidirect
193. #17986475C22semidirect
194. #17986475C22semidirect
196. C4×#11765866C22semidirect
202. C4×#11765865C22semidirect
206. C4×#11765864C22semidirect
209. C2×C4×Dic142C22semidirect
219. C4×Q8×D71C22semidirect
220. C4×Q8×D71C22semidirect
223. #557×C71C22semidirect
224. #556×C71C22semidirect
226. #552×C71C22semidirect
229. #548×C71C22semidirect
231. #533×C71C22semidirect
233. #529×C71C22semidirect
235. C4×#41×C71C22semidirect
237. C2×C4×Q8×C71C22semidirect
650. Q8×D71#41semidirect
945. C4×D712−1+4semidirect
1033. #3482D71semidirect
1045. C71#62788semidirect
1062. #557C2×D71semidirect
1071. #556C2×D71semidirect
1098. #552C2×D71semidirect
1122. #548C2×D71semidirect
1164. #533C2×D71semidirect
1196. #529C2×D71semidirect
1233. C4×#41C2×D71semidirect
1249. C2×C4×Q8C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226024292
#226024272
#226024182
#226024162
#226023362
#226023322
#226023282
#226023262
#226022012
#226021992
#226021472
#226021082
#226020422
#226020402
#226019902
#226019862
#226019572
#226019552
#226019532
#226019382
#226019312
Q8×#117658652
#226019182
#226017712
#226017652
#226016342
#226016332
C4×#145561762
C4×#145561752
C2×C4×Q8×D712
C71×#34822
#6278871