Finite Group Databasebeta

← #32905679

Subgroups — #32905679

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#22602432C213yesmaximal, complemented
2#22602430C211yesmaximal, characteristic, complemented
3#22602421C213yesmaximal, complemented
4#22602419C211yesmaximal, characteristic, complemented
5#22602333C211yesmaximal, characteristic, complemented
6#22602329C213yesmaximal, complemented
7#22602323C213yesmaximal, complemented
8#22602201C213yesmaximal, complemented
9#22602199C213yesmaximal, complemented
10#22602147C211yesmaximal, characteristic, complemented
11#22602108C211yesmaximal, characteristic, complemented
12#22602048C213yesmaximal, complemented
13#22602044C213yesmaximal, complemented
14#22601990C211yesmaximal, characteristic, complemented
15#22601986C211yesmaximal, characteristic, complemented
16#22601960C211yesmaximal, characteristic, complemented
17#22601959C213yesmaximal, complemented
18#22601956C211yesmaximal, characteristic, complemented
19#22601954C213yesmaximal, complemented
20#22601934C213yesmaximal, complemented
21#22601930C211yesmaximal, characteristic, complemented
22#22601919C213yesmaximal, complemented
23Q8×#11765864C211yesmaximal, characteristic, complemented
24#22601772C213yesmaximal, complemented
25#22601766C213yesmaximal, complemented
26#22601634C213yesmaximal, complemented
27#22601634C213yesmaximal, complemented
28#22601551C211yesmaximal, characteristic, complemented
29#22601549C211yesmaximal, characteristic, complemented
30C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
31C71×#3516C211yesmaximal, 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#17986708C2216yes—
57#17986707C2213yes—
58#17986707C2213yescomplemented
59#17986706C2213yes—
60#17986704C2213yes—
61#17986704C2213yescomplemented
62#17986703C2216yes—
63#17986703C2216yescomplemented
64#17986701C2213yes—
65#17986698C2216yes—
66#17986697C2213yes—
67#17986695C2213yes—
68#17986692C2216yes—
69#17986690C2213yes—
70#17986690C2213yescomplemented
71#17986689C2213yescomplemented
72#17986688C2213yes—
73#17986687C2213yes—
74#17986687C2213yescomplemented
75#17986685C2216yes—
76#17986685C2216yescomplemented
77#17986683C2213yes—
78#17986682C2216yescomplemented
79#17986681C2216yes—
80#17986668C2211yescharacteristic, complemented
81#17986667C2213yescomplemented
82Q8×D284C2211yescharacteristic
83D4×Dic142C2213yes—
84#17986664C2213yes—
85Q8×C22⋊D71C2211yescharacteristic
86Q8×C22⋊D71C2211yescharacteristic
87Q8×C22⋊D71C2211yescharacteristic, complemented
88#17986662C2213yes—
89#17986662C2213yes—
90#17986662C2213yescomplemented
91#17986661C2211yescharacteristic
92#17986661C2211yescharacteristic, complemented
93#17986660C2211yescharacteristic
94#17986659C2213yes—
95#17986658C2213yes—
96#17986658C2213yescomplemented
97#17986657C2213yes—
98#17986657C2213yescomplemented
99#17986656C2211yescharacteristic
100#17986655C2213yes—
101#17986654C2213yes—
102#17986652C2213yes—
103#17986651C2216yes—
104#17986650C2213yes—
105#17986649C2213yes—
106#17986647C2216yes—
107#17986629C2213yes—
108#17986626C2213yes—
109#17986621C2213yescomplemented
110#17986620C2213yescomplemented
111#17986615C2216yescomplemented
112#17986614C2213yescomplemented
113#17986613C2216yescomplemented
114#17986611C2213yescomplemented
115#17986608C2216yescomplemented
116#17986607C2213yescomplemented
117#17986607C2213yescomplemented
118#17986606C2216yescomplemented
119#17986597C2216yes—
120#17986595C2216yes—
121#17986592C2216yes—
122#17986590C2216yes—
123#17986579C2213yes—
124#17986578C2213yes—
125#17986574C2213yes—
126#17986572C2213yes—
127#17986572C2213yes—
128#17986569C2213yes—
129#17986555C2213yes—
130#17986555C2213yes—
131#17986555C2216yescomplemented
132#17986554C2213yescomplemented
133#17986554C2213yescomplemented
134#17986553C2213yes—
135#17986553C2213yes—
136#17986551C2213yes—
137#17986551C2213yes—
138#17986551C2213yescomplemented
139#17986551C2216yescomplemented
140#17986551C2213yescomplemented
141#17986548C2213yes—
142#17986548C2213yes—
143#17986546C2213yes—
144#17986546C2213yes—
145#17986544C2213yes—
146#17986544C2213yes—
147#17986535C2213yescomplemented
148#17986534C2213yes—
149#17986534C2213yes—
150#17986534C2213yescomplemented
151#17986533C2213yes—
152#17986533C2213yes—
153#17986532C2216yes—
154#17986532C2216yes—
155#17986532C2213yes—
156#17986532C2213yes—
157#17986532C2213yes—
158#17986532C2213yes—
159#17986532C2216yescomplemented
160#17986530C2213yescomplemented
161#17986528C2213yes—
162#17986528C2213yes—
163#17986528C2213yescomplemented
164#17986527C2213yes—
165#17986527C2213yes—
166#17986527C2216yes—
167#17986526C2213yes—
168#17986526C2216yes—
169#17986526C2213yes—
170#17986526C2216yescomplemented
171#17986512C2213yes—
172#17986512C2213yes—
173#17986509C2213yes—
174#17986509C2213yes—
175#17986508C2213yes—
176#17986508C2213yes—
177#17986508C2216yes—
178#17986507C2211yescharacteristic
179#17986507C2213yes—
180#17986481C2213yes—
181#17986481C2211yescharacteristic, complemented
182#17986480C2213yes—
183#17986479C2213yes—
184#17986479C2213yescomplemented
185#17986478C2213yes—
186#17986478C2213yescomplemented
187#17986476C2213yescomplemented
188#17986475C2211yescharacteristic
189#17986475C2211yescharacteristic
190#17986475C2213yescomplemented
191#17986475C2211yescharacteristic, complemented
192#41×Dic71C2211yescharacteristic, complemented
193C4×#11765866C2213yes—
194C4×#11765866C2213yes—
195C4×#11765866C2211yescharacteristic, complemented
196#17986467C2213yes—
197#17986467C2213yes—
198#17986467C2216yes—
199#17986467C2213yescomplemented
200C4×#11765864C2213yes—
201C4×#11765864C2213yes—
202C4×#11765864C2213yes—
203C4×#11765864C2216yes—
204C4×#11765864C2213yes—
205C4×#11765864C2213yescomplemented
206C2×Q8×Dic71C2211yescharacteristic
207C2×Q8×Dic71C2211yescharacteristic, complemented
208C2×C4×Dic142C2213yes—
209C2×#14556093C2213yes—
210C2×#14556093C2213yescomplemented
211C4×Q8×D71C2213yes—
212C4×Q8×D71C2211yescharacteristic
213C4×Q8×D71C2211yescharacteristic
214C4×Q8×D71C2211yescharacteristic
215C4×Q8×D71C2213yes—
216C4×Q8×D71C2213yes—
217C4×Q8×D71C2213yes—
218C4×Q8×D71C2211yescharacteristic
219C4×Q8×D71C2213yescomplemented
220C4×Q8×D71C2211yescharacteristic, complemented
221C2×C4⋊C4×D71C2213yes—
222C2×C42×D71C2213yes—
223#557×C71C2211yescharacteristic, complemented
224#556×C71C2213yescomplemented
225#554×C71C2213yes—
226#553×C71C2213yes—
227#552×C71C2213yescomplemented
228D4×Q8×C71C2211yescharacteristic
229#548×C71C2211yescharacteristic
230#548×C71C2211yescharacteristic, complemented
231#542×C71C2213yescomplemented
232#541×C71C2213yescomplemented
233#529×C71C2213yes—
234#529×C71C2213yes—
235#520×C71C2211yescharacteristic, complemented
236#519×C71C2211yescharacteristic, complemented
237C2×C4×Q8×C71C2211yescharacteristic
238#14556176—28no—
239#14556175—28no—
240C2×#11765866C2313yes—
241C2×#11765866C2311yescharacteristic
242C2×#11765866C2313yes—
243C2×#11765865C2313yes—
244C2×#11765865C2313yes—
245C2×#11765865C2313yes—
246C2×#11765865C2316yes—
247C2×#11765864C2313yes—
248C2×#11765864C2313yes—
249C2×#11765864C2311yescharacteristic
250C2×#11765864C2313yes—
251C2×#11765864C2313yes—
252C22×Dic142C2313yes—
253C22×Dic142C2313yes—
254C2×Q8×D71—28no—
255C2×Q8×D71C2313yes—
256C2×Q8×D71C2311yescharacteristic
257C2×Q8×D71C2313yes—
258C2×Q8×D71C2311yescharacteristic
259C2×Q8×D71C2313yes—
260C2×Q8×D71C2311yescharacteristic
261C22×C4×D71C2313yes—
262C22×C4×D71C2311yescharacteristic
263C22×C4×D71C2313yes—
264#14556128C2313yes—
265#14556128C2313yes—
266#14556127C2316yes—
267#14556127C2316yes—
268#14556127C2313yes—
269#14556127C2316yes—
270#14556127C2313yes—
271#14556127C2313yes—
272#14556127C2313yes—
273#14556127C2313yes—
274#14556127C2313yes—
275#14556126C2313yes—
276#14556126C2313yes—
277#14556126C2316yes—
278#14556126C2313yes—
279#14556126C2313yes—
280#14556124C2313yes—
281#14556124C2313yes—
282#14556123C2316yes—
283#14556123C2316yes—
284#14556123C2316yes—
285#14556123C2313yes—
286#14556123C2313yes—
287#14556123C2316yes—
288#14556122C2316yes—
289#14556122C2316yes—
290#14556122C2313yes—
291#14556122C2313yes—
292#14556121C2316yes—
293#14556121C2316yes—
294#14556121C2316yes—
295#14556121C2313yes—
296#14556121C2313yes—
297#14556121C2316yes—
298#14556120C2316yes—
299#14556120C2313yes—
300#14556120C2313yes—
301#14556120C2313yes—
302#14556119C2316yes—
303#14556119C2316yes—
304#14556119C2313yes—
305#14556119C2313yes—
306#14556118C2316yes—
307#14556118C2316yes—
308#14556118C2316yes—
309#14556118C2316yes—
310#14556118C2316yes—
311#14556118C2316yes—
312#14556118C2316yes—
313#14556118C2313yes—
314#14556118C2313yes—
315#14556118C2313yes—
316#14556118C2316yes—
317#14556118C2313yes—
318#14556117C2313yes—
319#14556116C2313yes—
320#14556116C2313yes—
321#14556116C2313yes—
322#14556115C2313yes—
323#14556114C2316yes—
324#14556114C2316yes—
325#14556114C2316yes—
326#14556114C2313yes—
327#14556114C2313yes—
328#14556114C2313yes—
329#14556114C2316yes—
330#14556114C2313yes—
331#14556113C2313yes—
332#14556113C2316yes—
333#14556113C2313yes—
334#14556113C2316yes—
335#14556113C2316yes—
336#14556113C2316yes—
337#14556113C2313yes—
338#14556113C2313yes—
339#14556112C2316yes—
340#14556111C2316yes—
341#14556111C2311yescharacteristic
342#14556111C2313yes—
343#14556110C2313yes—
344#14556110C2316yes—
345#14556110C2313yes—
346#14556110C2316yes—
347#14556110C2316yes—
348#14556110C2313yes—
349#14556110C2316yes—
350#14556110C2313yes—
351#14556109C2316yes—
352#14556108C2313yes—
353#14556108C2313yes—
354#14556108C2313yes—
355#14556108C2313yes—
356#14556108C2316yes—
357#14556108C2313yes—
358#14556107C2313yes—
359#14556107C2313yes—
360#14556107C2313yes—
361#14556107C2316yes—
362#14556107C2313yes—
363#14556107C2313yes—
364#14556106C2316yes—
365#14556106C2316yes—
366#14556106C2316yes—
367#14556106C2316yes—
368#14556106C2316yes—
369#14556106C2316yes—
370#14556106C2313yes—
371#14556106C2313yes—
372#14556106C2311yescharacteristic
373#14556106C2313yes—
374#14556106C2313yes—
375#14556106C2311yescharacteristic
376#14556105C2316yes—
377#14556105C2316yes—
378#14556105C2316yes—
379#14556105C2316yes—
380#14556105C2316yes—
381#14556105C2313yes—
382#14556105C2313yes—
383#14556105C2316yes—
384#14556104C2313yes—
385#14556104C2313yes—
386#14556104C2313yes—
387#14556104C2313yes—
388#14556104C2316yes—
389#14556104C2313yes—
390#14556103C2313yes—
391#14556103C2313yes—
392#14556103C2313yes—
393#14556102C2313yes—
394#14556102C2313yes—
395#14556102C2313yes—
396#14556101C2316yes—
397#14556101C2316yes—
398#14556101C2313yes—
399#14556101C2313yes—
400#14556101C2311yescharacteristic
401#14556101C2313yes—
402#14556101C2313yes—
403#14556101C2311yescharacteristic
404#14556100C2316yes—
405#14556100C2313yes—
406#14556100C2313yes—
407#14556100C2316yes—
408#14556099C2313yes—
409#14556099C2313yes—
410#14556099C2313yes—
411#14556098C2311yescharacteristic
412#14556098C2313yes—
413#14556096C2311yescharacteristic
414#14556096C2313yes—
415Q8×Dic71C2311yescharacteristic
416Q8×Dic71C2311yescharacteristic
417Q8×Dic71C2311yescharacteristic
418Q8×Dic71C2313yes—
419Q8×Dic71C2313yes—
420Q8×Dic71C2311yescharacteristic
421Q8×Dic71C2313yes—
422Q8×Dic71C2313yes—
423Q8×Dic71C2313yes—
424C4×Dic142C2316yes—
425C4×Dic142C2313yes—
426C4×Dic142C2313yes—
427C4×Dic142C2313yes—
428C4×Dic142C2313yes—
429C4×Dic142C2313yes—
430C4×Dic142C2316yes—
431C4×Dic142C2316yes—
432C4×Dic142C2313yes—
433C4×Dic142C2313yes—
434C4×Dic142C2316yes—
435C4×Dic142C2313yes—
436C4×Dic142C2313yes—
437C4×Dic142C2313yes—
438C4×Dic142C2313yes—
439#14556093C2313yes—
440#14556093C2313yes—
441#14556093C2313yes—
442#14556093C2313yes—
443#14556093C2313yes—
444#14556093C2316yes—
445#14556093C2313yes—
446#14556093C2316yes—
447#14556093C2313yes—
448#14556093C2313yes—
449#14556093C2316yes—
450#14556093C2313yes—
451#14556093C2316yes—
452#14556093C2313yes—
453#14556093C2313yes—
454#14556093C2313yes—
455#14556093C2313yes—
456#14556093C2313yes—
457#14556093C2316yes—
458#14556093C2313yes—
459#14556093C2316yes—
460C4×D284C2316yes—
461C4×D284C2313yes—
462C4×D284C2313yes—
463C4×D284C2313yes—
464C4×D284C2313yes—
465C4×D284C2313yes—
466D4×Dic71C2313yes—
467D4×Dic71C2316yes—
468D4×Dic71C2313yes—
469D4×Dic71C2313yes—
470D4×Dic71C2313yes—
471D4×Dic71C2313yes—
472#14556090C2313yes—
473#14556090C2313yes—
474#14556090C2313yes—
475#14556090C2316yes—
476#14556090C2311yescharacteristic
477#14556090C2313yes—
478#14556090C2313yes—
479#14556090C2313yes—
480#14556090C2311yescharacteristic
481#14556090C2313yes—
482C4×C22⋊D71C2316yes—
483C4×C22⋊D71C2313yes—
484C4×C22⋊D71C2313yes—
485C4×C22⋊D71C2316yes—
486C4×C22⋊D71C2313yes—
487C4×C22⋊D71C2313yes—
488C4×C22⋊D71C2313yes—
489C4×C22⋊D71C2313yes—
490C4×C22⋊D71C2316yes—
491C4×C22⋊D71C2316yes—
492(C22⋊D71)⋊C4C2313yes—
493(C22⋊D71)⋊C4C2313yes—
494(C22⋊D71)⋊C4C2313yes—
495(C22⋊D71)⋊C4C2313yes—
496(C22⋊D71)⋊C4C2316yes—
497(C22⋊D71)⋊C4C2316yes—
498(C22⋊D71)⋊C4C2316yes—
499(C22⋊D71)⋊C4C2316yes—
500(C22⋊D71)⋊C4C2316yes—
501(C22⋊D71)⋊C4C2313yes—
502(C22⋊D71)⋊C4C2313yes—
503(C22⋊D71)⋊C4C2313yes—
504(C22⋊D71)⋊C4C2313yes—
505(C22⋊D71)⋊C4C2311yescharacteristic
506(C22⋊D71)⋊C4C2313yes—
507(C22⋊D71)⋊C4C2313yes—
508(C22⋊D71)⋊C4C2313yes—
509(C22⋊D71)⋊C4C2311yescharacteristic
510(C22⋊D71)⋊C4C2313yes—
511(C22⋊D71)⋊C4C2316yes—
512#14556087C2313yes—
513#14556086C2313yes—
514#14556086C2313yes—
515#14556086C2316yes—
516#14556086C2313yes—
517#14556086C2313yes—
518#14556086C2313yes—
519#14556086C2313yes—
520#14556086C2313yes—
521#14556086C2313yes—
522#14556086C2316yes—
523#14556086C2313yes—
524#14556086C2313yes—
525#14556085C2313yes—
526#14556085C2313yes—
527#14556085C2313yes—
528#14556085C2313yes—
529#14556085C2316yes—
530#14556085C2316yes—
531#14556085C2316yes—
532#14556084C2316yes—
533#14556084C2313yes—
534#14556084C2316yes—
535#14556084C2313yes—
536#14556084C2311yescharacteristic
537#14556084C2313yes—
538#14556084C2313yes—
539#14556084C2313yes—
540#14556084C2316yes—
541C2×C4⋊Dic71C2313yes—
542C2×C4⋊Dic71C2313yes—
543C2×Dic71⋊C4C2316yes—
544C2×Dic71⋊C4C2316yes—
545C4⋊C4×D71C2313yes—
546C4⋊C4×D71C2316yes—
547C4⋊C4×D71C2316yes—
548C4⋊C4×D71C2313yes—
549C4⋊C4×D71C2313yes—
550C4⋊C4×D71C2316yes—
551C4⋊C4×D71C2313yes—
552C4⋊C4×D71C2313yes—
553C4⋊C4×D71C2313yes—
554C2×C4×Dic71C2313yes—
555C2×C4×Dic71C2313yes—
556C2×C4×Dic71C2313yes—
557C2×C4×Dic71C2316yes—
558C2×C4×Dic71C2313yes—
559C2×C4×Dic71C2313yes—
560C42×D71C2313yes—
561C42×D71C2313yes—
562C42×D71C2313yes—
563C42×D71C2313yes—
564C42×D71C2313yes—
565C42×D71C2313yes—
566C42×D71C2313yes—
567C42×D71C2313yes—
568C42×D71C2313yes—
569C42×D71C2316yes—
570C42×D71C2313yes—
571C2×#41×C71C2311yescharacteristic
572C22×Q8×C71C2311yescharacteristic
573C22×Q8×C71C2311yescharacteristic
574C4⋊Q8×C71C2313yes—
575C4⋊Q8×C71C2313yes—
576#126×C71C2316yes—
577#126×C71C2316yes—
578#126×C71C2313yes—
579#126×C71C2313yes—
580#125×C71C2316yes—
581#125×C71C2313yes—
582#125×C71C2313yes—
583#125×C71C2313yes—
584#124×C71C2313yes—
585#124×C71C2313yes—
586#124×C71C2313yes—
587#123×C71C2316yes—
588#123×C71C2311yescharacteristic
589#123×C71C2313yes—
590C22⋊Q8×C71C2313yes—
591C22⋊Q8×C71C2313yes—
592C22⋊Q8×C71C2313yes—
593C22⋊Q8×C71C2316yes—
594C22⋊Q8×C71C2313yes—
595C22⋊Q8×C71C2313yes—
596#121×C71C2313yes—
597#121×C71C2313yes—
598#121×C71C2313yes—
599C4×Q8×C71C2313yes—
600C4×Q8×C71C2313yes—
601C4×Q8×C71C2311yescharacteristic
602C4×Q8×C71C2311yescharacteristic
603C4×Q8×C71C2311yescharacteristic
604C4×Q8×C71C2311yescharacteristic
605C4×Q8×C71C2313yes—
606C4×Q8×C71C2313yes—
607C4×Q8×C71C2313yes—
608C4×D4×C71C2313yes—
609C4×D4×C71C2313yes—
610C4×D4×C71C2313yes—
611C4×D4×C71C2313yes—
612C4×D4×C71C2313yes—
613C4×D4×C71C2316yes—
614#117×C71C2313yes—
615#117×C71C2313yes—
616#117×C71C2313yes—
617#117×C71C2316yes—
618C2×C4⋊C4×C71C2313yes—
619C2×C4⋊C4×C71C2313yes—
620C2×C42×C71C2313yes—
621C23×D71C2411yescharacteristic
622#11765866—24no—
623#11765866—212no—
624#11765866—46no—
625#11765865—212no—
626#11765865—212no—
627#11765865—212no—
628#11765865—412no—
629#11765864—24no—
630#11765864—212no—
631#11765864—212no—
632#11765864—212no—
633#11765864—46no—
634C2×Dic142—212no—
635C2×Dic142—212no—
636C2×Dic142C2416yes—
637C2×Dic142C2413yes—
638C2×Dic142C2413yes—
639C2×Dic142C2413yes—
640C2×Dic142C2413yes—
641C2×Dic142C2411yescharacteristic
642C2×Dic142C2413yes—
643C2×Dic142C2413yes—
644C2×Dic142C2416yes—
645C2×Dic142C2413yes—
646Q8×D71—24no—
647Q8×D71—24no—
648Q8×D71—212no—
649Q8×D71—212no—
650Q8×D71—212no—
651Q8×D71#4118yescomplemented
652C2×D284C2411yescharacteristic
653C2×D284C2413yes—
654C2×D284C2413yes—
655C2×D284C2413yes—
656C2×D284C2411yescharacteristic
657C2×D284C2413yes—
658C2×C22⋊D71C2411yescharacteristic
659C2×C22⋊D71C2413yes—
660C2×C22⋊D71C2413yes—
661C2×C22⋊D71C2413yes—
662C2×C22⋊D71C2413yes—
663C2×C22⋊D71C2411yescharacteristic
664C2×C22⋊D71C2413yes—
665C2×C22⋊D71C2411yescharacteristic
666C2×C22⋊D71C2411yescharacteristic
667C2×C22⋊D71C2413yes—
668C2×C22⋊D71C2416yes—
669C22×Dic71C2413yes—
670C22×Dic71C2416yes—
671C22×Dic71C2413yes—
672C22×Dic71C2411yescharacteristic
673C22×Dic71C2413yes—
674C22×Dic71C2413yes—
675C22×Dic71C2413yes—
676C22×Dic71C2411yescharacteristic
677C2×C4×D71—24no—
678C2×C4×D71—212no—
679C2×C4×D71—46no—
680C2×C4×D71C2413yes—
681C2×C4×D71C2413yes—
682C2×C4×D71C2413yes—
683C2×C4×D71C2413yes—
684C2×C4×D71C2413yes—
685C2×C4×D71C2411yescharacteristic
686C2×C4×D71C2411yescharacteristic
687C2×C4×D71C2411yescharacteristic
688C2×C4×D71C2411yescharacteristic
689C2×C4×D71C2413yes—
690C2×C4×D71C2416yes—
691C2×C4×D71C2413yes—
692C2×C4×D71C2411yescharacteristic
693C2×C4×D71C2413yes—
694C2×C4×D71C2413yes—
695C2×C4×D71C2413yes—
696C2×C4×D71C2416yes—
697C2×C4×D71C2413yes—
698C2×C4×D71C2413yes—
699C2×C4×D71C2413yes—
700C4⋊Dic71C2413yes—
701C4⋊Dic71C2413yes—
702C4⋊Dic71C2416yes—
703C4⋊Dic71C2413yes—
704C4⋊Dic71C2416yes—
705C4⋊Dic71C2413yes—
706C4⋊Dic71C2413yes—
707C4⋊Dic71C2416yes—
708C4⋊Dic71C2413yes—
709C4⋊Dic71C2413yes—
710C4⋊Dic71C2413yes—
711C4⋊Dic71C2413yes—
712C4⋊Dic71C2413yes—
713Dic71⋊C4C2416yes—
714Dic71⋊C4C2416yes—
715Dic71⋊C4C2416yes—
716Dic71⋊C4C2416yes—
717Dic71⋊C4C2413yes—
718Dic71⋊C4C2413yes—
719Dic71⋊C4C2416yes—
720Dic71⋊C4C2413yes—
721Dic71⋊C4C2413yes—
722Dic71⋊C4C2411yescharacteristic
723Dic71⋊C4C2413yes—
724Dic71⋊C4C2413yes—
725Dic71⋊C4C2413yes—
726Dic71⋊C4C2411yescharacteristic
727Dic71⋊C4C2413yes—
728Dic71⋊C4C2413yes—
729Dic71⋊C4C2416yes—
730Dic71⋊C4C2413yes—
731Dic71⋊C4C2413yes—
732Dic71⋊C4C2411yescharacteristic
733Dic71⋊C4C2413yes—
734Dic71⋊C4C2413yes—
735Dic71⋊C4C2413yes—
736Dic71⋊C4C2413yes—
737Dic71⋊C4C2416yes—
738Dic71⋊C4C2413yes—
739Dic71⋊C4C2411yescharacteristic
740Dic71⋊C4C2416yes—
741Dic71⋊C4C2416yes—
742Dic71⋊C4C2416yes—
743C22⋊Dic71C2416yes—
744C22⋊Dic71C2411yescharacteristic
745C22⋊Dic71C2413yes—
746C22⋊Dic71C2413yes—
747C22⋊Dic71C2413yes—
748C22⋊Dic71C2416yes—
749C22⋊Dic71C2413yes—
750C22⋊Dic71C2413yes—
751(C2×D71)⋊C4C2411yescharacteristic
752(C2×D71)⋊C4C2411yescharacteristic
753(C2×D71)⋊C4C2411yescharacteristic
754(C2×D71)⋊C4C2413yes—
755(C2×D71)⋊C4C2413yes—
756(C2×D71)⋊C4C2413yes—
757(C2×D71)⋊C4C2413yes—
758(C2×D71)⋊C4C2413yes—
759(C2×D71)⋊C4C2413yes—
760(C2×D71)⋊C4C2413yes—
761(C2×D71)⋊C4C2416yes—
762(C2×D71)⋊C4C2413yes—
763(C2×D71)⋊C4C2416yes—
764(C2×D71)⋊C4C2411yescharacteristic
765(C2×D71)⋊C4C2411yescharacteristic
766(C2×D71)⋊C4C2411yescharacteristic
767(C2×D71)⋊C4C2416yes—
768(C2×D71)⋊C4C2413yes—
769(C2×D71)⋊C4C2413yes—
770(C2×D71)⋊C4C2413yes—
771(C2×D71)⋊C4C2413yes—
772(C2×D71)⋊C4C2416yes—
773(C2×D71)⋊C4C2413yes—
774(C2×D71)⋊C4C2413yes—
775C4×Dic71C2413yes—
776C4×Dic71C2413yes—
777C4×Dic71C2411yescharacteristic
778C4×Dic71C2413yes—
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×Dic71C2413yes—
792C4×Dic71C2416yes—
793C4×Dic71C2411yescharacteristic
794C4×Dic71C2413yes—
795C4×Dic71C2416yes—
796C4×Dic71C2413yes—
797C4×Dic71C2416yes—
798C4×Dic71C2413yes—
799C4×Dic71C2413yes—
800#41×C71—24no—
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×C71C2411yescharacteristic
809C2×D4×C71C2413yes—
810C2×D4×C71C2413yes—
811C22×C4×C71C2413yes—
812C22×C4×C71C2411yescharacteristic
813C22×C4×C71C2413yes—
814C22×C4×C71C2413yes—
815C22×C4×C71C2413yes—
816C22×C4×C71C2416yes—
817C4⋊C4×C71C2413yes—
818C4⋊C4×C71C2413yes—
819C4⋊C4×C71C2413yes—
820C4⋊C4×C71C2413yes—
821C4⋊C4×C71C2416yes—
822C4⋊C4×C71C2411yescharacteristic
823C4⋊C4×C71C2413yes—
824C4⋊C4×C71C2413yes—
825C4⋊C4×C71C2413yes—
826C4⋊C4×C71C2413yes—
827C4⋊C4×C71C2416yes—
828C4⋊C4×C71C2413yes—
829C4⋊C4×C71C2413yes—
830C4⋊C4×C71C2416yes—
831C4⋊C4×C71C2413yes—
832C4⋊C4×C71C2411yescharacteristic
833C4⋊C4×C71C2413yes—
834C22⋊C4×C71C2413yes—
835C22⋊C4×C71C2411yescharacteristic
836C22⋊C4×C71C2413yes—
837C22⋊C4×C71C2413yes—
838C22⋊C4×C71C2413yes—
839C22⋊C4×C71C2416yes—
840C22⋊C4×C71C2411yescharacteristic
841C22⋊C4×C71C2413yes—
842C22⋊C4×C71C2411yescharacteristic
843C22⋊C4×C71C2416yes—
844C22⋊C4×C71C2413yes—
845C22⋊C4×C71C2413yes—
846C42×C71C2413yes—
847C42×C71C2413yes—
848C42×C71C2413yes—
849C42×C71C2413yes—
850C42×C71C2416yes—
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—22no—
872C2×C4×C71—26no—
873C2×C4×C71—26no—
874C2×C4×C71—26no—
875C2×C4×C71—43no—
876C2×C4×C71—46no—
877C2×C4×C71C2511yescharacteristic
878C2×C4×C71C2511yescharacteristic
879C2×C4×C71C2513yes—
880C2×C4×C71C2511yescharacteristic
881C2×C4×C71C2513yes—
882C2×C4×C71C2511yescharacteristic
883C2×C4×C71C2513yes—
884C2×C4×C71C2513yes—
885C2×C4×C71C2513yes—
886C2×C4×C71C2513yes—
887C2×C4×C71C2511yescharacteristic
888C2×C4×C71C2513yes—
889C22⋊D71—26no—
890C22⋊D71—22no—
891C22⋊D71—26no—
892C22⋊D71—22no—
893C22⋊D71—22no—
894C22⋊D71—26no—
895C22⋊D71—26no—
896C22⋊D71—26no—
897C22⋊D71—26no—
898C22⋊D71—22no—
899C22⋊D71—46no—
900C2×Dic71—26no—
901C2×Dic71—212no—
902C2×Dic71—26no—
903C2×Dic71—22no—
904C2×Dic71—43no—
905C2×Dic71—43no—
906C2×Dic71—43no—
907C2×Dic712−1+414yescomplemented
908C2×Dic71C2513yes—
909C2×Dic71C2511yescharacteristic
910C2×Dic71C2513yes—
911C2×Dic71C2511yescharacteristic
912C2×Dic71C2513yes—
913C2×Dic71C2513yes—
914C2×Dic71C2513yes—
915C2×Dic71C2511yescharacteristic
916C2×Dic71C2513yes—
917C2×Dic71C2513yes—
918C2×Dic71C2511yescharacteristic
919C2×Dic71C2511yescharacteristic
920D284—22no—
921D284—26no—
922D284—26no—
923D284—22no—
924D284—26no—
925D284—43no—
926C4×D71—26no—
927C4×D71—26no—
928C4×D71—26no—
929C4×D71—26no—
930C4×D71—26no—
931C4×D71—26no—
932C4×D71—26no—
933C4×D71—212no—
934C4×D71—22no—
935C4×D71—22no—
936C4×D71—22no—
937C4×D71—22no—
938C4×D71—22no—
939C4×D71—26no—
940C4×D71—43no—
941C4×D71—43no—
942C4×D71—46no—
943C4×D71—43no—
944C4×D71—43no—
945C4×D71C2×#41112yes—
946Dic142—26no—
947Dic142—26no—
948Dic142—212no—
949Dic142—26no—
950Dic142—26no—
951Dic142—22no—
952Dic142—26no—
953Dic142—43no—
954Dic142—46no—
955Dic142C2×#41112yes—
956C22×C71—21no—
957C22×C71—21no—
958C22×C71—23no—
959C22×C71—21no—
960C22×C71—23no—
961C22×C71—21no—
962C22×C71—21no—
963C22×C71—23no—
964C22×C71C2×2−1+412yes—
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×D71#58512yes—
979C4×C71—21no—
980C4×C71—23no—
981C4×C71—23no—
982C4×C71—23no—
983C4×C71—21no—
984C4×C71—21no—
985C4×C71—21no—
986C4×C71—23no—
987C4×C71—23no—
988C4×C71—23no—
989C4×C71—21no—
990C4×C71C22×#4116yes—
991Dic71—23no—
992Dic71—21no—
993Dic71—23no—
994Dic71—21no—
995Dic71—23no—
996Dic71—23no—
997Dic71—21no—
998Dic71—23no—
999Dic71—23no—
1000Dic71C22×#4116yes—
1001Dic71C2×2−1+412yes—
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—713no—
1017#3522—711no—
1018#3516—713no—
1019#3516—713no—
1020#3516—711no—
1021#3516D7111yescharacteristic, complemented
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—711no—
1031#3482—713no—
1032#3482—713no—
1033#3482—711no—
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—716no—
1073#554—716no—
1074#554—713no—
1075#554—713no—
1076#554—713no—
1077#554—716no—
1078#554—713no—
1079#554—713no—
1080#554C2×D7113yes—
1081#553—716no—
1082#553—713no—
1083#553—713no—
1084#553—716no—
1085#553—713no—
1086#553C2×D7113yes—
1087#552—716no—
1088#552—716no—
1089#552—716no—
1090#552—713no—
1091#552—713no—
1092#552—713no—
1093#552—713no—
1094#552—713no—
1095#552—713no—
1096#552—716no—
1097#552—713no—
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—713no—
1124#547—716no—
1125#547—716no—
1126#547—713no—
1127#547—713no—
1128#547—713no—
1129#544—713no—
1130#544—713no—
1131#542—716no—
1132#542—716no—
1133#542—713no—
1134#542—713no—
1135#542—713no—
1136#542C2×D7113yescomplemented
1137#541—716no—
1138#541—716no—
1139#541—713no—
1140#541—713no—
1141#541—713no—
1142#541C2×D7113yescomplemented
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—716no—
1158#533—713no—
1159#533—713no—
1160#533—713no—
1161#533—713no—
1162#533—716no—
1163#533—713no—
1164#533—713no—
1165#532—713no—
1166#532—713no—
1167#532—713no—
1168#532—713no—
1169#532—713no—
1170#532—713no—
1171#529—716no—
1172#529—713no—
1173#529—713no—
1174#529—713no—
1175#529—713no—
1176#529—716no—
1177#529—716no—
1178#529—713no—
1179#529—713no—
1180#529—713no—
1181#529—713no—
1182#529—713no—
1183#529—713no—
1184#529—716no—
1185#529—713no—
1186#529—713no—
1187#529—716no—
1188#529—713no—
1189#529—713no—
1190#529—716no—
1191#529—713no—
1192#529—713no—
1193#529—713no—
1194#529—713no—
1195#529C2×D7113yes—
1196#529C2×D7113yes—
1197#525—711no—
1198#525—713no—
1199#525—713no—
1200#525—713no—
1201#525—713no—
1202#525—713no—
1203#525—713no—
1204#525—713no—
1205#525—716no—
1206#520—713no—
1207#520—711no—
1208#520—713no—
1209#520—713no—
1210#520—713no—
1211#520—713no—
1212#520—713no—
1213#520C2×D7111yescharacteristic, complemented
1214#519—711no—
1215#519—711no—
1216#519—713no—
1217#519—711no—
1218#519—713no—
1219#519C2×D7111yescharacteristic, complemented
1220C4×#41—711no—
1221C4×#41—713no—
1222C4×#41—711no—
1223C4×#41—713no—
1224C4×#41—713no—
1225C4×#41—713no—
1226C4×#41—716no—
1227C4×#41—713no—
1228C4×#41—713no—
1229C4×#41—713no—
1230C4×#41—713no—
1231C4×#41—713no—
1232C4×#41—713no—
1233C4×#41—716no—
1234C2×C4×Q8—711no—
1235C2×C4×Q8—711no—
1236C2×C4×Q8—711no—
1237C2×C4×Q8—713no—
1238C2×C4×Q8—711no—
1239C2×C4×Q8—713no—
1240C2×C4×Q8—711no—
1241C2×C4×Q8—713no—
1242C2×C4×Q8—711no—
1243C2×C4×Q8—713no—
1244C2×C4×Q8—711no—
1245C2×C4×Q8—713no—
1246C2×C4×Q8—713no—
1247C2×C4×Q8—713no—
1248C2×C4×Q8—713no—
1249C2×C4×Q8C2×D7111yescharacteristic
1250C22×C4⋊C4—713no—
1251C22×C42—713no—
12522−1+4—1428no—
12532−1+4—1428no—
1254C2×#41—713no—
1255C2×#41—713no—
1256C2×#41—711no—
1257C2×#41—713no—
1258C2×#41—713no—
1259C2×#41—711no—
1260C2×#41—713no—
1261C2×#41—713no—
1262C2×#41—716no—
1263C2×#41—713no—
1264C2×#41—713no—
1265C2×#41—713no—
1266C2×#41C22×D7111yescharacteristic
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—713no—
1302#126—713no—
1303#126—716no—
1304#126—716no—
1305#126—716no—
1306#126—716no—
1307#126—713no—
1308#126—713no—
1309#126—716no—
1310#126—716no—
1311#126—716no—
1312#126—716no—
1313#126—716no—
1314#126—713no—
1315#126—713no—
1316#126—716no—
1317#126C22×D7116yes—
1318#126C22×D7113yes—
1319#126C22×D7113yes—
1320#126C22×D7116yes—
1321#125—716no—
1322#125—713no—
1323#125—713no—
1324#125—716no—
1325#125—713no—
1326#125—713no—
1327#125—716no—
1328#125—716no—
1329#125—713no—
1330#125—713no—
1331#125—716no—
1332#125—716no—
1333#125—716no—
1334#125—716no—
1335#125—716no—
1336#125—716no—
1337#125—713no—
1338#125—713no—
1339#125—713no—
1340#125—716no—
1341#125C22×D7113yes—
1342#125C22×D7113yes—
1343#125C22×D7113yes—
1344#125C22×D7116yes—
1345#124—713no—
1346#124—713no—
1347#124—716no—
1348#124—713no—
1349#124—713no—
1350#124—716no—
1351#124—713no—
1352#124—713no—
1353#124—716no—
1354#124—716no—
1355#124—713no—
1356#124—713no—
1357#124—713no—
1358#124C22×D7113yes—
1359#124C22×D7113yes—
1360#124C22×D7113yes—
1361#123—716no—
1362#123—713no—
1363#123—711no—
1364#123—716no—
1365#123—713no—
1366#123—713no—
1367#123—716no—
1368#123—716no—
1369#123—713no—
1370#123—713no—
1371#123—716no—
1372#123—716no—
1373#123—716no—
1374#123—713no—
1375#123—713no—
1376#123—716no—
1377#123—713no—
1378#123—713no—
1379#123—716no—
1380#123—716no—
1381#123—716no—
1382#123C22×D7111yescharacteristic
1383#123C22×D7113yes—
1384#123C22×D7116yes—
1385C22⋊Q8—713no—
1386C22⋊Q8—713no—
1387C22⋊Q8—713no—
1388C22⋊Q8—713no—
1389C22⋊Q8—713no—
1390C22⋊Q8—716no—
1391C22⋊Q8—713no—
1392C22⋊Q8—713no—
1393C22⋊Q8—713no—
1394C22⋊Q8—713no—
1395C22⋊Q8—713no—
1396C22⋊Q8—716no—
1397C22⋊Q8—711no—
1398C22⋊Q8—713no—
1399C22⋊Q8—713no—
1400C22⋊Q8—711no—
1401C22⋊Q8—716no—
1402C22⋊Q8—713no—
1403C22⋊Q8—713no—
1404C22⋊Q8—713no—
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—713no—
1417C22⋊Q8—716no—
1418C22⋊Q8—716no—
1419C22⋊Q8—716no—
1420C22⋊Q8—716no—
1421C22⋊Q8—716no—
1422C22⋊Q8—716no—
1423C22⋊Q8C22×D7113yes—
1424C22⋊Q8C22×D7113yes—
1425C22⋊Q8C22×D7113yes—
1426C22⋊Q8C22×D7113yes—
1427C22⋊Q8C22×D7113yes—
1428C22⋊Q8C22×D7116yes—
1429#121—713no—
1430#121—713no—
1431#121—713no—
1432#121—713no—
1433#121—716no—
1434#121—713no—
1435#121—716no—
1436#121—713no—
1437#121—713no—
1438#121—713no—
1439#121—713no—
1440#121—713no—
1441#121—713no—
1442#121—711no—
1443#121—713no—
1444#121—713no—
1445#121—711no—
1446#121—716no—
1447#121—713no—
1448#121—713no—
1449#121—716no—
1450#121C22×D7113yes—
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—713no—
1462C4×Q8—711no—
1463C4×Q8—713no—
1464C4×Q8—711no—
1465C4×Q8—713no—
1466C4×Q8—713no—
1467C4×Q8—716no—
1468C4×Q8—713no—
1469C4×Q8—713no—
1470C4×Q8—716no—
1471C4×Q8—713no—
1472C4×Q8—713no—
1473C4×Q8—713no—
1474C4×Q8—713no—
1475C4×Q8—713no—
1476C4×Q8—716no—
1477C4×Q8—713no—
1478C4×Q8—713no—
1479C4×Q8—713no—
1480C4×Q8—713no—
1481C4×Q8—716no—
1482C4×Q8—713no—
1483C4×Q8—713no—
1484C4×Q8—713no—
1485C4×Q8—716no—
1486C4×Q8—716no—
1487C4×Q8—713no—
1488C4×Q8—716no—
1489C4×Q8—713no—
1490C4×Q8—713no—
1491C4×Q8—713no—
1492C4×Q8—716no—
1493C4×Q8—713no—
1494C4×Q8—713no—
1495C4×Q8—716no—
1496C4×Q8—713no—
1497C4×Q8—713no—
1498C4×Q8—716no—
1499C4×Q8—713no—
1500C4×Q8—713no—
1501C4×Q8—713no—
1502C4×Q8C22×D7111yescharacteristic
1503C4×Q8C22×D7113yes—
1504C4×Q8C22×D7111yescharacteristic
1505C4×Q8C22×D7113yes—
1506C4×Q8C22×D7111yescharacteristic
1507C4×Q8C22×D7113yes—
1508C4×Q8C22×D7113yes—
1509C4×Q8C22×D7111yescharacteristic
1510C4×Q8C22×D7113yes—
1511C4×D4—713no—
1512C4×D4—713no—
1513C4×D4—716no—
1514C4×D4—713no—
1515C4×D4—713no—
1516C4×D4—713no—
1517C4×D4—716no—
1518C4×D4—716no—
1519C4×D4—713no—
1520C4×D4—713no—
1521C4×D4—713no—
1522C4×D4—713no—
1523C4×D4—716no—
1524C4×D4—713no—
1525C4×D4—713no—
1526C4×D4—716no—
1527C4×D4—711no—
1528C4×D4—713no—
1529C4×D4—713no—
1530C4×D4—711no—
1531C4×D4—713no—
1532C4×D4—713no—
1533C4×D4—713no—
1534C4×D4—713no—
1535C4×D4—716no—
1536C4×D4—713no—
1537C4×D4—711no—
1538C4×D4—713no—
1539C4×D4—713no—
1540C4×D4—711no—
1541C4×D4—713no—
1542C4×D4—713no—
1543C4×D4—713no—
1544C4×D4—713no—
1545C4×D4—713no—
1546C4×D4—713no—
1547C4×D4—716no—
1548C4×D4—716no—
1549C4×D4—716no—
1550C4×D4—713no—
1551C4×D4—713no—
1552C4×D4—716no—
1553C4×D4—716no—
1554C4×D4—716no—
1555C4×D4—713no—
1556C4×D4—713no—
1557C4×D4—716no—
1558C4×D4—713no—
1559C4×D4—713no—
1560C4×D4—713no—
1561C4×D4—713no—
1562C4×D4—713no—
1563C4×D4C22×D7113yes—
1564C4×D4C22×D7113yes—
1565C4×D4C22×D7113yes—
1566C4×D4C22×D7113yes—
1567C4×D4C22×D7116yes—
1568C4×D4C22×D7113yes—
1569#117—713no—
1570#117—713no—
1571#117—713no—
1572#117—716no—
1573#117—713no—
1574#117—713no—
1575#117—713no—
1576#117—713no—
1577#117—716no—
1578#117—713no—
1579#117—713no—
1580#117—713no—
1581#117—713no—
1582#117—711no—
1583#117—713no—
1584#117—716no—
1585#117—716no—
1586#117—713no—
1587#117—713no—
1588#117—716no—
1589#117—713no—
1590#117—713no—
1591#117—713no—
1592#117—713no—
1593#117—713no—
1594#117—713no—
1595#117—716no—
1596#117—716no—
1597#117—716no—
1598#117C22×D7113yes—
1599#117C22×D7113yes—
1600#117C22×D7113yes—
1601#117C22×D7116yes—
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—713no—
1621C2×C42—713no—
1622C2×C42—716no—
1623C2×C42—713no—
1624C2×C42—713no—
1625C2×C42—713no—
1626C2×C42—713no—
1627C2×C42—713no—
1628C2×C42—713no—
1629C2×C42—713no—
1630C2×C42—713no—
1631C2×C42—713no—
1632C2×C42—713no—
1633C2×C42—716no—
1634C2×C42C22×D7113yes—
1635C24—711no—
1636#41—24no—
1637#41—28412no—
1638#41—2846no—
1639#41—2846no—
1640#41—14212no—
1641#41—14212no—
1642#41—14212no—
1643#41—14212no—
1644#41—1424no—
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—711no—
1656C2×Q8—713no—
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—711no—
1686C2×D4—713no—
1687C2×D4—713no—
1688C2×D4—711no—
1689C2×D4—713no—
1690C2×D4C23×D7113yes—
1691C2×D4C23×D7111yescharacteristic
1692C2×D4C23×D7113yes—
1693C2×D4C23×D7113yes—
1694C22×C4—2846no—
1695C22×C4—713no—
1696C22×C4—713no—
1697C22×C4—713no—
1698C22×C4—713no—
1699C22×C4—713no—
1700C22×C4—713no—
1701C22×C4—713no—
1702C22×C4—716no—
1703C22×C4—711no—
1704C22×C4—713no—
1705C22×C4—713no—
1706C22×C4—711no—
1707C22×C4—713no—
1708C22×C4—716no—
1709C22×C4—711no—
1710C22×C4—711no—
1711C22×C4—711no—
1712C22×C4—711no—
1713C22×C4—713no—
1714C22×C4—711no—
1715C22×C4—713no—
1716C22×C4—713no—
1717C22×C4—713no—
1718C22×C4—713no—
1719C22×C4—713no—
1720C22×C4—716no—
1721C22×C4—713no—
1722C22×C4—713no—
1723C22×C4—1424no—
1724C22×C4—14212no—
1725C22×C4C23×D7111yescharacteristic
1726C22×C4C23×D7113yes—
1727C22×C4C23×D7113yes—
1728C22×C4C23×D7113yes—
1729C22×C4C23×D7113yes—
1730C22×C4C23×D7116yes—
1731C4⋊C4—716no—
1732C4⋊C4—716no—
1733C4⋊C4—716no—
1734C4⋊C4—716no—
1735C4⋊C4—713no—
1736C4⋊C4—713no—
1737C4⋊C4—716no—
1738C4⋊C4—713no—
1739C4⋊C4—713no—
1740C4⋊C4—713no—
1741C4⋊C4—713no—
1742C4⋊C4—711no—
1743C4⋊C4—713no—
1744C4⋊C4—713no—
1745C4⋊C4—711no—
1746C4⋊C4—711no—
1747C4⋊C4—713no—
1748C4⋊C4—713no—
1749C4⋊C4—711no—
1750C4⋊C4—716no—
1751C4⋊C4—716no—
1752C4⋊C4—713no—
1753C4⋊C4—713no—
1754C4⋊C4—716no—
1755C4⋊C4—716no—
1756C4⋊C4—713no—
1757C4⋊C4—713no—
1758C4⋊C4—716no—
1759C4⋊C4—713no—
1760C4⋊C4—713no—
1761C4⋊C4—713no—
1762C4⋊C4—713no—
1763C4⋊C4—716no—
1764C4⋊C4—713no—
1765C4⋊C4—716no—
1766C4⋊C4—713no—
1767C4⋊C4—713no—
1768C4⋊C4—713no—
1769C4⋊C4—713no—
1770C4⋊C4—713no—
1771C4⋊C4—716no—
1772C4⋊C4—713no—
1773C4⋊C4—713no—
1774C4⋊C4C23×D7113yes—
1775C4⋊C4C23×D7113yes—
1776C4⋊C4C23×D7116yes—
1777C4⋊C4C23×D7113yes—
1778C4⋊C4C23×D7113yes—
1779C4⋊C4C23×D7113yes—
1780C4⋊C4C23×D7111yescharacteristic
1781C4⋊C4C23×D7113yes—
1782C4⋊C4C23×D7113yes—
1783C4⋊C4C23×D7113yes—
1784C4⋊C4C23×D7113yes—
1785C4⋊C4C23×D7113yes—
1786C4⋊C4C23×D7113yes—
1787C4⋊C4C23×D7113yes—
1788C4⋊C4C23×D7116yes—
1789C4⋊C4C23×D7111yescharacteristic
1790C4⋊C4C23×D7116yes—
1791C22⋊C4—716no—
1792C22⋊C4—713no—
1793C22⋊C4—711no—
1794C22⋊C4—713no—
1795C22⋊C4—713no—
1796C22⋊C4—716no—
1797C22⋊C4—713no—
1798C22⋊C4—713no—
1799C22⋊C4—711no—
1800C22⋊C4—713no—
1801C22⋊C4—713no—
1802C22⋊C4—711no—
1803C22⋊C4—711no—
1804C22⋊C4—713no—
1805C22⋊C4—713no—
1806C22⋊C4—711no—
1807C22⋊C4—716no—
1808C22⋊C4—713no—
1809C22⋊C4—713no—
1810C22⋊C4—711no—
1811C22⋊C4—713no—
1812C22⋊C4—713no—
1813C22⋊C4—711no—
1814C22⋊C4—716no—
1815C22⋊C4—713no—
1816C22⋊C4—713no—
1817C22⋊C4—716no—
1818C22⋊C4—713no—
1819C22⋊C4—713no—
1820C22⋊C4—716no—
1821C22⋊C4—713no—
1822C22⋊C4—713no—
1823C22⋊C4C23×D7111yescharacteristic
1824C22⋊C4C23×D7113yes—
1825C22⋊C4C23×D7113yes—
1826C22⋊C4C23×D7113yes—
1827C22⋊C4C23×D7111yescharacteristic
1828C22⋊C4C23×D7113yes—
1829C22⋊C4C23×D7116yes—
1830C22⋊C4C23×D7113yes—
1831C22⋊C4C23×D7113yes—
1832C22⋊C4C23×D7111yescharacteristic
1833C22⋊C4C23×D7113yes—
1834C22⋊C4C23×D7116yes—
1835C42—713no—
1836C42—713no—
1837C42—713no—
1838C42—711no—
1839C42—713no—
1840C42—713no—
1841C42—711no—
1842C42—713no—
1843C42—713no—
1844C42—713no—
1845C42—713no—
1846C42—713no—
1847C42—713no—
1848C42—713no—
1849C42—713no—
1850C42—713no—
1851C42—713no—
1852C42—713no—
1853C42—713no—
1854C42—713no—
1855C42—716no—
1856C42—716no—
1857C42—716no—
1858C42—713no—
1859C42—713no—
1860C42C23×D7113yes—
1861C42C23×D7113yes—
1862C42C23×D7113yes—
1863C42C23×D7113yes—
1864C42C23×D7116yes—
1865C42C23×D7113yes—
1866C42C23×D7113yes—
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—2846no—
1881Q8—2843no—
1882Q8—7112no—
1883Q8—14212no—
1884Q8—1426no—
1885Q8—1426no—
1886Q8—1422no—
1887Q8—1426no—
1888Q8—1426no—
1889Q8—1426no—
1890Q8#41×D7114yes—
1891D4—26no—
1892D4—22no—
1893D4—26no—
1894D4—43no—
1895D4—2843no—
1896D4—2846no—
1897D4—1426no—
1898D4—1422no—
1899D4—1422no—
1900D4—1426no—
1901D4—1426no—
1902D4—1426no—
1903D4—1422no—
1904D4—1426no—
1905D4—1426no—
1906D4—1422no—
1907D4—1422no—
1908D4—1426no—
1909D4—1422no—
1910D4—1426no—
1911D4—1426no—
1912C2×C4—22no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—26no—
1916C2×C4—43no—
1917C2×C4—46no—
1918C2×C4—2843no—
1919C2×C4—2843no—
1920C2×C4—2846no—
1921C2×C4—2843no—
1922C2×C4—2843no—
1923C2×C4—2843no—
1924C2×C4—2843no—
1925C2×C4—2843no—
1926C2×C4—714no—
1927C2×C4—711no—
1928C2×C4—711no—
1929C2×C4—713no—
1930C2×C4—7112no—
1931C2×C4—713no—
1932C2×C4—713no—
1933C2×C4—711no—
1934C2×C4—713no—
1935C2×C4—711no—
1936C2×C4—713no—
1937C2×C4—713no—
1938C2×C4—711no—
1939C2×C4—713no—
1940C2×C4—1426no—
1941C2×C4—1422no—
1942C2×C4—1422no—
1943C2×C4—1422no—
1944C2×C4—1422no—
1945C2×C4—14212no—
1946C2×C4—1426no—
1947C2×C4—1422no—
1948C2×C4—1426no—
1949C2×C4—1426no—
1950C2×C4—1426no—
1951C2×C4—1426no—
1952C2×C4—14212no—
1953C2×C4—1426no—
1954C2×C4—1422no—
1955C2×C4—1426no—
1956C2×C4—1426no—
1957C2×C4—1426no—
1958C2×C4C24×D7111yescharacteristic
1959C2×C4C24×D7111yescharacteristic
1960C2×C4C24×D7113yes—
1961C2×C4C24×D7111yescharacteristic
1962C2×C4C24×D7111yescharacteristic
1963C2×C4C24×D7113yes—
1964C2×C4C24×D7113yes—
1965C2×C4C24×D7113yes—
1966C2×C4C24×D7113yes—
1967C2×C4C24×D7113yes—
1968C2×C4C24×D7111yescharacteristic
1969C2×C4C24×D7113yes—
1970C22—21no—
1971C22—21no—
1972C22—21no—
1973C22—23no—
1974C22—21no—
1975C22—23no—
1976C22—23no—
1977C22—21no—
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—
1991C222−1+4×D7112yes—
1992C22C25×D7111yescharacteristic
1993C4—21no—
1994C4—23no—
1995C4—23no—
1996C4—21no—
1997C4—21no—
1998C4—21no—
1999C4—23no—
2000C4—23no—
2001C4—23no—
2002C4—23no—
2003C4—21no—
2004C4—716no—
2005C4—712no—
2006C4—712no—
2007C4—1423no—
2008C4—1421no—
2009C4—1423no—
2010C4—1423no—
2011C4—1421no—
2012C4—1423no—
2013C4—1423no—
2014C4—1421no—
2015C4—1423no—
2016C4C2×#41×D7116yes—
2017C2—22no—
2018C2—41no—
2019C2—43no—
2020C2—2843no—
2021C2—2841no—
2022C2—1422no—
2023C2—1422no—
2024C2C22×#41×D7111yescharacteristic
2025C2C2×2−1+4×D7111yescharacteristic
2026C2#585×D7111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3516C2
hypercenter#3516D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3516

Complements

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

NH ≅ G/Ntype
1. #22602432C2semidirect
2. #22602430C2semidirect
3. #22602421C2semidirect
4. #22602419C2semidirect
5. #22602333C2semidirect
6. #22602329C2semidirect
7. #22602323C2semidirect
8. #22602201C2semidirect
9. #22602199C2semidirect
10. #22602147C2semidirect
11. #22602108C2semidirect
12. #22602048C2semidirect
13. #22602044C2semidirect
14. #22601990C2semidirect
15. #22601986C2semidirect
16. #22601960C2semidirect
17. #22601959C2semidirect
18. #22601956C2semidirect
19. #22601954C2semidirect
20. #22601934C2semidirect
21. #22601930C2semidirect
22. #22601919C2semidirect
23. Q8×#11765864C2semidirect
24. #22601772C2semidirect
25. #22601766C2semidirect
26. #22601634C2semidirect
27. #22601634C2semidirect
28. #22601551C2semidirect
29. #22601549C2semidirect
30. C2×C4×Q8×D71C2semidirect
31. C71×#3516C2semidirect
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
58. #17986707C22semidirect
61. #17986704C22semidirect
63. #17986703C22semidirect
70. #17986690C22semidirect
71. #17986689C22semidirect
74. #17986687C22semidirect
76. #17986685C22semidirect
78. #17986682C22semidirect
80. #17986668C22semidirect
81. #17986667C22semidirect
87. Q8×C22⋊D71C22semidirect
90. #17986662C22semidirect
92. #17986661C22semidirect
96. #17986658C22semidirect
98. #17986657C22semidirect
109. #17986621C22semidirect
110. #17986620C22semidirect
111. #17986615C22semidirect
112. #17986614C22semidirect
113. #17986613C22semidirect
114. #17986611C22semidirect
115. #17986608C22semidirect
116. #17986607C22semidirect
117. #17986607C22semidirect
118. #17986606C22semidirect
131. #17986555C22semidirect
132. #17986554C22semidirect
133. #17986554C22semidirect
138. #17986551C22semidirect
139. #17986551C22semidirect
140. #17986551C22semidirect
147. #17986535C22semidirect
150. #17986534C22semidirect
159. #17986532C22semidirect
160. #17986530C22semidirect
163. #17986528C22semidirect
170. #17986526C22semidirect
181. #17986481C22semidirect
184. #17986479C22semidirect
186. #17986478C22semidirect
187. #17986476C22semidirect
190. #17986475C22semidirect
191. #17986475C22semidirect
192. #41×Dic71C22semidirect
195. C4×#11765866C22semidirect
199. #17986467C22semidirect
205. C4×#11765864C22semidirect
207. C2×Q8×Dic71C22semidirect
210. C2×#14556093C22semidirect
219. C4×Q8×D71C22semidirect
220. C4×Q8×D71C22semidirect
223. #557×C71C22semidirect
224. #556×C71C22semidirect
227. #552×C71C22semidirect
230. #548×C71C22semidirect
231. #542×C71C22semidirect
232. #541×C71C22semidirect
235. #520×C71C22semidirect
236. #519×C71C22semidirect
651. Q8×D71#41semidirect
907. C2×Dic712−1+4semidirect
1021. #3516D71semidirect
1045. C71#62788semidirect
1062. #557C2×D71semidirect
1071. #556C2×D71semidirect
1098. #552C2×D71semidirect
1122. #548C2×D71semidirect
1136. #542C2×D71semidirect
1142. #541C2×D71semidirect
1213. #520C2×D71semidirect
1219. #519C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226024322
#226024302
#226024212
#226024192
#226023332
#226023292
#226023232
#226022012
#226021992
#226021472
#226021082
#226020482
#226020442
#226019902
#226019862
#226019602
#226019592
#226019562
#226019542
#226019342
#226019302
#226019192
Q8×#117658642
#226017722
#226017662
#226016342
#226015512
#226015492
C2×C4×Q8×D712
C71×#35162
#6278871