Finite Group Databasebeta

← #32905687

Subgroups — #32905687

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602432C214yesmaximal, complemented
2#22602421C214yesmaximal, complemented
3#22602331C214yesmaximal, complemented
4#22602327C214yesmaximal, complemented
5#22602204C212yesmaximal, complemented
6#22602200C214yesmaximal, complemented
7#22602148C211yesmaximal, characteristic, complemented
8#22602109C211yesmaximal, characteristic, complemented
9#22602050C211yesmaximal, characteristic, complemented
10#22602047C211yesmaximal, characteristic, complemented
11#22602045C214yesmaximal, complemented
12#22601989C212yesmaximal, complemented
13#22601958C214yesmaximal, complemented
14#22601953C214yesmaximal, complemented
15#22601931C214yesmaximal, complemented
16#22601918C214yesmaximal, complemented
17#22601773C211yesmaximal, characteristic, complemented
18#22601769C214yesmaximal, complemented
19#22601634C214yesmaximal, complemented
20#22601633C212yesmaximal, complemented
21C4×#14556175C212yesmaximal, complemented
22C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
23C71×#3461C211yesmaximal, characteristic, complemented
24C2×#14556175C2212yes—
25C22×Q8×D71C2211yescharacteristic
26#17986733C2218yescomplemented
27#17986731C2214yescomplemented
28#17986729C2214yescomplemented
29#17986726C2214yescomplemented
30#17986726C2214yescomplemented
31#17986726C2218yescomplemented
32#17986724C2214yescomplemented
33#17986724C2214yescomplemented
34#17986723C2214yescomplemented
35#17986720C2218yescomplemented
36#17986720C2214yescomplemented
37#17986718C2214yescomplemented
38#17986716C2218yescomplemented
39#17986716C2218yescomplemented
40#17986710C2214yes—
41#17986707C2214yes—
42#17986707C2214yescomplemented
43#17986705C2218yes—
44#17986703C2218yes—
45#17986703C2218yescomplemented
46#17986702C2214yes—
47#17986700C2218yes—
48#17986696C2214yes—
49#17986694C2218yes—
50#17986691C2214yescomplemented
51#17986687C2214yes—
52#17986686C2218yescomplemented
53#17986685C2218yes—
54#17986683C2214yes—
55#17986683C2214yescomplemented
56#17986681C2218yes—
57#17986681C2218yescomplemented
58#17986667C2214yescomplemented
59#17986664C2214yes—
60#17986664C2214yes—
61#17986662C2214yes—
62#17986662C2214yes—
63#17986662C2214yescomplemented
64#17986659C2214yes—
65#17986659C2214yes—
66#17986659C2214yescomplemented
67#17986657C2214yes—
68#17986657C2214yes—
69#17986655C2214yescomplemented
70#17986652C2214yes—
71#17986651C2218yes—
72#17986649C2214yes—
73#17986647C2218yes—
74#17986630C2211yescharacteristic
75#17986628C2214yes—
76#17986621C2214yescomplemented
77#17986615C2218yescomplemented
78#17986613C2218yescomplemented
79#17986608C2218yescomplemented
80#17986607C2214yescomplemented
81#17986606C2218yescomplemented
82#17986598C2214yes—
83#17986596C2214yes—
84#17986594C2214yes—
85#17986593C2218yes—
86#17986580C2211yescharacteristic
87#17986576C2214yes—
88#17986573C2212yes—
89#17986571C2218yes—
90#17986555C2214yes—
91#17986553C2212yes—
92#17986553C2212yes—
93#17986553C2214yes—
94#17986553C2218yescomplemented
95#17986553C2214yescomplemented
96#17986552C2212yes—
97#17986552C2218yescomplemented
98#17986551C2214yes—
99#17986548C2214yes—
100#17986546C2212yes—
101#17986546C2212yes—
102#17986546C2214yes—
103#17986545C2212yes—
104#17986544C2214yes—
105#17986536C2212yes—
106#17986536C2212yes—
107#17986536C2214yescomplemented
108#17986534C2214yes—
109#17986533C2214yes—
110#17986532C2218yes—
111#17986532C2218yes—
112#17986531C2212yes—
113#17986531C2212yes—
114#17986529C2214yes—
115#17986529C2214yes—
116#17986529C2218yescomplemented
117#17986528C2214yes—
118#17986527C2214yes—
119#17986527C2214yes—
120#17986527C2218yes—
121#17986527C2218yescomplemented
122#17986526C2218yes—
123#17986512C2214yes—
124#17986511C2212yes—
125#17986509C2214yes—
126#17986508C2214yes—
127#17986508C2214yes—
128#17986507C2218yes—
129#17986506C2212yes—
130#17986482C2212yes—
131#17986479C2212yes—
132#17986479C2214yescomplemented
133#17986478C2218yes—
134#17986478C2214yescomplemented
135#17986476C2212yes—
136#17986476C2214yescomplemented
137#17986475C2214yescomplemented
138C4×#11765866C2214yes—
139C4×#11765865C2212yes—
140C4×#11765865C2214yes—
141C4×#11765865C2214yes—
142C4×#11765865C2214yescomplemented
143#17986467C2218yes—
144C4×#11765864C2218yes—
145C4×#11765864C2214yes—
146C4×#11765864C2214yescomplemented
147C2×Q8×Dic71C2211yescharacteristic
148C2×C4×Dic142C2212yes—
149C2×C4×Dic142C2211yescharacteristic
150C2×C4×Dic142C2214yescomplemented
151C2×#14556093C2211yescharacteristic
152C2×#14556093C2212yes—
153C4×Q8×D71C2214yes—
154C4×Q8×D71C2214yes—
155C4×Q8×D71C2214yes—
156C4×Q8×D71C2214yes—
157C4×Q8×D71C2214yescomplemented
158C2×C4⋊C4×D71C2212yes—
159C2×C4⋊C4×D71C2211yescharacteristic
160C2×C42×D71C2211yescharacteristic
161C2×C42×D71C2212yes—
162#544×C71C2211yescharacteristic
163#542×C71C2214yescomplemented
164#541×C71C2214yescomplemented
165#539×C71C2214yes—
166#537×C71C2211yescharacteristic
167#536×C71C2212yes—
168#533×C71C2214yescomplemented
169#529×C71C2214yes—
170#529×C71C2214yescomplemented
171C4×#41×C71C2212yes—
172C2×C4×Q8×C71C2211yescharacteristic
173#14556175—216no—
174C2×#11765866C2314yes—
175C2×#11765865C2312yes—
176C2×#11765865C2314yes—
177C2×#11765865C2314yes—
178C2×#11765865C2314yes—
179C2×#11765864C2318yes—
180C2×#11765864C2314yes—
181C2×#11765864C2314yes—
182C22×Dic142C2312yes—
183C22×Dic142C2314yes—
184C22×Dic142C2311yescharacteristic
185C2×Q8×D71—28no—
186C2×Q8×D71C2314yes—
187C2×Q8×D71C2314yes—
188C2×Q8×D71C2314yes—
189C22×C4×D71C2311yescharacteristic
190C22×C4×D71C2312yes—
191C22×C4×D71C2311yescharacteristic
192C22×C4×D71C2311yescharacteristic
193C22×C4×D71C2312yes—
194#14556127C2318yes—
195#14556127C2318yes—
196#14556127C2318yes—
197#14556127C2314yes—
198#14556127C2314yes—
199#14556127C2312yes—
200#14556127C2314yes—
201#14556127C2312yes—
202#14556126C2314yes—
203#14556126C2318yes—
204#14556126C2312yes—
205#14556126C2314yes—
206#14556124C2312yes—
207#14556124C2314yes—
208#14556123C2318yes—
209#14556123C2318yes—
210#14556123C2318yes—
211#14556123C2314yes—
212#14556123C2314yes—
213#14556123C2318yes—
214#14556122C2318yes—
215#14556121C2318yes—
216#14556121C2318yes—
217#14556121C2314yes—
218#14556121C2318yes—
219#14556121C2314yes—
220#14556120C2314yes—
221#14556119C2318yes—
222#14556119C2318yes—
223#14556119C2314yes—
224#14556119C2312yes—
225#14556119C2312yes—
226#14556118C2318yes—
227#14556118C2318yes—
228#14556118C2318yes—
229#14556118C2314yes—
230#14556118C2318yes—
231#14556118C2318yes—
232#14556118C2318yes—
233#14556118C2314yes—
234#14556118C2318yes—
235#14556117C2314yes—
236#14556117C2312yes—
237#14556116C2314yes—
238#14556115C2312yes—
239#14556114C2318yes—
240#14556114C2318yes—
241#14556114C2314yes—
242#14556114C2318yes—
243#14556114C2314yes—
244#14556114C2318yes—
245#14556113C2318yes—
246#14556113C2318yes—
247#14556113C2318yes—
248#14556113C2314yes—
249#14556113C2314yes—
250#14556112C2314yes—
251#14556112C2318yes—
252#14556111C2318yes—
253#14556110C2318yes—
254#14556110C2314yes—
255#14556110C2318yes—
256#14556110C2314yes—
257#14556109C2314yes—
258#14556109C2318yes—
259#14556108C2314yes—
260#14556108C2318yes—
261#14556108C2312yes—
262#14556108C2312yes—
263#14556108C2314yes—
264#14556107C2314yes—
265#14556106C2318yes—
266#14556106C2318yes—
267#14556106C2318yes—
268#14556106C2318yes—
269#14556106C2318yes—
270#14556106C2318yes—
271#14556106C2314yes—
272#14556106C2314yes—
273#14556105C2318yes—
274#14556105C2318yes—
275#14556105C2318yes—
276#14556105C2314yes—
277#14556105C2318yes—
278#14556105C2318yes—
279#14556105C2314yes—
280#14556104C2314yes—
281#14556104C2314yes—
282#14556104C2318yes—
283#14556104C2312yes—
284#14556104C2312yes—
285#14556104C2314yes—
286#14556103C2314yes—
287#14556103C2312yes—
288#14556103C2312yes—
289#14556103C2314yes—
290#14556102C2314yes—
291#14556101C2318yes—
292#14556101C2318yes—
293#14556101C2318yes—
294#14556101C2314yes—
295#14556101C2314yes—
296#14556100C2314yes—
297#14556100C2318yes—
298#14556100C2314yes—
299#14556099C2312yes—
300#14556099C2312yes—
301#14556099C2314yes—
302#14556098C2314yes—
303#14556096C2314yes—
304Q8×Dic71C2314yes—
305Q8×Dic71C2314yes—
306Q8×Dic71C2314yes—
307Q8×Dic71C2314yes—
308C4×Dic142C2318yes—
309C4×Dic142C2312yes—
310C4×Dic142C2314yes—
311C4×Dic142C2314yes—
312C4×Dic142C2318yes—
313C4×Dic142C2314yes—
314C4×Dic142C2314yes—
315C4×Dic142C2314yes—
316C4×Dic142C2314yes—
317C4×Dic142C2318yes—
318C4×Dic142C2318yes—
319C4×Dic142C2314yes—
320C4×Dic142C2312yes—
321C4×Dic142C2314yes—
322C4×Dic142C2314yes—
323C4×Dic142C2314yes—
324#14556093C2318yes—
325#14556093C2314yes—
326#14556093C2314yes—
327#14556093C2314yes—
328#14556093C2314yes—
329#14556093C2318yes—
330#14556093C2318yes—
331#14556093C2318yes—
332#14556093C2314yes—
333#14556093C2318yes—
334#14556093C2318yes—
335C4×D284C2312yes—
336C4×D284C2314yes—
337C4×D284C2314yes—
338C4×D284C2314yes—
339C4×D284C2314yes—
340C4×D284C2312yes—
341C4×D284C2314yes—
342C4×D284C2314yes—
343D4×Dic71C2318yes—
344D4×Dic71C2314yes—
345D4×Dic71C2314yes—
346#14556090C2318yes—
347#14556090C2318yes—
348#14556090C2314yes—
349#14556090C2318yes—
350C4×C22⋊D71C2314yes—
351C4×C22⋊D71C2314yes—
352C4×C22⋊D71C2318yes—
353C4×C22⋊D71C2314yes—
354C4×C22⋊D71C2314yes—
355C4×C22⋊D71C2314yes—
356C4×C22⋊D71C2314yes—
357C4×C22⋊D71C2314yes—
358C4×C22⋊D71C2314yes—
359C4×C22⋊D71C2314yes—
360C4×C22⋊D71C2318yes—
361C4×C22⋊D71C2314yes—
362(C22⋊D71)⋊C4C2318yes—
363(C22⋊D71)⋊C4C2318yes—
364(C22⋊D71)⋊C4C2318yes—
365(C22⋊D71)⋊C4C2318yes—
366(C22⋊D71)⋊C4C2318yes—
367(C22⋊D71)⋊C4C2318yes—
368(C22⋊D71)⋊C4C2318yes—
369(C22⋊D71)⋊C4C2318yes—
370#14556087C2312yes—
371#14556087C2314yes—
372#14556087C2314yes—
373#14556087C2314yes—
374#14556086C2318yes—
375#14556086C2314yes—
376#14556086C2318yes—
377#14556086C2314yes—
378#14556086C2314yes—
379#14556085C2314yes—
380#14556085C2314yes—
381#14556085C2318yes—
382#14556085C2314yes—
383#14556085C2314yes—
384#14556085C2318yes—
385#14556085C2314yes—
386#14556084C2318yes—
387#14556084C2318yes—
388#14556084C2318yes—
389#14556084C2318yes—
390C2×C4⋊Dic71C2312yes—
391C2×C4⋊Dic71C2314yes—
392C2×C4⋊Dic71C2311yescharacteristic
393C2×Dic71⋊C4C2312yes—
394C2×Dic71⋊C4C2312yes—
395C2×Dic71⋊C4C2318yes—
396C2×Dic71⋊C4C2312yes—
397C4⋊C4×D71C2318yes—
398C4⋊C4×D71C2314yes—
399C4⋊C4×D71C2318yes—
400C4⋊C4×D71C2314yes—
401C4⋊C4×D71C2318yes—
402C4⋊C4×D71C2314yes—
403C2×C4×Dic71C2311yescharacteristic
404C2×C4×Dic71C2312yes—
405C2×C4×Dic71C2312yes—
406C2×C4×Dic71C2311yescharacteristic
407C2×C4×Dic71C2312yes—
408C2×C4×Dic71C2311yescharacteristic
409C2×C4×Dic71C2318yes—
410C42×D71C2314yes—
411C42×D71C2314yes—
412C42×D71C2312yes—
413C42×D71C2312yes—
414C42×D71C2312yes—
415C42×D71C2312yes—
416C42×D71C2314yes—
417C42×D71C2314yes—
418C42×D71C2318yes—
419C42×D71C2314yes—
420C2×#41×C71C2312yes—
421C22×Q8×C71C2311yescharacteristic
422C4⋊Q8×C71C2314yes—
423C4⋊Q8×C71C2314yes—
424#126×C71C2318yes—
425#126×C71C2318yes—
426#125×C71C2314yes—
427#125×C71C2318yes—
428#125×C71C2314yes—
429#124×C71C2314yes—
430#124×C71C2314yes—
431#123×C71C2318yes—
432#123×C71C2318yes—
433C22⋊Q8×C71C2314yes—
434C22⋊Q8×C71C2318yes—
435C22⋊Q8×C71C2314yes—
436C22⋊Q8×C71C2314yes—
437C22⋊Q8×C71C2314yes—
438#121×C71C2314yes—
439#121×C71C2314yes—
440C4×Q8×C71C2314yes—
441C4×Q8×C71C2314yes—
442C4×Q8×C71C2312yes—
443C4×Q8×C71C2312yes—
444C4×Q8×C71C2314yes—
445C4×D4×C71C2314yes—
446C4×D4×C71C2312yes—
447C4×D4×C71C2314yes—
448C4×D4×C71C2312yes—
449C4×D4×C71C2314yes—
450#117×C71C2312yes—
451#117×C71C2314yes—
452#117×C71C2318yes—
453C2×C4⋊C4×C71C2311yescharacteristic
454C2×C4⋊C4×C71C2312yes—
455C2×C42×C71C2311yescharacteristic
456C2×C42×C71C2312yes—
457C2×C42×C71C2314yes—
458C23×D71C2411yescharacteristic
459#11765866—48no—
460#11765865—28no—
461#11765865—216no—
462#11765865—216no—
463#11765865—48no—
464#11765864—232no—
465#11765864—216no—
466#11765864—48no—
467C2×Dic142—28no—
468C2×Dic142—216no—
469C2×Dic142#4118yescomplemented
470C2×Dic142C2418yes—
471C2×Dic142C2418yes—
472C2×Dic142C2412yes—
473C2×Dic142C2414yes—
474C2×Dic142C2414yes—
475C2×Dic142C2414yes—
476C2×Dic142C2414yes—
477Q8×D71—216no—
478Q8×D71—216no—
479Q8×D71—216no—
480C2×D284C2412yes—
481C2×D284C2414yes—
482C2×D284C2414yes—
483C2×D284C2414yes—
484C2×C22⋊D71C2414yes—
485C2×C22⋊D71C2414yes—
486C2×C22⋊D71C2418yes—
487C2×C22⋊D71C2414yes—
488C2×C22⋊D71C2414yes—
489C2×C22⋊D71C2414yes—
490C22×Dic71C2411yescharacteristic
491C22×Dic71C2411yescharacteristic
492C22×Dic71C2418yes—
493C22×Dic71C2412yes—
494C22×Dic71C2411yescharacteristic
495C22×Dic71C2418yes—
496C22×Dic71C2412yes—
497C2×C4×D71—24no—
498C2×C4×D71—28no—
499C2×C4×D71—24no—
500C2×C4×D71—44no—
501C2×C4×D71—42no—
502C2×C4×D71C2414yes—
503C2×C4×D71C2414yes—
504C2×C4×D71C2412yes—
505C2×C4×D71C2412yes—
506C2×C4×D71C2414yes—
507C2×C4×D71C2412yes—
508C2×C4×D71C2411yescharacteristic
509C2×C4×D71C2411yescharacteristic
510C2×C4×D71C2411yescharacteristic
511C2×C4×D71C2418yes—
512C2×C4×D71C2414yes—
513C2×C4×D71C2414yes—
514C2×C4×D71C2414yes—
515C2×C4×D71C2412yes—
516C2×C4×D71C2414yes—
517C2×C4×D71C2418yes—
518C2×C4×D71C2411yescharacteristic
519C4⋊Dic71C2414yes—
520C4⋊Dic71C2418yes—
521C4⋊Dic71C2418yes—
522C4⋊Dic71C2412yes—
523C4⋊Dic71C2414yes—
524C4⋊Dic71C2414yes—
525C4⋊Dic71C2414yes—
526C4⋊Dic71C2412yes—
527C4⋊Dic71C2414yes—
528C4⋊Dic71C2414yes—
529C4⋊Dic71C2414yes—
530Dic71⋊C4C2418yes—
531Dic71⋊C4C2418yes—
532Dic71⋊C4C2418yes—
533Dic71⋊C4C2418yes—
534Dic71⋊C4C2418yes—
535Dic71⋊C4C2414yes—
536Dic71⋊C4C2418yes—
537Dic71⋊C4C2414yes—
538Dic71⋊C4C2414yes—
539Dic71⋊C4C2418yes—
540Dic71⋊C4C2414yes—
541Dic71⋊C4C2414yes—
542Dic71⋊C4C2418yes—
543Dic71⋊C4C2418yes—
544Dic71⋊C4C2414yes—
545Dic71⋊C4C2414yes—
546Dic71⋊C4C2414yes—
547Dic71⋊C4C2414yes—
548Dic71⋊C4C2414yes—
549C22⋊Dic71C2414yes—
550C22⋊Dic71C2418yes—
551C22⋊Dic71C2414yes—
552C22⋊Dic71C2414yes—
553C22⋊Dic71C2414yes—
554C22⋊Dic71C2414yes—
555(C2×D71)⋊C4C2414yes—
556(C2×D71)⋊C4C2414yes—
557(C2×D71)⋊C4C2414yes—
558(C2×D71)⋊C4C2418yes—
559(C2×D71)⋊C4C2414yes—
560(C2×D71)⋊C4C2414yes—
561(C2×D71)⋊C4C2414yes—
562(C2×D71)⋊C4C2414yes—
563(C2×D71)⋊C4C2418yes—
564(C2×D71)⋊C4C2418yes—
565(C2×D71)⋊C4C2414yes—
566(C2×D71)⋊C4C2414yes—
567(C2×D71)⋊C4C2414yes—
568(C2×D71)⋊C4C2418yes—
569C4×Dic71C2414yes—
570C4×Dic71C2414yes—
571C4×Dic71C2414yes—
572C4×Dic71C2412yes—
573C4×Dic71C2412yes—
574C4×Dic71C2414yes—
575C4×Dic71C2414yes—
576C4×Dic71C2412yes—
577C4×Dic71C2412yes—
578C4×Dic71C2412yes—
579C4×Dic71C2414yes—
580C4×Dic71C2412yes—
581C4×Dic71C2414yes—
582C4×Dic71C2414yes—
583C4×Dic71C2418yes—
584C4×Dic71C2418yes—
585C4×Dic71C2414yes—
586C4×Dic71C2418yes—
587C4×Dic71C2418yes—
588#41×C71—28no—
589C2×Q8×C71—24no—
590C2×Q8×C71C2414yes—
591C2×Q8×C71C2412yes—
592C2×Q8×C71C2414yes—
593C2×D4×C71C2414yes—
594C2×D4×C71C2412yes—
595C2×D4×C71C2414yes—
596C22×C4×C71C2412yes—
597C22×C4×C71C2411yescharacteristic
598C22×C4×C71C2414yes—
599C22×C4×C71C2414yes—
600C22×C4×C71C2411yescharacteristic
601C22×C4×C71C2412yes—
602C22×C4×C71C2414yes—
603C22×C4×C71C2411yescharacteristic
604C4⋊C4×C71C2414yes—
605C4⋊C4×C71C2418yes—
606C4⋊C4×C71C2414yes—
607C4⋊C4×C71C2412yes—
608C4⋊C4×C71C2412yes—
609C4⋊C4×C71C2414yes—
610C4⋊C4×C71C2418yes—
611C4⋊C4×C71C2418yes—
612C4⋊C4×C71C2414yes—
613C4⋊C4×C71C2414yes—
614C4⋊C4×C71C2418yes—
615C22⋊C4×C71C2414yes—
616C22⋊C4×C71C2414yes—
617C22⋊C4×C71C2414yes—
618C22⋊C4×C71C2418yes—
619C22⋊C4×C71C2418yes—
620C22⋊C4×C71C2418yes—
621C42×C71C2412yes—
622C42×C71C2412yes—
623C42×C71C2414yes—
624C42×C71C2414yes—
625C42×C71C2414yes—
626C42×C71C2414yes—
627C42×C71C2414yes—
628C23×C71C2514yes—
629C23×C71C2511yescharacteristic
630C22×D71—22no—
631C22×D71—22no—
632C22×D71—22no—
633C22×D71C2514yes—
634C22×D71C2511yescharacteristic
635C22×D71C2511yescharacteristic
636Q8×C71—28no—
637Q8×C71—24no—
638Q8×C71—44no—
639D4×C71—28no—
640D4×C71—24no—
641D4×C71—44no—
642C2×C4×C71—24no—
643C2×C4×C71—28no—
644C2×C4×C71—22no—
645C2×C4×C71—28no—
646C2×C4×C71—42no—
647C2×C4×C71—41no—
648C2×C4×C71—44no—
649C2×C4×C71C2×#4114yes—
650C2×C4×C71C2511yescharacteristic
651C2×C4×C71C2512yes—
652C2×C4×C71C2514yes—
653C2×C4×C71C2514yes—
654C2×C4×C71C2514yes—
655C2×C4×C71C2514yes—
656C2×C4×C71C2514yes—
657C2×C4×C71C2512yes—
658C2×C4×C71C2511yescharacteristic
659C22⋊D71—28no—
660C22⋊D71—28no—
661C22⋊D71—28no—
662C22⋊D71—216no—
663C22⋊D71—28no—
664C22⋊D71—44no—
665C2×Dic71—22no—
666C2×Dic71—216no—
667C2×Dic71—22no—
668C2×Dic71—41no—
669C2×Dic71—42no—
670C2×Dic71—48no—
671C2×Dic71C2×#4118yes—
672C2×Dic71C2511yescharacteristic
673C2×Dic71C2514yes—
674C2×Dic71C2514yes—
675C2×Dic71C2512yes—
676C2×Dic71C2514yes—
677C2×Dic71C2514yes—
678C2×Dic71C2512yes—
679C2×Dic71C2514yes—
680C2×Dic71C2511yescharacteristic
681D284—28no—
682D284—28no—
683D284—24no—
684D284—44no—
685C4×D71—22no—
686C4×D71—28no—
687C4×D71—24no—
688C4×D71—24no—
689C4×D71—24no—
690C4×D71—28no—
691C4×D71—22no—
692C4×D71—28no—
693C4×D71—28no—
694C4×D71—28no—
695C4×D71—216no—
696C4×D71—22no—
697C4×D71—42no—
698C4×D71—44no—
699C4×D71—44no—
700C4×D71—48no—
701C4×D712−1+414yescomplemented
702Dic142—24no—
703Dic142—216no—
704Dic142—216no—
705Dic142—28no—
706Dic142—44no—
707Dic142—44no—
708Dic142C2×#41116yes—
709C22×C71—21no—
710C22×C71—21no—
711C22×C71—24no—
712C22×C71—24no—
713C22×C71—24no—
714C22×C71C22×#4112yes—
715C22×C71C2611yescharacteristic
716C2×D71—28no—
717C2×D71—21no—
718C2×D71—21no—
719C2×D71—21no—
720C2×D71—21no—
721C2×D71—24no—
722C2×D71—24no—
723C2×D71—24no—
724C2×D71C2×2−1+412yes—
725C2×D71#58512yes—
726C4×C71—24no—
727C4×C71—24no—
728C4×C71—24no—
729C4×C71—21no—
730C4×C71—24no—
731C4×C71—24no—
732C4×C71—22no—
733C4×C71C22×#4114yes—
734C4×C71C2×2−1+412yes—
735Dic71—22no—
736Dic71—24no—
737Dic71—24no—
738Dic71—21no—
739Dic71—24no—
740Dic71—22no—
741Dic71—24no—
742Dic71C22×#4118yes—
743Dic71C2×2−1+412yes—
744#62788—711nomaximal, Sylow
745C2×C71—22no—
746C2×C71—44no—
747C2×C71C23×#4111yescharacteristic
748C2×C71C22×2−1+411yescharacteristic
749C2×C71C2×#58511yescharacteristic
750D71—22no—
751D71—22no—
752D71—44no—
753#3523—714no—
754#3522—714no—
755#3516—714no—
756#3516—714no—
757#3507—714no—
758#3507—712no—
759#3502—711no—
760#3497—711no—
761#3492—711no—
762#3492—714no—
763#3492—711no—
764#3486—712no—
765#3482—714no—
766#3482—714no—
767#3480—714no—
768Q8×#41—714no—
769#3461—714no—
770#3461—711no—
771#3461D7111yescharacteristic, complemented
772#3444—714no—
773#3444—712no—
774C4×2−1+4—712no—
775C22×C4×Q8—711no—
776C71#6278811yescharacteristic, complemented, Sylow
777C2×2−1+4—712no—
778C23×Q8—711no—
779#559—714no—
780#559—718no—
781Q82—714no—
782#557—714no—
783#557—714no—
784#557—718no—
785#557—714no—
786#557—714no—
787#556—714no—
788#556—718no—
789#556—718no—
790#556—714no—
791#556—714no—
792#556—718no—
793#554—714no—
794#554—718no—
795#554—718no—
796#554—718no—
797#554—714no—
798#554—714no—
799#553—718no—
800#553—714no—
801#553—718no—
802#553—714no—
803#552—718no—
804#552—718no—
805#552—718no—
806#552—714no—
807#552—718no—
808#552—714no—
809#552—714no—
810#552—714no—
811#550—714no—
812D4×Q8—714no—
813D4×Q8—714no—
814D4×Q8—714no—
815D4×Q8—714no—
816D4×Q8—714no—
817#548—714no—
818#548—714no—
819#548—714no—
820#548—714no—
821#548—714no—
822#548—714no—
823#547—714no—
824#547—718no—
825#547—718no—
826#547—714no—
827#544—714no—
828#544—711no—
829#544C2×D7111yescharacteristic
830#542—718no—
831#542—718no—
832#542—714no—
833#542C2×D7114yescomplemented
834#541—718no—
835#541—718no—
836#541—714no—
837#541C2×D7114yescomplemented
838#539—718no—
839#539—714no—
840#539—714no—
841#539—714no—
842#539C2×D7114yes—
843#537—714no—
844#537—711no—
845#537C2×D7111yescharacteristic
846#536—712no—
847#536—718no—
848#536C2×D7112yes—
849#533—714no—
850#533—714no—
851#533—714no—
852#533—712no—
853#533—712no—
854#533—718no—
855#533—714no—
856#533—712no—
857#533—718no—
858#533C2×D7114yescomplemented
859#532—712no—
860#532—714no—
861#532—714no—
862#532—714no—
863#532—712no—
864#532—712no—
865#529—718no—
866#529—718no—
867#529—714no—
868#529—714no—
869#529—718no—
870#529—712no—
871#529—712no—
872#529—714no—
873#529—714no—
874#529—712no—
875#529—714no—
876#529—712no—
877#529—718no—
878#529—718no—
879#529—714no—
880#529—714no—
881#529—718no—
882#529—714no—
883#529C2×D7114yes—
884#529C2×D7114yescomplemented
885#525—712no—
886#525—718no—
887#525—714no—
888#525—714no—
889#525—714no—
890#525—714no—
891#525—712no—
892#520—712no—
893#520—718no—
894#520—714no—
895#520—712no—
896#520—714no—
897#519—714no—
898#519—712no—
899#519—714no—
900C4×#41—714no—
901C4×#41—718no—
902C4×#41—714no—
903C4×#41—714no—
904C4×#41—718no—
905C4×#41—712no—
906C4×#41—714no—
907C4×#41—714no—
908C4×#41—714no—
909C4×#41C2×D7112yes—
910C2×C4×Q8—711no—
911C2×C4×Q8—714no—
912C2×C4×Q8—714no—
913C2×C4×Q8—714no—
914C2×C4×Q8—714no—
915C2×C4×Q8—714no—
916C2×C4×Q8—711no—
917C2×C4×Q8—712no—
918C2×C4×Q8—711no—
919C2×C4×Q8—712no—
920C2×C4×Q8—714no—
921C2×C4×Q8C2×D7111yescharacteristic
922C22×C4⋊C4—712no—
923C22×C4⋊C4—711no—
924C22×C42—712no—
925C22×C42—711no—
9262−1+4—14216no—
927C2×#41—714no—
928C2×#41—714no—
929C2×#41—718no—
930C2×#41—714no—
931C2×#41—714no—
932C2×#41—714no—
933C2×#41—712no—
934C2×#41—714no—
935C2×#41C22×D7112yes—
936C22×Q8—714no—
937C22×Q8—714no—
938C22×Q8—714no—
939C22×Q8—711no—
940C22×Q8—712no—
941C22×Q8—714no—
942C22×Q8—1428no—
943C22×Q8C22×D7111yescharacteristic
944C23×C4—712no—
945C23×C4—711no—
946C23×C4—712no—
947C23×C4—711no—
948C23×C4—711no—
949C4⋊Q8—712no—
950C4⋊Q8—714no—
951C4⋊Q8—714no—
952C4⋊Q8—718no—
953C4⋊Q8—714no—
954C4⋊Q8—712no—
955C4⋊Q8—714no—
956C4⋊Q8—712no—
957C4⋊Q8—718no—
958C4⋊Q8—718no—
959C4⋊Q8—718no—
960C4⋊Q8—714no—
961C4⋊Q8C22×D7114yes—
962C4⋊Q8C22×D7114yes—
963#127—712no—
964#127—714no—
965#126—714no—
966#126—718no—
967#126—714no—
968#126—718no—
969#126—718no—
970#126—718no—
971#126—714no—
972#126—718no—
973#126—714no—
974#126—718no—
975#126—718no—
976#126—718no—
977#126C22×D7118yes—
978#126C22×D7118yes—
979#125—714no—
980#125—718no—
981#125—712no—
982#125—712no—
983#125—718no—
984#125—714no—
985#125—718no—
986#125—718no—
987#125—714no—
988#125—718no—
989#125—718no—
990#125—718no—
991#125—718no—
992#125—718no—
993#125—714no—
994#125C22×D7114yes—
995#125C22×D7114yes—
996#125C22×D7118yes—
997#124—712no—
998#124—714no—
999#124—712no—
1000#124—714no—
1001#124—718no—
1002#124—718no—
1003#124—714no—
1004#124—718no—
1005#124—718no—
1006#124—714no—
1007#124C22×D7114yes—
1008#124C22×D7114yes—
1009#123—714no—
1010#123—718no—
1011#123—718no—
1012#123—714no—
1013#123—718no—
1014#123—714no—
1015#123—718no—
1016#123—718no—
1017#123—714no—
1018#123—714no—
1019#123—718no—
1020#123—714no—
1021#123—718no—
1022#123—718no—
1023#123C22×D7118yes—
1024#123C22×D7118yes—
1025C22⋊Q8—712no—
1026C22⋊Q8—712no—
1027C22⋊Q8—714no—
1028C22⋊Q8—714no—
1029C22⋊Q8—714no—
1030C22⋊Q8—718no—
1031C22⋊Q8—714no—
1032C22⋊Q8—714no—
1033C22⋊Q8—718no—
1034C22⋊Q8—712no—
1035C22⋊Q8—718no—
1036C22⋊Q8—712no—
1037C22⋊Q8—714no—
1038C22⋊Q8—714no—
1039C22⋊Q8—718no—
1040C22⋊Q8—718no—
1041C22⋊Q8—718no—
1042C22⋊Q8—714no—
1043C22⋊Q8—718no—
1044C22⋊Q8—718no—
1045C22⋊Q8—714no—
1046C22⋊Q8—714no—
1047C22⋊Q8—718no—
1048C22⋊Q8—718no—
1049C22⋊Q8—718no—
1050C22⋊Q8—718no—
1051C22⋊Q8—718no—
1052C22⋊Q8C22×D7114yes—
1053C22⋊Q8C22×D7114yes—
1054C22⋊Q8C22×D7114yes—
1055C22⋊Q8C22×D7114yes—
1056C22⋊Q8C22×D7118yes—
1057#121—714no—
1058#121—714no—
1059#121—712no—
1060#121—712no—
1061#121—714no—
1062#121—718no—
1063#121—714no—
1064#121—712no—
1065#121—712no—
1066#121—714no—
1067#121—714no—
1068#121—714no—
1069#121—718no—
1070#121—718no—
1071#121—714no—
1072#121—718no—
1073#121C22×D7114yes—
1074#121C22×D7114yes—
1075#120—714no—
1076#120—714no—
1077C4×Q8—714no—
1078C4×Q8—714no—
1079C4×Q8—714no—
1080C4×Q8—714no—
1081C4×Q8—714no—
1082C4×Q8—714no—
1083C4×Q8—718no—
1084C4×Q8—718no—
1085C4×Q8—714no—
1086C4×Q8—718no—
1087C4×Q8—718no—
1088C4×Q8—714no—
1089C4×Q8—718no—
1090C4×Q8—714no—
1091C4×Q8—718no—
1092C4×Q8—714no—
1093C4×Q8—714no—
1094C4×Q8—718no—
1095C4×Q8—718no—
1096C4×Q8—718no—
1097C4×Q8—712no—
1098C4×Q8—714no—
1099C4×Q8—714no—
1100C4×Q8—718no—
1101C4×Q8—712no—
1102C4×Q8—714no—
1103C4×Q8—714no—
1104C4×Q8—714no—
1105C4×Q8—714no—
1106C4×Q8—714no—
1107C4×Q8—714no—
1108C4×Q8C22×D7114yes—
1109C4×Q8C22×D7114yes—
1110C4×Q8C22×D7112yes—
1111C4×Q8C22×D7114yes—
1112C4×Q8C22×D7112yes—
1113C4×D4—718no—
1114C4×D4—714no—
1115C4×D4—714no—
1116C4×D4—714no—
1117C4×D4—714no—
1118C4×D4—718no—
1119C4×D4—714no—
1120C4×D4—718no—
1121C4×D4—714no—
1122C4×D4—714no—
1123C4×D4—714no—
1124C4×D4—714no—
1125C4×D4—714no—
1126C4×D4—714no—
1127C4×D4—714no—
1128C4×D4—718no—
1129C4×D4—718no—
1130C4×D4—718no—
1131C4×D4—714no—
1132C4×D4—718no—
1133C4×D4—718no—
1134C4×D4—718no—
1135C4×D4—718no—
1136C4×D4—718no—
1137C4×D4—718no—
1138C4×D4—718no—
1139C4×D4—718no—
1140C4×D4—714no—
1141C4×D4—712no—
1142C4×D4—712no—
1143C4×D4—714no—
1144C4×D4—714no—
1145C4×D4—714no—
1146C4×D4—714no—
1147C4×D4—714no—
1148C4×D4C22×D7114yes—
1149C4×D4C22×D7112yes—
1150C4×D4C22×D7114yes—
1151C4×D4C22×D7114yes—
1152C4×D4C22×D7112yes—
1153#117—712no—
1154#117—714no—
1155#117—714no—
1156#117—714no—
1157#117—718no—
1158#117—714no—
1159#117—714no—
1160#117—714no—
1161#117—718no—
1162#117—718no—
1163#117—718no—
1164#117—718no—
1165#117—718no—
1166#117—714no—
1167#117—714no—
1168#117—718no—
1169#117—714no—
1170#117—718no—
1171#117—714no—
1172#117—714no—
1173#117C22×D7118yes—
1174#117C22×D7112yes—
1175#117C22×D7114yes—
1176C2×C4⋊C4—712no—
1177C2×C4⋊C4—711no—
1178C2×C4⋊C4—712no—
1179C2×C4⋊C4—712no—
1180C2×C4⋊C4—712no—
1181C2×C4⋊C4—718no—
1182C2×C4⋊C4—714no—
1183C2×C4⋊C4—718no—
1184C2×C4⋊C4—714no—
1185C2×C4⋊C4—718no—
1186C2×C4⋊C4—714no—
1187C2×C4⋊C4—718no—
1188C2×C4⋊C4—714no—
1189C2×C4⋊C4C22×D7111yescharacteristic
1190C2×C4⋊C4C22×D7112yes—
1191C2×C42—712no—
1192C2×C42—712no—
1193C2×C42—711no—
1194C2×C42—711no—
1195C2×C42—711no—
1196C2×C42—712no—
1197C2×C42—718no—
1198C2×C42—714no—
1199C2×C42—712no—
1200C2×C42—714no—
1201C2×C42—712no—
1202C2×C42—714no—
1203C2×C42—712no—
1204C2×C42—714no—
1205C2×C42—712no—
1206C2×C42—718no—
1207C2×C42—714no—
1208C2×C42C22×D7111yescharacteristic
1209C2×C42C22×D7112yes—
1210C2×C42C22×D7114yes—
1211C24—711no—
1212#41—28no—
1213#41—2848no—
1214#41—2848no—
1215#41—2848no—
1216#41—14216no—
1217#41—14216no—
1218#41—14232no—
1219#41—14216no—
1220#41—1428no—
1221C2×Q8—24no—
1222C2×Q8—718no—
1223C2×Q8—714no—
1224C2×Q8—714no—
1225C2×Q8—714no—
1226C2×Q8—714no—
1227C2×Q8—718no—
1228C2×Q8—718no—
1229C2×Q8—712no—
1230C2×Q8—1428no—
1231C2×Q8—14216no—
1232C2×Q8—14216no—
1233C2×Q8—14216no—
1234C2×Q8—14216no—
1235C2×Q8C23×D7114yes—
1236C2×Q8C23×D7112yes—
1237C2×Q8C23×D7114yes—
1238C2×D4—714no—
1239C2×D4—714no—
1240C2×D4—714no—
1241C2×D4—714no—
1242C2×D4—714no—
1243C2×D4—718no—
1244C2×D4—714no—
1245C2×D4—714no—
1246C2×D4—714no—
1247C2×D4—712no—
1248C2×D4C23×D7114yes—
1249C2×D4C23×D7112yes—
1250C2×D4C23×D7114yes—
1251C22×C4—2842no—
1252C22×C4—2844no—
1253C22×C4—712no—
1254C22×C4—711no—
1255C22×C4—718no—
1256C22×C4—714no—
1257C22×C4—712no—
1258C22×C4—718no—
1259C22×C4—714no—
1260C22×C4—712no—
1261C22×C4—711no—
1262C22×C4—711no—
1263C22×C4—711no—
1264C22×C4—718no—
1265C22×C4—711no—
1266C22×C4—711no—
1267C22×C4—714no—
1268C22×C4—712no—
1269C22×C4—714no—
1270C22×C4—714no—
1271C22×C4—712no—
1272C22×C4—712no—
1273C22×C4—718no—
1274C22×C4—714no—
1275C22×C4—711no—
1276C22×C4—714no—
1277C22×C4—1424no—
1278C22×C4—1428no—
1279C22×C4—1424no—
1280C22×C4C23×D7112yes—
1281C22×C4C23×D7114yes—
1282C22×C4C23×D7111yescharacteristic
1283C22×C4C23×D7114yes—
1284C22×C4C23×D7111yescharacteristic
1285C22×C4C23×D7112yes—
1286C22×C4C23×D7114yes—
1287C22×C4C23×D7111yescharacteristic
1288C4⋊C4—718no—
1289C4⋊C4—718no—
1290C4⋊C4—718no—
1291C4⋊C4—718no—
1292C4⋊C4—718no—
1293C4⋊C4—714no—
1294C4⋊C4—718no—
1295C4⋊C4—714no—
1296C4⋊C4—714no—
1297C4⋊C4—714no—
1298C4⋊C4—714no—
1299C4⋊C4—714no—
1300C4⋊C4—714no—
1301C4⋊C4—714no—
1302C4⋊C4—718no—
1303C4⋊C4—714no—
1304C4⋊C4—718no—
1305C4⋊C4—718no—
1306C4⋊C4—714no—
1307C4⋊C4—714no—
1308C4⋊C4—718no—
1309C4⋊C4—712no—
1310C4⋊C4—718no—
1311C4⋊C4—712no—
1312C4⋊C4—714no—
1313C4⋊C4—714no—
1314C4⋊C4—714no—
1315C4⋊C4—714no—
1316C4⋊C4—714no—
1317C4⋊C4—714no—
1318C4⋊C4C23×D7114yes—
1319C4⋊C4C23×D7118yes—
1320C4⋊C4C23×D7112yes—
1321C4⋊C4C23×D7114yes—
1322C4⋊C4C23×D7112yes—
1323C4⋊C4C23×D7114yes—
1324C4⋊C4C23×D7114yes—
1325C4⋊C4C23×D7118yes—
1326C4⋊C4C23×D7114yes—
1327C4⋊C4C23×D7118yes—
1328C4⋊C4C23×D7118yes—
1329C22⋊C4—714no—
1330C22⋊C4—718no—
1331C22⋊C4—714no—
1332C22⋊C4—714no—
1333C22⋊C4—714no—
1334C22⋊C4—714no—
1335C22⋊C4—714no—
1336C22⋊C4—714no—
1337C22⋊C4—718no—
1338C22⋊C4—714no—
1339C22⋊C4—714no—
1340C22⋊C4—714no—
1341C22⋊C4—714no—
1342C22⋊C4—714no—
1343C22⋊C4—718no—
1344C22⋊C4—714no—
1345C22⋊C4—714no—
1346C22⋊C4—718no—
1347C22⋊C4—718no—
1348C22⋊C4—714no—
1349C22⋊C4C23×D7114yes—
1350C22⋊C4C23×D7114yes—
1351C22⋊C4C23×D7114yes—
1352C22⋊C4C23×D7118yes—
1353C22⋊C4C23×D7118yes—
1354C22⋊C4C23×D7118yes—
1355C42—714no—
1356C42—714no—
1357C42—712no—
1358C42—714no—
1359C42—712no—
1360C42—714no—
1361C42—712no—
1362C42—714no—
1363C42—712no—
1364C42—712no—
1365C42—718no—
1366C42—718no—
1367C42—714no—
1368C42—718no—
1369C42—718no—
1370C42—714no—
1371C42—714no—
1372C42—712no—
1373C42—714no—
1374C42C23×D7112yes—
1375C42C23×D7114yes—
1376C42C23×D7114yes—
1377C42C23×D7114yes—
1378C42C23×D7112yes—
1379C42C23×D7114yes—
1380C42C23×D7114yes—
1381C23—711no—
1382C23—711no—
1383C23—714no—
1384C23—1422no—
1385C23—1422no—
1386C23—1422no—
1387C23C24×D7114yes—
1388C23C24×D7111yescharacteristic
1389Q8—28no—
1390Q8—24no—
1391Q8—44no—
1392Q8—2844no—
1393Q8—2844no—
1394Q8—7116no—
1395Q8—14216no—
1396Q8—14216no—
1397Q8—1428no—
1398Q8—1424no—
1399D4—28no—
1400D4—24no—
1401D4—44no—
1402D4—2844no—
1403D4—2844no—
1404D4—1428no—
1405D4—1428no—
1406D4—14216no—
1407D4—1428no—
1408D4—1428no—
1409D4—1428no—
1410D4—1428no—
1411D4—1424no—
1412C2×C4—24no—
1413C2×C4—28no—
1414C2×C4—22no—
1415C2×C4—28no—
1416C2×C4—41no—
1417C2×C4—42no—
1418C2×C4—44no—
1419C2×C4—2842no—
1420C2×C4—2844no—
1421C2×C4—2844no—
1422C2×C4—2848no—
1423C2×C4—2842no—
1424C2×C4—2841no—
1425C2×C4—2848no—
1426C2×C4—718no—
1427C2×C4—711no—
1428C2×C4—714no—
1429C2×C4—714no—
1430C2×C4—711no—
1431C2×C4—714no—
1432C2×C4—714no—
1433C2×C4—712no—
1434C2×C4—714no—
1435C2×C4—714no—
1436C2×C4—712no—
1437C2×C4—1428no—
1438C2×C4—1428no—
1439C2×C4—1422no—
1440C2×C4—14216no—
1441C2×C4—1424no—
1442C2×C4—1428no—
1443C2×C4—1422no—
1444C2×C4—1422no—
1445C2×C4—14216no—
1446C2×C4—1422no—
1447C2×C4—1424no—
1448C2×C4—1424no—
1449C2×C4—1428no—
1450C2×C4—1422no—
1451C2×C4—1428no—
1452C2×C4#41×D7114yes—
1453C2×C4C24×D7111yescharacteristic
1454C2×C4C24×D7112yes—
1455C2×C4C24×D7114yes—
1456C2×C4C24×D7114yes—
1457C2×C4C24×D7114yes—
1458C2×C4C24×D7114yes—
1459C2×C4C24×D7114yes—
1460C2×C4C24×D7112yes—
1461C2×C4C24×D7111yescharacteristic
1462C22—21no—
1463C22—21no—
1464C22—24no—
1465C22—24no—
1466C22—24no—
1467C22—712no—
1468C22—712no—
1469C22—1428no—
1470C22—1424no—
1471C22—1424no—
1472C22—1424no—
1473C22—1421no—
1474C22—1421no—
1475C22—1421no—
1476C22—1421no—
1477C22C2×#41×D7112yes—
1478C22C25×D7111yescharacteristic
1479C4—24no—
1480C4—24no—
1481C4—21no—
1482C4—24no—
1483C4—22no—
1484C4—24no—
1485C4—24no—
1486C4—718no—
1487C4—712no—
1488C4—1424no—
1489C4—1422no—
1490C4—1421no—
1491C4—1424no—
1492C4—1424no—
1493C4—1424no—
1494C4—1422no—
1495C4C2×#41×D7114yes—
1496C42−1+4×D7112yes—
1497C2—22no—
1498C2—44no—
1499C2—2844no—
1500C2—1422no—
1501C2—1422no—
1502C2C22×#41×D7111yescharacteristic
1503C2C2×2−1+4×D7111yescharacteristic
1504C2#585×D7111yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3461C2
hypercenter#3461D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #22602432C2semidirect
2. #22602421C2semidirect
3. #22602331C2semidirect
4. #22602327C2semidirect
5. #22602204C2semidirect
6. #22602200C2semidirect
7. #22602148C2semidirect
8. #22602109C2semidirect
9. #22602050C2semidirect
10. #22602047C2semidirect
11. #22602045C2semidirect
12. #22601989C2semidirect
13. #22601958C2semidirect
14. #22601953C2semidirect
15. #22601931C2semidirect
16. #22601918C2semidirect
17. #22601773C2semidirect
18. #22601769C2semidirect
19. #22601634C2semidirect
20. #22601633C2semidirect
21. C4×#14556175C2semidirect
22. C2×C4×Q8×D71C2semidirect
23. C71×#3461C2semidirect
26. #17986733C22semidirect
27. #17986731C22semidirect
28. #17986729C22semidirect
29. #17986726C22semidirect
30. #17986726C22semidirect
31. #17986726C22semidirect
32. #17986724C22semidirect
33. #17986724C22semidirect
34. #17986723C22semidirect
35. #17986720C22semidirect
36. #17986720C22semidirect
37. #17986718C22semidirect
38. #17986716C22semidirect
39. #17986716C22semidirect
42. #17986707C22semidirect
45. #17986703C22semidirect
50. #17986691C22semidirect
52. #17986686C22semidirect
55. #17986683C22semidirect
57. #17986681C22semidirect
58. #17986667C22semidirect
63. #17986662C22semidirect
66. #17986659C22semidirect
69. #17986655C22semidirect
76. #17986621C22semidirect
77. #17986615C22semidirect
78. #17986613C22semidirect
79. #17986608C22semidirect
80. #17986607C22semidirect
81. #17986606C22semidirect
94. #17986553C22semidirect
95. #17986553C22semidirect
97. #17986552C22semidirect
107. #17986536C22semidirect
116. #17986529C22semidirect
121. #17986527C22semidirect
132. #17986479C22semidirect
134. #17986478C22semidirect
136. #17986476C22semidirect
137. #17986475C22semidirect
142. C4×#11765865C22semidirect
146. C4×#11765864C22semidirect
150. C2×C4×Dic142C22semidirect
157. C4×Q8×D71C22semidirect
163. #542×C71C22semidirect
164. #541×C71C22semidirect
168. #533×C71C22semidirect
170. #529×C71C22semidirect
469. C2×Dic142#41semidirect
701. C4×D712−1+4semidirect
771. #3461D71semidirect
776. C71#62788semidirect
833. #542C2×D71semidirect
837. #541C2×D71semidirect
858. #533C2×D71semidirect
884. #529C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226024322
#226024212
#226023312
#226023272
#226022042
#226022002
#226021482
#226021092
#226020502
#226020472
#226020452
#226019892
#226019582
#226019532
#226019312
#226019182
#226017732
#226017692
#226016342
#226016332
C4×#145561752
C2×C4×Q8×D712
C71×#34612
#6278871