Finite Group Databasebeta

← #3444×D71 #32904159

Subgroups — #3444×D71 #32904159

Order 18176.

8518 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601637C213yesmaximal, complemented
2#22601636C211yesmaximal, characteristic, complemented
3#22601635C213yesmaximal, complemented
4#22601634C2112yesmaximal, complemented
5#22601633C216yesmaximal, complemented
6#22601632C216yesmaximal, complemented
7#533×D71C213yesmaximal, complemented
8#532×D71C213yesmaximal, complemented
9#529×D71C2112yesmaximal, complemented
10#525×D71C216yesmaximal, complemented
11C4×#41×D71C216yesmaximal, complemented
12C22×C42×D71C211yesmaximal, characteristic, complemented
13C71×#3444C211yesmaximal, characteristic, complemented
14C2×#41×D71C2216yes—
15C23×C4×D71C2213yes—
16#17986556C2213yescomplemented
17#17986555C2216yescomplemented
18#17986554C2216yescomplemented
19#17986553C22112yescomplemented
20#17986552C2216yescomplemented
21#17986551C22112yescomplemented
22#17986550C2213yescomplemented
23#17986549C2213yescomplemented
24#17986548C2216yescomplemented
25#17986547C2213yescomplemented
26#17986546C22112yescomplemented
27#17986545C2216yescomplemented
28#17986544C22112yescomplemented
29C4⋊Q8×D71C2213yescomplemented
30#127×D71C2211yescharacteristic, complemented
31#17986536C22112yescomplemented
32#17986535C22112yescomplemented
33#17986534C22112yescomplemented
34#17986533C22112yescomplemented
35#17986532C22124yescomplemented
36#17986531C22112yescomplemented
37#17986530C22112yescomplemented
38#17986529C22124yescomplemented
39#17986528C22112yescomplemented
40#17986527C22124yescomplemented
41#17986526C22124yescomplemented
42#126×D71C2218yescomplemented
43#125×D71C2216yescomplemented
44#124×D71C2216yescomplemented
45#17986512C22112yescomplemented
46#17986511C2216yescomplemented
47#17986510C2216yescomplemented
48#17986509C22112yescomplemented
49#17986508C22124yescomplemented
50#17986507C22112yescomplemented
51#17986506C2216yescomplemented
52#17986505C22112yescomplemented
53#123×D71C22112yes—
54C22⋊Q8×D71C22112yes—
55#121×D71C22112yes—
56#120×D71C2214yes—
57#41×Dic71C2216yescomplemented
58C4×#11765866C22112yescomplemented
59C4×#11765865C2216yescomplemented
60C4×#11765865C22112yescomplemented
61#17986467C2216yescomplemented
62#17986467C22112yescomplemented
63C4×#11765864C22124yescomplemented
64C4×#11765864C22112yescomplemented
65C4×Q8×D71C22112yescomplemented
66C4×D4×D71C22124yes—
67C4×D4×D71C22112yescomplemented
68#117×D71C2216yes—
69#117×D71C22112yescomplemented
70C22×C4×Dic71C2213yescomplemented
71C2×C42×D71C2213yes—
72C2×C42×D71C2216yes—
73C2×C42×D71C2213yes—
74C2×C42×D71C2213yescomplemented
75C2×C42×D71C2216yescomplemented
76C2×C42×D71C2213yescomplemented
77C2×C42×D71C2214yescomplemented
78#533×C71C2213yescomplemented
79#532×C71C2213yescomplemented
80#529×C71C22112yescomplemented
81#525×C71C2216yescomplemented
82C4×#41×C71C2216yescomplemented
83C22×C42×C71C2211yescharacteristic, complemented
84C24×D71C2311yescharacteristic
85C2×#11765866C2316yes—
86C2×#11765865C23112yes—
87C2×#11765865C2316yes—
88C2×#11765864C23112yes—
89C2×#11765864C2316yes—
90#41×D71—248no—
91C2×Q8×D71C2316yes—
92C2×D4×D71C23112yes—
93C2×D4×D71C2316yes—
94C23×Dic71C2313yes—
95C22×C4×D71—224no—
96C22×C4×D71C2316yes—
97C22×C4×D71C2316yes—
98C22×C4×D71C2313yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2313yes—
101C22×C4×D71C2316yes—
102C22×C4×D71C2316yes—
103C22×C4×D71C23112yes—
104C22×C4×D71C2313yes—
105#14556128C2313yescomplemented
106#14556127C23112yescomplemented
107#14556126C2316yescomplemented
108#14556125C2311yescharacteristic, complemented
109#14556124C2316yescomplemented
110#14556123C23124yescomplemented
111#14556122C2318yescomplemented
112#14556121C23124yescomplemented
113#14556120C2316yescomplemented
114#14556119C23112yescomplemented
115#14556118C23124yescomplemented
116#14556117C2316yescomplemented
117#14556116C2316yescomplemented
118#14556115C2316yescomplemented
119#14556114C23124yescomplemented
120#14556113C23124yes—
121#14556112C23112yes—
122#14556111C23112yes—
123#14556110C23124yes—
124#14556109C23112yes—
125#14556108C23112yes—
126#14556107C23112yes—
127#14556106C23124yes—
128#14556105C23124yes—
129#14556104C23112yes—
130#14556103C23112yes—
131#14556102C23112yes—
132#14556101C23124yes—
133#14556100C23124yes—
134#14556099C23112yes—
135#14556098C23112yes—
136#14556097C2314yes—
137#14556096C23112yes—
138Q8×Dic71C23112yescomplemented
139C4×Dic142C23124yescomplemented
140C4×Dic142C23112yescomplemented
141#14556093C23124yescomplemented
142#14556093C23112yescomplemented
143C4×D284C23124yes—
144C4×D284C23112yescomplemented
145D4×Dic71C23124yes—
146D4×Dic71C23112yescomplemented
147#14556090C23124yes—
148#14556090C23112yescomplemented
149C4×C22⋊D71C23124yes—
150C4×C22⋊D71C23124yes—
151C4×C22⋊D71C23124yescomplemented
152(C22⋊D71)⋊C4C23124yes—
153(C22⋊D71)⋊C4C23124yes—
154(C22⋊D71)⋊C4C23124yescomplemented
155#14556087C2316yes—
156#14556087C23112yescomplemented
157#14556086C23112yes—
158#14556086C23124yescomplemented
159#14556085C23112yes—
160#14556085C23112yescomplemented
161#14556085C23112yescomplemented
162#14556084C23112yes—
163#14556084C23124yescomplemented
164C4⋊C4×D71C23112yes—
165C4⋊C4×D71C23124yes—
166C22⋊C4×D71C23112yes—
167C22⋊C4×D71C23124yes—
168C2×C4×Dic71C2316yes—
169C2×C4×Dic71C2313yes—
170C2×C4×Dic71C2316yes—
171C2×C4×Dic71C2316yes—
172C2×C4×Dic71C2316yes—
173C2×C4×Dic71C2316yes—
174C2×C4×Dic71C2313yes—
175C2×C4×Dic71C23112yescomplemented
176C42×D71C2311yescharacteristic
177C42×D71C2313yes—
178C42×D71C2316yes—
179C42×D71C2313yes—
180C42×D71C2312yes—
181C42×D71C2311yescharacteristic
182C42×D71C2316yes—
183C42×D71C2313yes—
184C42×D71C2313yes—
185C42×D71C2316yes—
186C42×D71C2316yes—
187C42×D71C2316yes—
188C42×D71C2316yes—
189C42×D71C2316yes—
190C42×D71C2313yes—
191C42×D71C2313yes—
192C42×D71C23112yes—
193C42×D71C23112yescomplemented
194C42×D71C2314yescomplemented
195C2×#41×C71C2316yes—
196C23×C4×C71C2313yes—
197C4⋊Q8×C71C2313yescomplemented
198#127×C71C2311yescharacteristic, complemented
199#126×C71C2318yescomplemented
200#125×C71C2316yescomplemented
201#124×C71C2316yescomplemented
202#123×C71C23112yes—
203C22⋊Q8×C71C23112yes—
204#121×C71C23112yes—
205#120×C71C2314yes—
206C4×Q8×C71C23112yescomplemented
207C4×D4×C71C23124yes—
208C4×D4×C71C23112yescomplemented
209#117×C71C2316yes—
210#117×C71C23112yescomplemented
211C2×C42×C71C2313yes—
212C2×C42×C71C2316yes—
213C2×C42×C71C2313yes—
214C2×C42×C71C2314yescomplemented
215C23×D71—212no—
216C23×D71C2413yes—
217C23×D71C2414yes—
218C23×D71C2413yes—
219#11765866—224no—
220#11765865—224no—
221#11765865—248no—
222#11765864—248no—
223#11765864—224no—
224C2×Dic142C24112yes—
225C2×Dic142C2416yes—
226Q8×D71—224no—
227C2×D284C24112yes—
228C2×D284C2416yes—
229C2×C22⋊D71C24112yes—
230C2×C22⋊D71C24112yes—
231C2×C22⋊D71C24112yes—
232D4×D71—248no—
233D4×D71—224no—
234C22×Dic71—212no—
235C22×Dic71C2416yes—
236C22×Dic71C2416yes—
237C22×Dic71C2413yes—
238C22×Dic71C24112yes—
239C22×Dic71C2413yes—
240C2×C4×D71—212no—
241C2×C4×D71—212no—
242C2×C4×D71—212no—
243C2×C4×D71—224no—
244C2×C4×D71—224no—
245C2×C4×D71—248no—
246C2×C4×D71—224no—
247C2×C4×D71—224no—
248C2×C4×D71#41124yescomplemented
249C2×C4×D71C2416yes—
250C2×C4×D71C2416yes—
251C2×C4×D71C2416yes—
252C2×C4×D71C2416yes—
253C2×C4×D71C2416yes—
254C2×C4×D71C2416yes—
255C2×C4×D71C24112yes—
256C2×C4×D71C24112yes—
257C2×C4×D71C24112yes—
258C2×C4×D71C2413yes—
259C2×C4×D71C2413yes—
260C2×C4×D71C2413yes—
261C2×C4×D71C2413yes—
262C4⋊Dic71C24112yes—
263C4⋊Dic71C24124yes—
264Dic71⋊C4C24124yes—
265Dic71⋊C4C24124yes—
266Dic71⋊C4C24124yes—
267C22⋊Dic71C24112yes—
268C22⋊Dic71C24124yes—
269(C2×D71)⋊C4C24124yes—
270(C2×D71)⋊C4C24124yes—
271(C2×D71)⋊C4C24124yes—
272C4×Dic71C2413yes—
273C4×Dic71C2416yes—
274C4×Dic71C2413yes—
275C4×Dic71C2416yes—
276C4×Dic71C2416yes—
277C4×Dic71C2416yes—
278C4×Dic71C2416yes—
279C4×Dic71C2413yes—
280C4×Dic71C2416yes—
281C4×Dic71C2413yes—
282C4×Dic71C24124yes—
283C4×Dic71C24112yes—
284C24×C71C2411yescharacteristic
285#41×C71—224no—
286C2×Q8×C71C2416yes—
287C2×D4×C71C24112yes—
288C2×D4×C71C2416yes—
289C22×C4×C71—212no—
290C22×C4×C71C2416yes—
291C22×C4×C71C2416yes—
292C22×C4×C71C2413yes—
293C22×C4×C71C24112yes—
294C22×C4×C71C2413yes—
295C4⋊C4×C71C24112yes—
296C4⋊C4×C71C24124yes—
297C22⋊C4×C71C24112yes—
298C22⋊C4×C71C24124yes—
299C42×C71C2413yes—
300C42×C71C2416yes—
301C42×C71C2413yes—
302C42×C71C2412yes—
303C42×C71C2411yescharacteristic
304C42×C71C24112yes—
305C42×C71C2411yescharacteristic
306C23×C71—26no—
307C23×C71C2514yes—
308C23×C71C2513yes—
309C22×D71—232no—
310C22×D71—26no—
311C22×D71—212no—
312C22×D71—212no—
313C22×D71—224no—
314C22×D71C2×#41112yes—
315C22×D71C2514yes—
316C22×D71C2513yes—
317C22×D71C2511yescharacteristic
318Q8×C71—212no—
319D4×C71—224no—
320D4×C71—212no—
321C2×C4×C71—26no—
322C2×C4×C71—212no—
323C2×C4×C71—212no—
324C2×C4×C71—224no—
325C2×C4×C71C2×#41112yescomplemented
326C2×C4×C71C2516yes—
327C2×C4×C71C25112yes—
328C2×C4×C71C2513yes—
329C2×C4×C71C2513yes—
330C22⋊D71—224no—
331C22⋊D71—224no—
332C22⋊D71—224no—
333C2×Dic71—26no—
334C2×Dic71—212no—
335C2×Dic71—212no—
336C2×Dic71—224no—
337C2×Dic71C2×#41112yescomplemented
338C2×Dic71C2516yes—
339C2×Dic71C25112yes—
340C2×Dic71C2513yes—
341C2×Dic71C2513yes—
342D284—224no—
343D284—212no—
344C4×D71—212no—
345C4×D71—212no—
346C4×D71—224no—
347C4×D71—212no—
348C4×D71—212no—
349C4×D71—224no—
350C4×D71—212no—
351C4×D71—212no—
352C4×D71—224no—
353C4×D71C2×#41112yes—
354C4×D71C2×#41112yes—
355C4×D71C2×#41112yescomplemented
356C4×D71C2×#41112yescomplemented
357Dic142—212no—
358Dic142—224no—
359C22×C71—28no—
360C22×C71—26no—
361C22×C71—212no—
362C22×C71C22×#4116yes—
363C22×C71C2611yescharacteristic
364C2×D71—224no—
365C2×D71—26no—
366C2×D71—224no—
367C2×D71—212no—
368C2×D71—416no—
369C2×D71C22×#4116yes—
370C2×D71C22×#4116yes—
371C4×C71—212no—
372C4×C71—26no—
373C4×C71C22×#4116yes—
374C4×C71C22×#4116yes—
375Dic71—212no—
376Dic71—26no—
377Dic71C22×#4116yes—
378Dic71C22×#4116yes—
379C2×#3444—711nomaximal, Sylow
380C2×C71—26no—
381C2×C71—44no—
382C2×C71C23×#4113yes—
383D71—26no—
384D71—44no—
385D71#344414yesdirect product factor
386#3444—711no—
387#3444—713no—
388#3444—713no—
389#3444—7112no—
390#3444—716no—
391#3444—716no—
392#3444D7111yescharacteristic, direct product factor
393C2×#533—713no—
394C2×#532—713no—
395C2×#529—7112no—
396C2×#525—716no—
397C2×C4×#41—716no—
398C23×C42—711no—
399C71C2×#344411yescharacteristic, complemented, Sylow
400C22×#41—716no—
401C24×C4—713no—
402#533—716no—
403#533—716no—
404#533—7112no—
405#533—7112no—
406#533—716no—
407#533—713no—
408#533C2×D7113yescomplemented
409#532—716no—
410#532—713no—
411#532—713no—
412#532—716no—
413#532—7112no—
414#532—7112no—
415#532—713no—
416#532C2×D7113yescomplemented
417C2×C4⋊Q8—713no—
418C2×#127—711no—
419#529—7124no—
420#529—7112no—
421#529—7112no—
422#529—7124no—
423#529—7112no—
424#529—7112no—
425#529—7112no—
426#529—7124no—
427#529—7112no—
428#529—7124no—
429#529—7112no—
430#529C2×D71112yescomplemented
431C2×#126—718no—
432C2×#125—716no—
433C2×#124—716no—
434#525—716no—
435#525—716no—
436#525—7112no—
437#525—7112no—
438#525—7112no—
439#525—7112no—
440#525—7124no—
441#525—716no—
442#525C2×D7116yescomplemented
443C2×#123—7112no—
444C2×C22⋊Q8—7112no—
445C2×#121—7112no—
446C2×#120—714no—
447C4×#41—716no—
448C4×#41—7112no—
449C4×#41—7124no—
450C4×#41—7112no—
451C4×#41—716no—
452C4×#41—7112no—
453C4×#41—716no—
454C4×#41—7112no—
455C4×#41C2×D7116yescomplemented
456C2×C4×Q8—7112no—
457C2×C4×D4—7124no—
458C2×C4×D4—7112no—
459C2×#117—716no—
460C2×#117—7112no—
461C22×C42—713no—
462C22×C42—713no—
463C22×C42—716no—
464C22×C42—713no—
465C22×C42—713no—
466C22×C42—716no—
467C22×C42—713no—
468C22×C42—714no—
469C22×C42C2×D7111yescharacteristic, complemented
470C25—711no—
471C2×#41—716no—
472C2×#41—7112no—
473C2×#41—716no—
474C2×#41—7112no—
475C2×#41—716no—
476C2×#41—14248no—
477C2×#41C22×D7116yes—
478C22×Q8—716no—
479C22×D4—7112no—
480C22×D4—716no—
481C23×C4—713no—
482C23×C4—713no—
483C23×C4—7112no—
484C23×C4—716no—
485C23×C4—716no—
486C23×C4—713no—
487C23×C4—713no—
488C23×C4—716no—
489C23×C4—716no—
490C23×C4—713no—
491C23×C4—14224no—
492C23×C4C22×D7113yes—
493C4⋊Q8—716no—
494C4⋊Q8—7112no—
495C4⋊Q8—713no—
496C4⋊Q8C22×D7113yescomplemented
497#127—716no—
498#127—711no—
499#127C22×D7111yescharacteristic, complemented
500#126—7124no—
501#126—7124no—
502#126—718no—
503#126C22×D7118yescomplemented
504#125—7124no—
505#125—7112no—
506#125—716no—
507#125C22×D7116yescomplemented
508#124—716no—
509#124—716no—
510#124—7124no—
511#124—716no—
512#124C22×D7116yescomplemented
513#123—7112no—
514#123—7112no—
515#123—7124no—
516#123—7124no—
517#123—7112no—
518#123C22×D71112yes—
519C22⋊Q8—7112no—
520C22⋊Q8—7112no—
521C22⋊Q8—7124no—
522C22⋊Q8—7112no—
523C22⋊Q8—7124no—
524C22⋊Q8C22×D71112yes—
525#121—7112no—
526#121—7124no—
527#121—7112no—
528#121—7112no—
529#121—7124no—
530#121C22×D71112yes—
531#120—714no—
532#120—7112no—
533#120—7112no—
534#120C22×D7114yes—
535C4×Q8—7112no—
536C4×Q8—7124no—
537C4×Q8—7112no—
538C4×Q8—7124no—
539C4×Q8—7112no—
540C4×Q8C22×D71112yescomplemented
541C4×D4—7124no—
542C4×D4—7112no—
543C4×D4—7124no—
544C4×D4—7124no—
545C4×D4—7124no—
546C4×D4—7124no—
547C4×D4—7112no—
548C4×D4—7124no—
549C4×D4—7124no—
550C4×D4—7124no—
551C4×D4—7124no—
552C4×D4—7112no—
553C4×D4C22×D71124yes—
554C4×D4C22×D71112yescomplemented
555#117—716no—
556#117—7112no—
557#117—7112no—
558#117—7124no—
559#117—7112no—
560#117—7124no—
561#117—7112no—
562#117—7112no—
563#117—7112no—
564#117C22×D7116yes—
565#117C22×D71112yescomplemented
566C2×C4⋊C4—7112no—
567C2×C4⋊C4—7124no—
568C2×C22⋊C4—7112no—
569C2×C22⋊C4—7124no—
570C2×C42—7112no—
571C2×C42—716no—
572C2×C42—713no—
573C2×C42—716no—
574C2×C42—716no—
575C2×C42—716no—
576C2×C42—716no—
577C2×C42—713no—
578C2×C42—713no—
579C2×C42—7112no—
580C2×C42—716no—
581C2×C42—7112no—
582C2×C42—716no—
583C2×C42—713no—
584C2×C42—713no—
585C2×C42—712no—
586C2×C42—716no—
587C2×C42—716no—
588C2×C42—716no—
589C2×C42—716no—
590C2×C42—711no—
591C2×C42—713no—
592C2×C42—713no—
593C2×C42—716no—
594C2×C42—714no—
595C2×C42—713no—
596C2×C42—711no—
597C2×C42C22×D7116yes—
598C2×C42C22×D7113yes—
599C2×C42C22×D7113yes—
600C2×C42C22×D7114yescomplemented
601C24—713no—
602C24—714no—
603C24—713no—
604C24—14212no—
605C24C23×D7111yescharacteristic
606#41—224no—
607#41—14248no—
608#41—14248no—
609#41—14224no—
610#41—14224no—
611#41—14224no—
612C2×Q8—7112no—
613C2×Q8—716no—
614C2×Q8—14224no—
615C2×Q8C23×D7116yes—
616C2×D4—7112no—
617C2×D4—7112no—
618C2×D4—7112no—
619C2×D4—7112no—
620C2×D4—716no—
621C2×D4—14224no—
622C2×D4—14248no—
623C2×D4C23×D71112yes—
624C2×D4C23×D7116yes—
625C22×C4—212no—
626C22×C4—713no—
627C22×C4—7124no—
628C22×C4—713no—
629C22×C4—713no—
630C22×C4—713no—
631C22×C4—713no—
632C22×C4—716no—
633C22×C4—716no—
634C22×C4—713no—
635C22×C4—7112no—
636C22×C4—716no—
637C22×C4—716no—
638C22×C4—716no—
639C22×C4—716no—
640C22×C4—716no—
641C22×C4—716no—
642C22×C4—7112no—
643C22×C4—7112no—
644C22×C4—7112no—
645C22×C4—14212no—
646C22×C4—14224no—
647C22×C4—14224no—
648C22×C4—14224no—
649C22×C4—14224no—
650C22×C4—14248no—
651C22×C4—14212no—
652C22×C4—14212no—
653C22×C4—14212no—
654C22×C4C23×D7116yes—
655C22×C4C23×D7116yes—
656C22×C4C23×D7113yes—
657C22×C4C23×D71112yes—
658C22×C4C23×D7113yes—
659C4⋊C4—7124no—
660C4⋊C4—7124no—
661C4⋊C4—7124no—
662C4⋊C4—7112no—
663C4⋊C4—7124no—
664C4⋊C4C23×D71112yes—
665C4⋊C4C23×D71124yes—
666C22⋊C4—7112no—
667C22⋊C4—7124no—
668C22⋊C4—7124no—
669C22⋊C4—7124no—
670C22⋊C4—7124no—
671C22⋊C4C23×D71112yes—
672C22⋊C4C23×D71124yes—
673C42—713no—
674C42—716no—
675C42—713no—
676C42—716no—
677C42—716no—
678C42—716no—
679C42—716no—
680C42—713no—
681C42—716no—
682C42—713no—
683C42—7124no—
684C42—7112no—
685C42C23×D7113yes—
686C42C23×D7116yes—
687C42C23×D7113yes—
688C42C23×D7112yes—
689C42C23×D7111yescharacteristic
690C42C23×D71112yes—
691C42C23×D7111yescharacteristic
692C23—26no—
693C23—711no—
694C23—7112no—
695C23—713no—
696C23—714no—
697C23—14224no—
698C23—14212no—
699C23—14212no—
700C23—14232no—
701C23—1426no—
702C23C24×D7114yes—
703C23C24×D7113yes—
704Q8—212no—
705Q8—14224no—
706Q8—14212no—
707D4—224no—
708D4—212no—
709D4—14224no—
710D4—14224no—
711D4—14224no—
712D4—14224no—
713D4—14212no—
714C2×C4—26no—
715C2×C4—212no—
716C2×C4—212no—
717C2×C4—224no—
718C2×C4—7112no—
719C2×C4—713no—
720C2×C4—713no—
721C2×C4—7112no—
722C2×C4—7112no—
723C2×C4—7112no—
724C2×C4—7112no—
725C2×C4—716no—
726C2×C4—7112no—
727C2×C4—14212no—
728C2×C4—14212no—
729C2×C4—14224no—
730C2×C4—14212no—
731C2×C4—14212no—
732C2×C4—14224no—
733C2×C4—14212no—
734C2×C4—14212no—
735C2×C4—14224no—
736C2×C4—1426no—
737C2×C4—14212no—
738C2×C4—14212no—
739C2×C4—14224no—
740C2×C4#41×D71112yescomplemented
741C2×C4C24×D7116yes—
742C2×C4C24×D71112yes—
743C2×C4C24×D7113yes—
744C2×C4C24×D7113yes—
745C22—28no—
746C22—26no—
747C22—212no—
748C22—28416no—
749C22—716no—
750C22—716no—
751C22—14224no—
752C22—14224no—
753C22—14212no—
754C22—1426no—
755C22C2×#41×D7116yes—
756C22C25×D7111yescharacteristic
757C4—26no—
758C4—212no—
759C4—716no—
760C4—716no—
761C4—1426no—
762C4—14212no—
763C4C2×#41×D7116yes—
764C4C2×#41×D7116yes—
765C2—26no—
766C2—44no—
767C2—2844no—
768C2—714no—
769C2—1426no—
770C2C22×#41×D7113yes—
subgroupG/H
centerC42C23×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC71×#3444C2
hypercenter#3444D71
hypocenterC71C2×#3444
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #22601637C2semidirect
2. #22601636C2semidirect
3. #22601635C2semidirect
4. #22601634C2semidirect
5. #22601633C2semidirect
6. #22601632C2semidirect
7. #533×D71C2semidirect
8. #532×D71C2semidirect
9. #529×D71C2semidirect
10. #525×D71C2semidirect
11. C4×#41×D71C2semidirect
12. C22×C42×D71C2semidirect
13. C71×#3444C2semidirect
16. #17986556C22semidirect
17. #17986555C22semidirect
18. #17986554C22semidirect
19. #17986553C22semidirect
20. #17986552C22semidirect
21. #17986551C22semidirect
22. #17986550C22semidirect
23. #17986549C22semidirect
24. #17986548C22semidirect
25. #17986547C22semidirect
26. #17986546C22semidirect
27. #17986545C22semidirect
28. #17986544C22semidirect
29. C4⋊Q8×D71C22semidirect
30. #127×D71C22semidirect
31. #17986536C22semidirect
32. #17986535C22semidirect
33. #17986534C22semidirect
34. #17986533C22semidirect
35. #17986532C22semidirect
36. #17986531C22semidirect
37. #17986530C22semidirect
38. #17986529C22semidirect
39. #17986528C22semidirect
40. #17986527C22semidirect
41. #17986526C22semidirect
42. #126×D71C22semidirect
43. #125×D71C22semidirect
44. #124×D71C22semidirect
45. #17986512C22semidirect
46. #17986511C22semidirect
47. #17986510C22semidirect
48. #17986509C22semidirect
49. #17986508C22semidirect
50. #17986507C22semidirect
51. #17986506C22semidirect
52. #17986505C22semidirect
57. #41×Dic71C22semidirect
58. C4×#11765866C22semidirect
59. C4×#11765865C22semidirect
60. C4×#11765865C22semidirect
61. #17986467C22semidirect
62. #17986467C22semidirect
63. C4×#11765864C22semidirect
64. C4×#11765864C22semidirect
65. C4×Q8×D71C22semidirect
67. C4×D4×D71C22semidirect
69. #117×D71C22semidirect
70. C22×C4×Dic71C22semidirect
74. C2×C42×D71C22semidirect
75. C2×C42×D71C22semidirect
76. C2×C42×D71C22semidirect
77. C2×C42×D71C22semidirect
78. #533×C71C22semidirect
79. #532×C71C22semidirect
80. #529×C71C22semidirect
81. #525×C71C22semidirect
82. C4×#41×C71C22semidirect
83. C22×C42×C71C22semidirect
105. #14556128C23semidirect
106. #14556127C23semidirect
107. #14556126C23semidirect
108. #14556125C23semidirect
109. #14556124C23semidirect
110. #14556123C23semidirect
111. #14556122C23semidirect
112. #14556121C23semidirect
113. #14556120C23semidirect
114. #14556119C23semidirect
115. #14556118C23semidirect
116. #14556117C23semidirect
117. #14556116C23semidirect
118. #14556115C23semidirect
119. #14556114C23semidirect
138. Q8×Dic71C23semidirect
139. C4×Dic142C23semidirect
140. C4×Dic142C23semidirect
141. #14556093C23semidirect
142. #14556093C23semidirect
144. C4×D284C23semidirect
146. D4×Dic71C23semidirect
148. #14556090C23semidirect
151. C4×C22⋊D71C23semidirect
154. (C22⋊D71)⋊C4C23semidirect
156. #14556087C23semidirect
158. #14556086C23semidirect
160. #14556085C23semidirect
161. #14556085C23semidirect
163. #14556084C23semidirect
175. C2×C4×Dic71C23semidirect
193. C42×D71C23semidirect
194. C42×D71C23semidirect
197. C4⋊Q8×C71C23semidirect
198. #127×C71C23semidirect
199. #126×C71C23semidirect
200. #125×C71C23semidirect
201. #124×C71C23semidirect
206. C4×Q8×C71C23semidirect
208. C4×D4×C71C23semidirect
210. #117×C71C23semidirect
214. C2×C42×C71C23semidirect
248. C2×C4×D71#41semidirect
325. C2×C4×C71C2×#41semidirect
337. C2×Dic71C2×#41semidirect
355. C4×D71C2×#41semidirect
356. C4×D71C2×#41semidirect
385. D71#3444direct (N × H)
392. #3444D71direct (N × H)
399. C71C2×#3444semidirect
408. #533C2×D71semidirect
416. #532C2×D71semidirect
430. #529C2×D71semidirect
442. #525C2×D71semidirect
455. C4×#41C2×D71semidirect
469. C22×C42C2×D71semidirect
496. C4⋊Q8C22×D71semidirect
499. #127C22×D71semidirect
503. #126C22×D71semidirect
507. #125C22×D71semidirect
512. #124C22×D71semidirect
540. C4×Q8C22×D71semidirect
554. C4×D4C22×D71semidirect
565. #117C22×D71semidirect
600. C2×C42C22×D71semidirect
740. C2×C4#41×D71semidirect

Maximal subgroups

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

subgroupindex
#226016372
#226016362
#226016352
#226016342
#226016332
#226016322
#533×D712
#532×D712
#529×D712
#525×D712
C4×#41×D712
C22×C42×D712
C71×#34442
C2×#344471