Finite Group Databasebeta

← #32905846

Subgroups — #32905846

Order 18176.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602425C212yesmaximal, complemented
2#22602372C216yesmaximal, complemented
3#22602346C212yesmaximal, complemented
4#22602301C216yesmaximal, complemented
5#22602251C213yesmaximal, complemented
6#22602216C213yesmaximal, complemented
7#22602159C211yesmaximal, characteristic, complemented
8#22602118C211yesmaximal, characteristic, complemented
9#22602075C216yesmaximal, complemented
10#22602009C212yesmaximal, complemented
11#22601966C212yesmaximal, complemented
12#22601950C216yesmaximal, complemented
13#22601935C212yesmaximal, complemented
14D4×#11765865C216yesmaximal, complemented
15#22601756C216yesmaximal, complemented
16#22601636C213yesmaximal, complemented
17C2×#17986549C213yesmaximal, complemented
18C4×#14556174C212yesmaximal, complemented
19C2×C4×#41×C71C211yesmaximal, characteristic, complemented
20C2×#14556174C2212yes—
21C22×#11765865C2216yescomplemented
22#17986734C2216yescomplemented
23#17986734C2216yescomplemented
24Q8×Dic142C2212yescomplemented
25#17986728C2212yescomplemented
26#17986722C2216yescomplemented
27#17986714C2216yescomplemented
28#17986712C22112yescomplemented
29#17986709C2216yescomplemented
30#17986706C2216yescomplemented
31#17986697C22112yescomplemented
32#17986695C22112yescomplemented
33#17986693C22112yescomplemented
34#17986673C22124yescomplemented
35#17986671C2212yescomplemented
36#17986671C2212yescomplemented
37#17986670C2216yescomplemented
38#17986670C2216yescomplemented
39#17986668C2214yescomplemented
40D4×Dic142C2216yescomplemented
41#17986660C2214yescomplemented
42#17986658C22112yescomplemented
43#17986654C2216yescomplemented
44#17986650C22112yescomplemented
45#17986645C22112yescomplemented
46#17986645C22112yescomplemented
47#17986639C22124yescomplemented
48#17986637C22112yescomplemented
49D4×D284C2216yescomplemented
50D4×D284C2216yescomplemented
51D4×C22⋊D71C22112yescomplemented
52#17986627C2216yescomplemented
53#17986621C22112yescomplemented
54#17986620C22112yescomplemented
55#17986604C22112yescomplemented
56#17986600C22112yescomplemented
57#17986582C22124yescomplemented
58#17986577C2216yescomplemented
59#17986568C2216yescomplemented
60#17986563C2216yescomplemented
61#17986556C2213yescomplemented
62#17986556C2211yescharacteristic, complemented
63#17986556C2213yescomplemented
64#17986549C2213yescomplemented
65#17986549C2216yescomplemented
66#17986549C2216yescomplemented
67#17986549C2216yescomplemented
68#17986549C2216yescomplemented
69#17986549C2216yescomplemented
70#17986549C2216yescomplemented
71#17986549C2213yescomplemented
72#17986549C2216yescomplemented
73#17986549C2213yescomplemented
74#17986546C22112yescomplemented
75C2×#14556128C2213yescomplemented
76C2×#14556125C2213yescomplemented
77#17986536C22112yescomplemented
78#17986533C2216yescomplemented
79#17986533C2216yescomplemented
80#17986533C2216yescomplemented
81#17986533C2216yescomplemented
82#17986533C2216yescomplemented
83#17986533C2216yescomplemented
84C2×#14556116C2216yescomplemented
85#17986510C2216yescomplemented
86#17986510C2216yescomplemented
87#17986510C2216yescomplemented
88#17986508C22124yescomplemented
89C2×#14556102C2216yescomplemented
90C2×#14556102C2216yescomplemented
91#17986482C2212yes—
92#17986481C2214yescomplemented
93#17986479C2216yescomplemented
94#17986473C2216yescomplemented
95#17986471C22112yescomplemented
96C4×#11765866C2214yescomplemented
97C4×#11765865C2216yescomplemented
98C4×#11765865C2216yescomplemented
99C4×#11765865C2216yescomplemented
100C2×C4×D284C2216yescomplemented
101C2×C4×D284C2216yescomplemented
102C4×D4×D71C22112yescomplemented
103C22×#41×C71C2211yescharacteristic
104C4×#41×C71C2211yescharacteristic
105C4×#41×C71C2211yescharacteristic
106C4×#41×C71C2213yescomplemented
107C4×#41×C71C2213yescomplemented
108C4×#41×C71C2213yescomplemented
109C4×#41×C71C2211yescharacteristic, complemented
110C4×#41×C71C2213yescomplemented
111C4×#41×C71C2211yescharacteristic, complemented
112C2×C4×Q8×C71C2211yescharacteristic, complemented
113C2×C4×Q8×C71C2211yescharacteristic, complemented
114C2×C4×D4×C71C2213yescomplemented
115C2×C4×D4×C71C2213yescomplemented
116C2×#117×C71C2213yescomplemented
117C22×C42×C71C2213yescomplemented
118#14556174—216no—
119C2×#11765866C2314yes—
120C2×#11765865—424no—
121C2×#11765865C2316yes—
122C2×#11765865C2316yes—
123C2×#11765865C23112yes—
124C2×#11765865C23112yes—
125C2×#11765865C23112yes—
126C2×#11765865C2316yes—
127C22×Dic142C2316yes—
128C22×D284C2316yes—
129C22×D284C2316yes—
130C22×D284C2316yes—
131C22×C22⋊D71C23112yes—
132C2×D4×D71C23112yes—
133C22×C4×D71C23112yes—
134#14556128C2316yes—
135#14556128C2316yes—
136#14556128C2316yes—
137#14556128C2313yes—
138#14556128C2311yescharacteristic
139#14556128C2311yescharacteristic
140#14556127C23112yes—
141#14556125C2316yes—
142#14556125C2316yes—
143#14556125C2316yes—
144#14556125C2313yes—
145#14556124C23112yes—
146#14556123C23124yes—
147#14556122C23112yes—
148#14556122C23112yes—
149#14556120C2316yes—
150#14556120C2316yes—
151#14556120C2312yes—
152#14556119C23112yes—
153#14556117C23112yes—
154#14556116C2316yes—
155#14556116C23112yes—
156#14556116C2316yes—
157#14556116C23112yes—
158#14556116C23112yes—
159#14556116C2316yes—
160#14556114C23124yes—
161#14556113C23124yes—
162#14556113C23124yes—
163#14556111C23112yes—
164#14556111C23112yes—
165#14556111C23112yes—
166#14556110C23124yes—
167#14556107C2316yes—
168#14556107C2316yes—
169#14556107C2316yes—
170#14556107C2316yes—
171#14556107C2312yes—
172#14556107C2312yes—
173#14556106C23124yes—
174#14556105C23124yes—
175#14556104C23112yes—
176#14556103C23112yes—
177#14556103C23112yes—
178#14556102C2316yes—
179#14556102C23112yes—
180#14556102C23112yes—
181#14556102C23112yes—
182#14556102C2316yes—
183#14556102C2316yes—
184#14556102C23112yes—
185#14556102C23112yes—
186#14556102C2316yes—
187#14556102C23112yes—
188#14556102C2316yes—
189#14556102C2316yes—
190#14556101C23124yes—
191#14556101C23124yes—
192#14556100C23124yes—
193#14556099C23112yes—
194#14556098C23124yes—
195#14556097C23112yes—
196#14556096C23124yes—
197Q8×Dic71C2314yes—
198C4×Dic142C2316yes—
199C4×Dic142C2316yes—
200C4×Dic142C2316yes—
201C4×Dic142C2316yes—
202C4×Dic142C2312yes—
203C4×Dic142C2312yes—
204C4×D284C23112yes—
205C4×D284C2316yes—
206C4×D284C23112yes—
207C4×D284C2316yes—
208C4×D284C2316yes—
209C4×D284C2316yes—
210C4×D284C23112yes—
211C4×D284C23112yes—
212C4×D284C23112yes—
213C4×D284C2316yes—
214C4×D284C2316yes—
215C4×D284C23112yes—
216D4×Dic71C23112yes—
217#14556090C23112yes—
218#14556090C23112yes—
219C4×C22⋊D71C23112yes—
220C4×C22⋊D71C23112yes—
221C4×C22⋊D71C23112yes—
222C4×C22⋊D71C23112yes—
223C4×C22⋊D71C23112yes—
224C4×C22⋊D71C23112yes—
225(C22⋊D71)⋊C4C23124yes—
226#14556087C2316yes—
227#14556087C2316yes—
228#14556087C2312yes—
229#14556086C23112yes—
230#14556085C23112yes—
231#14556085C23112yes—
232#14556085C23112yes—
233C2×C4⋊Dic71C2316yes—
234C2×C4⋊Dic71C2316yes—
235C4⋊C4×D71C23112yes—
236C2×(C2×D71)⋊C4C23112yes—
237C2×(C2×D71)⋊C4C23112yes—
238C22⋊C4×D71C23124yes—
239C42×D71C23112yes—
240C2×#41×C71—28no—
241C2×#41×C71C2313yes—
242C2×#41×C71C2313yes—
243C2×#41×C71C2311yescharacteristic
244C2×#41×C71C2311yescharacteristic
245C22×Q8×C71C2311yescharacteristic
246C22×D4×C71C2313yes—
247C23×C4×C71C2313yes—
248C23×C4×C71C2313yes—
249C23×C4×C71C2313yes—
250C4×Q8×C71C2313yes—
251C4×Q8×C71C2311yescharacteristic
252C4×Q8×C71C2311yescharacteristic
253C4×Q8×C71C2311yescharacteristic
254C4×Q8×C71C2311yescharacteristic
255C4×Q8×C71C2313yes—
256C4×Q8×C71C2313yes—
257C4×Q8×C71C2313yes—
258C4×D4×C71C2316yes—
259C4×D4×C71C2313yes—
260C4×D4×C71C2313yes—
261C4×D4×C71C2313yes—
262C4×D4×C71C2316yes—
263C4×D4×C71C2316yes—
264C4×D4×C71C2313yes—
265C4×D4×C71C2313yes—
266C4×D4×C71C2313yes—
267C4×D4×C71C2313yes—
268C4×D4×C71C2316yes—
269C4×D4×C71C2313yes—
270#117×C71C2313yes—
271#117×C71C2316yes—
272#117×C71C2313yes—
273#117×C71C2316yes—
274#117×C71C2313yes—
275#117×C71C2313yes—
276C2×C4⋊C4×C71C2313yes—
277C2×C4⋊C4×C71C2313yes—
278C2×C22⋊C4×C71C2316yes—
279C2×C42×C71C2311yescharacteristic
280C2×C42×C71C2313yes—
281C2×C42×C71C2313yes—
282C2×C42×C71C2313yes—
283C2×C42×C71C2313yes—
284C2×C42×C71C2313yes—
285C2×C42×C71C2313yes—
286C2×C42×C71C2313yes—
287C2×C42×C71C2313yes—
288C2×C42×C71C2313yes—
289C2×C42×C71C2313yes—
290C2×C42×C71C2313yes—
291C23×D71C24112yes—
292#11765866—216no—
293#11765865—224no—
294#11765865—224no—
295#11765865—424no—
296#11765865—412no—
297#11765865—424no—
298#11765865—424no—
299C2×Dic142—412no—
300C2×Dic142C2416yes—
301C2×Dic142C2412yes—
302C2×Dic142C2412yes—
303C2×Dic142C24112yes—
304C2×D284—224no—
305C2×D284—412no—
306C2×D284—412no—
307C2×D284C24112yes—
308C2×D284C2416yes—
309C2×D284C2416yes—
310C2×D284C2416yes—
311C2×D284C24112yes—
312C2×D284C24112yes—
313C2×C22⋊D71—424no—
314C2×C22⋊D71C24112yes—
315C2×C22⋊D71C24112yes—
316C2×C22⋊D71C24124yes—
317C2×C22⋊D71C24112yes—
318D4×D71—248no—
319C22×Dic71C24112yes—
320C2×C4×D71—424no—
321C2×C4×D71C24112yes—
322C2×C4×D71C24112yes—
323C2×C4×D71C24124yes—
324C2×C4×D71C24112yes—
325C4⋊Dic71C24112yes—
326C4⋊Dic71C2416yes—
327C4⋊Dic71C2416yes—
328C4⋊Dic71C24112yes—
329C4⋊Dic71C2412yes—
330C4⋊Dic71C2412yes—
331C4⋊Dic71C2412yes—
332C4⋊Dic71C2412yes—
333Dic71⋊C4C24112yes—
334Dic71⋊C4C2414yes—
335Dic71⋊C4C2414yes—
336Dic71⋊C4C24112yes—
337Dic71⋊C4C24112yes—
338Dic71⋊C4C24112yes—
339C22⋊Dic71C24112yes—
340C22⋊Dic71C2414yes—
341C22⋊Dic71C24112yes—
342(C2×D71)⋊C4C24112yes—
343(C2×D71)⋊C4C24124yes—
344(C2×D71)⋊C4C24112yes—
345(C2×D71)⋊C4C24112yes—
346(C2×D71)⋊C4C24124yes—
347(C2×D71)⋊C4C24112yes—
348(C2×D71)⋊C4C24112yes—
349(C2×D71)⋊C4C24112yes—
350C4×Dic71C2414yes—
351C4×Dic71C24112yes—
352C4×Dic71C24112yes—
353C24×C71C2413yes—
354#41×C71—24no—
355#41×C71—212no—
356#41×C71—212no—
357#41×C71#4118yescomplemented
358C2×Q8×C71—24no—
359C2×Q8×C71C2413yes—
360C2×Q8×C71C2411yescharacteristic
361C2×D4×C71—212no—
362C2×D4×C71C2416yes—
363C2×D4×C71C2413yes—
364C2×D4×C71C2413yes—
365C22×C4×C71—212no—
366C22×C4×C71—212no—
367C22×C4×C71—46no—
368C22×C4×C71C2413yes—
369C22×C4×C71C2413yes—
370C22×C4×C71C2413yes—
371C22×C4×C71C2413yes—
372C22×C4×C71C2413yes—
373C22×C4×C71C2413yes—
374C22×C4×C71C2413yes—
375C22×C4×C71C2411yescharacteristic
376C22×C4×C71C2411yescharacteristic
377C22×C4×C71C2413yes—
378C22×C4×C71C2413yes—
379C22×C4×C71C2413yes—
380C22×C4×C71C2413yes—
381C22×C4×C71C2413yes—
382C22×C4×C71C2413yes—
383C22×C4×C71C2413yes—
384C22×C4×C71C2413yes—
385C22×C4×C71C2411yescharacteristic
386C4⋊C4×C71C2413yes—
387C4⋊C4×C71C2413yes—
388C4⋊C4×C71C2413yes—
389C4⋊C4×C71C2413yes—
390C4⋊C4×C71C2416yes—
391C4⋊C4×C71C2416yes—
392C22⋊C4×C71C2416yes—
393C22⋊C4×C71C2416yes—
394C22⋊C4×C71C2416yes—
395C22⋊C4×C71C2416yes—
396C42×C71C2411yescharacteristic
397C42×C71C2411yescharacteristic
398C42×C71C2411yescharacteristic
399C42×C71C2411yescharacteristic
400C42×C71C2413yes—
401C42×C71C2413yes—
402C42×C71C2413yes—
403C42×C71C2413yes—
404C42×C71C2413yes—
405C42×C71C2413yes—
406C42×C71C2413yes—
407C42×C71C2413yes—
408C42×C71C2413yes—
409C42×C71C2413yes—
410C42×C71C2413yes—
411C42×C71C2413yes—
412C23×C71—26no—
413C23×C71—26no—
414C23×C71—43no—
415C23×C71C2513yes—
416C23×C71C2513yes—
417C23×C71C2511yescharacteristic
418C22×D71—224no—
419C22×D71—412no—
420C22×D71—412no—
421C22×D71C25112yes—
422Q8×C71—26no—
423Q8×C71C2×#4114yescomplemented
424D4×C71—212no—
425D4×C71—26no—
426D4×C71C2×#41112yescomplemented
427C2×C4×C71—26no—
428C2×C4×C71—26no—
429C2×C4×C71—22no—
430C2×C4×C71—26no—
431C2×C4×C71—26no—
432C2×C4×C71—26no—
433C2×C4×C71—26no—
434C2×C4×C71—26no—
435C2×C4×C71—26no—
436C2×C4×C71—26no—
437C2×C4×C71—22no—
438C2×C4×C71—26no—
439C2×C4×C71—26no—
440C2×C4×C71—43no—
441C2×C4×C71—43no—
442C2×C4×C71—43no—
443C2×C4×C71C2×#41112yescomplemented
444C2×C4×C71H(5,𝔽2)14yescomplemented
445C2×C4×C71C2511yescharacteristic
446C2×C4×C71C2511yescharacteristic
447C2×C4×C71C2513yes—
448C2×C4×C71C2513yes—
449C2×C4×C71C2513yes—
450C2×C4×C71C2513yes—
451C2×C4×C71C2513yes—
452C2×C4×C71C2511yescharacteristic
453C2×C4×C71C2513yes—
454C2×C4×C71C2511yescharacteristic
455C2×C4×C71C2511yescharacteristic
456C2×C4×C71C2511yescharacteristic
457C22⋊D71—224no—
458C22⋊D71—224no—
459C22⋊D71—424no—
460C22⋊D71—412no—
461C2×Dic71—412no—
462C2×Dic71C2514yes—
463C2×Dic71C2514yes—
464C2×Dic71C25112yes—
465D284—224no—
466D284—212no—
467D284—212no—
468D284—212no—
469D284—412no—
470D284—412no—
471C4×D71—224no—
472C4×D71—224no—
473C4×D71—424no—
474C4×D71—412no—
475Dic142—24no—
476Dic142—212no—
477Dic142—24no—
478Dic142—412no—
479C22×C71—21no—
480C22×C71—23no—
481C22×C71—21no—
482C22×C71—23no—
483C22×C71—23no—
484C22×C71—23no—
485C22×C71—23no—
486C22×C71—412no—
487C22×C71C22×#4116yes—
488C22×C71C2×H(5,𝔽2)12yes—
489C22×C71C2611yescharacteristic
490C2×D71—212no—
491C2×D71—212no—
492C2×D71—212no—
493C2×D71—824no—
494C4×C71—21no—
495C4×C71—23no—
496C4×C71—23no—
497C4×C71—23no—
498C4×C71—23no—
499C4×C71—23no—
500C4×C71—21no—
501C4×C71C22×#4112yes—
502C4×C71C22×#4116yes—
503C4×C71C2×H(5,𝔽2)12yes—
504C4×C71C2×H(5,𝔽2)12yes—
505C4×C71#58512yes—
506Dic71—24no—
507Dic71—212no—
508Dic71—24no—
509#62800—711nomaximal, Sylow
510C2×C71—26no—
511C2×C71—22no—
512C2×C71—43no—
513C2×C71C23×#4111yescharacteristic
514C2×C71C22×H(5,𝔽2)11yescharacteristic
515C2×C71C2×#58511yescharacteristic
516D71—412no—
517#3522—712no—
518#3519—716no—
519#3517—712no—
520#3514—716no—
521#3511—713no—
522#3508—713no—
523#3503—711no—
524#3498—711no—
525#3494—716no—
526#3488—712no—
527#3483—712no—
528#3481—716no—
529#3480—712no—
530D4×#41—716no—
531#3460—716no—
532#3444—713no—
533C2×#532—713no—
534C4×H(5,𝔽2)—712no—
535C2×C4×#41D7111yescharacteristic, complemented
536C71#6280011yescharacteristic, complemented, Sylow
537C2×H(5,𝔽2)—712no—
538C22×#41—716no—
539C22×#41C2×D7111yescharacteristic
540#559—716no—
541#559—716no—
542Q82—712no—
543#557—712no—
544#556—716no—
545#555—716no—
546#555—7112no—
547#554—716no—
548#554—716no—
549#553—7112no—
550#553—7112no—
551#553—7112no—
552#551—7124no—
553#550—714no—
554#550—712no—
555#550—712no—
556#550—716no—
557#550—716no—
558D4×Q8—716no—
559#548—714no—
560#548—7112no—
561#547—716no—
562#547—7112no—
563#546—7112no—
564#546—7112no—
565#546—7112no—
566#546—7124no—
567D42—7112no—
568D42—716no—
569D42—716no—
570#544—716no—
571#542—7112no—
572#542—7112no—
573#540—7112no—
574#540—7112no—
575#538—7124no—
576#537—716no—
577#535—716no—
578#535—716no—
579#533—711no—
580#533—713no—
581#533—713no—
582#532—7112no—
583#532—713no—
584#532—716no—
585#532—716no—
586#532—716no—
587#532—716no—
588#532—716no—
589#532—716no—
590#532—716no—
591#532—713no—
592#532—713no—
593C2×C4⋊Q8—713no—
594C2×#127—713no—
595#529—7112no—
596#529—716no—
597#529—716no—
598#529—716no—
599#529—716no—
600#529—716no—
601#529—716no—
602C2×#124—716no—
603#525—716no—
604#525—716no—
605#525—716no—
606#525—7124no—
607C2×#121—716no—
608C2×#121—716no—
609#520—712no—
610#520—714no—
611#520—716no—
612#518—7112no—
613#518—716no—
614C4×#41—714no—
615C4×#41—716no—
616C4×#41—716no—
617C4×#41—716no—
618C4×#41C2×D7111yescharacteristic
619C4×#41C2×D7111yescharacteristic
620C4×#41C2×D7113yescomplemented
621C4×#41C2×D7113yescomplemented
622C4×#41C2×D7111yescharacteristic, complemented
623C4×#41C2×D7113yescomplemented
624C4×#41C2×D7113yescomplemented
625C4×#41C2×D7111yescharacteristic, complemented
626C2×C4×Q8C2×D7111yescharacteristic, complemented
627C2×C4×Q8C2×D7111yescharacteristic, complemented
628C2×C4×D4—7112no—
629C2×C4×D4—716no—
630C2×C4×D4—716no—
631C2×C4×D4C2×D7113yescomplemented
632C2×C4×D4C2×D7113yescomplemented
633C2×#117C2×D7113yescomplemented
634C22×C42C2×D7113yescomplemented
635H(5,𝔽2)—14216no—
636C2×#41—28no—
637C2×#41—28424no—
638C2×#41—714no—
639C2×#41—716no—
640C2×#41—7112no—
641C2×#41—7112no—
642C2×#41—7112no—
643C2×#41—716no—
644C2×#41—716no—
645C2×#41C22×D7113yes—
646C2×#41C22×D7113yes—
647C2×#41C22×D7111yescharacteristic
648C2×#41C22×D7111yescharacteristic
649C22×Q8—716no—
650C22×Q8C22×D7111yescharacteristic
651C22×D4—7112no—
652C22×D4—7112no—
653C22×D4—716no—
654C22×D4—716no—
655C22×D4—716no—
656C22×D4C22×D7113yes—
657C23×C4—7112no—
658C23×C4C22×D7113yes—
659C23×C4C22×D7113yes—
660C23×C4C22×D7113yes—
661C4⋊Q8—7112no—
662C4⋊Q8—713no—
663C4⋊Q8—716no—
664C4⋊Q8—716no—
665C4⋊Q8—716no—
666C4⋊Q8—711no—
667C4⋊Q8—711no—
668#127—7112no—
669#127—713no—
670#127—716no—
671#127—716no—
672#127—716no—
673#126—7124no—
674#126—7112no—
675#126—7112no—
676#125—7112no—
677#125—712no—
678#125—716no—
679#125—716no—
680#124—7112no—
681#124—7124no—
682#124—716no—
683#124—7112no—
684#124—7112no—
685#124—7112no—
686#124—716no—
687#124—716no—
688#123—7112no—
689#123—7112no—
690#123—7112no—
691#123—7124no—
692#123—7124no—
693#123—7124no—
694C22⋊Q8—7112no—
695C22⋊Q8—712no—
696C22⋊Q8—712no—
697C22⋊Q8—716no—
698C22⋊Q8—716no—
699C22⋊Q8—716no—
700C22⋊Q8—716no—
701C22⋊Q8—7124no—
702C22⋊Q8—7124no—
703#121—7124no—
704#121—7112no—
705#121—716no—
706#121—716no—
707#121—7112no—
708#121—7112no—
709#121—7112no—
710#121—7112no—
711#121—7112no—
712#121—7112no—
713#121—716no—
714#121—716no—
715#121—716no—
716#121—716no—
717#121—7112no—
718#121—7112no—
719#121—7124no—
720#121—7124no—
721#120—7112no—
722#120—7124no—
723#120—7124no—
724C4×Q8—714no—
725C4×Q8—712no—
726C4×Q8—712no—
727C4×Q8—716no—
728C4×Q8—716no—
729C4×Q8—716no—
730C4×Q8—716no—
731C4×Q8C22×D7111yescharacteristic
732C4×Q8C22×D7111yescharacteristic
733C4×Q8C22×D7111yescharacteristic
734C4×Q8C22×D7111yescharacteristic
735C4×Q8C22×D7113yes—
736C4×Q8C22×D7113yes—
737C4×Q8C22×D7113yes—
738C4×Q8C22×D7113yes—
739C4×D4—7112no—
740C4×D4—7112no—
741C4×D4—7112no—
742C4×D4—7112no—
743C4×D4—7112no—
744C4×D4—7112no—
745C4×D4—7112no—
746C4×D4—7112no—
747C4×D4—7112no—
748C4×D4—7124no—
749C4×D4—7112no—
750C4×D4—716no—
751C4×D4—716no—
752C4×D4—7112no—
753C4×D4—7112no—
754C4×D4—7112no—
755C4×D4—7112no—
756C4×D4—7112no—
757C4×D4—716no—
758C4×D4—716no—
759C4×D4—716no—
760C4×D4—716no—
761C4×D4C22×D7113yes—
762C4×D4C22×D7113yes—
763C4×D4C22×D7113yes—
764C4×D4C22×D7113yes—
765C4×D4C22×D7116yes—
766C4×D4C22×D7113yes—
767C4×D4C22×D7116yes—
768C4×D4C22×D7113yes—
769C4×D4C22×D7116yes—
770C4×D4C22×D7116yes—
771C4×D4C22×D7113yes—
772C4×D4C22×D7113yes—
773#117—712no—
774#117—716no—
775#117—716no—
776#117—7112no—
777#117—7112no—
778#117—7112no—
779#117—7112no—
780#117C22×D7113yes—
781#117C22×D7113yes—
782#117C22×D7116yes—
783#117C22×D7116yes—
784#117C22×D7113yes—
785#117C22×D7113yes—
786C2×C4⋊C4—716no—
787C2×C4⋊C4—716no—
788C2×C4⋊C4—7112no—
789C2×C4⋊C4C22×D7113yes—
790C2×C4⋊C4C22×D7113yes—
791C2×C22⋊C4—7112no—
792C2×C22⋊C4—7112no—
793C2×C22⋊C4—7124no—
794C2×C22⋊C4C22×D7116yes—
795C2×C42—7112no—
796C2×C42C22×D7113yes—
797C2×C42C22×D7113yes—
798C2×C42C22×D7113yes—
799C2×C42C22×D7113yes—
800C2×C42C22×D7113yes—
801C2×C42C22×D7113yes—
802C2×C42C22×D7113yes—
803C2×C42C22×D7113yes—
804C2×C42C22×D7113yes—
805C2×C42C22×D7113yes—
806C2×C42C22×D7113yes—
807C2×C42C22×D7111yescharacteristic
808C24—7112no—
809C24C23×D7113yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—28424no—
814#41—28412no—
815#41—28424no—
816#41—28424no—
817#41—14216no—
818#41—14224no—
819#41—14224no—
820#41#1176586518yescomplemented
821C2×Q8—24no—
822C2×Q8—28412no—
823C2×Q8—7112no—
824C2×Q8—712no—
825C2×Q8—712no—
826C2×Q8—716no—
827C2×Q8C23×D7113yes—
828C2×Q8C23×D7111yescharacteristic
829C2×D4—212no—
830C2×D4—28412no—
831C2×D4—28412no—
832C2×D4—28424no—
833C2×D4—7112no—
834C2×D4—7124no—
835C2×D4—7112no—
836C2×D4—7112no—
837C2×D4—7112no—
838C2×D4—7112no—
839C2×D4—7112no—
840C2×D4—716no—
841C2×D4—716no—
842C2×D4—716no—
843C2×D4—14248no—
844C2×D4—14224no—
845C2×D4C23×D7116yes—
846C2×D4C23×D7113yes—
847C2×D4C23×D7113yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—28424no—
852C22×C4—7112no—
853C22×C4—7112no—
854C22×C4—7124no—
855C22×C4—7112no—
856C22×C4—7112no—
857C22×C4C23×D7111yescharacteristic
858C22×C4C23×D7111yescharacteristic
859C22×C4C23×D7113yes—
860C22×C4C23×D7113yes—
861C22×C4C23×D7113yes—
862C22×C4C23×D7113yes—
863C22×C4C23×D7113yes—
864C22×C4C23×D7113yes—
865C22×C4C23×D7113yes—
866C22×C4C23×D7113yes—
867C22×C4C23×D7113yes—
868C22×C4C23×D7113yes—
869C22×C4C23×D7113yes—
870C22×C4C23×D7113yes—
871C22×C4C23×D7113yes—
872C22×C4C23×D7113yes—
873C22×C4C23×D7113yes—
874C22×C4C23×D7111yescharacteristic
875C4⋊C4—7112no—
876C4⋊C4—714no—
877C4⋊C4—714no—
878C4⋊C4—7112no—
879C4⋊C4—7112no—
880C4⋊C4—7112no—
881C4⋊C4—7112no—
882C4⋊C4—716no—
883C4⋊C4—716no—
884C4⋊C4—7112no—
885C4⋊C4—712no—
886C4⋊C4—712no—
887C4⋊C4—712no—
888C4⋊C4—712no—
889C4⋊C4C23×D7113yes—
890C4⋊C4C23×D7113yes—
891C4⋊C4C23×D7113yes—
892C4⋊C4C23×D7113yes—
893C4⋊C4C23×D7116yes—
894C4⋊C4C23×D7116yes—
895C22⋊C4—7112no—
896C22⋊C4—714no—
897C22⋊C4—7112no—
898C22⋊C4—7112no—
899C22⋊C4—7124no—
900C22⋊C4—7112no—
901C22⋊C4—7112no—
902C22⋊C4—7124no—
903C22⋊C4—7112no—
904C22⋊C4—7112no—
905C22⋊C4—7112no—
906C22⋊C4C23×D7116yes—
907C22⋊C4C23×D7116yes—
908C22⋊C4C23×D7116yes—
909C22⋊C4C23×D7116yes—
910C42—7112no—
911C42—7112no—
912C42—714no—
913C42C23×D7111yescharacteristic
914C42C23×D7111yescharacteristic
915C42C23×D7113yes—
916C42C23×D7113yes—
917C42C23×D7113yes—
918C42C23×D7113yes—
919C42C23×D7113yes—
920C42C23×D7113yes—
921C42C23×D7113yes—
922C42C23×D7113yes—
923C42C23×D7113yes—
924C42C23×D7113yes—
925C42C23×D7113yes—
926C42C23×D7111yescharacteristic
927C42C23×D7111yescharacteristic
928C42C23×D7113yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—28412no—
933C23—28412no—
934C23—7112no—
935C23—14224no—
936C23C24×D7113yes—
937C23C24×D7113yes—
938C23C24×D7111yescharacteristic
939Q8—26no—
940Q8—28412no—
941Q8—1424no—
942Q8—14212no—
943Q8—1424no—
944Q8C2×#1176586514yescomplemented
945D4—212no—
946D4—26no—
947D4—28412no—
948D4—28412no—
949D4—28424no—
950D4—28412no—
951D4—14224no—
952D4—14224no—
953D4—14212no—
954D4—14224no—
955D4—14212no—
956D4—14212no—
957D4C2×#11765865112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—28424no—
975C2×C4—28412no—
976C2×C4—28412no—
977C2×C4—714no—
978C2×C4—714no—
979C2×C4—7112no—
980C2×C4—14224no—
981C2×C4—14224no—
982C2×C4C2×#11765865112yescomplemented
983C2×C4#1455617414yescomplemented
984C2×C4C24×D7113yes—
985C2×C4C24×D7111yescharacteristic
986C2×C4C24×D7111yescharacteristic
987C2×C4C24×D7113yes—
988C2×C4C24×D7113yes—
989C2×C4C24×D7113yes—
990C2×C4C24×D7113yes—
991C2×C4C24×D7113yes—
992C2×C4C24×D7111yescharacteristic
993C2×C4C24×D7111yescharacteristic
994C2×C4C24×D7111yescharacteristic
995C2×C4C24×D7111yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—56824no—
1005C22—14212no—
1006C22—14212no—
1007C22—14212no—
1008C22C22×#1176586516yes—
1009C22C2×#1455617412yes—
1010C22C25×D7111yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—1424no—
1019C4—14212no—
1020C4—1424no—
1021C4C22×#1176586512yes—
1022C4C22×#1176586516yes—
1023C4C2×#1455617412yes—
1024C4C2×#1455617412yes—
1025C4#1798683512yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—28412no—
1030C2C23×#1176586511yescharacteristic
1031C2C22×#1455617411yescharacteristic
1032C2C2×#1798683511yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×C4×#41×C71C2
hypercenterC2×C4×#41D71
hypocenterC71#62800
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22602425C2semidirect
2. #22602372C2semidirect
3. #22602346C2semidirect
4. #22602301C2semidirect
5. #22602251C2semidirect
6. #22602216C2semidirect
7. #22602159C2semidirect
8. #22602118C2semidirect
9. #22602075C2semidirect
10. #22602009C2semidirect
11. #22601966C2semidirect
12. #22601950C2semidirect
13. #22601935C2semidirect
14. D4×#11765865C2semidirect
15. #22601756C2semidirect
16. #22601636C2semidirect
17. C2×#17986549C2semidirect
18. C4×#14556174C2semidirect
19. C2×C4×#41×C71C2semidirect
21. C22×#11765865C22semidirect
22. #17986734C22semidirect
23. #17986734C22semidirect
24. Q8×Dic142C22semidirect
25. #17986728C22semidirect
26. #17986722C22semidirect
27. #17986714C22semidirect
28. #17986712C22semidirect
29. #17986709C22semidirect
30. #17986706C22semidirect
31. #17986697C22semidirect
32. #17986695C22semidirect
33. #17986693C22semidirect
34. #17986673C22semidirect
35. #17986671C22semidirect
36. #17986671C22semidirect
37. #17986670C22semidirect
38. #17986670C22semidirect
39. #17986668C22semidirect
40. D4×Dic142C22semidirect
41. #17986660C22semidirect
42. #17986658C22semidirect
43. #17986654C22semidirect
44. #17986650C22semidirect
45. #17986645C22semidirect
46. #17986645C22semidirect
47. #17986639C22semidirect
48. #17986637C22semidirect
49. D4×D284C22semidirect
50. D4×D284C22semidirect
51. D4×C22⋊D71C22semidirect
52. #17986627C22semidirect
53. #17986621C22semidirect
54. #17986620C22semidirect
55. #17986604C22semidirect
56. #17986600C22semidirect
57. #17986582C22semidirect
58. #17986577C22semidirect
59. #17986568C22semidirect
60. #17986563C22semidirect
61. #17986556C22semidirect
62. #17986556C22semidirect
63. #17986556C22semidirect
64. #17986549C22semidirect
65. #17986549C22semidirect
66. #17986549C22semidirect
67. #17986549C22semidirect
68. #17986549C22semidirect
69. #17986549C22semidirect
70. #17986549C22semidirect
71. #17986549C22semidirect
72. #17986549C22semidirect
73. #17986549C22semidirect
74. #17986546C22semidirect
75. C2×#14556128C22semidirect
76. C2×#14556125C22semidirect
77. #17986536C22semidirect
78. #17986533C22semidirect
79. #17986533C22semidirect
80. #17986533C22semidirect
81. #17986533C22semidirect
82. #17986533C22semidirect
83. #17986533C22semidirect
84. C2×#14556116C22semidirect
85. #17986510C22semidirect
86. #17986510C22semidirect
87. #17986510C22semidirect
88. #17986508C22semidirect
89. C2×#14556102C22semidirect
90. C2×#14556102C22semidirect
92. #17986481C22semidirect
93. #17986479C22semidirect
94. #17986473C22semidirect
95. #17986471C22semidirect
96. C4×#11765866C22semidirect
97. C4×#11765865C22semidirect
98. C4×#11765865C22semidirect
99. C4×#11765865C22semidirect
100. C2×C4×D284C22semidirect
101. C2×C4×D284C22semidirect
102. C4×D4×D71C22semidirect
106. C4×#41×C71C22semidirect
107. C4×#41×C71C22semidirect
108. C4×#41×C71C22semidirect
109. C4×#41×C71C22semidirect
110. C4×#41×C71C22semidirect
111. C4×#41×C71C22semidirect
112. C2×C4×Q8×C71C22semidirect
113. C2×C4×Q8×C71C22semidirect
114. C2×C4×D4×C71C22semidirect
115. C2×C4×D4×C71C22semidirect
116. C2×#117×C71C22semidirect
117. C22×C42×C71C22semidirect
357. #41×C71#41semidirect
423. Q8×C71C2×#41semidirect
426. D4×C71C2×#41semidirect
443. C2×C4×C71C2×#41semidirect
444. C2×C4×C71H(5,𝔽2)semidirect
535. C2×C4×#41D71semidirect
536. C71#62800semidirect
620. C4×#41C2×D71semidirect
621. C4×#41C2×D71semidirect
622. C4×#41C2×D71semidirect
623. C4×#41C2×D71semidirect
624. C4×#41C2×D71semidirect
625. C4×#41C2×D71semidirect
626. C2×C4×Q8C2×D71semidirect
627. C2×C4×Q8C2×D71semidirect
631. C2×C4×D4C2×D71semidirect
632. C2×C4×D4C2×D71semidirect
633. C2×#117C2×D71semidirect
634. C22×C42C2×D71semidirect
820. #41#11765865semidirect
944. Q8C2×#11765865semidirect
957. D4C2×#11765865semidirect
982. C2×C4C2×#11765865semidirect
983. C2×C4#14556174semidirect

Maximal subgroups

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

subgroupindex
#226024252
#226023722
#226023462
#226023012
#226022512
#226022162
#226021592
#226021182
#226020752
#226020092
#226019662
#226019502
#226019352
D4×#117658652
#226017562
#226016362
C2×#179865492
C4×#145561742
C2×C4×#41×C712
#6280071