Finite Group Databasebeta

← #32905683

Subgroups — #32905683

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602430C214yesmaximal, complemented
2#22602419C214yesmaximal, complemented
3#22602335C214yesmaximal, complemented
4#22602325C214yesmaximal, complemented
5#22602198C216yesmaximal, complemented
6#22602146C211yesmaximal, characteristic, complemented
7#22602107C211yesmaximal, characteristic, complemented
8#22602043C216yesmaximal, complemented
9#22601992C211yesmaximal, characteristic, complemented
10#22601988C211yesmaximal, characteristic, complemented
11#22601962C214yesmaximal, complemented
12#22601957C214yesmaximal, complemented
13#22601938C214yesmaximal, complemented
14Q8×#11765865C214yesmaximal, complemented
15#22601767C216yesmaximal, complemented
16#22601633C216yesmaximal, complemented
17C4×#14556176C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
19C4×2−1+4×C71C211yesmaximal, characteristic, complemented
20C2×#14556176C2211yescharacteristic
21C22×Q8×D71C2211yescharacteristic
22#17986732C22112yescomplemented
23Q8×Dic142C2214yescomplemented
24#17986728C2214yescomplemented
25#17986727C22112yescomplemented
26#17986725C2214yescomplemented
27#17986725C2214yescomplemented
28#17986721C22112yescomplemented
29#17986719C22112yescomplemented
30#17986717C22112yescomplemented
31#17986709C22112yes—
32#17986704C22112yes—
33#17986704C22112yescomplemented
34#17986699C22112yes—
35#17986693C22112yes—
36#17986690C22112yes—
37#17986688C22112yes—
38#17986688C22112yescomplemented
39#17986684C22112yescomplemented
40#17986668C2214yescomplemented
41Q8×D284C2214yes—
42Q8×D284C2214yes—
43Q8×C22⋊D71C2214yes—
44Q8×C22⋊D71C2214yes—
45Q8×C22⋊D71C2214yescomplemented
46#17986661C2214yes—
47#17986661C2214yes—
48#17986660C2214yescomplemented
49#17986656C2214yes—
50#17986656C2214yes—
51#17986656C2214yescomplemented
52#17986654C22112yes—
53#17986650C22112yes—
54#17986627C2216yes—
55#17986620C22112yescomplemented
56#17986614C22112yescomplemented
57#17986611C22112yescomplemented
58#17986607C22112yescomplemented
59#17986591C22124yes—
60#17986577C2216yes—
61#17986575C2216yes—
62#17986570C2216yes—
63#17986556C22112yescomplemented
64#17986553C2216yes—
65#17986553C2216yes—
66#17986553C22112yescomplemented
67#17986552C2216yes—
68#17986546C2216yes—
69#17986546C2216yes—
70#17986545C2216yes—
71#17986536C2216yes—
72#17986536C2216yes—
73#17986533C22112yescomplemented
74#17986531C2216yes—
75#17986531C2216yes—
76#17986531C22112yescomplemented
77#17986529C22112yes—
78#17986529C22112yes—
79#17986527C22112yes—
80#17986527C22112yes—
81#17986511C2216yes—
82#17986508C22112yes—
83#17986508C2214yes—
84#17986506C2216yes—
85#17986481C2214yescomplemented
86#17986480C2216yes—
87#17986477C2211yescharacteristic
88#17986475C2214yescomplemented
89C4×#11765866C2214yescomplemented
90C4×#11765865C2216yes—
91C4×#11765865C22112yes—
92C4×#11765865C22112yes—
93C2×Q8×Dic71C2211yescharacteristic
94C2×C4×Dic142C2213yes—
95C2×#14556093C2213yes—
96C4×Q8×D71C2214yes—
97C4×Q8×D71C2214yes—
98C4×Q8×D71C2214yes—
99C4×Q8×D71C2214yes—
100C4×Q8×D71C2214yescomplemented
101C2×C4⋊C4×D71C2213yes—
102C2×C42×D71C2213yes—
103C2×2−1+4×C71C2211yescharacteristic
104#520×C71C2216yes—
105#520×C71C2214yescomplemented
106#519×C71C2211yescharacteristic
107#519×C71C2214yescomplemented
108C4×#41×C71C2216yes—
109C4×#41×C71C2214yescomplemented
110C2×C4×Q8×C71C2211yescharacteristic
111C2×C4×Q8×C71C2214yescomplemented
112#14556176—28no—
113C2×#11765866C2314yes—
114C2×#11765865C2316yes—
115C2×#11765865C2314yes—
116C2×#11765865C23112yes—
117C22×Dic142C2313yes—
118C2×Q8×D71—28no—
119C2×Q8×D71C2314yes—
120C2×Q8×D71C2314yes—
121C2×Q8×D71C2314yes—
122C22×C4×D71C2313yes—
123C22×C4×D71C2311yescharacteristic
124C22×C4×D71C2313yes—
125#14556128C23112yes—
126#14556128C23112yes—
127#14556127C23112yes—
128#14556127C2316yes—
129#14556127C2316yes—
130#14556126C23112yes—
131#14556126C2316yes—
132#14556124C2316yes—
133#14556123C23112yes—
134#14556123C23112yes—
135#14556122C23124yes—
136#14556121C23124yes—
137#14556121C23112yes—
138#14556121C23112yes—
139#14556120C23124yes—
140#14556120C23112yes—
141#14556119C23112yes—
142#14556119C2316yes—
143#14556119C2316yes—
144#14556118C23124yes—
145#14556118C23112yes—
146#14556118C23112yes—
147#14556117C2316yes—
148#14556116C23112yes—
149#14556115C23112yes—
150#14556115C2316yes—
151#14556114C23112yes—
152#14556114C23112yes—
153#14556113C23112yes—
154#14556113C2314yes—
155#14556112C23112yes—
156#14556111C23124yes—
157#14556110C23124yes—
158#14556110C23112yes—
159#14556110C2314yes—
160#14556109C23112yes—
161#14556108C23112yes—
162#14556108C23112yes—
163#14556108C2316yes—
164#14556108C2316yes—
165#14556107C23112yes—
166#14556107C23112yes—
167#14556107C23112yes—
168#14556107C23124yes—
169#14556106C23124yes—
170#14556106C23112yes—
171#14556106C2314yes—
172#14556105C23112yes—
173#14556105C2314yes—
174#14556104C23112yes—
175#14556104C2316yes—
176#14556104C2316yes—
177#14556103C2316yes—
178#14556103C2316yes—
179#14556102C23112yes—
180#14556101C23112yes—
181#14556101C2314yes—
182#14556100C23112yes—
183#14556100C2314yes—
184#14556099C23112yes—
185#14556099C2316yes—
186#14556099C2316yes—
187#14556098C2314yes—
188#14556096C2314yes—
189Q8×Dic71C2314yes—
190Q8×Dic71C2314yes—
191Q8×Dic71C2314yes—
192Q8×Dic71C2314yes—
193C4×Dic142C23112yes—
194C4×Dic142C2316yes—
195C4×Dic142C23112yes—
196C4×Dic142C23112yes—
197C4×Dic142C2316yes—
198C4×Dic142C23112yes—
199C4×Dic142C23112yes—
200C4×Dic142C23112yes—
201#14556093C23112yes—
202#14556093C23112yes—
203#14556093C23112yes—
204C4×D284C2316yes—
205C4×D284C23112yes—
206C4×D284C23112yes—
207C4×D284C23112yes—
208C4×D284C2314yes—
209C4×D284C2316yes—
210#14556090C23112yes—
211C4×C22⋊D71C23112yes—
212C4×C22⋊D71C23112yes—
213C4×C22⋊D71C23112yes—
214C4×C22⋊D71C23112yes—
215C4×C22⋊D71C23112yes—
216C4×C22⋊D71C23112yes—
217C4×C22⋊D71C23112yes—
218C4×C22⋊D71C2314yes—
219C4×C22⋊D71C2314yes—
220C4×C22⋊D71C23112yes—
221#14556087C2316yes—
222#14556087C23112yes—
223#14556087C23112yes—
224#14556086C23112yes—
225#14556085C23112yes—
226#14556085C23112yes—
227#14556085C23112yes—
228#14556085C2314yes—
229#14556085C23112yes—
230C2×C4⋊Dic71C2313yes—
231C2×Dic71⋊C4C2316yes—
232C4⋊C4×D71C23112yes—
233C4⋊C4×D71C23112yes—
234C4⋊C4×D71C23112yes—
235C2×C4×Dic71C2313yes—
236C2×C4×Dic71C2313yes—
237C2×C4×Dic71C2313yes—
238C42×D71C2316yes—
239C42×D71C2316yes—
240C42×D71C2316yes—
241C42×D71C2316yes—
242C42×D71C23112yes—
2432−1+4×C71—28no—
244C2×#41×C71C2316yes—
245C2×#41×C71C2314yes—
246C22×Q8×C71C2314yes—
247C22×Q8×C71C2311yescharacteristic
248C4×Q8×C71C2316yes—
249C4×Q8×C71C2314yes—
250C4×Q8×C71C2314yes—
251C4×Q8×C71C2314yes—
252C4×Q8×C71C2314yes—
253C4×Q8×C71C2316yes—
254C4×Q8×C71C23112yes—
255C4×D4×C71C23112yes—
256C4×D4×C71C2316yes—
257C4×D4×C71C23112yes—
258C4×D4×C71C2314yes—
259C4×D4×C71C2316yes—
260#117×C71C2316yes—
261#117×C71C23112yes—
262#117×C71C23112yes—
263C2×C4⋊C4×C71C23112yes—
264C2×C4⋊C4×C71C2313yes—
265C2×C42×C71C2313yes—
266C2×C42×C71C23112yes—
267C23×D71C2411yescharacteristic
268#11765866—216no—
269#11765865—224no—
270#11765865—216no—
271#11765865—424no—
272C2×Dic142—212no—
273C2×Dic142C24112yes—
274C2×Dic142C2416yes—
275C2×Dic142C2414yes—
276C2×Dic142C24112yes—
277Q8×D71—216no—
278Q8×D71—216no—
279Q8×D71—216no—
280C2×D284C2414yes—
281C2×D284C2416yes—
282C2×D284C2414yes—
283C2×C22⋊D71C2414yes—
284C2×C22⋊D71C2414yes—
285C2×C22⋊D71C2414yes—
286C2×C22⋊D71C2414yes—
287C2×C22⋊D71C24112yes—
288C22×Dic71C2413yes—
289C22×Dic71C2411yescharacteristic
290C22×Dic71C2413yes—
291C2×C4×D71—212no—
292C2×C4×D71—24no—
293C2×C4×D71—46no—
294C2×C4×D71C2416yes—
295C2×C4×D71C2416yes—
296C2×C4×D71C2416yes—
297C2×C4×D71C2411yescharacteristic
298C2×C4×D71C2411yescharacteristic
299C2×C4×D71C2411yescharacteristic
300C2×C4×D71C24112yes—
301C2×C4×D71C2414yes—
302C2×C4×D71C2416yes—
303C2×C4×D71C24112yes—
304C2×C4×D71C2411yescharacteristic
305C4⋊Dic71C24112yes—
306C4⋊Dic71C2416yes—
307C4⋊Dic71C2416yes—
308C4⋊Dic71C2414yes—
309C4⋊Dic71C24112yes—
310C4⋊Dic71C24112yes—
311C4⋊Dic71C24112yes—
312Dic71⋊C4C24124yes—
313Dic71⋊C4C24112yes—
314Dic71⋊C4C2414yes—
315Dic71⋊C4C2414yes—
316Dic71⋊C4C2414yes—
317Dic71⋊C4C2414yes—
318Dic71⋊C4C24112yes—
319Dic71⋊C4C24112yes—
320Dic71⋊C4C24112yes—
321Dic71⋊C4C24112yes—
322Dic71⋊C4C24112yes—
323C22⋊Dic71C2414yes—
324C22⋊Dic71C2414yes—
325C22⋊Dic71C24112yes—
326C22⋊Dic71C24112yes—
327C22⋊Dic71C24112yes—
328(C2×D71)⋊C4C2414yes—
329(C2×D71)⋊C4C2414yes—
330(C2×D71)⋊C4C2414yes—
331(C2×D71)⋊C4C2414yes—
332(C2×D71)⋊C4C24112yes—
333(C2×D71)⋊C4C2414yes—
334(C2×D71)⋊C4C2414yes—
335(C2×D71)⋊C4C24112yes—
336(C2×D71)⋊C4C24112yes—
337(C2×D71)⋊C4C24112yes—
338C4×Dic71C2414yes—
339C4×Dic71C2416yes—
340C4×Dic71C2416yes—
341C4×Dic71C2416yes—
342C4×Dic71C2416yes—
343C4×Dic71C2416yes—
344C4×Dic71C2416yes—
345C4×Dic71C24112yes—
346C4×Dic71C24112yes—
347#41×C71—216no—
348#41×C71—224no—
349C2×Q8×C71—216no—
350C2×Q8×C71#4118yescomplemented
351C2×Q8×C71C2416yes—
352C2×Q8×C71C2414yes—
353C2×D4×C71C2414yes—
354C2×D4×C71C2416yes—
355C22×C4×C71C2411yescharacteristic
356C22×C4×C71C2414yes—
357C22×C4×C71C24112yes—
358C22×C4×C71C2413yes—
359C22×C4×C71C24112yes—
360C22×C4×C71C2413yes—
361C4⋊C4×C71C24112yes—
362C4⋊C4×C71C2416yes—
363C4⋊C4×C71C24112yes—
364C4⋊C4×C71C2416yes—
365C4⋊C4×C71C2414yes—
366C22⋊C4×C71C2414yes—
367C22⋊C4×C71C24112yes—
368C22⋊C4×C71C2414yes—
369C42×C71C2416yes—
370C42×C71C2414yes—
371C42×C71C2416yes—
372C42×C71C24112yes—
373C42×C71C24112yes—
374C23×C71C2514yes—
375C23×C71C2511yescharacteristic
376C22×D71—22no—
377C22×D71—22no—
378C22×D71—22no—
379C22×D71C2514yes—
380C22×D71C2511yescharacteristic
381C22×D71C2511yescharacteristic
382Q8×C71—212no—
383Q8×C71C2×#41116yes—
384D4×C71—28no—
385D4×C71—212no—
386C2×C4×C71—224no—
387C2×C4×C71—22no—
388C2×C4×C71—28no—
389C2×C4×C71—43no—
390C2×C4×C71—412no—
391C2×C4×C71C2×#41112yes—
392C2×C4×C71C2511yescharacteristic
393C2×C4×C71C2514yes—
394C2×C4×C71C2516yes—
395C2×C4×C71C2514yes—
396C2×C4×C71C2514yes—
397C2×C4×C71C2516yes—
398C2×C4×C71C2511yescharacteristic
399C22⋊D71—28no—
400C22⋊D71—28no—
401C22⋊D71—28no—
402C22⋊D71—28no—
403C22⋊D71—412no—
404C2×Dic71—26no—
405C2×Dic71—22no—
406C2×Dic71—43no—
407C2×Dic71C2511yescharacteristic
408C2×Dic71C2514yes—
409C2×Dic71C2516yes—
410C2×Dic71C2514yes—
411C2×Dic71C2514yes—
412C2×Dic71C2516yes—
413C2×Dic71C2511yescharacteristic
414D284—28no—
415D284—28no—
416D284—212no—
417C4×D71—22no—
418C4×D71—212no—
419C4×D71—212no—
420C4×D71—212no—
421C4×D71—224no—
422C4×D71—22no—
423C4×D71—28no—
424C4×D71—22no—
425C4×D71—46no—
426C4×D71—412no—
427C4×D712−1+414yescomplemented
428Dic142—224no—
429Dic142—212no—
430Dic142—28no—
431Dic142—412no—
432C22×C71—21no—
433C22×C71—21no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71C22×#4112yes—
438C22×C71C2611yescharacteristic
439C2×D71—28no—
440C2×D71—21no—
441C2×D71—21no—
442C2×D71—21no—
443C2×D71—21no—
444C2×D71—24no—
445C2×D71—24no—
446C2×D71—24no—
447C2×D71C2×2−1+412yes—
448C2×D71#58512yes—
449C4×C71—24no—
450C4×C71—24no—
451C4×C71—21no—
452C4×C71—24no—
453C4×C71—26no—
454C4×C71C22×#41112yes—
455C4×C71C2×2−1+412yes—
456Dic71—26no—
457Dic71—24no—
458Dic71—24no—
459Dic71—21no—
460Dic71—24no—
461Dic71—26no—
462Dic71C2×2−1+412yes—
463#62788—711nomaximal, Sylow
464C2×C71—22no—
465C2×C71—44no—
466C2×C71C23×#4111yescharacteristic
467C2×C71C22×2−1+411yescharacteristic
468C2×C71C2×#58511yescharacteristic
469D71—22no—
470D71—22no—
471D71—44no—
472#3523—714no—
473#3522—714no—
474#3516—714no—
475#3516—714no—
476#3507—716no—
477#3502—711no—
478#3497—711no—
479#3492—716no—
480#3486—711no—
481#3486—711no—
482#3482—714no—
483#3482—714no—
484#3480—714no—
485Q8×#41—714no—
486#3461—716no—
487#3444—716no—
488C4×2−1+4—711no—
489C4×2−1+4D7111yescharacteristic, complemented
490C22×C4×Q8—711no—
491C71#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—711no—
493C2×2−1+4C2×D7111yescharacteristic
494C23×Q8—711no—
495#559—7112no—
496Q82—714no—
497#557—7112no—
498#557—714no—
499#557—714no—
500#557—714no—
501#556—7112no—
502#556—7112no—
503#556—7112no—
504#554—7112no—
505#554—7112no—
506#554—7112no—
507#553—7112no—
508#553—7112no—
509#552—7112no—
510#552—7112no—
511#552—7112no—
512#552—7112no—
513#550—714no—
514D4×Q8—714no—
515D4×Q8—714no—
516D4×Q8—714no—
517D4×Q8—714no—
518D4×Q8—714no—
519#548—714no—
520#548—714no—
521#548—714no—
522#548—714no—
523#548—714no—
524#548—714no—
525#547—7112no—
526#547—7112no—
527#544—716no—
528#542—7112no—
529#542—7112no—
530#541—7112no—
531#541—7112no—
532#539—7124no—
533#537—716no—
534#536—716no—
535#536—716no—
536#533—716no—
537#533—716no—
538#533—7112no—
539#533—716no—
540#533—7112no—
541#532—716no—
542#532—716no—
543#532—716no—
544#529—716no—
545#529—716no—
546#529—7112no—
547#529—716no—
548#529—7112no—
549#529—716no—
550#529—7112no—
551#529—7112no—
552#529—7112no—
553#529—7112no—
554#525—716no—
555#525—714no—
556#525—7112no—
557#525—716no—
558#520—714no—
559#520—716no—
560#520C2×D7116yes—
561#520C2×D7114yescomplemented
562#519—711no—
563#519—714no—
564#519C2×D7111yescharacteristic
565#519C2×D7114yescomplemented
566C4×#41—714no—
567C4×#41—716no—
568C4×#41—7112no—
569C4×#41—7112no—
570C4×#41C2×D7116yes—
571C4×#41C2×D7114yescomplemented
572C2×C4×Q8—711no—
573C2×C4×Q8—714no—
574C2×C4×Q8—714no—
575C2×C4×Q8—714no—
576C2×C4×Q8—714no—
577C2×C4×Q8—714no—
578C2×C4×Q8—713no—
579C2×C4×Q8—713no—
580C2×C4×Q8C2×D7111yescharacteristic
581C2×C4×Q8C2×D7114yescomplemented
582C22×C4⋊C4—713no—
583C22×C42—713no—
5842−1+4—28no—
5852−1+4—1428no—
586C2×#41—714no—
587C2×#41—7112no—
588C2×#41—714no—
589C2×#41—716no—
590C2×#41C22×D7116yes—
591C2×#41C22×D7114yes—
592C22×Q8—714no—
593C22×Q8—714no—
594C22×Q8—714no—
595C22×Q8—713no—
596C22×Q8—1428no—
597C22×Q8C22×D7114yes—
598C22×Q8C22×D7111yescharacteristic
599C23×C4—713no—
600C23×C4—713no—
601C23×C4—711no—
602C4⋊Q8—716no—
603C4⋊Q8—7112no—
604C4⋊Q8—716no—
605C4⋊Q8—716no—
606C4⋊Q8—7112no—
607C4⋊Q8—7112no—
608C4⋊Q8—7112no—
609#127—716no—
610#126—7112no—
611#126—7112no—
612#126—7112no—
613#126—7112no—
614#126—7124no—
615#126—7124no—
616#125—7112no—
617#125—716no—
618#125—716no—
619#125—7112no—
620#125—7112no—
621#125—7124no—
622#125—7112no—
623#125—7124no—
624#124—716no—
625#124—716no—
626#124—7112no—
627#124—7112no—
628#124—7112no—
629#124—7112no—
630#123—7112no—
631#123—7124no—
632#123—714no—
633#123—7112no—
634#123—714no—
635#123—7112no—
636#123—7112no—
637#123—7124no—
638C22⋊Q8—716no—
639C22⋊Q8—716no—
640C22⋊Q8—7112no—
641C22⋊Q8—7112no—
642C22⋊Q8—7112no—
643C22⋊Q8—7112no—
644C22⋊Q8—7124no—
645C22⋊Q8—714no—
646C22⋊Q8—716no—
647C22⋊Q8—716no—
648C22⋊Q8—7112no—
649C22⋊Q8—7112no—
650C22⋊Q8—7112no—
651C22⋊Q8—7124no—
652C22⋊Q8—714no—
653C22⋊Q8—7112no—
654#121—714no—
655#121—7112no—
656#121—716no—
657#121—716no—
658#121—7112no—
659#121—7112no—
660#121—716no—
661#121—716no—
662#121—714no—
663#121—7112no—
664#120—714no—
665#120—714no—
666C4×Q8—714no—
667C4×Q8—714no—
668C4×Q8—714no—
669C4×Q8—714no—
670C4×Q8—7112no—
671C4×Q8—7112no—
672C4×Q8—7112no—
673C4×Q8—7112no—
674C4×Q8—7112no—
675C4×Q8—716no—
676C4×Q8—716no—
677C4×Q8—7112no—
678C4×Q8—7112no—
679C4×Q8—7112no—
680C4×Q8—7112no—
681C4×Q8C22×D7114yes—
682C4×Q8C22×D7114yes—
683C4×Q8C22×D7116yes—
684C4×Q8C22×D7114yes—
685C4×Q8C22×D71112yes—
686C4×Q8C22×D7116yes—
687C4×Q8C22×D7114yes—
688C4×D4—714no—
689C4×D4—714no—
690C4×D4—7112no—
691C4×D4—7112no—
692C4×D4—7112no—
693C4×D4—7112no—
694C4×D4—7112no—
695C4×D4—7112no—
696C4×D4—7112no—
697C4×D4—7112no—
698C4×D4—7112no—
699C4×D4—714no—
700C4×D4—716no—
701C4×D4—716no—
702C4×D4—7112no—
703C4×D4—7112no—
704C4×D4—7112no—
705C4×D4C22×D7114yes—
706C4×D4C22×D7116yes—
707C4×D4C22×D71112yes—
708C4×D4C22×D7116yes—
709C4×D4C22×D71112yes—
710#117—716no—
711#117—7112no—
712#117—7112no—
713#117—7112no—
714#117—714no—
715#117—7112no—
716#117—7112no—
717#117—7112no—
718#117—7112no—
719#117C22×D7116yes—
720#117C22×D71112yes—
721#117C22×D71112yes—
722C2×C4⋊C4—713no—
723C2×C4⋊C4—716no—
724C2×C4⋊C4—7112no—
725C2×C4⋊C4—7112no—
726C2×C4⋊C4—7112no—
727C2×C4⋊C4C22×D7113yes—
728C2×C4⋊C4C22×D71112yes—
729C2×C42—713no—
730C2×C42—713no—
731C2×C42—713no—
732C2×C42—716no—
733C2×C42—716no—
734C2×C42—716no—
735C2×C42—716no—
736C2×C42—7112no—
737C2×C42C22×D7113yes—
738C2×C42C22×D71112yes—
739C24—711no—
740#41—216no—
741#41—224no—
742#41—28424no—
743#41—14216no—
744#41—14216no—
745#41—14224no—
746C2×Q8—216no—
747C2×Q8—7112no—
748C2×Q8—714no—
749C2×Q8—7112no—
750C2×Q8—716no—
751C2×Q8—14216no—
752C2×Q8—14216no—
753C2×Q8—14216no—
754C2×Q8—14212no—
755C2×Q8#1176586518yescomplemented
756C2×Q8C23×D7116yes—
757C2×Q8C23×D7114yes—
758C2×D4—7112no—
759C2×D4—714no—
760C2×D4—714no—
761C2×D4—714no—
762C2×D4—714no—
763C2×D4—714no—
764C2×D4—714no—
765C2×D4—716no—
766C2×D4C23×D7114yes—
767C2×D4C23×D7116yes—
768C22×C4—2846no—
769C22×C4—713no—
770C22×C4—716no—
771C22×C4—7112no—
772C22×C4—711no—
773C22×C4—711no—
774C22×C4—713no—
775C22×C4—711no—
776C22×C4—711no—
777C22×C4—716no—
778C22×C4—716no—
779C22×C4—716no—
780C22×C4—7112no—
781C22×C4—711no—
782C22×C4—714no—
783C22×C4—1424no—
784C22×C4—14212no—
785C22×C4C23×D71112yes—
786C22×C4C23×D7111yescharacteristic
787C22×C4C23×D7114yes—
788C22×C4C23×D7113yes—
789C22×C4C23×D71112yes—
790C22×C4C23×D7113yes—
791C4⋊C4—7124no—
792C4⋊C4—7112no—
793C4⋊C4—714no—
794C4⋊C4—714no—
795C4⋊C4—714no—
796C4⋊C4—714no—
797C4⋊C4—7112no—
798C4⋊C4—7112no—
799C4⋊C4—7112no—
800C4⋊C4—7112no—
801C4⋊C4—7112no—
802C4⋊C4—7112no—
803C4⋊C4—716no—
804C4⋊C4—716no—
805C4⋊C4—714no—
806C4⋊C4—7112no—
807C4⋊C4—7112no—
808C4⋊C4—7112no—
809C4⋊C4C23×D71112yes—
810C4⋊C4C23×D7116yes—
811C4⋊C4C23×D71112yes—
812C4⋊C4C23×D7116yes—
813C4⋊C4C23×D7114yes—
814C22⋊C4—714no—
815C22⋊C4—714no—
816C22⋊C4—7112no—
817C22⋊C4—7112no—
818C22⋊C4—7112no—
819C22⋊C4—714no—
820C22⋊C4—714no—
821C22⋊C4—7112no—
822C22⋊C4—714no—
823C22⋊C4—714no—
824C22⋊C4—714no—
825C22⋊C4—714no—
826C22⋊C4—7112no—
827C22⋊C4—7112no—
828C22⋊C4—7112no—
829C22⋊C4C23×D7114yes—
830C22⋊C4C23×D71112yes—
831C22⋊C4C23×D7114yes—
832C42—716no—
833C42—716no—
834C42—716no—
835C42—716no—
836C42—716no—
837C42—7112no—
838C42—7112no—
839C42—716no—
840C42—714no—
841C42C23×D7116yes—
842C42C23×D71112yes—
843C42C23×D71112yes—
844C42C23×D7116yes—
845C42C23×D7114yes—
846C23—711no—
847C23—711no—
848C23—714no—
849C23—1422no—
850C23—1422no—
851C23—1422no—
852C23C24×D7114yes—
853C23C24×D7111yescharacteristic
854Q8—212no—
855Q8—28412no—
856Q8—1428no—
857Q8—14224no—
858Q8—14212no—
859Q8C2×#11765865116yes—
860D4—28no—
861D4—212no—
862D4—28412no—
863D4—1428no—
864D4—1428no—
865D4—1428no—
866D4—1428no—
867D4—1428no—
868D4—1428no—
869D4—14212no—
870C2×C4—224no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—2846no—
876C2×C4—28412no—
877C2×C4—2843no—
878C2×C4—711no—
879C2×C4—714no—
880C2×C4—711no—
881C2×C4—714no—
882C2×C4—716no—
883C2×C4—714no—
884C2×C4—714no—
885C2×C4—716no—
886C2×C4—1422no—
887C2×C4—14212no—
888C2×C4—1422no—
889C2×C4—1422no—
890C2×C4—1426no—
891C2×C4—14212no—
892C2×C4—14212no—
893C2×C4—14224no—
894C2×C4—1422no—
895C2×C4—1428no—
896C2×C4C2×#11765865112yes—
897C2×C4C24×D7111yescharacteristic
898C2×C4C24×D7116yes—
899C2×C4C24×D7114yes—
900C2×C4C24×D7114yes—
901C2×C4C24×D7114yes—
902C2×C4C24×D7116yes—
903C2×C4C24×D7111yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—712no—
910C22—712no—
911C22—1428no—
912C22—1424no—
913C22—1424no—
914C22—1424no—
915C22—1421no—
916C22—1421no—
917C22—1421no—
918C22—1421no—
919C22C22×#1176586512yes—
920C22C25×D7111yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—712no—
927C4—1424no—
928C4—1426no—
929C4—1421no—
930C4—1424no—
931C4—1424no—
932C4—1426no—
933C4C22×#11765865112yes—
934C42−1+4×D7112yes—
935C2—22no—
936C2—44no—
937C2—2844no—
938C2—1422no—
939C2—1422no—
940C2C23×#1176586511yescharacteristic
941C2C2×2−1+4×D7111yescharacteristic
942C2#585×D7111yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC4×2−1+4×C71C2
hypercenterC4×2−1+4D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #22602430C2semidirect
2. #22602419C2semidirect
3. #22602335C2semidirect
4. #22602325C2semidirect
5. #22602198C2semidirect
6. #22602146C2semidirect
7. #22602107C2semidirect
8. #22602043C2semidirect
9. #22601992C2semidirect
10. #22601988C2semidirect
11. #22601962C2semidirect
12. #22601957C2semidirect
13. #22601938C2semidirect
14. Q8×#11765865C2semidirect
15. #22601767C2semidirect
16. #22601633C2semidirect
17. C4×#14556176C2semidirect
18. C2×C4×Q8×D71C2semidirect
19. C4×2−1+4×C71C2semidirect
22. #17986732C22semidirect
23. Q8×Dic142C22semidirect
24. #17986728C22semidirect
25. #17986727C22semidirect
26. #17986725C22semidirect
27. #17986725C22semidirect
28. #17986721C22semidirect
29. #17986719C22semidirect
30. #17986717C22semidirect
33. #17986704C22semidirect
38. #17986688C22semidirect
39. #17986684C22semidirect
40. #17986668C22semidirect
45. Q8×C22⋊D71C22semidirect
48. #17986660C22semidirect
51. #17986656C22semidirect
55. #17986620C22semidirect
56. #17986614C22semidirect
57. #17986611C22semidirect
58. #17986607C22semidirect
63. #17986556C22semidirect
66. #17986553C22semidirect
73. #17986533C22semidirect
76. #17986531C22semidirect
85. #17986481C22semidirect
88. #17986475C22semidirect
89. C4×#11765866C22semidirect
100. C4×Q8×D71C22semidirect
105. #520×C71C22semidirect
107. #519×C71C22semidirect
109. C4×#41×C71C22semidirect
111. C2×C4×Q8×C71C22semidirect
350. C2×Q8×C71#41semidirect
427. C4×D712−1+4semidirect
489. C4×2−1+4D71semidirect
491. C71#62788semidirect
561. #520C2×D71semidirect
565. #519C2×D71semidirect
571. C4×#41C2×D71semidirect
581. C2×C4×Q8C2×D71semidirect
755. C2×Q8#11765865semidirect

Maximal subgroups

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

subgroupindex
#226024302
#226024192
#226023352
#226023252
#226021982
#226021462
#226021072
#226020432
#226019922
#226019882
#226019622
#226019572
#226019382
Q8×#117658652
#226017672
#226016332
C4×#145561762
C2×C4×Q8×D712
C4×2−1+4×C712
#6278871