Finite Group Databasebeta

← #27124566

Subgroups — #27124566

Order 12032.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257498C214yesmaximal, complemented
2#20257486C214yesmaximal, complemented
3#20257396C214yesmaximal, complemented
4#20257385C214yesmaximal, complemented
5#20257239C216yesmaximal, complemented
6#20257194C211yesmaximal, characteristic, complemented
7#20257155C211yesmaximal, characteristic, complemented
8#20257105C216yesmaximal, complemented
9#20257046C211yesmaximal, characteristic, complemented
10#20257011C214yesmaximal, complemented
11#20257004C214yesmaximal, complemented
12#20256987C214yesmaximal, complemented
13#20256978C214yesmaximal, complemented
14#20256801C216yesmaximal, complemented
15#20256680C216yesmaximal, complemented
162−1+4×Dic47C211yesmaximal, characteristic, complemented
17#20256597C211yesmaximal, characteristic, complemented
18C2×#41×Dic47C211yesmaximal, characteristic, complemented
19C47×#3487C211yesmaximal, characteristic, complemented
20C2×#13094072C2211yescharacteristic
21#15689859C22112yescomplemented
22#15689855C22112yescomplemented
23Q8×Dic94C2214yescomplemented
24#15689852C2214yescomplemented
25#15689849C2214yescomplemented
26#15689849C2214yescomplemented
27#15689844C22112yescomplemented
28#15689843C22112yescomplemented
29#15689842C22112yescomplemented
30#15689838C22112yescomplemented
31#15689837C22112yescomplemented
32#15689837C22112yescomplemented
33#15689825C22112yescomplemented
34#15689820C22112yescomplemented
35#15689820C22112yescomplemented
36#15689819C22112yescomplemented
37#15689813C22112yescomplemented
38#15689807C22112yescomplemented
39#15689793C22112yescomplemented
40#15689792C2214yes—
41#15689792C2214yes—
42#15689792C2214yescomplemented
43Q8×C22⋊D47C2214yescomplemented
44#15689784C2214yescomplemented
45#15689780C2214yes—
46#15689780C2214yes—
47#15689780C2214yescomplemented
48#15689773C22112yescomplemented
49#15689751C2216yes—
50#15689742C22112yescomplemented
51#15689740C22112yescomplemented
52#15689727C22112yescomplemented
53#15689726C22112yescomplemented
54#15689708C22124yes—
55#15689701C2216yes—
56#15689690C2216yes—
57#15689676C2216yes—
58#15689675C2216yescomplemented
59#15689675C2216yescomplemented
60#15689671C22112yescomplemented
61#15689669C2216yes—
62#15689668C22112yescomplemented
63#15689668C2216yescomplemented
64#15689668C2216yescomplemented
65#15689659C2216yescomplemented
66#15689659C2216yescomplemented
67#15689654C22112yescomplemented
68#15689654C2216yescomplemented
69#15689654C2216yescomplemented
70#15689653C22112yescomplemented
71#15689653C22112yescomplemented
72#15689652C22112yescomplemented
73#15689650C22112yes—
74#15689650C2214yes—
75#15689634C2216yes—
76#15689629C22112yes—
77#15689629C22112yes—
78#15689606C2216yes—
79#15689606C2214yescomplemented
80#15689605C2214yescomplemented
81#15689603C2216yes—
82#15689601C2211yescharacteristic
83#15689601C2214yescomplemented
84#15689599C2214yescomplemented
85#41×Dic47C2216yes—
86#41×Dic47C2214yes—
87#41×Dic47C2214yes—
88#41×Dic47C2214yes—
89#41×Dic47C2214yes—
90#41×Dic47C2214yescomplemented
91C4×#10625354C2214yescomplemented
92#15689591C2216yes—
93C4×#10625352C22112yescomplemented
94C4×#10625352C22112yescomplemented
95C2×Q8×Dic47C2211yescharacteristic
96C2×Q8×Dic47C2211yescharacteristic
97C2×Q8×Dic47C2214yescomplemented
98C4×Q8×D47C2214yescomplemented
99C2×D4×Dic47C2213yes—
100C2×D4×Dic47C2213yes—
101C2×#13093983C2213yes—
102C22×C4×Dic47C2213yes—
103C2×2−1+4×C47C2211yescharacteristic
104C22×#41×C47C2211yescharacteristic
105C47×#550C2214yes—
106C47×#550C2214yes—
107C47×#548C2214yes—
108C47×#548C2214yes—
109C47×#535C2216yes—
110C47×#525C2216yes—
111C47×#519C2211yescharacteristic
112#13094072—28no—
113C2×#10625354C2314yes—
114C2×#10625350C2316yes—
115C2×#10625352C23112yes—
116C2×#10625352C23112yes—
117C2×Q8×D47C2314yes—
118C23×Dic47C2313yes—
119C23×Dic47C2313yes—
120#13094024C23112yes—
121#13094023C23112yes—
122#13094023C2316yes—
123#13094023C2316yes—
124#13094022C2316yes—
125#13094020C23112yes—
126#13094020C2316yes—
127#13094019C23112yes—
128#13094019C2314yes—
129#13094017C23124yes—
130#13094017C23124yes—
131#13094017C23112yes—
132#13094017C2314yes—
133#13094016C23112yes—
134#13094015C23112yes—
135#13094015C2316yes—
136#13094015C2316yes—
137#13094014C23112yes—
138#13094014C2314yes—
139#13094013C2316yes—
140#13094011C23112yes—
141#13094011C23124yes—
142#13094011C2316yes—
143#13094010C23124yes—
144#13094010C23112yes—
145#13094010C2314yes—
146#13094008C23112yes—
147#13094008C23112yes—
148#13094007C2314yes—
149#13094006C23124yes—
150#13094005C23112yes—
151#13094005C23124yes—
152#13094005C23112yes—
153#13094003C23112yes—
154#13094003C2316yes—
155#13094003C2316yes—
156#13094001C23112yes—
157#13094001C23112yes—
158#13094001C23112yes—
159#13094001C2314yes—
160#13094000C23112yes—
161#13093998C23112yes—
162#13093998C2316yes—
163#13093998C2316yes—
164#13093996C23112yes—
165#13093996C23124yes—
166#13093996C2314yes—
167#13093996C23112yes—
168#13093996C23112yes—
169#13093995C23112yes—
170#13093995C23112yes—
171#13093995C23112yes—
172#13093995C23124yes—
173#13093993C23112yes—
174Q8×Dic47C2316yes—
175Q8×Dic47C2314yes—
176Q8×Dic47C2314yes—
177Q8×Dic47C2314yes—
178Q8×Dic47C2314yes—
179Q8×Dic47C23112yes—
180Q8×Dic47C2314yes—
181Q8×Dic47C2314yes—
182Q8×Dic47C2316yes—
183C4×Dic94C23112yes—
184C4×Dic94C23112yes—
185C4×Dic94C23112yes—
186#13093989C2316yes—
187#13093989C2316yes—
188#13093989C23112yes—
189#13093989C2314yes—
190C4×D188C23112yes—
191D4×Dic47C23112yes—
192D4×Dic47C23112yes—
193D4×Dic47C23112yes—
194D4×Dic47C23112yes—
195D4×Dic47C23112yes—
196D4×Dic47C23112yes—
197D4×Dic47C23112yes—
198D4×Dic47C2314yes—
199D4×Dic47C2316yes—
200D4×Dic47C23112yes—
201D4×Dic47C2316yes—
202#13093986C2316yes—
203#13093986C2316yes—
204C4×C22⋊D47C23112yes—
205C4×C22⋊D47C23112yes—
206C4×C22⋊D47C23112yes—
207C4×C22⋊D47C23112yes—
208(C22⋊D47)⋊C4C23112yes—
209(C22⋊D47)⋊C4C23112yes—
210(C22⋊D47)⋊C4C2314yes—
211(C22⋊D47)⋊C4C23112yes—
212(C22⋊D47)⋊C4C2314yes—
213(C22⋊D47)⋊C4C23112yes—
214#13093983C23112yes—
215#13093983C2316yes—
216#13093983C23112yes—
217#13093983C23112yes—
218#13093983C23112yes—
219#13093982C23112yes—
220#13093982C23112yes—
221#13093982C2314yes—
222#13093981C23112yes—
223#13093980C23112yes—
224#13093980C23112yes—
225#13093980C2314yes—
226#13093980C23112yes—
227C2×C4⋊Dic47C2313yes—
228C2×C4⋊Dic47C23112yes—
229C2×C4⋊Dic47C2313yes—
230C4⋊C4×D47C23112yes—
231C2×C22⋊Dic47C2316yes—
232C2×C4×Dic47C2311yescharacteristic
233C2×C4×Dic47C2313yes—
234C2×C4×Dic47C2313yes—
235C2×C4×Dic47C2313yes—
236C2×C4×Dic47C2316yes—
237C2×C4×Dic47C2316yes—
238C2×C4×Dic47C2316yes—
239C2×C4×Dic47C2316yes—
240C2×C4×Dic47C23112yes—
241C42×D47C23112yes—
2422−1+4×C47—28no—
243C2×#41×C47—28no—
244C2×#41×C47C2314yes—
245C2×#41×C47C2314yes—
246C2×#41×C47C2314yes—
247C2×#41×C47C2316yes—
248C22×Q8×C47C2314yes—
249C22×Q8×C47C2311yescharacteristic
250C22×D4×C47C2313yes—
251C23×C4×C47C2313yes—
252#127×C47C23112yes—
253#124×C47C23112yes—
254#123×C47C2314yes—
255C22⋊Q8×C47C2316yes—
256C22⋊Q8×C47C2316yes—
257#121×C47C23112yes—
258#121×C47C23112yes—
259#121×C47C2316yes—
260#121×C47C2316yes—
261#120×C47C23112yes—
262C4×Q8×C47C2314yes—
263C4×Q8×C47C2314yes—
264C4×D4×C47C23112yes—
265C4×D4×C47C23112yes—
266#117×C47C2316yes—
267C24×C47C2413yes—
268#41×C47—216no—
269#41×C47—216no—
270#41×C47—216no—
271#41×C47—224no—
272C2×Q8×C47—216no—
273C2×Q8×C47#4118yescomplemented
274C2×Q8×C47C2416yes—
275C2×Q8×C47C2414yes—
276C2×D4×C47—212no—
277C2×D4×C47C2414yes—
278C2×D4×C47C24112yes—
279C2×D4×C47C2416yes—
280C2×D4×C47C24112yes—
281C2×D4×C47C24112yes—
282C22×C4×C47—212no—
283C22×C4×C47C24112yes—
284C22×C4×C47C2416yes—
285C22×C4×C47C2416yes—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2413yes—
288C2×C22⋊D47C2414yes—
289C2×C22⋊D47C2414yes—
290C2×C22⋊D47C24112yes—
291C2×C22⋊D47C24112yes—
292C2×C22⋊D47C24112yes—
293C22×Dic47—46no—
294C22×Dic47—46no—
295C22×Dic47C2411yescharacteristic
296C22×Dic47C2411yescharacteristic
297C22×Dic47C2414yes—
298C22×Dic47C2416yes—
299C22×Dic47C2416yes—
300C22×Dic47C2413yes—
301C22×Dic47C2413yes—
302C22×Dic47C2416yes—
303C22×Dic47C2416yes—
304C22×Dic47C24112yes—
305#10625354—216no—
306Q8×D47—216no—
307#10625352—424no—
308#10625352—424no—
309#10625350—224no—
310C2×D188C2416yes—
311C2×C4×D47C2414yes—
312C2×C4×D47C24112yes—
313C2×C4×D47C24112yes—
314C2×Dic94C2416yes—
315C2×Dic94C2414yes—
316C2×Dic94C24112yes—
317C4⋊C4×C47C2416yes—
318C4⋊C4×C47C2416yes—
319C4⋊C4×C47C2414yes—
320C4⋊C4×C47C2414yes—
321C22⋊C4×C47C2414yes—
322C22⋊C4×C47C2414yes—
323C22⋊C4×C47C2414yes—
324C22⋊C4×C47C24112yes—
325C22⋊C4×C47C24112yes—
326C42×C47C24112yes—
327C22⋊Dic47C24124yes—
328C22⋊Dic47C2414yes—
329C22⋊Dic47C24112yes—
330C22⋊Dic47C24112yes—
331C22⋊Dic47C24112yes—
332C22⋊Dic47C2414yes—
333C22⋊Dic47C24112yes—
334C22⋊Dic47C2414yes—
335(C2×D47)⋊C4C2414yes—
336(C2×D47)⋊C4C24112yes—
337(C2×D47)⋊C4C2414yes—
338(C2×D47)⋊C4C2414yes—
339(C2×D47)⋊C4C2414yes—
340(C2×D47)⋊C4C24112yes—
341C4⋊Dic47C24112yes—
342C4⋊Dic47C2416yes—
343C4⋊Dic47C24112yes—
344C4⋊Dic47C24112yes—
345C4⋊Dic47C2414yes—
346C4⋊Dic47C24112yes—
347C4⋊Dic47C2416yes—
348C4⋊Dic47C2414yes—
349Dic47⋊C4C24112yes—
350Dic47⋊C4C2414yes—
351Dic47⋊C4C2414yes—
352Dic47⋊C4C2414yes—
353Dic47⋊C4C2414yes—
354Dic47⋊C4C24112yes—
355Dic47⋊C4C24112yes—
356Dic47⋊C4C2414yes—
357Dic47⋊C4C24112yes—
358Dic47⋊C4C2414yes—
359C4×Dic47C2414yes—
360C4×Dic47C2416yes—
361C4×Dic47C24112yes—
362C4×Dic47C2411yescharacteristic
363C4×Dic47C2411yescharacteristic
364C4×Dic47C2411yescharacteristic
365C4×Dic47C2411yescharacteristic
366C4×Dic47C2414yes—
367C4×Dic47C2416yes—
368C4×Dic47C2416yes—
369C4×Dic47C2416yes—
370C4×Dic47C2416yes—
371C4×Dic47C2416yes—
372C4×Dic47C24112yes—
373C4×Dic47C24112yes—
374C23×C47—26no—
375C23×C47—43no—
376C23×C47—43no—
377C23×C47C2516yes—
378C23×C47C2514yes—
379C23×C47C2511yescharacteristic
380C22×D47C2514yes—
381Q8×C47—212no—
382Q8×C47C2×#41116yes—
383D4×C47—28no—
384D4×C47—224no—
385D4×C47—212no—
386D4×C47—412no—
387D4×C47—412no—
388C2×C4×C47—22no—
389C2×C4×C47—212no—
390C2×C4×C47—212no—
391C2×C4×C47—224no—
392C2×C4×C47C2×#41112yes—
393C2×C4×C47C2511yescharacteristic
394C2×C4×C47C2511yescharacteristic
395C2×C4×C47C2514yes—
396C2×C4×C47C2514yes—
397C2×C4×C47C2514yes—
398C2×C4×C47C2516yes—
399C22⋊D47—28no—
400C22⋊D47—28no—
401C22⋊D47—412no—
402C22⋊D47—412no—
403C22⋊D47—412no—
404C2×Dic47—28no—
405C2×Dic47—212no—
406C2×Dic47—212no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—412no—
410C2×Dic47—43no—
411C2×Dic47—46no—
412C2×Dic47—43no—
413C2×Dic47—46no—
414C2×Dic47C2511yescharacteristic
415C2×Dic47C2511yescharacteristic
416C2×Dic47C2516yes—
417C2×Dic47C2514yes—
418C2×Dic47C2514yes—
419C2×Dic47C2514yes—
420C2×Dic47C2516yes—
421C2×Dic47C2511yescharacteristic
422C2×Dic47C2511yescharacteristic
423D188—212no—
424C4×D47—224no—
425C4×D47—28no—
426C4×D47—412no—
427Dic94—212no—
428Dic94—28no—
429Dic94—412no—
430#62793—471nomaximal, Sylow
431C22×C47—21no—
432C22×C47—21no—
433C22×C47—24no—
434C22×C47—26no—
435C22×C47—26no—
436C22×C47—26no—
437C22×C47—24no—
438C22×C47—24no—
439C22×C47—412no—
440C22×C47C22×#4112yes—
441C22×C47C2611yescharacteristic
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—24no—
445C4×C47—21no—
446C4×C47—21no—
447C4×C47—24no—
448C4×C47—24no—
449C4×C47—24no—
450C4×C47C22×#41112yes—
451Dic47—24no—
452Dic47—24no—
453Dic47—24no—
454Dic47—26no—
455Dic47—26no—
456Dic47—21no—
457Dic47—21no—
458Dic47#58512yes—
459Dic47#58512yes—
460#3524—474no—
461#3524—474no—
462#3518—474no—
463#3517—474no—
464#3506—476no—
465#3502—471no—
466#3497—471no—
467#3493—476no—
468#3487—471no—
469#3487D4711yescharacteristic, complemented
470#3483—474no—
471#3482—474no—
472#3480—474no—
473#3480—474no—
474#3460—476no—
475#3444—476no—
476C4×2−1+4—471no—
477C4×2−1+4—471no—
478C2×C4×#41—471no—
479C2×C47—22no—
480C2×C47—44no—
481C2×C47—46no—
482C2×C47C23×#4111yescharacteristic
483C2×C47C2×#58511yescharacteristic
484C2×C47C2×#58511yescharacteristic
485D47—44no—
486C2×2−1+4—471no—
487C2×2−1+4C2×D4711yescharacteristic
488C22×#41C2×D4711yescharacteristic
489#559—4712no—
490#559—4712no—
491Q82—474no—
492#557—474no—
493#557—474no—
494#557—474no—
495#556—4712no—
496#556—4712no—
497#556—4712no—
498#555—4712no—
499#555—4712no—
500#555—4712no—
501#553—4712no—
502#553—4712no—
503#553—4712no—
504#553—4712no—
505#552—4712no—
506#552—4712no—
507#550—474no—
508#550—474no—
509#550—474no—
510#550—4712no—
511#550C2×D4714yes—
512#550C2×D4714yes—
513D4×Q8—474no—
514#548—474no—
515#548—474no—
516#548—474no—
517#548—474no—
518#548C2×D4714yes—
519#548C2×D4714yes—
520#547—4712no—
521#544—476no—
522#542—4712no—
523#542—4712no—
524#540—4712no—
525#540—4712no—
526#538—4724no—
527#537—476no—
528#535—476no—
529#535C2×D4716yes—
530#533—476no—
531#533—476no—
532#533—476no—
533#532—476no—
534#532—4712no—
535#532—476no—
536#532—476no—
537#532—4712no—
538#529—4712no—
539#529—474no—
540#529—4712no—
541#529—476no—
542#529—476no—
543#529—476no—
544#529—476no—
545#529—4712no—
546#529—4712no—
547#529—4712no—
548#525—476no—
549#525—4712no—
550#525—4712no—
551#525C2×D4716yes—
552#520—476no—
553#520—474no—
554#520—474no—
555#520—476no—
556#519—471no—
557#519—474no—
558#519—474no—
559#519C2×D4711yescharacteristic
560C4×#41—474no—
561C4×#41—474no—
562C4×#41—474no—
563C4×#41—474no—
564C4×#41—476no—
565C4×#41—474no—
566C4×#41—474no—
567C4×#41—4712no—
568C4×#41—4712no—
569C4×#41—476no—
570C2×C4×Q8—471no—
571C2×C4×Q8—471no—
572C2×C4×Q8—474no—
573C2×C4×Q8—474no—
574C2×C4×D4—473no—
575C2×C4×D4—473no—
576C2×#117—473no—
577C22×C42—473no—
578C47#6279311yescharacteristic, complemented, Sylow
5792−1+4—28no—
5802−1+4—948no—
581C2×#41—28no—
582C2×#41—474no—
583C2×#41—4712no—
584C2×#41—4712no—
585C2×#41—476no—
586C2×#41C22×D4714yes—
587C2×#41C22×D4714yes—
588C2×#41C22×D4716yes—
589C2×#41C22×D4714yes—
590C22×Q8—474no—
591C22×Q8C22×D4714yes—
592C22×Q8C22×D4711yescharacteristic
593C22×D4C22×D4713yes—
594C23×C4—473no—
595C23×C4—473no—
596C23×C4C22×D4713yes—
597C4⋊Q8—476no—
598C4⋊Q8—476no—
599C4⋊Q8—476no—
600C4⋊Q8—4712no—
601C4⋊Q8—4712no—
602#127—476no—
603#127—4712no—
604#127C22×D47112yes—
605#126—474no—
606#126—4712no—
607#126—474no—
608#126—4712no—
609#126—4724no—
610#126—4724no—
611#125—474no—
612#125—4712no—
613#125—476no—
614#125—476no—
615#125—4712no—
616#125—4712no—
617#124—476no—
618#124—476no—
619#124—4712no—
620#124—4724no—
621#124—474no—
622#124—4712no—
623#124—4724no—
624#124C22×D47112yes—
625#123—4712no—
626#123—4712no—
627#123—4724no—
628#123—474no—
629#123—4712no—
630#123—4712no—
631#123—4724no—
632#123C22×D4714yes—
633C22⋊Q8—4712no—
634C22⋊Q8—476no—
635C22⋊Q8—476no—
636C22⋊Q8—4712no—
637C22⋊Q8—474no—
638C22⋊Q8—4712no—
639C22⋊Q8—4712no—
640C22⋊Q8—4712no—
641C22⋊Q8C22×D4716yes—
642C22⋊Q8C22×D4716yes—
643#121—474no—
644#121—4712no—
645#121—4712no—
646#121—4712no—
647#121—4712no—
648#121—4712no—
649#121—4712no—
650#121—4724no—
651#121—4724no—
652#121—476no—
653#121—476no—
654#121—4712no—
655#121C22×D4716yes—
656#121C22×D4716yes—
657#121C22×D47112yes—
658#121C22×D47112yes—
659#120—4712no—
660#120C22×D47112yes—
661C4×Q8—474no—
662C4×Q8—476no—
663C4×Q8—474no—
664C4×Q8—474no—
665C4×Q8—474no—
666C4×Q8—474no—
667C4×Q8—4712no—
668C4×Q8—476no—
669C4×Q8—474no—
670C4×Q8—476no—
671C4×Q8—474no—
672C4×Q8—476no—
673C4×Q8—4712no—
674C4×Q8—4712no—
675C4×Q8—4712no—
676C4×Q8—4712no—
677C4×Q8C22×D4714yes—
678C4×Q8C22×D4714yes—
679C4×D4—4712no—
680C4×D4—4712no—
681C4×D4—4712no—
682C4×D4—4712no—
683C4×D4—474no—
684C4×D4—476no—
685C4×D4—4712no—
686C4×D4—476no—
687C4×D4—4712no—
688C4×D4—4712no—
689C4×D4—4712no—
690C4×D4—4712no—
691C4×D4—4712no—
692C4×D4—4712no—
693C4×D4—4712no—
694C4×D4—476no—
695C4×D4—476no—
696C4×D4—474no—
697C4×D4—474no—
698C4×D4—4712no—
699C4×D4—4712no—
700C4×D4—4712no—
701C4×D4—4712no—
702C4×D4—4712no—
703C4×D4C22×D47112yes—
704C4×D4C22×D47112yes—
705#117—4712no—
706#117—4712no—
707#117—476no—
708#117—4712no—
709#117—4712no—
710#117—474no—
711#117—4712no—
712#117—4712no—
713#117—474no—
714#117—4712no—
715#117—4712no—
716#117—4712no—
717#117—4712no—
718#117C22×D4716yes—
719C2×C4⋊C4—473no—
720C2×C4⋊C4—473no—
721C2×C4⋊C4—4712no—
722C2×C4⋊C4—4712no—
723C2×C22⋊C4—476no—
724C2×C42—473no—
725C2×C42—473no—
726C2×C42—473no—
727C2×C42—4712no—
728C2×C42—476no—
729C2×C42—476no—
730C2×C42—476no—
731C2×C42—476no—
732C2×C42—471no—
733C2×C42—4712no—
734C24C23×D4713yes—
735#41—216no—
736#41—216no—
737#41—216no—
738#41—224no—
739#41—9416no—
740#41—9424no—
741#41—18824no—
742#41—18824no—
743C2×Q8—216no—
744C2×Q8—476no—
745C2×Q8—474no—
746C2×Q8—4712no—
747C2×Q8—9416no—
748C2×Q8#1062535218yescomplemented
749C2×Q8C23×D4716yes—
750C2×Q8C23×D4714yes—
751C2×D4—212no—
752C2×D4—474no—
753C2×D4—474no—
754C2×D4—4712no—
755C2×D4—4712no—
756C2×D4—4712no—
757C2×D4—476no—
758C2×D4C23×D4714yes—
759C2×D4C23×D47112yes—
760C2×D4C23×D4716yes—
761C2×D4C23×D47112yes—
762C2×D4C23×D47112yes—
763C22×C4—212no—
764C22×C4—471no—
765C22×C4—471no—
766C22×C4—474no—
767C22×C4—476no—
768C22×C4—476no—
769C22×C4—473no—
770C22×C4—473no—
771C22×C4—476no—
772C22×C4—476no—
773C22×C4—4712no—
774C22×C4—474no—
775C22×C4—4712no—
776C22×C4—4712no—
777C22×C4—1886no—
778C22×C4—1886no—
779C22×C4C23×D4711yescharacteristic
780C22×C4C23×D4716yes—
781C22×C4C23×D4716yes—
782C22×C4C23×D47112yes—
783C22×C4C23×D4713yes—
784C4⋊C4—4712no—
785C4⋊C4—474no—
786C4⋊C4—474no—
787C4⋊C4—474no—
788C4⋊C4—474no—
789C4⋊C4—474no—
790C4⋊C4—474no—
791C4⋊C4—4712no—
792C4⋊C4—4712no—
793C4⋊C4—4712no—
794C4⋊C4—4712no—
795C4⋊C4—476no—
796C4⋊C4—4712no—
797C4⋊C4—4712no—
798C4⋊C4—476no—
799C4⋊C4—474no—
800C4⋊C4—474no—
801C4⋊C4—4712no—
802C4⋊C4C23×D4716yes—
803C4⋊C4C23×D4714yes—
804C4⋊C4C23×D4716yes—
805C4⋊C4C23×D4714yes—
806C22⋊C4—4724no—
807C22⋊C4—474no—
808C22⋊C4—474no—
809C22⋊C4—4712no—
810C22⋊C4—474no—
811C22⋊C4—4712no—
812C22⋊C4—4712no—
813C22⋊C4—4712no—
814C22⋊C4—474no—
815C22⋊C4—4712no—
816C22⋊C4—474no—
817C22⋊C4—474no—
818C22⋊C4—474no—
819C22⋊C4—4712no—
820C22⋊C4C23×D4714yes—
821C22⋊C4C23×D4714yes—
822C22⋊C4C23×D47112yes—
823C22⋊C4C23×D47112yes—
824C22⋊C4C23×D4714yes—
825C42—471no—
826C42—471no—
827C42—476no—
828C42—471no—
829C42—471no—
830C42—476no—
831C42—474no—
832C42—474no—
833C42—476no—
834C42—476no—
835C42—476no—
836C42—476no—
837C42—4712no—
838C42—4712no—
839C42—4712no—
840C42C23×D47112yes—
841C23—26no—
842C23—43no—
843C23—43no—
844C23—474no—
845C23C24×D4716yes—
846C23C24×D4714yes—
847C23C24×D4711yescharacteristic
848Q8—212no—
849Q8—948no—
850Q8—9412no—
851Q8—18812no—
852Q8C2×#10625352116yes—
853D4—28no—
854D4—224no—
855D4—212no—
856D4—412no—
857D4—412no—
858D4—948no—
859D4—948no—
860D4—9412no—
861D4—18812no—
862D4—18812no—
863D4—18812no—
864C2×C4—22no—
865C2×C4—212no—
866C2×C4—212no—
867C2×C4—224no—
868C2×C4—471no—
869C2×C4—471no—
870C2×C4—471no—
871C2×C4—471no—
872C2×C4—476no—
873C2×C4—474no—
874C2×C4—474no—
875C2×C4—476no—
876C2×C4—474no—
877C2×C4—948no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—9412no—
881C2×C4—9412no—
882C2×C4—948no—
883C2×C4—9424no—
884C2×C4—18812no—
885C2×C4—1883no—
886C2×C4—1886no—
887C2×C4—1886no—
888C2×C4—1883no—
889C2×C4—18812no—
890C2×C4C2×#10625352112yes—
891C2×C4C24×D4711yescharacteristic
892C2×C4C24×D4711yescharacteristic
893C2×C4C24×D4714yes—
894C2×C4C24×D4714yes—
895C2×C4C24×D4714yes—
896C2×C4C24×D4716yes—
897C22—21no—
898C22—21no—
899C22—24no—
900C22—26no—
901C22—26no—
902C22—26no—
903C22—24no—
904C22—24no—
905C22—412no—
906C22—944no—
907C22—944no—
908C22—944no—
909C22C22×#1062535212yes—
910C22C25×D4711yescharacteristic
911C4—21no—
912C4—21no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—472no—
917C4—472no—
918C4—944no—
919C4—941no—
920C4—941no—
921C4—946no—
922C4—946no—
923C4—944no—
924C4—944no—
925C4C22×#10625352112yes—
926C2—22no—
927C2—46no—
928C2—44no—
929C2—1884no—
930C2C23×#1062535211yescharacteristic
931C2#585×D4711yescharacteristic
932C2#585×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3487C2
hypercenter#3487D47
hypocenterC47#62793
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #20257498C2semidirect
2. #20257486C2semidirect
3. #20257396C2semidirect
4. #20257385C2semidirect
5. #20257239C2semidirect
6. #20257194C2semidirect
7. #20257155C2semidirect
8. #20257105C2semidirect
9. #20257046C2semidirect
10. #20257011C2semidirect
11. #20257004C2semidirect
12. #20256987C2semidirect
13. #20256978C2semidirect
14. #20256801C2semidirect
15. #20256680C2semidirect
16. 2−1+4×Dic47C2semidirect
17. #20256597C2semidirect
18. C2×#41×Dic47C2semidirect
19. C47×#3487C2semidirect
21. #15689859C22semidirect
22. #15689855C22semidirect
23. Q8×Dic94C22semidirect
24. #15689852C22semidirect
25. #15689849C22semidirect
26. #15689849C22semidirect
27. #15689844C22semidirect
28. #15689843C22semidirect
29. #15689842C22semidirect
30. #15689838C22semidirect
31. #15689837C22semidirect
32. #15689837C22semidirect
33. #15689825C22semidirect
34. #15689820C22semidirect
35. #15689820C22semidirect
36. #15689819C22semidirect
37. #15689813C22semidirect
38. #15689807C22semidirect
39. #15689793C22semidirect
42. #15689792C22semidirect
43. Q8×C22⋊D47C22semidirect
44. #15689784C22semidirect
47. #15689780C22semidirect
48. #15689773C22semidirect
50. #15689742C22semidirect
51. #15689740C22semidirect
52. #15689727C22semidirect
53. #15689726C22semidirect
58. #15689675C22semidirect
59. #15689675C22semidirect
60. #15689671C22semidirect
62. #15689668C22semidirect
63. #15689668C22semidirect
64. #15689668C22semidirect
65. #15689659C22semidirect
66. #15689659C22semidirect
67. #15689654C22semidirect
68. #15689654C22semidirect
69. #15689654C22semidirect
70. #15689653C22semidirect
71. #15689653C22semidirect
72. #15689652C22semidirect
79. #15689606C22semidirect
80. #15689605C22semidirect
83. #15689601C22semidirect
84. #15689599C22semidirect
90. #41×Dic47C22semidirect
91. C4×#10625354C22semidirect
93. C4×#10625352C22semidirect
94. C4×#10625352C22semidirect
97. C2×Q8×Dic47C22semidirect
98. C4×Q8×D47C22semidirect
273. C2×Q8×C47#41semidirect
469. #3487D47semidirect
578. C47#62793semidirect
748. C2×Q8#10625352semidirect

Maximal subgroups

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

subgroupindex
#202574982
#202574862
#202573962
#202573852
#202572392
#202571942
#202571552
#202571052
#202570462
#202570112
#202570042
#202569872
#202569782
#202568012
#202566802
2−1+4×Dic472
#202565972
C2×#41×Dic472
C47×#34872
#6279347