Finite Group Databasebeta

← D47×#3504 #27124752

Subgroups — D47×#3504 #27124752

Order 12032.

6958 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257214C211yesmaximal, characteristic, complemented
2#20257213C214yesmaximal, complemented
3#20257212C213yesmaximal, complemented
4#20257211C216yesmaximal, complemented
5#20257210C212yesmaximal, complemented
6#20257209C213yesmaximal, complemented
7#20257208C2112yesmaximal, complemented
8#557×D47C214yesmaximal, complemented
9#554×D47C2112yesmaximal, complemented
10#544×D47C216yesmaximal, complemented
11#533×D47C213yesmaximal, complemented
12C2×#125×D47C213yesmaximal, complemented
13#520×D47C212yesmaximal
14C4×#41×D47C211yesmaximal, characteristic
15C47×#3504C211yesmaximal, characteristic, complemented
16C2×#41×D47C2211yescharacteristic
17#15689852C2214yescomplemented
18#15689851C22112yescomplemented
19#15689850C22112yescomplemented
20#15689850C22112yescomplemented
21#15689849C2214yescomplemented
22#15689849C2214yescomplemented
23#15689848C22112yescomplemented
24#15689834C22112yescomplemented
25#15689833C22112yescomplemented
26#15689832C22112yescomplemented
27#15689832C22112yescomplemented
28#15689831C22124yescomplemented
29#15689830C22112yescomplemented
30#15689829C22112yescomplemented
31#15689829C22112yescomplemented
32#15689828C22124yescomplemented
33#15689827C22124yescomplemented
34#15689827C22124yescomplemented
35#15689754C2216yescomplemented
36#15689753C22112yescomplemented
37#15689753C22112yescomplemented
38#15689752C22124yescomplemented
39#15689751C2216yescomplemented
40#15689751C2216yescomplemented
41#15689750C22112yescomplemented
42#15689750C22112yescomplemented
43#15689680C2213yescomplemented
44#15689679C2213yescomplemented
45#15689679C2213yescomplemented
46#15689678C2216yescomplemented
47#15689677C22112yescomplemented
48#15689676C2216yescomplemented
49#15689675C22112yescomplemented
50C4⋊Q8×D47C2216yes—
51C4⋊Q8×D47C22112yes—
52C2×#13094016C2213yescomplemented
53C2×#13094015C2216yescomplemented
54C2×#13094014C22112yescomplemented
55#125×D47C2216yes—
56#125×D47C22112yes—
57#125×D47C2213yes—
58#125×D47C22112yes—
59#125×D47C2211yescharacteristic
60#125×D47C22112yescomplemented
61#125×D47C2216yescomplemented
62#125×D47C2216yescomplemented
63C22⋊Q8×D47C22124yes—
64C22⋊Q8×D47C22112yes—
65#15689606C2212yes—
66#15689605C2214yes—
67#15689604C2216yes—
68#15689603C2216yes—
69#15689602C22112yes—
70#41×Dic47C2211yescharacteristic
71C4×#10625354C2212yes—
72C4×#10625350C2213yes—
73#15689591C2213yes—
74C4×#10625352C2216yes—
75C4×Q8×D47C2212yes—
76C4×Q8×D47C2214yes—
77C4×Q8×D47C22112yes—
78C4×D4×D47C2216yes—
79C4×D4×D47C22112yes—
80#117×D47C2213yes—
81#117×D47C2216yes—
82C2×C4⋊C4×D47C2216yes—
83C2×C4⋊C4×D47C22112yes—
84C2×C42×D47C2213yes—
85C47×#557C2214yescomplemented
86C47×#554C22112yescomplemented
87C47×#544C2216yescomplemented
88C47×#533C2213yescomplemented
89C2×#125×C47C2213yescomplemented
90C47×#520C2212yes—
91C4×#41×C47C2211yescharacteristic
92C2×#10625354C2311yescharacteristic
93C2×#10625350C2313yes—
94C2×#10625352C2313yes—
95#41×D47Q8116yescomplemented
96C2×Q8×D47C23112yes—
97C2×Q8×D47C2311yescharacteristic
98C2×D4×D47C2313yes—
99C22×C4×D47C2316yes—
100C22×C4×D47C23112yes—
101C22×C4×D47C2313yes—
102#13094024C2316yes—
103#13094024C23112yes—
104#13094023C2316yes—
105#13094023C23112yes—
106#13094023C23112yes—
107#13094023C23124yes—
108#13094023C2316yes—
109#13094023C23112yes—
110#13094022C23112yes—
111#13094022C23124yes—
112#13094016C2316yes—
113#13094016C23112yes—
114#13094016C23112yes—
115#13094016C2313yes—
116#13094016C2311yescharacteristic
117#13094015C23112yes—
118#13094015C23112yes—
119#13094015C23112yes—
120#13094015C23112yes—
121#13094015C23112yes—
122#13094015C2316yes—
123#13094015C2312yes—
124#13094014C23124yes—
125#13094014C23124yes—
126#13094014C23124yes—
127#13094014C23124yes—
128#13094014C23124yes—
129#13094014C23112yes—
130#13094014C2314yes—
131#13094004C23124yes—
132#13094004C23112yes—
133#13094003C23124yes—
134#13094003C23112yes—
135#13094002C23124yes—
136#13094002C23124yes—
137#13094002C23112yes—
138#13094002C23112yes—
139#13094001C23124yes—
140#13094001C23124yes—
141#13094001C23112yes—
142#13094001C23112yes—
143#13094000C23124yes—
144#13094000C23112yes—
145Q8×Dic47C23112yes—
146Q8×Dic47C2312yes—
147Q8×Dic47C2314yes—
148C4×Dic94C23112yes—
149C4×Dic94C23112yes—
150C4×Dic94C23112yes—
151C4×Dic94C2316yes—
152C4×Dic94C23112yes—
153#13093989C23112yes—
154#13093989C23112yes—
155#13093989C23112yes—
156#13093989C2316yes—
157#13093989C23112yes—
158C4×D188C2316yes—
159C4×D188C23112yes—
160D4×Dic47C2316yes—
161D4×Dic47C23112yes—
162#13093986C23112yes—
163#13093986C2316yes—
164C4×C22⋊D47C23112yes—
165C4×C22⋊D47C23124yes—
166(C22⋊D47)⋊C4C23124yes—
167(C22⋊D47)⋊C4C23112yes—
168#13093983C2313yes—
169#13093983C2316yes—
170#13093982C2316yes—
171#13093982C2316yes—
172#13093982C2316yes—
173#13093981C2316yes—
174#13093981C23112yes—
175#13093980C2316yes—
176#13093980C23112yes—
177C2×C4⋊Dic47C2316yes—
178C2×C4⋊Dic47C23112yes—
179C2×Dic47⋊C4C23112yes—
180C2×Dic47⋊C4C23112yes—
181C2×Dic47⋊C4C23112yes—
182C4⋊C4×D47C23112yes—
183C4⋊C4×D47C23112yes—
184C4⋊C4×D47C23124yes—
185C4⋊C4×D47C23124yes—
186C4⋊C4×D47C2316yes—
187C4⋊C4×D47C23112yes—
188C4⋊C4×D47C23112yes—
189C4⋊C4×D47C23124yes—
190C4⋊C4×D47C2312yes—
191C4⋊C4×D47C2316yes—
192C4⋊C4×D47C2314yes—
193C4⋊C4×D47C23112yes—
194C22⋊C4×D47C23112yes—
195C22⋊C4×D47C2316yes—
196C2×C4×Dic47C2316yes—
197C2×C4×Dic47C2313yes—
198C42×D47C2311yescharacteristic
199C42×D47C2313yes—
200C42×D47C2316yes—
201C42×D47C2316yes—
202C42×D47C2313yes—
203C42×D47C2313yes—
204C42×D47C23112yes—
205C2×#41×C47C2311yescharacteristic
206C4⋊Q8×C47C2316yes—
207C4⋊Q8×C47C23112yes—
208#125×C47C2316yes—
209#125×C47C23112yes—
210#125×C47C2313yes—
211#125×C47C23112yes—
212#125×C47C2311yescharacteristic
213C22⋊Q8×C47C23124yes—
214C22⋊Q8×C47C23112yes—
215C4×Q8×C47C2312yes—
216C4×Q8×C47C2314yes—
217C4×Q8×C47C23112yes—
218C4×D4×C47C2316yes—
219C4×D4×C47C23112yes—
220#117×C47C2313yes—
221#117×C47C2316yes—
222C2×C4⋊C4×C47C2316yes—
223C2×C4⋊C4×C47C23112yes—
224C2×C42×C47C2313yes—
225C23×D47C2413yes—
226#41×C47C2×Q818yescomplemented
227C2×Q8×C47C24112yes—
228C2×Q8×C47C2411yescharacteristic
229C2×D4×C47C2413yes—
230C22×C4×C47C2416yes—
231C22×C4×C47C24112yes—
232C22×C4×C47C2413yes—
233C2×C22⋊D47C2416yes—
234C22×Dic47C2416yes—
235C22×Dic47C24112yes—
236C22×Dic47C2413yes—
237#10625354C2×Q818yescomplemented
238Q8×D47—424no—
239Q8×D47C2×Q818yes—
240#10625352C2×Q8124yescomplemented
241D4×D47C2×Q8124yes—
242#10625350C2×Q8124yescomplemented
243C2×D188C2413yes—
244C2×C4×D47—412no—
245C2×C4×D47—424no—
246C2×C4×D47C2×Q8124yes—
247C2×C4×D47C2412yes—
248C2×C4×D47C2414yes—
249C2×C4×D47C2416yes—
250C2×C4×D47C24112yes—
251C2×C4×D47C2416yes—
252C2×C4×D47C2416yes—
253C2×C4×D47C24124yes—
254C2×C4×D47C2413yes—
255C2×C4×D47C2411yescharacteristic
256C2×C4×D47C2413yes—
257C2×C4×D47C2413yes—
258C2×Dic94C24112yes—
259C2×Dic94C24112yes—
260C2×Dic94C24112yes—
261C2×Dic94C2413yes—
262C4⋊C4×C47C2416yes—
263C4⋊C4×C47C24112yes—
264C4⋊C4×C47C24112yes—
265C4⋊C4×C47C24124yes—
266C4⋊C4×C47C2412yes—
267C4⋊C4×C47C2416yes—
268C4⋊C4×C47C2414yes—
269C4⋊C4×C47C24112yes—
270C22⋊C4×C47C24112yes—
271C22⋊C4×C47C2416yes—
272C42×C47C2411yescharacteristic
273C42×C47C2413yes—
274C42×C47C2416yes—
275C42×C47C24112yes—
276C22⋊Dic47C24112yes—
277C22⋊Dic47C2416yes—
278(C2×D47)⋊C4C24112yes—
279(C2×D47)⋊C4C24112yes—
280(C2×D47)⋊C4C24112yes—
281C4⋊Dic47C2416yes—
282C4⋊Dic47C24112yes—
283C4⋊Dic47C24112yes—
284C4⋊Dic47C24124yes—
285C4⋊Dic47C2412yes—
286C4⋊Dic47C2416yes—
287C4⋊Dic47C2414yes—
288C4⋊Dic47C24112yes—
289Dic47⋊C4C24112yes—
290Dic47⋊C4C24112yes—
291Dic47⋊C4C24112yes—
292Dic47⋊C4C24124yes—
293Dic47⋊C4C24124yes—
294Dic47⋊C4C24124yes—
295Dic47⋊C4C2414yes—
296Dic47⋊C4C24112yes—
297Dic47⋊C4C2414yes—
298Dic47⋊C4C2414yes—
299Dic47⋊C4C24112yes—
300Dic47⋊C4C24112yes—
301C4×Dic47C2412yes—
302C4×Dic47C2411yescharacteristic
303C4×Dic47C2416yes—
304C4×Dic47C2413yes—
305C4×Dic47C2416yes—
306C4×Dic47C2416yes—
307C4×Dic47C2416yes—
308C4×Dic47C24112yes—
309C4×Dic47C24112yes—
310C4×Dic47C24112yes—
311C23×C47C2513yes—
312C22×D47—212no—
313C22×D47C22×Q8112yes—
314C22×D47C2513yes—
315C22×D47C2511yescharacteristic
316Q8×C47—412no—
317Q8×C47C22×Q814yes—
318D4×C47C22×Q8112yes—
319C2×C4×C47—46no—
320C2×C4×C47—412no—
321C2×C4×C47C22×Q8112yes—
322C2×C4×C47C2512yes—
323C2×C4×C47C2514yes—
324C2×C4×C47C2516yes—
325C2×C4×C47C25112yes—
326C2×C4×C47C2513yes—
327C2×C4×C47C2511yescharacteristic
328C22⋊D47C22×Q8124yes—
329C2×Dic47—46no—
330C2×Dic47—412no—
331C2×Dic47C22×Q8112yes—
332C2×Dic47C2512yes—
333C2×Dic47C2514yes—
334C2×Dic47C2516yes—
335C2×Dic47C25112yes—
336C2×Dic47C2513yes—
337C2×Dic47C2511yescharacteristic
338D188C22×Q8112yes—
339C4×D47—24no—
340C4×D47—224no—
341C4×D47—212no—
342C4×D47—28no—
343C4×D47—46no—
344C4×D47—424no—
345C4×D47—46no—
346C4×D47C22×Q814yes—
347C4×D47C22×Q8112yes—
348C4×D47C22×Q8112yes—
349C4×D47C22×Q8112yes—
350Dic94—412no—
351Dic94—412no—
352Dic94—412no—
353Dic94C22×Q8112yes—
354C2×#3504—471nomaximal, Sylow
355C22×C47—26no—
356C22×C47C23×Q816yes—
357C22×C47C2611yescharacteristic
358C2×D47—26no—
359C2×D47—224no—
360C2×D47C23×Q816yes—
361C2×D47C23×Q812yes—
362C2×D47#58514yes—
363C4×C47—24no—
364C4×C47—26no—
365C4×C47—212no—
366C4×C47—22no—
367C4×C47C23×Q816yes—
368C4×C47C23×Q812yes—
369Dic47—24no—
370Dic47—26no—
371Dic47—212no—
372Dic47—22no—
373Dic47C23×Q816yes—
374Dic47C23×Q812yes—
375#3504—474no—
376#3504—4712no—
377#3504—476no—
378#3504—473no—
379#3504—473no—
380#3504—472no—
381#3504—471no—
382#3504D4711yescharacteristic, direct product factor
383C2×#557—474no—
384C2×#554—4712no—
385C2×#544—476no—
386C2×#533—473no—
387C22×#125—473no—
388C2×#520—472no—
389C2×C4×#41—471no—
390C2×C47—26no—
391C2×C47C24×Q811yescharacteristic
392C2×C47C2×#58512yes—
393D47—26no—
394D47#350414yesdirect product factor
395C22×#41—471no—
396#557—4712no—
397#557—4712no—
398#557—4712no—
399#557—474no—
400#557—474no—
401#557—4712no—
402#557—474no—
403#557C2×D4714yescomplemented
404#554—4712no—
405#554—4712no—
406#554—4712no—
407#554—4724no—
408#554—4724no—
409#554—4724no—
410#554—4712no—
411#554—4712no—
412#554—4712no—
413#554—4712no—
414#554—4724no—
415#554C2×D47112yescomplemented
416#544—4712no—
417#544—4712no—
418#544—4712no—
419#544—4712no—
420#544—4724no—
421#544—476no—
422#544—476no—
423#544—476no—
424#544C2×D4716yescomplemented
425#533—476no—
426#533—473no—
427#533—473no—
428#533—4712no—
429#533—4712no—
430#533—476no—
431#533—473no—
432#533C2×D4713yescomplemented
433C2×C4⋊Q8—476no—
434C2×C4⋊Q8—4712no—
435C2×#125—473no—
436C2×#125—476no—
437C2×#125—4712no—
438C2×#125—4712no—
439C2×#125—476no—
440C2×#125—476no—
441C2×#125—471no—
442C2×#125—4712no—
443C2×#125—4712no—
444C2×#125—476no—
445C2×#125—473no—
446C2×#125C2×D4713yescomplemented
447C2×C22⋊Q8—4712no—
448C2×C22⋊Q8—4724no—
449#520—472no—
450#520—474no—
451#520—4712no—
452#520—476no—
453#520—476no—
454#520C2×D4712yes—
455C4×#41—471no—
456C4×#41—472no—
457C4×#41—476no—
458C4×#41—473no—
459C4×#41—473no—
460C4×#41C2×D4711yescharacteristic
461C2×C4×Q8—472no—
462C2×C4×Q8—474no—
463C2×C4×Q8—4712no—
464C2×C4×D4—476no—
465C2×C4×D4—4712no—
466C2×#117—473no—
467C2×#117—476no—
468C22×C4⋊C4—476no—
469C22×C4⋊C4—4712no—
470C22×C42—473no—
471C47C2×#350411yescharacteristic, complemented, Sylow
472C2×#41—4716no—
473C2×#41—471no—
474C2×#41—473no—
475C2×#41—473no—
476C2×#41C22×D4711yescharacteristic
477C22×Q8—471no—
478C22×Q8—4712no—
479C22×D4—473no—
480C23×C4—473no—
481C23×C4—4712no—
482C23×C4—476no—
483C4⋊Q8—4712no—
484C4⋊Q8—4724no—
485C4⋊Q8—4712no—
486C4⋊Q8—476no—
487C4⋊Q8—476no—
488C4⋊Q8—4724no—
489C4⋊Q8—4712no—
490C4⋊Q8—4712no—
491C4⋊Q8—476no—
492C4⋊Q8—4712no—
493C4⋊Q8C22×D4716yes—
494C4⋊Q8C22×D47112yes—
495#125—4712no—
496#125—476no—
497#125—4724no—
498#125—4712no—
499#125—4724no—
500#125—4724no—
501#125—4712no—
502#125—4712no—
503#125—474no—
504#125—472no—
505#125—4724no—
506#125—4724no—
507#125—4712no—
508#125—4712no—
509#125—473no—
510#125—476no—
511#125—4712no—
512#125—471no—
513#125—4712no—
514#125C22×D4713yes—
515#125C22×D4716yes—
516#125C22×D47112yes—
517#125C22×D4711yescharacteristic
518#125C22×D47112yes—
519C22⋊Q8—4712no—
520C22⋊Q8—4724no—
521C22⋊Q8—4712no—
522C22⋊Q8—4724no—
523C22⋊Q8—4712no—
524C22⋊Q8—4712no—
525C22⋊Q8—4712no—
526C22⋊Q8—4724no—
527C22⋊Q8—4724no—
528C22⋊Q8—4724no—
529C22⋊Q8—4712no—
530C22⋊Q8—4712no—
531C22⋊Q8—4724no—
532C22⋊Q8—4724no—
533C22⋊Q8C22×D47112yes—
534C22⋊Q8C22×D47124yes—
535C4×Q8—472no—
536C4×Q8—474no—
537C4×Q8—4712no—
538C4×Q8—476no—
539C4×Q8—4712no—
540C4×Q8—4712no—
541C4×Q8—4712no—
542C4×Q8—4712no—
543C4×Q8—476no—
544C4×Q8—4712no—
545C4×Q8—4712no—
546C4×Q8—4712no—
547C4×Q8—4712no—
548C4×Q8C22×D4712yes—
549C4×Q8C22×D4714yes—
550C4×Q8C22×D47112yes—
551C4×D4—476no—
552C4×D4—4712no—
553C4×D4—4712no—
554C4×D4—4724no—
555C4×D4—476no—
556C4×D4—4712no—
557C4×D4—4712no—
558C4×D4—4724no—
559C4×D4—476no—
560C4×D4—4712no—
561C4×D4C22×D4716yes—
562C4×D4C22×D47112yes—
563#117—473no—
564#117—476no—
565#117—476no—
566#117—476no—
567#117—476no—
568#117—476no—
569#117—4712no—
570#117—476no—
571#117—4712no—
572#117C22×D4713yes—
573#117C22×D4716yes—
574C2×C4⋊C4—4712no—
575C2×C4⋊C4—476no—
576C2×C4⋊C4—4712no—
577C2×C4⋊C4—4712no—
578C2×C4⋊C4—4712no—
579C2×C4⋊C4—476no—
580C2×C4⋊C4—4712no—
581C2×C4⋊C4—4712no—
582C2×C4⋊C4—4712no—
583C2×C4⋊C4—4712no—
584C2×C4⋊C4—4724no—
585C2×C4⋊C4—4724no—
586C2×C4⋊C4—4724no—
587C2×C4⋊C4—472no—
588C2×C4⋊C4—476no—
589C2×C4⋊C4—474no—
590C2×C4⋊C4—4712no—
591C2×C4⋊C4C22×D4716yes—
592C2×C4⋊C4C22×D47112yes—
593C2×C22⋊C4—4712no—
594C2×C22⋊C4—476no—
595C2×C42—476no—
596C2×C42—473no—
597C2×C42—473no—
598C2×C42—4712no—
599C2×C42—476no—
600C2×C42—476no—
601C2×C42—473no—
602C2×C42—473no—
603C2×C42—471no—
604C2×C42C22×D4713yes—
605C24—473no—
606#41—478no—
607#41—4724no—
608#41—4724no—
609#41Q8×D4718yescomplemented
610C2×Q8—478no—
611C2×Q8—473no—
612C2×Q8—4712no—
613C2×Q8—4712no—
614C2×Q8—4712no—
615C2×Q8—18824no—
616C2×Q8C23×D47112yes—
617C2×Q8C23×D4711yescharacteristic
618C2×D4—476no—
619C2×D4—4724no—
620C2×D4—473no—
621C2×D4C23×D4713yes—
622C22×C4—473no—
623C22×C4—4724no—
624C22×C4—473no—
625C22×C4—471no—
626C22×C4—473no—
627C22×C4—473no—
628C22×C4—476no—
629C22×C4—4712no—
630C22×C4—472no—
631C22×C4—474no—
632C22×C4—476no—
633C22×C4—4712no—
634C22×C4—476no—
635C22×C4—476no—
636C22×C4—4724no—
637C22×C4—18812no—
638C22×C4—18824no—
639C22×C4C23×D4716yes—
640C22×C4C23×D47112yes—
641C22×C4C23×D4713yes—
642C4⋊C4—4712no—
643C4⋊C4—4712no—
644C4⋊C4—4712no—
645C4⋊C4—4724no—
646C4⋊C4—4724no—
647C4⋊C4—4724no—
648C4⋊C4—474no—
649C4⋊C4—4712no—
650C4⋊C4—474no—
651C4⋊C4—474no—
652C4⋊C4—4712no—
653C4⋊C4—4712no—
654C4⋊C4—476no—
655C4⋊C4—4712no—
656C4⋊C4—4712no—
657C4⋊C4—4724no—
658C4⋊C4—472no—
659C4⋊C4—476no—
660C4⋊C4—474no—
661C4⋊C4—4712no—
662C4⋊C4C23×D4716yes—
663C4⋊C4C23×D47112yes—
664C4⋊C4C23×D47112yes—
665C4⋊C4C23×D47124yes—
666C4⋊C4C23×D4712yes—
667C4⋊C4C23×D4716yes—
668C4⋊C4C23×D4714yes—
669C4⋊C4C23×D47112yes—
670C22⋊C4—4712no—
671C22⋊C4—476no—
672C22⋊C4—4712no—
673C22⋊C4—4712no—
674C22⋊C4—4712no—
675C22⋊C4C23×D47112yes—
676C22⋊C4C23×D4716yes—
677C42—472no—
678C42—471no—
679C42—476no—
680C42—473no—
681C42—476no—
682C42—476no—
683C42—476no—
684C42—4712no—
685C42—4712no—
686C42—4712no—
687C42C23×D4711yescharacteristic
688C42C23×D4713yes—
689C42C23×D4716yes—
690C42C23×D47112yes—
691C23—471no—
692C23—4712no—
693C23—473no—
694C23—9412no—
695C23C24×D4713yes—
696Q8—412no—
697Q8—4712no—
698Q8—18812no—
699Q8—18812no—
700Q8—18812no—
701Q8C2×Q8×D4714yes—
702D4—4724no—
703D4—4712no—
704D4C2×Q8×D47112yes—
705C2×C4—46no—
706C2×C4—412no—
707C2×C4—4712no—
708C2×C4—473no—
709C2×C4—471no—
710C2×C4—474no—
711C2×C4—4712no—
712C2×C4—4712no—
713C2×C4—4712no—
714C2×C4—472no—
715C2×C4—474no—
716C2×C4—476no—
717C2×C4—4712no—
718C2×C4—944no—
719C2×C4—9424no—
720C2×C4—9412no—
721C2×C4—948no—
722C2×C4—1886no—
723C2×C4—18824no—
724C2×C4—1886no—
725C2×C4—1886no—
726C2×C4—18812no—
727C2×C4C2×Q8×D47112yes—
728C2×C4C24×D4712yes—
729C2×C4C24×D4714yes—
730C2×C4C24×D4716yes—
731C2×C4C24×D47112yes—
732C2×C4C24×D4713yes—
733C2×C4C24×D4711yescharacteristic
734C22—26no—
735C22—472no—
736C22—474no—
737C22—476no—
738C22—9424no—
739C22—946no—
740C22C22×Q8×D4716yes—
741C22C25×D4711yescharacteristic
742C4—22no—
743C4—212no—
744C4—26no—
745C4—24no—
746C4—472no—
747C4—476no—
748C4—942no—
749C4—9412no—
750C4—946no—
751C4—944no—
752C4C22×Q8×D4712yes—
753C4C22×Q8×D4716yes—
754C2—26no—
755C2—474no—
756C2—946no—
757C2C23×Q8×D4711yescharacteristic
758C2#585×D4712yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3504C2
prime radicalC2×#41×D47C22
hypercenter#3504D47
hypocenterC47C2×#3504
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #20257214C2semidirect
2. #20257213C2semidirect
3. #20257212C2semidirect
4. #20257211C2semidirect
5. #20257210C2semidirect
6. #20257209C2semidirect
7. #20257208C2semidirect
8. #557×D47C2semidirect
9. #554×D47C2semidirect
10. #544×D47C2semidirect
11. #533×D47C2semidirect
12. C2×#125×D47C2semidirect
15. C47×#3504C2semidirect
17. #15689852C22semidirect
18. #15689851C22semidirect
19. #15689850C22semidirect
20. #15689850C22semidirect
21. #15689849C22semidirect
22. #15689849C22semidirect
23. #15689848C22semidirect
24. #15689834C22semidirect
25. #15689833C22semidirect
26. #15689832C22semidirect
27. #15689832C22semidirect
28. #15689831C22semidirect
29. #15689830C22semidirect
30. #15689829C22semidirect
31. #15689829C22semidirect
32. #15689828C22semidirect
33. #15689827C22semidirect
34. #15689827C22semidirect
35. #15689754C22semidirect
36. #15689753C22semidirect
37. #15689753C22semidirect
38. #15689752C22semidirect
39. #15689751C22semidirect
40. #15689751C22semidirect
41. #15689750C22semidirect
42. #15689750C22semidirect
43. #15689680C22semidirect
44. #15689679C22semidirect
45. #15689679C22semidirect
46. #15689678C22semidirect
47. #15689677C22semidirect
48. #15689676C22semidirect
49. #15689675C22semidirect
52. C2×#13094016C22semidirect
53. C2×#13094015C22semidirect
54. C2×#13094014C22semidirect
60. #125×D47C22semidirect
61. #125×D47C22semidirect
62. #125×D47C22semidirect
85. C47×#557C22semidirect
86. C47×#554C22semidirect
87. C47×#544C22semidirect
88. C47×#533C22semidirect
89. C2×#125×C47C22semidirect
95. #41×D47Q8semidirect
226. #41×C47C2×Q8semidirect
237. #10625354C2×Q8semidirect
240. #10625352C2×Q8semidirect
242. #10625350C2×Q8semidirect
382. #3504D47direct (N × H)
394. D47#3504direct (N × H)
403. #557C2×D47semidirect
415. #554C2×D47semidirect
424. #544C2×D47semidirect
432. #533C2×D47semidirect
446. C2×#125C2×D47semidirect
471. C47C2×#3504semidirect
609. #41Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#202572142
#202572132
#202572122
#202572112
#202572102
#202572092
#202572082
#557×D472
#554×D472
#544×D472
#533×D472
C2×#125×D472
#520×D472
C4×#41×D472
C47×#35042
C2×#350447