Finite Group Databasebeta

← D47×#3497 #27124447

Subgroups — D47×#3497 #27124447

Order 12032.

11210 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
1C2×2−1+4×D47C212yesmaximal, complemented
2#20257159C211yesmaximal, characteristic, complemented
3#20257158C214yesmaximal, complemented
4#20257157C216yesmaximal, complemented
5#20257156C218yesmaximal, complemented
6#20257155C212yesmaximal, complemented
7#20257154C216yesmaximal, complemented
8#20257153C214yesmaximal, complemented
9#550×D47C214yesmaximal, complemented
10D4×Q8×D47C214yesmaximal, complemented
11#548×D47C218yesmaximal, complemented
12#537×D47C216yesmaximal, complemented
13#532×D47C216yesmaximal, complemented
14C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
15C47×#3497C211yesmaximal, characteristic, complemented
16C2×#13094072C2212yescomplemented
17C2×#13094072C2218yescomplemented
18C2×#13094071C2218yescomplemented
19C2×#13094071C22112yescomplemented
202−1+4×D47—232no—
21C2×#41×D47C2218yes—
22C2×#41×D47C22112yes—
23C22×Q8×D47C2218yes—
24C22×Q8×D47C2211yescharacteristic
25#15689795C2214yescomplemented
26#15689794C22112yescomplemented
27#15689793C22112yescomplemented
28#15689792C2218yescomplemented
29#15689791C22124yescomplemented
30Q8×D188C2214yescomplemented
31D4×Dic94C22112yescomplemented
32#15689788C22112yescomplemented
33Q8×C22⋊D47C2218yescomplemented
34#15689786C22124yescomplemented
35#15689785C2218yescomplemented
36#15689784C2218yescomplemented
37#15689783C22124yescomplemented
38#15689782C22124yescomplemented
39#15689781C22124yescomplemented
40#15689780C2218yescomplemented
41#15689779C22124yescomplemented
42#15689704C2216yescomplemented
43#15689703C22124yescomplemented
44#15689702C22124yescomplemented
45#15689701C22112yescomplemented
46#15689700C22124yescomplemented
47#15689674C2216yescomplemented
48#15689673C2216yescomplemented
49#15689672C22112yescomplemented
50#15689671C2216yescomplemented
51#15689670C22112yescomplemented
52#15689670C22112yescomplemented
53#15689669C22112yescomplemented
54#15689668C22112yescomplemented
55#15689668C22112yescomplemented
56C4⋊Q8×D47C2216yes—
57#127×D47C2216yes—
58#124×D47C22112yes—
59C22⋊Q8×D47C22124yes—
60#121×D47C22124yes—
61#121×D47C2214yes—
62#121×D47C22112yes—
63C2×Q8×Dic47C2211yescharacteristic, complemented
64C2×C4×Dic94C2213yescomplemented
65C2×#13093989C2213yescomplemented
66C4×Q8×D47C2214yes—
67C4×Q8×D47C2214yes—
68C4×Q8×D47C2214yescomplemented
69C4×Q8×D47C2214yescomplemented
70C4×D4×D47C22112yes—
71C4×D4×D47C22112yes—
72C2×C4⋊C4×D47C2213yes—
73C2×C42×D47C2213yes—
74C2×2−1+4×C47C2212yescomplemented
75C47×#550C2214yescomplemented
76D4×Q8×C47C2214yescomplemented
77C47×#548C2218yescomplemented
78C47×#537C2216yescomplemented
79C47×#532C2216yescomplemented
80C2×C4×Q8×C47C2211yescharacteristic, complemented
81#13094072—216no—
82#13094072—264no—
83#13094071—264no—
84#13094071—296no—
85C2×#10625354C2318yes—
86C2×#10625354C23112yes—
87C2×#10625350C23124yes—
88C2×#10625350C23112yes—
89C2×#10625350C23124yes—
90C2×#10625352C23124yes—
91C2×#10625352C23124yes—
92C2×#10625352C23112yes—
93#41×D47—264no—
94#41×D47—296no—
95C22×Dic94C23124yes—
96C22×Dic94C2313yes—
97C2×Q8×D47—264no—
98C2×Q8×D47D4116yescomplemented
99C2×Q8×D47C2318yes—
100C2×Q8×D47C23124yes—
101C2×Q8×D47C23112yes—
102C2×Q8×D47C2314yes—
103C2×Q8×D47C2314yes—
104C2×D4×D47C2314yes—
105C2×D4×D47C2318yes—
106C2×D4×D47C23112yes—
107C2×D4×D47C23112yes—
108C22×C4×D47C2311yescharacteristic
109C22×C4×D47C23124yes—
110C22×C4×D47C2313yes—
111C22×C4×D47C2313yes—
112#13094024C2316yes—
113#13094023C23112yes—
114#13094023C23112yes—
115#13094022C23112yes—
116#13094021C2316yes—
117#13094020C23112yes—
118#13094020C23112yes—
119#13094020C23112yes—
120#13094013C23112yes—
121#13094012C23112yes—
122#13094011C23112yes—
123#13094010C23124yes—
124#13094010C23124yes—
125#13094004C23124yes—
126#13094003C23124yes—
127#13094002C23148yes—
128#13094001C23148yes—
129#13094000C23124yes—
130#13093999C23124yes—
131#13093999C2314yes—
132#13093999C23112yes—
133#13093998C23124yes—
134#13093998C2314yes—
135#13093998C23112yes—
136#13093997C23148yes—
137#13093997C2318yes—
138#13093997C23124yes—
139#13093996C23148yes—
140#13093996C2318yes—
141#13093996C23124yes—
142#13093995C23124yes—
143#13093995C2314yes—
144#13093995C23112yes—
145Q8×Dic47C2314yes—
146Q8×Dic47C2314yes—
147C4×Dic94C23112yes—
148C4×Dic94C23112yes—
149#13093989C23112yes—
150#13093989C23112yes—
151C4×D188C23112yes—
152C4×D188C23112yes—
153D4×Dic47C23112yes—
154D4×Dic47C23112yes—
155#13093986C23112yes—
156#13093986C23112yes—
157C4×C22⋊D47C23124yes—
158C4×C22⋊D47C23124yes—
159(C22⋊D47)⋊C4C23124yes—
160(C22⋊D47)⋊C4C23124yes—
161C2×C4⋊Dic47C2313yes—
162C2×Dic47⋊C4C2316yes—
163C4⋊C4×D47C23112yes—
164C4⋊C4×D47C23112yes—
165C4⋊C4×D47C2314yes—
166C4⋊C4×D47C23112yes—
167C22⋊C4×D47C2318yes—
168C22⋊C4×D47C23124yes—
169C2×C4×Dic47C2313yes—
170C2×C4×Dic47C2313yes—
171C2×C4×Dic47C2313yes—
172C42×D47C2316yes—
173C42×D47C2316yes—
174C42×D47C2316yes—
175C42×D47C2316yes—
1762−1+4×C47—216no—
177C2×#41×C47C2318yes—
178C2×#41×C47C23112yes—
179C22×Q8×C47C2318yes—
180C22×Q8×C47C2311yescharacteristic
181C4⋊Q8×C47C2316yes—
182#127×C47C2316yes—
183#124×C47C23112yes—
184C22⋊Q8×C47C23124yes—
185#121×C47C23124yes—
186#121×C47C2314yes—
187#121×C47C23112yes—
188C4×Q8×C47C2314yes—
189C4×Q8×C47C2314yes—
190C4×D4×C47C23112yes—
191C4×D4×C47C23112yes—
192C2×C4⋊C4×C47C2313yes—
193C2×C42×C47C2313yes—
194C23×D47C2418yes—
195C23×D47C2411yescharacteristic
196#41×C47—232no—
197#41×C47—248no—
198C2×Q8×C47—232no—
199C2×Q8×C47C2×D418yescomplemented
200C2×Q8×C47C24112yes—
201C2×Q8×C47C2414yes—
202C2×D4×C47C2414yes—
203C2×D4×C47C2418yes—
204C2×D4×C47C24112yes—
205C2×D4×C47C24112yes—
206C22×C4×C47C2411yescharacteristic
207C22×C4×C47C24124yes—
208C22×C4×C47C2413yes—
209C22×C4×C47C2413yes—
210C2×C22⋊D47C2418yes—
211C2×C22⋊D47C2418yes—
212C2×C22⋊D47C2418yes—
213C2×C22⋊D47C24124yes—
214C2×C22⋊D47C24124yes—
215C22×Dic47C2411yescharacteristic
216C22×Dic47C24124yes—
217C22×Dic47C2413yes—
218C22×Dic47C2413yes—
219#10625354—232no—
220#10625354—248no—
221Q8×D47—232no—
222Q8×D47—248no—
223Q8×D47—296no—
224Q8×D47C2×D4132yes—
225Q8×D47C2×D4132yescomplemented
226#10625352—296no—
227#10625352—248no—
228#10625352—296no—
229D4×D47—232no—
230D4×D47—248no—
231D4×D47—216no—
232D4×D47—424no—
233#10625350—248no—
234#10625350—296no—
235#10625350—296no—
236C2×D188C2414yes—
237C2×D188C2418yes—
238C2×D188C24112yes—
239C2×D188C24112yes—
240C2×C4×D47—296no—
241C2×C4×D47—24no—
242C2×C4×D47—46no—
243C2×C4×D47C2×D4124yes—
244C2×C4×D47C2411yescharacteristic
245C2×C4×D47C2411yescharacteristic
246C2×C4×D47C2411yescharacteristic
247C2×C4×D47C2416yes—
248C2×C4×D47C2418yes—
249C2×C4×D47C24124yes—
250C2×C4×D47C24124yes—
251C2×C4×D47C2416yes—
252C2×C4×D47C2416yes—
253C2×C4×D47C2416yes—
254C2×C4×D47C2411yescharacteristic
255C2×Dic94—296no—
256C2×Dic94C2×D4124yescomplemented
257C2×Dic94C24124yes—
258C2×Dic94C24112yes—
259C2×Dic94C24112yes—
260C4⋊C4×C47C24112yes—
261C4⋊C4×C47C2414yes—
262C4⋊C4×C47C24112yes—
263C22⋊C4×C47C2418yes—
264C22⋊C4×C47C24124yes—
265C42×C47C2416yes—
266C42×C47C2416yes—
267C22⋊Dic47C2418yes—
268C22⋊Dic47C24124yes—
269(C2×D47)⋊C4C2418yes—
270(C2×D47)⋊C4C24124yes—
271(C2×D47)⋊C4C2418yes—
272(C2×D47)⋊C4C24124yes—
273C4⋊Dic47C24112yes—
274C4⋊Dic47C2414yes—
275C4⋊Dic47C24112yes—
276Dic47⋊C4C24124yes—
277Dic47⋊C4C2418yes—
278Dic47⋊C4C24124yes—
279C4×Dic47C2416yes—
280C4×Dic47C2416yes—
281C4×Dic47C2416yes—
282C4×Dic47C2416yes—
283C4×Dic47C2416yes—
284C4×Dic47C2416yes—
285C23×C47C2518yes—
286C23×C47C2511yescharacteristic
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—216no—
290C22×D47—216no—
291C22×D47—216no—
292C22×D47C22×D414yes—
293C22×D47C2518yes—
294C22×D47C2511yescharacteristic
295C22×D47C2511yescharacteristic
296Q8×C47—224no—
297Q8×C47C22×D4116yes—
298D4×C47—216no—
299D4×C47—224no—
300D4×C47—28no—
301D4×C47—412no—
302C2×C4×C47—248no—
303C2×C4×C47—22no—
304C2×C4×C47—43no—
305C2×C4×C47C22×D4112yes—
306C2×C4×C47C2511yescharacteristic
307C2×C4×C47C2516yes—
308C2×C4×C47C2518yes—
309C2×C4×C47C2516yes—
310C2×C4×C47C2511yescharacteristic
311C22⋊D47—216no—
312C22⋊D47—216no—
313C22⋊D47—248no—
314C22⋊D47—216no—
315C22⋊D47—424no—
316C2×Dic47—248no—
317C2×Dic47—22no—
318C2×Dic47—43no—
319C2×Dic47C22×D4112yes—
320C2×Dic47C2511yescharacteristic
321C2×Dic47C2516yes—
322C2×Dic47C2518yes—
323C2×Dic47C2516yes—
324C2×Dic47C2511yescharacteristic
325D188—216no—
326D188—224no—
327D188—28no—
328D188—412no—
329C4×D47—216no—
330C4×D47—22no—
331C4×D47—212no—
332C4×D47—248no—
333C4×D47—22no—
334C4×D47—248no—
335C4×D47—22no—
336C4×D47—46no—
337C4×D47C22×D4124yes—
338C4×D47C22×D4124yes—
339C4×D472−1+414yescomplemented
340Dic94—224no—
341Dic94—248no—
342Dic94C22×D4148yes—
343C2×#3497—471nomaximal, Sylow
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—28no—
347C22×C47—28no—
348C22×C47—28no—
349C22×C47C23×D412yes—
350C22×C47C2611yescharacteristic
351C2×D47—21no—
352C2×D47—21no—
353C2×D47—28no—
354C2×D47—28no—
355C2×D47—28no—
356C2×D47—28no—
357C2×D47—432no—
358C2×D47C23×D412yes—
359C2×D47C23×D412yes—
360C2×D47C2×2−1+412yes—
361C2×D47#58512yes—
362C4×C47—28no—
363C4×C47—21no—
364C4×C47—26no—
365C4×C47C23×D4112yes—
366C4×C47C2×2−1+412yescomplemented
367Dic47—28no—
368Dic47—21no—
369Dic47—26no—
370Dic47C23×D4112yes—
371Dic47C2×2−1+412yescomplemented
372C22×2−1+4—472no—
373#3497—472no—
374#3497—474no—
375#3497—474no—
376#3497—478no—
377#3497—476no—
378#3497—476no—
379#3497—471no—
380#3497D4711yescharacteristic, direct product factor
381C2×#550—474no—
382C2×D4×Q8—474no—
383C2×#548—478no—
384C2×#537—476no—
385C2×#532—476no—
386C22×C4×Q8—471no—
387C2×C47—22no—
388C2×C47—48no—
389C2×C47C24×D411yescharacteristic
390C2×C47C22×2−1+411yescharacteristic
391C2×C47C2×#58511yescharacteristic
392D47—22no—
393D47—48no—
394D47#349714yesdirect product factor
395C2×2−1+4—478no—
396C2×2−1+4—4712no—
397C2×2−1+4—478no—
398C2×2−1+4—472no—
399C2×2−1+4—9432no—
400C2×2−1+4C2×D4712yescomplemented
401C22×#41—4712no—
402C22×#41—478no—
403C23×Q8—471no—
404C23×Q8—478no—
405#550—478no—
406#550—4712no—
407#550—4724no—
408#550—474no—
409#550—4712no—
410#550C2×D4714yescomplemented
411D4×Q8—478no—
412D4×Q8—4712no—
413D4×Q8—4724no—
414D4×Q8—474no—
415D4×Q8—4712no—
416D4×Q8C2×D4714yescomplemented
417#548—478no—
418#548—478no—
419#548—4724no—
420#548—4724no—
421#548—4724no—
422#548—478no—
423#548—4724no—
424#548C2×D4718yescomplemented
425#537—4712no—
426#537—4724no—
427#537—4724no—
428#537—4724no—
429#537—476no—
430#537C2×D4716yescomplemented
431#532—4712no—
432#532—476no—
433#532—476no—
434#532—4712no—
435#532—4712no—
436#532—4712no—
437#532—4712no—
438#532—4712no—
439#532—476no—
440#532C2×D4716yescomplemented
441C2×C4⋊Q8—476no—
442C2×#127—476no—
443C2×#124—4712no—
444C2×C22⋊Q8—4724no—
445C2×#121—474no—
446C2×#121—4712no—
447C2×#121—4724no—
448C2×C4×Q8—471no—
449C2×C4×Q8—474no—
450C2×C4×Q8—474no—
451C2×C4×Q8—474no—
452C2×C4×Q8—474no—
453C2×C4×Q8—473no—
454C2×C4×Q8—473no—
455C2×C4×Q8C2×D4711yescharacteristic, complemented
456C2×C4×D4—4712no—
457C2×C4×D4—4712no—
458C22×C4⋊C4—473no—
459C22×C42—473no—
460C47C2×#349711yescharacteristic, complemented, Sylow
4612−1+4—216no—
4622−1+4—9464no—
4632−1+4—9464no—
4642−1+4—9496no—
4652−1+4—9416no—
466C2×#41—4712no—
467C2×#41—478no—
468C2×#41—4724no—
469C2×#41—4712no—
470C2×#41—4724no—
471C2×#41—4724no—
472C2×#41—4712no—
473C2×#41—4724no—
474C2×#41—9496no—
475C2×#41—9464no—
476C2×#41C22×D47112yes—
477C2×#41C22×D4718yes—
478C22×Q8—4716no—
479C22×Q8—474no—
480C22×Q8—474no—
481C22×Q8—4712no—
482C22×Q8—4724no—
483C22×Q8—478no—
484C22×Q8—473no—
485C22×Q8—4724no—
486C22×Q8—9464no—
487C22×Q8C22×D4718yes—
488C22×Q8C22×D4711yescharacteristic
489C22×D4—474no—
490C22×D4—478no—
491C22×D4—4712no—
492C22×D4—4712no—
493C23×C4—473no—
494C23×C4—4724no—
495C23×C4—471no—
496C23×C4—473no—
497C4⋊Q8—4712no—
498C4⋊Q8—4712no—
499C4⋊Q8—4712no—
500C4⋊Q8—476no—
501C4⋊Q8C22×D4716yes—
502#127—4712no—
503#127—4712no—
504#127—4712no—
505#127—476no—
506#127C22×D4716yes—
507#124—4712no—
508#124—4712no—
509#124—4724no—
510#124—4724no—
511#124—4712no—
512#124C22×D47112yes—
513C22⋊Q8—4724no—
514C22⋊Q8—4724no—
515C22⋊Q8—4748no—
516C22⋊Q8—4724no—
517C22⋊Q8—4748no—
518C22⋊Q8C22×D47124yes—
519#121—474no—
520#121—478no—
521#121—4712no—
522#121—4724no—
523#121—4724no—
524#121—4748no—
525#121—474no—
526#121—4712no—
527#121—4724no—
528#121—474no—
529#121—4712no—
530#121—4724no—
531#121—478no—
532#121—4724no—
533#121—4748no—
534#121C22×D4714yes—
535#121C22×D47112yes—
536#121C22×D47124yes—
537C4×Q8—474no—
538C4×Q8—474no—
539C4×Q8—4712no—
540C4×Q8—4712no—
541C4×Q8—4712no—
542C4×Q8—4712no—
543C4×Q8C22×D4714yes—
544C4×Q8C22×D4714yes—
545C4×D4—4712no—
546C4×D4—4712no—
547C4×D4—4724no—
548C4×D4—4724no—
549C4×D4—4712no—
550C4×D4—4712no—
551C4×D4—4724no—
552C4×D4—4724no—
553C4×D4—4712no—
554C4×D4—4712no—
555C4×D4C22×D47112yes—
556C4×D4C22×D47112yes—
557C2×C4⋊C4—476no—
558C2×C4⋊C4—473no—
559C2×C4⋊C4—4712no—
560C2×C4⋊C4—4712no—
561C2×C4⋊C4—474no—
562C2×C4⋊C4—4712no—
563C2×C4⋊C4C22×D4713yes—
564C2×C22⋊C4—478no—
565C2×C22⋊C4—4724no—
566C2×C42—473no—
567C2×C42—473no—
568C2×C42—473no—
569C2×C42—476no—
570C2×C42—476no—
571C2×C42—476no—
572C2×C42—476no—
573C2×C42C22×D4713yes—
574C24—471no—
575C24—478no—
576#41—232no—
577#41—248no—
578#41—9496no—
579#41—9496no—
580#41—9496no—
581#41—9448no—
582#41—9448no—
583#41—9496no—
584#41—9432no—
585#41—9448no—
586C2×Q8—232no—
587C2×Q8—4732no—
588C2×Q8—4732no—
589C2×Q8—4724no—
590C2×Q8—4712no—
591C2×Q8—4724no—
592C2×Q8—4712no—
593C2×Q8—9496no—
594C2×Q8—9448no—
595C2×Q8—9496no—
596C2×Q8—9432no—
597C2×Q8D4×D4718yescomplemented
598C2×Q8C23×D47112yes—
599C2×Q8C23×D4714yes—
600C2×D4—478no—
601C2×D4—478no—
602C2×D4—478no—
603C2×D4—4724no—
604C2×D4—4724no—
605C2×D4—474no—
606C2×D4—478no—
607C2×D4—4712no—
608C2×D4—4712no—
609C2×D4—9416no—
610C2×D4—9448no—
611C2×D4—9432no—
612C2×D4—18824no—
613C2×D4C23×D4714yes—
614C2×D4C23×D4718yes—
615C2×D4C23×D47112yes—
616C2×D4C23×D47112yes—
617C22×C4—473no—
618C22×C4—4724no—
619C22×C4—471no—
620C22×C4—476no—
621C22×C4—476no—
622C22×C4—471no—
623C22×C4—4724no—
624C22×C4—473no—
625C22×C4—471no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—476no—
629C22×C4—478no—
630C22×C4—4724no—
631C22×C4—4724no—
632C22×C4—476no—
633C22×C4—944no—
634C22×C4—9496no—
635C22×C4—1886no—
636C22×C4C23×D4711yescharacteristic
637C22×C4C23×D47124yes—
638C22×C4C23×D4713yes—
639C22×C4C23×D4713yes—
640C4⋊C4—4724no—
641C4⋊C4—478no—
642C4⋊C4—4724no—
643C4⋊C4—4712no—
644C4⋊C4—474no—
645C4⋊C4—4712no—
646C4⋊C4C23×D47112yes—
647C4⋊C4C23×D4714yes—
648C4⋊C4C23×D47112yes—
649C22⋊C4—478no—
650C22⋊C4—4724no—
651C22⋊C4—478no—
652C22⋊C4—478no—
653C22⋊C4—4724no—
654C22⋊C4—4724no—
655C22⋊C4C23×D4718yes—
656C22⋊C4C23×D47124yes—
657C42—476no—
658C42—476no—
659C42—476no—
660C42—476no—
661C42—476no—
662C42—476no—
663C42C23×D4716yes—
664C42C23×D4716yes—
665C23—471no—
666C23—474no—
667C23—471no—
668C23—478no—
669C23—942no—
670C23—942no—
671C23—9416no—
672C23—9416no—
673C23—9416no—
674C23C24×D4718yes—
675C23C24×D4711yescharacteristic
676Q8—224no—
677Q8—4748no—
678Q8—9448no—
679Q8—9424no—
680Q8C2×D4×D47116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—9416no—
686D4—9416no—
687D4—9448no—
688D4—9416no—
689D4—9416no—
690D4—9424no—
691D4—948no—
692D4—18812no—
693D4—18824no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—4712no—
698C2×C4—471no—
699C2×C4—476no—
700C2×C4—4724no—
701C2×C4—4724no—
702C2×C4—474no—
703C2×C4—471no—
704C2×C4—476no—
705C2×C4—478no—
706C2×C4—942no—
707C2×C4—9448no—
708C2×C4—942no—
709C2×C4—9416no—
710C2×C4—9412no—
711C2×C4—942no—
712C2×C4—9448no—
713C2×C4—9448no—
714C2×C4—942no—
715C2×C4—1886no—
716C2×C4—1883no—
717C2×C4C2×D4×D47112yes—
718C2×C4C24×D4711yescharacteristic
719C2×C4C24×D4716yes—
720C2×C4C24×D4718yes—
721C2×C4C24×D4716yes—
722C2×C4C24×D4711yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—472no—
729C22—472no—
730C22—472no—
731C22—472no—
732C22—948no—
733C22—941no—
734C22—941no—
735C22—948no—
736C22—948no—
737C22—948no—
738C22—18832no—
739C22C22×D4×D4712yes—
740C22C25×D4711yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—4712no—
745C4—472no—
746C4—948no—
747C4—941no—
748C4—946no—
749C4C22×D4×D47112yes—
750C42−1+4×D4712yescomplemented
751C2—22no—
752C2—48no—
753C2—474no—
754C2—942no—
755C2—1888no—
756C2C23×D4×D4711yescharacteristic
757C2C2×2−1+4×D4711yescharacteristic
758C2#585×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3497C2
hypercenter#3497D47
hypocenterC47C2×#3497
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D47C2semidirect
2. #20257159C2semidirect
3. #20257158C2semidirect
4. #20257157C2semidirect
5. #20257156C2semidirect
6. #20257155C2semidirect
7. #20257154C2semidirect
8. #20257153C2semidirect
9. #550×D47C2semidirect
10. D4×Q8×D47C2semidirect
11. #548×D47C2semidirect
12. #537×D47C2semidirect
13. #532×D47C2semidirect
14. C2×C4×Q8×D47C2semidirect
15. C47×#3497C2semidirect
16. C2×#13094072C22semidirect
17. C2×#13094072C22semidirect
18. C2×#13094071C22semidirect
19. C2×#13094071C22semidirect
25. #15689795C22semidirect
26. #15689794C22semidirect
27. #15689793C22semidirect
28. #15689792C22semidirect
29. #15689791C22semidirect
30. Q8×D188C22semidirect
31. D4×Dic94C22semidirect
32. #15689788C22semidirect
33. Q8×C22⋊D47C22semidirect
34. #15689786C22semidirect
35. #15689785C22semidirect
36. #15689784C22semidirect
37. #15689783C22semidirect
38. #15689782C22semidirect
39. #15689781C22semidirect
40. #15689780C22semidirect
41. #15689779C22semidirect
42. #15689704C22semidirect
43. #15689703C22semidirect
44. #15689702C22semidirect
45. #15689701C22semidirect
46. #15689700C22semidirect
47. #15689674C22semidirect
48. #15689673C22semidirect
49. #15689672C22semidirect
50. #15689671C22semidirect
51. #15689670C22semidirect
52. #15689670C22semidirect
53. #15689669C22semidirect
54. #15689668C22semidirect
55. #15689668C22semidirect
63. C2×Q8×Dic47C22semidirect
64. C2×C4×Dic94C22semidirect
65. C2×#13093989C22semidirect
68. C4×Q8×D47C22semidirect
69. C4×Q8×D47C22semidirect
74. C2×2−1+4×C47C22semidirect
75. C47×#550C22semidirect
76. D4×Q8×C47C22semidirect
77. C47×#548C22semidirect
78. C47×#537C22semidirect
79. C47×#532C22semidirect
80. C2×C4×Q8×C47C22semidirect
98. C2×Q8×D47D4semidirect
199. C2×Q8×C47C2×D4semidirect
225. Q8×D47C2×D4semidirect
256. C2×Dic94C2×D4semidirect
339. C4×D472−1+4semidirect
366. C4×C47C2×2−1+4semidirect
371. Dic47C2×2−1+4semidirect
380. #3497D47direct (N × H)
394. D47#3497direct (N × H)
400. C2×2−1+4C2×D47semidirect
410. #550C2×D47semidirect
416. D4×Q8C2×D47semidirect
424. #548C2×D47semidirect
430. #537C2×D47semidirect
440. #532C2×D47semidirect
455. C2×C4×Q8C2×D47semidirect
460. C47C2×#3497semidirect
597. C2×Q8D4×D47semidirect
750. C42−1+4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D472
#202571592
#202571582
#202571572
#202571562
#202571552
#202571542
#202571532
#550×D472
D4×Q8×D472
#548×D472
#537×D472
#532×D472
C2×C4×Q8×D472
C47×#34972
C2×#349747