Finite Group Databasebeta

← #27124822

Subgroups — #27124822

Order 12032.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689958C212yesmaximal, complemented
2#20257180C216yesmaximal, complemented
3#20257176C212yesmaximal, complemented
4#20257173C211yesmaximal, characteristic, complemented
5#20257168C213yesmaximal, complemented
6#20257164C213yesmaximal, complemented
7#20257153C214yesmaximal, complemented
8#20257144C2112yesmaximal, complemented
9#20256878C214yesmaximal, complemented
10D4×#10625352C2112yesmaximal, complemented
11#20256719C216yesmaximal, complemented
12C2×#15689671C213yesmaximal, complemented
13#532×D47C213yesmaximal, complemented
14C4×#41×D47C211yesmaximal, characteristic, complemented
15C47×#3498C211yesmaximal, characteristic, complemented
16#15689958—232no—
17C2×#13094071C2214yescomplemented
18C2×#13094071C2216yescomplemented
19C2×#13094071C2212yescomplemented
20C2×#13094069C22112yescomplemented
21C2×#13094069C2216yescomplemented
22C22×#10625352C22112yescomplemented
23C22×#10625352C2216yescomplemented
24C2×#41×D47C2211yescharacteristic
25C2×#41×D47C2214yescomplemented
26C2×#41×D47C2216yescomplemented
27#15689793C22112yescomplemented
28Q8×D188C2214yescomplemented
29D4×Dic94C22112yescomplemented
30#15689780C2218yescomplemented
31#15689779C22124yescomplemented
32#15689778C22112yescomplemented
33#15689777C22112yescomplemented
34#15689773C22124yescomplemented
35#15689770C22124yescomplemented
36#15689767C22124yescomplemented
37#15689760C22148yescomplemented
38#15689758C22112yescomplemented
39D4×C22⋊D47C22124yescomplemented
40#15689702C22124yescomplemented
41#15689699C2216yescomplemented
42#15689694C2216yescomplemented
43#15689693C22112yescomplemented
44#15689690C2216yescomplemented
45#15689686C22112yescomplemented
46#15689683C22124yescomplemented
47#15689674C2211yescharacteristic, complemented
48#15689673C2213yescomplemented
49#15689672C2216yescomplemented
50#15689671C22112yescomplemented
51#15689671C22112yescomplemented
52#15689671C2216yescomplemented
53#15689671C2213yescomplemented
54#15689671C2216yescomplemented
55#15689671C2216yescomplemented
56#15689670C22112yescomplemented
57#15689669C2216yescomplemented
58#15689668C22112yescomplemented
59C2×#13094024C2213yescomplemented
60C4⋊Q8×D47C2213yescomplemented
61#127×D47C2213yescomplemented
62C2×#13094011C2216yescomplemented
63#124×D47C2216yescomplemented
64#15689633C22124yescomplemented
65#15689629C22124yescomplemented
66C2×#13093995C22112yescomplemented
67#121×D47C22112yescomplemented
68#41×Dic47C2211yescharacteristic, complemented
69C4×#10625354C2212yescomplemented
70C4×#10625350C2213yescomplemented
71#15689591C2213yescomplemented
72C4×#10625352C2216yescomplemented
73C4×Q8×D47C2212yescomplemented
74C2×D4×Dic47C22112yescomplemented
75C4×D4×D47C2216yescomplemented
76C4×D4×D47C22112yescomplemented
77#117×D47C2213yescomplemented
78C2×C42×D47C2213yescomplemented
79C2×H(5,𝔽2)×C47C2212yescomplemented
80C47×#550C2214yescomplemented
81D42×C47C22112yescomplemented
82C47×#535C2216yescomplemented
83C47×#532C2213yescomplemented
84C2×#127×C47C2213yescomplemented
85C4×#41×C47C2211yescharacteristic, complemented
86#13094071—216no—
87#13094071—232no—
88#13094071—248no—
89#13094069—296no—
90#13094069—248no—
91C2×#10625354C2312yes—
92C2×#10625354C2311yescharacteristic
93C2×#10625350C23112yes—
94C2×#10625350C2316yes—
95C2×#10625350C23112yes—
96C2×#10625350C2313yes—
97C2×#10625352—296no—
98C2×#10625352—248no—
99C2×#10625352C23124yes—
100C2×#10625352C23112yes—
101C2×#10625352C23112yes—
102C2×#10625352C23112yes—
103C2×#10625352C23112yes—
104C2×#10625352C2316yes—
105C2×#10625352C23112yes—
106C2×#10625352C23112yes—
107C2×#10625352C2313yes—
108#41×D47—232no—
109#41×D47—248no—
110#41×D47D4116yescomplemented
111C22×Dic94C23112yes—
112C22×Dic94C2316yes—
113C2×Q8×D47C2314yes—
114C2×Q8×D47C2316yes—
115C2×Q8×D47C2311yescharacteristic
116C22×C22⋊D47C23124yes—
117C22×C22⋊D47C23112yes—
118C2×D4×D47C23112yes—
119C2×D4×D47C23112yes—
120C2×D4×D47C2316yes—
121C2×D4×D47C23112yes—
122C2×D4×D47C2313yes—
123C23×Dic47C23112yes—
124C22×C4×D47C23112yes—
125C22×C4×D47C2316yes—
126C22×C4×D47C2313yes—
127#13094024C23112yes—
128#13094024C2313yes—
129#13094024C2316yes—
130#13094023C23112yes—
131#13094022C2316yes—
132#13094021C2311yescharacteristic
133#13094020C23112yes—
134#13094020C2316yes—
135#13094013C2312yes—
136#13094012C2316yes—
137#13094011C23124yes—
138#13094011C2316yes—
139#13094011C23112yes—
140#13094010C23124yes—
141#13094008C23124yes—
142#13094006C23148yes—
143#13094005C23124yes—
144#13094004C23124yes—
145#13094003C23124yes—
146#13094001C23148yes—
147#13093999C2314yes—
148#13093998C23112yes—
149#13093997C23124yes—
150#13093996C23148yes—
151#13093996C23124yes—
152#13093995C23124yes—
153#13093995C23124yes—
154#13093995C23124yes—
155#13093995C23112yes—
156#13093995C23124yes—
157#13093993C23124yes—
158#13093992C23148yes—
159Q8×Dic47C2312yes—
160C4×Dic94C2316yes—
161#13093989C2316yes—
162C4×D188C2316yes—
163C4×D188C23112yes—
164D4×Dic47C23124yes—
165D4×Dic47C23124yes—
166D4×Dic47C2316yes—
167D4×Dic47C23112yes—
168D4×Dic47C23124yes—
169#13093986C2316yes—
170#13093986C2314yes—
171C4×C22⋊D47C23112yes—
172C4×C22⋊D47C23124yes—
173(C22⋊D47)⋊C4C23112yes—
174(C22⋊D47)⋊C4C23124yes—
175#13093983C2313yes—
176#13093982C2316yes—
177#13093981C2316yes—
178#13093980C2316yes—
179C2×C4⋊Dic47C23112yes—
180C4⋊C4×D47C23112yes—
181C4⋊C4×D47C2316yes—
182C2×C22⋊Dic47C23124yes—
183C22⋊C4×D47C23124yes—
184C22⋊C4×D47C2316yes—
185C2×C4×Dic47C2316yes—
186C2×C4×Dic47C2313yes—
187C42×D47C2311yescharacteristic
188C42×D47C2313yes—
189C42×D47C2316yes—
190C42×D47C2316yes—
191C42×D47C2313yes—
192C42×D47C2313yes—
193H(5,𝔽2)×C47—216no—
194C2×#41×C47C2314yes—
195C2×#41×C47C2316yes—
196C2×#41×C47C2311yescharacteristic
197C22×D4×C47C23112yes—
198C22×D4×C47C2316yes—
199C22×D4×C47C23112yes—
200C4⋊Q8×C47C2311yescharacteristic
201#127×C47C23112yes—
202#127×C47C2313yes—
203#127×C47C2316yes—
204#124×C47C2316yes—
205#121×C47C23124yes—
206#121×C47C23112yes—
207#120×C47C23124yes—
208C4×Q8×C47C2312yes—
209C4×D4×C47C2316yes—
210C4×D4×C47C23112yes—
211#117×C47C2313yes—
212C2×C42×C47C2313yes—
213C24×C47C24112yes—
214C23×D47C24112yes—
215C23×D47C2413yes—
216#41×C47—216no—
217#41×C47—224no—
218#41×C47C2×D418yescomplemented
219C2×Q8×C47C2412yes—
220C2×Q8×C47C2411yescharacteristic
221C2×D4×C47—248no—
222C2×D4×C47—224no—
223C2×D4×C47—424no—
224C2×D4×C47C24112yes—
225C2×D4×C47C24112yes—
226C2×D4×C47C24112yes—
227C2×D4×C47C2416yes—
228C2×D4×C47C24124yes—
229C2×D4×C47C2413yes—
230C22×C4×C47C2416yes—
231C22×C4×C47C24112yes—
232C22×C4×C47C2413yes—
233C2×C22⋊D47—248no—
234C2×C22⋊D47—296no—
235C2×C22⋊D47C24124yes—
236C2×C22⋊D47C24112yes—
237C2×C22⋊D47C24112yes—
238C2×C22⋊D47C24112yes—
239C2×C22⋊D47C24124yes—
240C2×C22⋊D47C2416yes—
241C22×Dic47—248no—
242C22×Dic47C24112yes—
243C22×Dic47C24112yes—
244C22×Dic47C24124yes—
245C22×Dic47C2416yes—
246C22×Dic47C2413yes—
247#10625354—28no—
248#10625354C2×D418yescomplemented
249Q8×D47—216no—
250Q8×D47—224no—
251Q8×D47C2×D418yescomplemented
252#10625352—248no—
253#10625352—296no—
254#10625352—248no—
255#10625352—248no—
256#10625352—224no—
257#10625352—248no—
258#10625352—248no—
259#10625352—248no—
260#10625352C2×D4124yescomplemented
261D4×D47—248no—
262D4×D47—248no—
263D4×D47—224no—
264D4×D47—424no—
265D4×D47C2×D4124yescomplemented
266#10625350—224no—
267#10625350—248no—
268#10625350—248no—
269#10625350C2×D4124yescomplemented
270C2×D188C2414yes—
271C2×D188C2414yes—
272C2×D188C2412yes—
273C2×D188C2413yes—
274C2×C4×D47—248no—
275C2×C4×D47—412no—
276C2×C4×D47C2×D4124yescomplemented
277C2×C4×D47C2412yes—
278C2×C4×D47C2416yes—
279C2×C4×D47C24112yes—
280C2×C4×D47C2414yes—
281C2×C4×D47C24112yes—
282C2×C4×D47C2416yes—
283C2×C4×D47C2416yes—
284C2×C4×D47C2411yescharacteristic
285C2×C4×D47C2413yes—
286C2×C4×D47C2413yes—
287C2×C4×D47C2413yes—
288C2×Dic94—224no—
289C2×Dic94—248no—
290C2×Dic94C24112yes—
291C2×Dic94C24112yes—
292C2×Dic94C2416yes—
293C2×Dic94C2413yes—
294C4⋊C4×C47C2416yes—
295C4⋊C4×C47C2414yes—
296C22⋊C4×C47C2416yes—
297C22⋊C4×C47C24124yes—
298C42×C47C2411yescharacteristic
299C42×C47C2413yes—
300C42×C47C2416yes—
301C22⋊Dic47C24124yes—
302C22⋊Dic47C2416yes—
303C22⋊Dic47C24148yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C24112yes—
306(C2×D47)⋊C4C24124yes—
307C4⋊Dic47C24112yes—
308C4⋊Dic47C2416yes—
309C4⋊Dic47C24124yes—
310Dic47⋊C4C24112yes—
311Dic47⋊C4C24124yes—
312C4×Dic47C2412yes—
313C4×Dic47C2411yescharacteristic
314C4×Dic47C2416yes—
315C4×Dic47C2413yes—
316C4×Dic47C2416yes—
317C4×Dic47C2416yes—
318C4×Dic47C2416yes—
319C23×C47—224no—
320C23×C47—424no—
321C23×C47C25112yes—
322C23×C47C2513yes—
323C22×D47—224no—
324C22×D47—46no—
325C22×D47—424no—
326C22×D47C22×D4112yes—
327C22×D47C2514yes—
328C22×D47C2513yes—
329C22×D47C2511yescharacteristic
330Q8×C47—24no—
331Q8×C47C22×D414yes—
332D4×C47—224no—
333D4×C47—212no—
334D4×C47—224no—
335D4×C47—224no—
336D4×C47—424no—
337D4×C47C22×D4112yes—
338C2×C4×C47—224no—
339C2×C4×C47—212no—
340C2×C4×C47C22×D4112yes—
341C2×C4×C47C2516yes—
342C2×C4×C47C2514yes—
343C2×C4×C47C2511yescharacteristic
344C2×C4×C47C2513yes—
345C2×C4×C47C2512yes—
346C22⋊D47—224no—
347C22⋊D47—248no—
348C22⋊D47—224no—
349C22⋊D47—224no—
350C22⋊D47—424no—
351C22⋊D47C22×D4124yes—
352C2×Dic47—224no—
353C2×Dic47—248no—
354C2×Dic47—224no—
355C2×Dic47—46no—
356C2×Dic47C22×D4112yes—
357C2×Dic47C2512yes—
358C2×Dic47C2516yes—
359C2×Dic47C25112yes—
360C2×Dic47C2511yescharacteristic
361C2×Dic47C2513yes—
362D188—28no—
363D188—24no—
364D188—28no—
365D188C22×D4112yes—
366C4×D47—224no—
367C4×D47—224no—
368C4×D47—24no—
369C4×D47—212no—
370C4×D47—28no—
371C4×D47—46no—
372C4×D47—46no—
373C4×D47C22×D4112yes—
374C4×D47C22×D414yes—
375C4×D47C22×D4112yes—
376C4×D47C22×D4112yes—
377Dic94—212no—
378Dic94—224no—
379Dic94—224no—
380Dic94C22×D4112yes—
381#62812—471nomaximal, Sylow
382C22×C47—26no—
383C22×C47—212no—
384C22×C47—224no—
385C22×C47—824no—
386C22×C47C23×D416yes—
387C22×C47C2611yescharacteristic
388C2×D47—22no—
389C2×D47—26no—
390C2×D47—24no—
391C2×D47—28no—
392C2×D47—412no—
393C2×D47—824no—
394C2×D47C23×D416yes—
395C2×D47C23×D412yes—
396C4×C47—24no—
397C4×C47—26no—
398C4×C47C23×D412yes—
399C4×C47C23×D416yes—
400C4×C47#58514yescomplemented
401Dic47—212no—
402Dic47—22no—
403Dic47—26no—
404Dic47C23×D416yes—
405Dic47C23×D412yes—
406C2×#585—472no—
407#3500—472no—
408#3500—476no—
409#3499—473no—
410#3499—471no—
411#3498—473no—
412#3498D4711yescharacteristic, complemented
413#3497—474no—
414#3496—4712no—
415D4×#41—474no—
416D4×#41—4712no—
417#3449—476no—
418C2×#532—473no—
419C2×#532—473no—
420C2×C4×#41—471no—
421C2×C47—26no—
422C2×C47—412no—
423C2×C47C24×D411yescharacteristic
424C2×C47C2×#58512yes—
425D47—22no—
426D47—26no—
427D47—44no—
428#585—9432no—
429C2×2−1+4—474no—
430C2×2−1+4—476no—
431C2×2−1+4—472no—
432C2×H(5,𝔽2)—4712no—
433C2×H(5,𝔽2)—476no—
434C2×H(5,𝔽2)C2×D4712yescomplemented
435C22×#41—471no—
436C22×#41—476no—
437C22×#41—474no—
438C22×#41—476no—
439C22×#41—4712no—
440#550—4712no—
441#550C2×D4714yescomplemented
442D4×Q8—474no—
443D4×Q8—4712no—
444#548—478no—
445#548—4724no—
446#547—4724no—
447#547—4712no—
448#547—4712no—
449#546—4724no—
450#546—4724no—
451#546—4748no—
452D42—4724no—
453D42—4712no—
454D42C2×D47112yescomplemented
455#537—4724no—
456#536—476no—
457#536—4712no—
458#536—476no—
459#535—476no—
460#535—4712no—
461#535C2×D4716yescomplemented
462#534—4724no—
463#532—476no—
464#532—471no—
465#532—473no—
466#532—476no—
467#532—4712no—
468#532—4712no—
469#532—476no—
470#532—476no—
471#532—476no—
472#532—4712no—
473#532—4712no—
474#532—473no—
475#532C2×D4713yescomplemented
476C2×C4⋊Q8—473no—
477C2×C4⋊Q8—473no—
478C2×#127—473no—
479C2×#127C2×D4713yescomplemented
480C2×#124—476no—
481C2×#124—476no—
482#525—4724no—
483#525—4724no—
484C2×#121—4712no—
485C2×#121—4712no—
486C4×#41—471no—
487C4×#41—472no—
488C4×#41—476no—
489C4×#41—473no—
490C4×#41—473no—
491C4×#41C2×D4711yescharacteristic, complemented
492C2×C4×Q8—472no—
493C2×C4×D4—4712no—
494C2×C4×D4—476no—
495C2×C4×D4—4712no—
496C2×#117—473no—
497C22×C42—473no—
498C47#6281211yescharacteristic, complemented, Sylow
4992−1+4—9432no—
5002−1+4—9448no—
5012−1+4—9416no—
502H(5,𝔽2)—216no—
503H(5,𝔽2)—9496no—
504H(5,𝔽2)—9448no—
505C2×#41—4716no—
506C2×#41—471no—
507C2×#41—472no—
508C2×#41—473no—
509C2×#41—4712no—
510C2×#41—4712no—
511C2×#41—476no—
512C2×#41—4712no—
513C2×#41—4712no—
514C2×#41—4712no—
515C2×#41—4724no—
516C2×#41—4712no—
517C2×#41—473no—
518C2×#41—476no—
519C2×#41—4712no—
520C2×#41—4712no—
521C2×#41—9448no—
522C2×#41—9448no—
523C2×#41—9496no—
524C2×#41—9432no—
525C2×#41C22×D4716yes—
526C2×#41C22×D4714yes—
527C2×#41C22×D4711yescharacteristic
528C22×Q8—471no—
529C22×Q8—476no—
530C22×Q8—474no—
531C22×Q8—476no—
532C22×Q8—4712no—
533C22×D4—473no—
534C22×D4—4712no—
535C22×D4—4724no—
536C22×D4—4712no—
537C22×D4—476no—
538C22×D4—4712no—
539C22×D4—4712no—
540C22×D4C22×D4716yes—
541C22×D4C22×D47112yes—
542C22×D4C22×D47112yes—
543C23×C4—473no—
544C23×C4—4712no—
545C23×C4—4712no—
546C23×C4—476no—
547C4⋊Q8—476no—
548C4⋊Q8—4712no—
549C4⋊Q8—473no—
550C4⋊Q8—476no—
551C4⋊Q8—4712no—
552C4⋊Q8C22×D4711yescharacteristic
553#127—476no—
554#127—4712no—
555#127—471no—
556#127C22×D4713yes—
557#127C22×D4716yes—
558#127C22×D47112yes—
559#124—472no—
560#124—476no—
561#124—4712no—
562#124—4724no—
563#124—4724no—
564#124—476no—
565#124C22×D4716yes—
566#123—4724no—
567#123—4748no—
568#123—4724no—
569C22⋊Q8—4724no—
570C22⋊Q8—4724no—
571C22⋊Q8—4748no—
572#121—4712no—
573#121—4724no—
574#121—4724no—
575#121—4724no—
576#121—4724no—
577#121—4724no—
578#121—4748no—
579#121—4712no—
580#121—474no—
581#121—4724no—
582#121C22×D47112yes—
583#121C22×D47124yes—
584#120—4724no—
585#120—4748no—
586#120C22×D47124yes—
587C4×Q8—472no—
588C4×Q8—476no—
589C4×Q8—476no—
590C4×Q8C22×D4712yes—
591C4×D4—4712no—
592C4×D4—476no—
593C4×D4—4724no—
594C4×D4—4724no—
595C4×D4—4724no—
596C4×D4—4712no—
597C4×D4—4724no—
598C4×D4—474no—
599C4×D4—476no—
600C4×D4—4712no—
601C4×D4—4724no—
602C4×D4—476no—
603C4×D4—4712no—
604C4×D4C22×D4716yes—
605C4×D4C22×D47112yes—
606#117—473no—
607#117—476no—
608#117—476no—
609#117—476no—
610#117C22×D4713yes—
611C2×C4⋊C4—4712no—
612C2×C4⋊C4—476no—
613C2×C4⋊C4—4712no—
614C2×C22⋊C4—4724no—
615C2×C22⋊C4—476no—
616C2×C22⋊C4—4724no—
617C2×C42—476no—
618C2×C42—473no—
619C2×C42—473no—
620C2×C42—476no—
621C2×C42—476no—
622C2×C42—473no—
623C2×C42—473no—
624C2×C42—471no—
625C2×C42C22×D4713yes—
626C24—473no—
627C24—4712no—
628C24C23×D47112yes—
629#41—216no—
630#41—224no—
631#41—478no—
632#41—4724no—
633#41—4724no—
634#41—9448no—
635#41—9448no—
636#41—9448no—
637#41—9424no—
638#41—9448no—
639#41—9448no—
640#41—9448no—
641#41—948no—
642#41—9496no—
643#41—9448no—
644#41—9448no—
645#41—9424no—
646#41D4×D4718yescomplemented
647C2×Q8—478no—
648C2×Q8—473no—
649C2×Q8—4712no—
650C2×Q8—4712no—
651C2×Q8—476no—
652C2×Q8—9448no—
653C2×Q8—9424no—
654C2×Q8—9416no—
655C2×Q8—9424no—
656C2×Q8C23×D4712yes—
657C2×Q8C23×D4711yescharacteristic
658C2×D4—248no—
659C2×D4—224no—
660C2×D4—424no—
661C2×D4—476no—
662C2×D4—4724no—
663C2×D4—4724no—
664C2×D4—4712no—
665C2×D4—4712no—
666C2×D4—4712no—
667C2×D4—4724no—
668C2×D4—473no—
669C2×D4—474no—
670C2×D4—474no—
671C2×D4—472no—
672C2×D4—9424no—
673C2×D4—9448no—
674C2×D4—9448no—
675C2×D4—9496no—
676C2×D4—9448no—
677C2×D4—18824no—
678C2×D4C23×D47112yes—
679C2×D4C23×D47112yes—
680C2×D4C23×D47112yes—
681C2×D4C23×D4716yes—
682C2×D4C23×D47124yes—
683C2×D4C23×D4713yes—
684C22×C4—473no—
685C22×C4—4724no—
686C22×C4—471no—
687C22×C4—473no—
688C22×C4—473no—
689C22×C4—473no—
690C22×C4—4712no—
691C22×C4—4712no—
692C22×C4—4724no—
693C22×C4—476no—
694C22×C4—472no—
695C22×C4—476no—
696C22×C4—4712no—
697C22×C4—474no—
698C22×C4—4712no—
699C22×C4—476no—
700C22×C4—476no—
701C22×C4—9448no—
702C22×C4—9448no—
703C22×C4—18812no—
704C22×C4C23×D4716yes—
705C22×C4C23×D47112yes—
706C22×C4C23×D4713yes—
707C4⋊C4—4712no—
708C4⋊C4—4724no—
709C4⋊C4—4712no—
710C4⋊C4—476no—
711C4⋊C4—4724no—
712C4⋊C4C23×D4714yes—
713C4⋊C4C23×D4716yes—
714C22⋊C4—4724no—
715C22⋊C4—476no—
716C22⋊C4—4748no—
717C22⋊C4—478no—
718C22⋊C4—4712no—
719C22⋊C4—4724no—
720C22⋊C4C23×D4716yes—
721C22⋊C4C23×D47124yes—
722C42—472no—
723C42—471no—
724C42—476no—
725C42—473no—
726C42—476no—
727C42—476no—
728C42—476no—
729C42C23×D4711yescharacteristic
730C42C23×D4713yes—
731C42C23×D4716yes—
732C23—224no—
733C23—424no—
734C23—473no—
735C23—471no—
736C23—4712no—
737C23—474no—
738C23—9424no—
739C23—18824no—
740C23—1886no—
741C23C24×D47112yes—
742C23C24×D4713yes—
743Q8—24no—
744Q8—4712no—
745Q8—9424no—
746Q8—9424no—
747Q8—9412no—
748Q8C2×D4×D4714yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—4724no—
755D4—4712no—
756D4—948no—
757D4—9424no—
758D4—9424no—
759D4—9448no—
760D4—9424no—
761D4—944no—
762D4—948no—
763D4—18824no—
764D4C2×D4×D47112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—4712no—
768C2×C4—471no—
769C2×C4—473no—
770C2×C4—474no—
771C2×C4—4712no—
772C2×C4—4712no—
773C2×C4—4712no—
774C2×C4—472no—
775C2×C4—476no—
776C2×C4—4712no—
777C2×C4—948no—
778C2×C4—9424no—
779C2×C4—9424no—
780C2×C4—9448no—
781C2×C4—9424no—
782C2×C4—9424no—
783C2×C4—944no—
784C2×C4—9412no—
785C2×C4—1886no—
786C2×C4—1886no—
787C2×C4—1886no—
788C2×C4C2×D4×D47112yes—
789C2×C4C24×D4716yes—
790C2×C4C24×D4714yes—
791C2×C4C24×D4711yescharacteristic
792C2×C4C24×D4713yes—
793C2×C4C24×D4712yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—472no—
799C22—476no—
800C22—942no—
801C22—946no—
802C22—944no—
803C22—948no—
804C22—37624no—
805C22—18812no—
806C22C22×D4×D4716yes—
807C22C25×D4711yescharacteristic
808C4—24no—
809C4—26no—
810C4—472no—
811C4—476no—
812C4—9412no—
813C4—942no—
814C4—946no—
815C4C22×D4×D4716yes—
816C4C22×D4×D4712yes—
817C4#1568995814yescomplemented
818C2—26no—
819C2—412no—
820C2—946no—
821C2—942no—
822C2—1884no—
823C2C23×D4×D4711yescharacteristic
824C2C2×#1568995812yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3498C2
hypercenter#3498D47
hypocenterC47#62812
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#15689958C2semidirect
2. #20257180C2semidirect
3. #20257176C2semidirect
4. #20257173C2semidirect
5. #20257168C2semidirect
6. #20257164C2semidirect
7. #20257153C2semidirect
8. #20257144C2semidirect
9. #20256878C2semidirect
10. D4×#10625352C2semidirect
11. #20256719C2semidirect
12. C2×#15689671C2semidirect
13. #532×D47C2semidirect
14. C4×#41×D47C2semidirect
15. C47×#3498C2semidirect
17. C2×#13094071C22semidirect
18. C2×#13094071C22semidirect
19. C2×#13094071C22semidirect
20. C2×#13094069C22semidirect
21. C2×#13094069C22semidirect
22. C22×#10625352C22semidirect
23. C22×#10625352C22semidirect
25. C2×#41×D47C22semidirect
26. C2×#41×D47C22semidirect
27. #15689793C22semidirect
28. Q8×D188C22semidirect
29. D4×Dic94C22semidirect
30. #15689780C22semidirect
31. #15689779C22semidirect
32. #15689778C22semidirect
33. #15689777C22semidirect
34. #15689773C22semidirect
35. #15689770C22semidirect
36. #15689767C22semidirect
37. #15689760C22semidirect
38. #15689758C22semidirect
39. D4×C22⋊D47C22semidirect
40. #15689702C22semidirect
41. #15689699C22semidirect
42. #15689694C22semidirect
43. #15689693C22semidirect
44. #15689690C22semidirect
45. #15689686C22semidirect
46. #15689683C22semidirect
47. #15689674C22semidirect
48. #15689673C22semidirect
49. #15689672C22semidirect
50. #15689671C22semidirect
51. #15689671C22semidirect
52. #15689671C22semidirect
53. #15689671C22semidirect
54. #15689671C22semidirect
55. #15689671C22semidirect
56. #15689670C22semidirect
57. #15689669C22semidirect
58. #15689668C22semidirect
59. C2×#13094024C22semidirect
60. C4⋊Q8×D47C22semidirect
61. #127×D47C22semidirect
62. C2×#13094011C22semidirect
63. #124×D47C22semidirect
64. #15689633C22semidirect
65. #15689629C22semidirect
66. C2×#13093995C22semidirect
67. #121×D47C22semidirect
68. #41×Dic47C22semidirect
69. C4×#10625354C22semidirect
70. C4×#10625350C22semidirect
71. #15689591C22semidirect
72. C4×#10625352C22semidirect
73. C4×Q8×D47C22semidirect
74. C2×D4×Dic47C22semidirect
75. C4×D4×D47C22semidirect
76. C4×D4×D47C22semidirect
77. #117×D47C22semidirect
78. C2×C42×D47C22semidirect
79. C2×H(5,𝔽2)×C47C22semidirect
80. C47×#550C22semidirect
81. D42×C47C22semidirect
82. C47×#535C22semidirect
83. C47×#532C22semidirect
84. C2×#127×C47C22semidirect
85. C4×#41×C47C22semidirect
110. #41×D47D4semidirect
218. #41×C47C2×D4semidirect
248. #10625354C2×D4semidirect
251. Q8×D47C2×D4semidirect
260. #10625352C2×D4semidirect
265. D4×D47C2×D4semidirect
269. #10625350C2×D4semidirect
276. C2×C4×D47C2×D4semidirect
400. C4×C47#585semidirect
412. #3498D47semidirect
434. C2×H(5,𝔽2)C2×D47semidirect
441. #550C2×D47semidirect
454. D42C2×D47semidirect
461. #535C2×D47semidirect
475. #532C2×D47semidirect
479. C2×#127C2×D47semidirect
491. C4×#41C2×D47semidirect
498. C47#62812semidirect
646. #41D4×D47semidirect
817. C4#15689958semidirect

Maximal subgroups

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

subgroupindex
C2×#156899582
#202571802
#202571762
#202571732
#202571682
#202571642
#202571532
#202571442
#202568782
D4×#106253522
#202567192
C2×#156896712
#532×D472
C4×#41×D472
C47×#34982
#6281247