Finite Group Databasebeta

← #27124830

Subgroups — #27124830

Order 12032.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257208C218yesmaximal, complemented
2#20257202C214yesmaximal, complemented
3#20257199C214yesmaximal, complemented
4#20257196C212yesmaximal, complemented
5#20257193C212yesmaximal, complemented
6#20257191C211yesmaximal, characteristic, complemented
7#20257188C214yesmaximal, complemented
8#20257186C212yesmaximal, complemented
9#20257184C214yesmaximal, complemented
10#20256967C214yesmaximal, complemented
11#20256967C218yesmaximal, complemented
12Q8×#10625352C214yesmaximal, complemented
13#20256792C212yesmaximal, complemented
14#20256790C214yesmaximal, complemented
15C2×#15689675C214yesmaximal, complemented
16#533×D47C212yesmaximal, complemented
17#20256586C212yesmaximal
18C2×C4×#10625352C211yesmaximal, characteristic
19C47×#3501C211yesmaximal, characteristic, complemented
20C22×#10625352C2211yescharacteristic
21Q8×Dic94C2214yescomplemented
22#15689853C2214yescomplemented
23#15689853C2218yescomplemented
24#15689851C2214yescomplemented
25#15689851C2218yescomplemented
26#15689850C2218yescomplemented
27#15689850C2218yescomplemented
28#15689850C2218yescomplemented
29#15689848C2214yescomplemented
30#15689848C2218yescomplemented
31#15689832C2218yescomplemented
32#15689832C2218yescomplemented
33#15689832C2218yescomplemented
34#15689831C2218yescomplemented
35#15689831C22116yescomplemented
36#15689830C2218yescomplemented
37#15689830C2214yescomplemented
38#15689828C2218yescomplemented
39#15689828C22116yescomplemented
40#15689827C22116yescomplemented
41#15689827C22116yescomplemented
42#15689827C22116yescomplemented
43D4×Dic94C2218yescomplemented
44D4×Dic94C2214yescomplemented
45Q8×C22⋊D47C2218yescomplemented
46#15689786C2218yescomplemented
47#15689786C22116yescomplemented
48#15689754C2212yes—
49#15689753C2218yescomplemented
50#15689752C2218yes—
51#15689752C2218yes—
52#15689752C22116yescomplemented
53#15689752C22116yescomplemented
54#15689751C2214yes—
55#15689750C2218yescomplemented
56#15689749C2218yes—
57#15689749C2214yes—
58#15689748C2218yes—
59#15689680C2212yes—
60#15689679C2218yescomplemented
61#15689679C2214yescomplemented
62#15689678C2218yescomplemented
63#15689678C2212yescomplemented
64#15689678C2212yescomplemented
65#15689677C2214yescomplemented
66#15689677C2214yescomplemented
67#15689676C2214yes—
68#15689675C2214yes—
69#15689675C2218yes—
70#15689675C2218yes—
71#15689675C2214yes—
72#15689675C2218yes—
73#15689675C22116yescomplemented
74#15689675C22116yescomplemented
75#15689675C2218yescomplemented
76#15689675C2218yescomplemented
77#15689675C2218yescomplemented
78#15689675C2218yescomplemented
79C2×#13094023C2214yescomplemented
80C2×#13094022C2214yescomplemented
81C4⋊Q8×D47C2212yescomplemented
82C4⋊Q8×D47C2212yescomplemented
83C2×#13094014C2218yescomplemented
84#125×D47C2214yescomplemented
85C2×#13094003C2214yes—
86C2×#13094001C2218yes—
87C22⋊Q8×D47C2214yes—
88C22⋊Q8×D47C2214yes—
89#15689602C2218yes—
90#15689602C2218yes—
91#15689600C2214yes—
92#15689598C2212yes—
93#15689596C2218yes—
94C4×#10625352C2214yes—
95C4×#10625352C2214yes—
96C4×#10625352C2214yes—
97C4×#10625352C2214yes—
98C4×#10625352C2218yes—
99C4×#10625352C2218yes—
100C2×Q8×Dic47C2214yescomplemented
101C2×C4×Dic94C2211yescharacteristic
102C2×#13093989C2211yescharacteristic
103C2×#13093989C2218yescomplemented
104C2×#13093989C2214yescomplemented
105C4×Q8×D47C2214yescomplemented
106C4×Q8×D47C2214yescomplemented
107C2×D4×Dic47C2211yescharacteristic
108C2×C4×C22⋊D47C2212yes—
109C2×(C22⋊D47)⋊C4C2212yes—
110C2×#13093982C2211yescharacteristic
111C2×#13093980C2212yes—
112C2×#13093980C2218yes—
113#117×D47C2214yes—
114C22×C4×Dic47C2212yes—
115C2×C42×D47C2211yescharacteristic
116C47×#554C2214yescomplemented
117C47×#554C2218yescomplemented
118D4×Q8×C47C2214yescomplemented
119C47×#544C2212yes—
120C47×#543C2214yes—
121C47×#533C2212yes—
122C2×C22⋊Q8×C47C2214yes—
123C47×#518C2212yes—
124C2×C4×D4×C47C2211yescharacteristic
125C2×#10625352Q8116yescomplemented
126C2×#10625352C2314yes—
127C2×#10625352C2314yes—
128C22×Dic94C2318yes—
129C22×Dic94C2314yes—
130C22×Dic94C2311yescharacteristic
131C2×Q8×D47C2314yes—
132C2×Q8×D47C2314yes—
133C22×C22⋊D47C2312yes—
134C23×Dic47C2312yes—
135C23×Dic47C2312yes—
136C22×C4×D47C2311yescharacteristic
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2311yescharacteristic
139#13094024C2318yes—
140#13094024C2312yes—
141#13094024C2312yes—
142#13094023C2318yes—
143#13094023C2318yes—
144#13094023C23116yes—
145#13094023C23116yes—
146#13094023C2314yes—
147#13094023C2318yes—
148#13094023C2318yes—
149#13094023C2314yes—
150#13094023C2318yes—
151#13094023C2314yes—
152#13094023C2314yes—
153#13094022C2318yes—
154#13094022C23116yes—
155#13094022C23116yes—
156#13094022C2314yes—
157#13094022C2318yes—
158#13094022C2318yes—
159#13094022C2314yes—
160#13094016C2318yes—
161#13094016C2314yes—
162#13094015C2318yes—
163#13094015C2318yes—
164#13094015C2314yes—
165#13094015C2314yes—
166#13094014C23116yes—
167#13094014C23116yes—
168#13094014C23116yes—
169#13094014C23116yes—
170#13094014C23116yes—
171#13094014C2318yes—
172#13094014C23116yes—
173#13094014C23116yes—
174#13094014C2318yes—
175#13094004C23116yes—
176#13094004C2314yes—
177#13094004C2314yes—
178#13094003C2318yes—
179#13094003C2314yes—
180#13094003C23116yes—
181#13094003C23116yes—
182#13094003C2318yes—
183#13094003C2318yes—
184#13094003C2314yes—
185#13094002C23116yes—
186#13094002C23116yes—
187#13094002C2318yes—
188#13094002C2318yes—
189#13094001C23116yes—
190#13094001C2318yes—
191#13094001C23116yes—
192#13094001C23116yes—
193#13094001C23116yes—
194#13094001C23116yes—
195#13094001C23116yes—
196#13094001C23116yes—
197#13094001C2318yes—
198#13094000C23116yes—
199#13094000C2314yes—
200#13094000C2314yes—
201Q8×Dic47C2318yes—
202Q8×Dic47C2318yes—
203Q8×Dic47C2314yes—
204Q8×Dic47C2314yes—
205Q8×Dic47C2318yes—
206C4×Dic94C2314yes—
207C4×Dic94C2318yes—
208C4×Dic94C2318yes—
209C4×Dic94C2314yes—
210C4×Dic94C2314yes—
211C4×Dic94C2314yes—
212C4×Dic94C2318yes—
213C4×Dic94C2318yes—
214#13093989C23116yes—
215#13093989C2318yes—
216#13093989C2318yes—
217#13093989C23116yes—
218#13093989C2314yes—
219#13093989C2318yes—
220#13093989C2314yes—
221#13093989C2318yes—
222#13093989C2314yes—
223#13093989C2314yes—
224#13093989C23116yes—
225#13093989C2318yes—
226#13093989C2318yes—
227#13093989C2318yes—
228D4×Dic47C2314yes—
229D4×Dic47C2318yes—
230D4×Dic47C2318yes—
231D4×Dic47C2314yes—
232C4×C22⋊D47C2318yes—
233C4×C22⋊D47C23116yes—
234C4×C22⋊D47C23116yes—
235C4×C22⋊D47C2318yes—
236(C22⋊D47)⋊C4C2318yes—
237(C22⋊D47)⋊C4C23116yes—
238(C22⋊D47)⋊C4C23116yes—
239(C22⋊D47)⋊C4C2318yes—
240#13093983C2314yes—
241#13093982C2314yes—
242#13093982C2314yes—
243#13093982C2314yes—
244#13093982C2314yes—
245#13093981C2318yes—
246#13093980C23116yes—
247#13093980C2318yes—
248#13093980C23116yes—
249#13093980C2318yes—
250#13093980C2318yes—
251#13093980C23116yes—
252C2×C4⋊Dic47C2311yescharacteristic
253C2×C4⋊Dic47C2318yes—
254C2×C4⋊Dic47C2314yes—
255C2×Dic47⋊C4C2312yes—
256C2×Dic47⋊C4C2312yes—
257C2×Dic47⋊C4C2318yes—
258C2×Dic47⋊C4C2318yes—
259C2×Dic47⋊C4C2318yes—
260C2×Dic47⋊C4C2318yes—
261C2×Dic47⋊C4C2318yes—
262C4⋊C4×D47C2314yes—
263C4⋊C4×D47C2314yes—
264C4⋊C4×D47C2314yes—
265C4⋊C4×D47C2318yes—
266C4⋊C4×D47C2318yes—
267C4⋊C4×D47C2314yes—
268C2×C22⋊Dic47C2312yes—
269C2×C22⋊Dic47C2318yes—
270C2×(C2×D47)⋊C4C2312yes—
271C22⋊C4×D47C2318yes—
272C2×C4×Dic47C2311yescharacteristic
273C2×C4×Dic47C2311yescharacteristic
274C2×C4×Dic47C2311yescharacteristic
275C2×C4×Dic47C2312yes—
276C2×C4×Dic47C2312yes—
277C2×C4×Dic47C2312yes—
278C2×C4×Dic47C2314yes—
279C2×C4×Dic47C2314yes—
280C2×C4×Dic47C2314yes—
281C2×C4×Dic47C2314yes—
282C2×C4×Dic47C2318yes—
283C2×C4×Dic47C2318yes—
284C42×D47C2312yes—
285C42×D47C2312yes—
286C42×D47C2312yes—
287C42×D47C2312yes—
288C42×D47C2318yes—
289C22×Q8×C47C2314yes—
290C22×D4×C47C2311yescharacteristic
291C23×C4×C47C2312yes—
292C4⋊Q8×C47C2318yes—
293C4⋊Q8×C47C2312yes—
294C4⋊Q8×C47C2312yes—
295#125×C47C2318yes—
296#125×C47C2314yes—
297C22⋊Q8×C47C2318yes—
298C22⋊Q8×C47C2314yes—
299C22⋊Q8×C47C23116yes—
300C22⋊Q8×C47C23116yes—
301C22⋊Q8×C47C2318yes—
302C22⋊Q8×C47C2314yes—
303C22⋊Q8×C47C2318yes—
304C4×Q8×C47C2314yes—
305C4×Q8×C47C2314yes—
306C4×D4×C47C2314yes—
307C4×D4×C47C2318yes—
308C4×D4×C47C2314yes—
309C4×D4×C47C2318yes—
310#117×C47C2314yes—
311C2×C4⋊C4×C47C2311yescharacteristic
312C2×C4⋊C4×C47C2318yes—
313C2×C4⋊C4×C47C2314yes—
314C2×C22⋊C4×C47C2312yes—
315C2×C22⋊C4×C47C2318yes—
316C2×C42×C47C2311yescharacteristic
317C24×C47C2412yes—
318C23×D47C2411yescharacteristic
319C2×Q8×C47—48no—
320C2×Q8×C47C2414yes—
321C2×Q8×C47C2414yes—
322C2×Q8×C47C2418yes—
323C2×D4×C47C2×Q818yescomplemented
324C2×D4×C47C2414yes—
325C22×C4×C47—44no—
326C22×C4×C47C2411yescharacteristic
327C22×C4×C47C2414yes—
328C22×C4×C47C2411yescharacteristic
329C22×C4×C47C2418yes—
330C22×C4×C47C2418yes—
331C22×C4×C47C2412yes—
332C22×C4×C47C2414yes—
333C22×C4×C47C2411yescharacteristic
334C2×C22⋊D47C2×Q8116yescomplemented
335C2×C22⋊D47C2418yes—
336C22×Dic47—44no—
337C22×Dic47C2×Q8116yescomplemented
338C22×Dic47C2411yescharacteristic
339C22×Dic47C2414yes—
340C22×Dic47C2412yes—
341C22×Dic47C2411yescharacteristic
342C22×Dic47C2414yes—
343C22×Dic47C2418yes—
344C22×Dic47C2418yes—
345C22×Dic47C2414yes—
346C22×Dic47C2411yescharacteristic
347C22×Dic47C2414yes—
348C22×Dic47C2412yes—
349Q8×D47—48no—
350Q8×D47—48no—
351#10625352C2×Q8132yescomplemented
352#10625352C2×Q8132yescomplemented
353C2×C4×D47—42no—
354C2×C4×D47—42no—
355C2×C4×D47C2×Q818yescomplemented
356C2×C4×D47C2412yes—
357C2×C4×D47C2412yes—
358C2×C4×D47C2412yes—
359C2×C4×D47C2412yes—
360C2×C4×D47C2418yes—
361C2×C4×D47C2418yes—
362C2×C4×D47C2412yes—
363C2×C4×D47C2412yes—
364C2×Dic94—416no—
365C2×Dic94—48no—
366C2×Dic94C2×Q818yescomplemented
367C2×Dic94C2418yes—
368C2×Dic94C2414yes—
369C2×Dic94C24116yes—
370C2×Dic94C2418yes—
371C2×Dic94C2414yes—
372C2×Dic94C2418yes—
373C2×Dic94C2414yes—
374C4⋊C4×C47C2418yes—
375C4⋊C4×C47C2414yes—
376C4⋊C4×C47C2414yes—
377C4⋊C4×C47C2418yes—
378C4⋊C4×C47C24116yes—
379C4⋊C4×C47C2414yes—
380C4⋊C4×C47C2414yes—
381C4⋊C4×C47C2418yes—
382C4⋊C4×C47C2414yes—
383C22⋊C4×C47C2418yes—
384C22⋊C4×C47C2418yes—
385C22⋊C4×C47C24116yes—
386C42×C47C2412yes—
387C42×C47C2412yes—
388C42×C47C2418yes—
389C22⋊Dic47C2418yes—
390C22⋊Dic47C24116yes—
391C22⋊Dic47C2418yes—
392(C2×D47)⋊C4C2418yes—
393(C2×D47)⋊C4C2418yes—
394(C2×D47)⋊C4C2418yes—
395C4⋊Dic47C2414yes—
396C4⋊Dic47C2418yes—
397C4⋊Dic47C2414yes—
398C4⋊Dic47C2414yes—
399C4⋊Dic47C2414yes—
400C4⋊Dic47C2418yes—
401C4⋊Dic47C2414yes—
402C4⋊Dic47C24116yes—
403C4⋊Dic47C2418yes—
404Dic47⋊C4C2418yes—
405Dic47⋊C4C2418yes—
406Dic47⋊C4C2418yes—
407Dic47⋊C4C2418yes—
408Dic47⋊C4C2418yes—
409Dic47⋊C4C2418yes—
410Dic47⋊C4C2418yes—
411Dic47⋊C4C2418yes—
412Dic47⋊C4C2418yes—
413Dic47⋊C4C24116yes—
414Dic47⋊C4C24116yes—
415Dic47⋊C4C2418yes—
416Dic47⋊C4C24116yes—
417Dic47⋊C4C24116yes—
418Dic47⋊C4C24116yes—
419C4×Dic47C2411yescharacteristic
420C4×Dic47C2411yescharacteristic
421C4×Dic47C2411yescharacteristic
422C4×Dic47C2411yescharacteristic
423C4×Dic47C2412yes—
424C4×Dic47C2412yes—
425C4×Dic47C2412yes—
426C4×Dic47C2412yes—
427C4×Dic47C2418yes—
428C4×Dic47C2418yes—
429C4×Dic47C2418yes—
430C4×Dic47C2414yes—
431C4×Dic47C2414yes—
432C4×Dic47C2414yes—
433C4×Dic47C2414yes—
434C4×Dic47C2414yes—
435C4×Dic47C2414yes—
436C4×Dic47C24116yes—
437C4×Dic47C24116yes—
438C23×C47—42no—
439C23×C47—42no—
440C23×C47C22×Q818yes—
441C23×C47C2511yescharacteristic
442C23×C47C2514yes—
443C22×D47—41no—
444C22×D47—41no—
445C22×D47C22×Q814yes—
446C22×D47C2512yes—
447Q8×C47—28no—
448Q8×C47—44no—
449Q8×C47—48no—
450D4×C47C22×Q8116yes—
451C2×C4×C47—28no—
452C2×C4×C47—22no—
453C2×C4×C47—48no—
454C2×C4×C47—41no—
455C2×C4×C47—42no—
456C2×C4×C47—44no—
457C2×C4×C47—48no—
458C2×C4×C47C22×Q814yes—
459C2×C4×C47C2511yescharacteristic
460C2×C4×C47C2514yes—
461C2×C4×C47C2518yes—
462C2×C4×C47C2518yes—
463C2×C4×C47C2512yes—
464C2×C4×C47C2512yes—
465C2×C4×C47C2511yescharacteristic
466C22⋊D47C22×Q8132yes—
467C2×Dic47—28no—
468C2×Dic47—22no—
469C2×Dic47—48no—
470C2×Dic47—48no—
471C2×Dic47—41no—
472C2×Dic47—42no—
473C2×Dic47—44no—
474C2×Dic47C22×Q818yes—
475C2×Dic47C22×Q814yes—
476C2×Dic47C22×Q8116yes—
477C2×Dic47C22×Q8116yes—
478C2×Dic47C2511yescharacteristic
479C2×Dic47C2518yes—
480C2×Dic47C2512yes—
481C2×Dic47C2514yes—
482C2×Dic47C2518yes—
483C2×Dic47C2511yescharacteristic
484C2×Dic47C2514yes—
485C2×Dic47C2511yescharacteristic
486C2×Dic47C2511yescharacteristic
487C4×D47—24no—
488C4×D47—24no—
489C4×D47—42no—
490C4×D47—42no—
491C4×D47—48no—
492C4×D47—48no—
493C4×D47C22×Q818yes—
494C4×D47C22×Q818yes—
495Dic94—28no—
496Dic94—216no—
497Dic94—48no—
498Dic94—416no—
499Dic94—44no—
500Dic94—48no—
501Dic94C22×Q8116yes—
502#62813—471nomaximal, Sylow
503C22×C47—24no—
504C22×C47—21no—
505C22×C47—24no—
506C22×C47—21no—
507C22×C47—48no—
508C22×C47C23×Q812yes—
509C22×C47C23×Q818yes—
510C22×C47C2611yescharacteristic
511C2×D47—22no—
512C2×D47—22no—
513C2×D47—44no—
514C2×D47C23×Q814yes—
515C4×C47—28no—
516C4×C47—22no—
517C4×C47—24no—
518C4×C47—28no—
519C4×C47—21no—
520C4×C47C23×Q814yes—
521C4×C47#58512yes—
522Dic47—28no—
523Dic47—28no—
524Dic47—22no—
525Dic47—24no—
526Dic47—21no—
527Dic47C23×Q818yes—
528Dic47C23×Q812yes—
529Dic47C23×Q812yes—
530Dic47#58512yes—
531#3504—478no—
532#3503—474no—
533#3503—474no—
534#3502—472no—
535#3502—472no—
536#3501—474no—
537#3501—474no—
538#3501—472no—
539#3501—471no—
540#3501D4711yescharacteristic, complemented
541Q8×#41—474no—
542Q8×#41—478no—
543Q8×#41—474no—
544#3458—472no—
545#3458—474no—
546C2×#533—472no—
547C2×#533—474no—
548#3428—472no—
549C2×C4×#41—471no—
550C2×C47—22no—
551C2×C47—28no—
552C2×C47C24×Q811yescharacteristic
553C2×C47C2×#58511yescharacteristic
554C2×C47C2×#58511yescharacteristic
555D47—24no—
556C22×#41—471no—
557Q82—478no—
558Q82—474no—
559Q82—474no—
560#557—474no—
561#557—478no—
562#557—478no—
563#557—478no—
564#557—478no—
565#557—474no—
566#557—478no—
567#554—4716no—
568#554—4716no—
569#554—4716no—
570#554—478no—
571#554—4716no—
572#554—474no—
573#554—478no—
574#554—478no—
575#554—478no—
576#554—478no—
577#554—478no—
578#554—4716no—
579#554C2×D4714yescomplemented
580#554C2×D4718yescomplemented
581D4×Q8—478no—
582D4×Q8—478no—
583D4×Q8—4716no—
584D4×Q8—478no—
585D4×Q8—474no—
586D4×Q8C2×D4714yescomplemented
587#544—478no—
588#544—478no—
589#544—478no—
590#544—478no—
591#544—4716no—
592#544—4716no—
593#544—474no—
594#544—472no—
595#544C2×D4712yes—
596#543—478no—
597#543—478no—
598#543—474no—
599#543C2×D4714yes—
600#533—472no—
601#533—472no—
602#533—478no—
603#533—474no—
604#533—478no—
605#533—474no—
606#533—474no—
607#533—478no—
608#533—478no—
609#533—478no—
610#533—478no—
611#533—478no—
612#533—478no—
613#533—478no—
614#533—4716no—
615#533—4716no—
616#533—474no—
617#533—474no—
618#533—474no—
619#533—472no—
620#533C2×D4712yes—
621C2×C4⋊Q8—474no—
622C2×C4⋊Q8—472no—
623C2×C4⋊Q8—472no—
624C2×C4⋊Q8—474no—
625C2×#125—474no—
626C2×#125—478no—
627C2×C22⋊Q8—474no—
628C2×C22⋊Q8—474no—
629C2×C22⋊Q8—474no—
630C2×C22⋊Q8—478no—
631C2×C22⋊Q8C2×D4714yes—
632#520—478no—
633#520—478no—
634#519—474no—
635#518—472no—
636#518—478no—
637#518C2×D4712yes—
638C4×#41—474no—
639C4×#41—474no—
640C4×#41—474no—
641C4×#41—474no—
642C4×#41—478no—
643C4×#41—478no—
644C2×C4×Q8—474no—
645C2×C4×Q8—474no—
646C2×C4×Q8—474no—
647C2×C4×Q8—471no—
648C2×C4×Q8—474no—
649C2×C4×Q8—478no—
650C2×C4×Q8—471no—
651C2×C4×D4—471no—
652C2×C4×D4—472no—
653C2×C4×D4—472no—
654C2×C4×D4C2×D4711yescharacteristic
655C2×#117—474no—
656C2×#117—471no—
657C2×#117—472no—
658C2×#117—478no—
659C22×C42—472no—
660C22×C42—471no—
661C47#6281311yescharacteristic, complemented, Sylow
662C2×#41—4716no—
663C2×#41—474no—
664C2×#41—474no—
665C22×Q8—474no—
666C22×Q8—474no—
667C22×Q8—471no—
668C22×Q8—478no—
669C22×Q8—474no—
670C22×Q8C22×D4714yes—
671C22×D4—472no—
672C22×D4C22×D4711yescharacteristic
673C23×C4—472no—
674C23×C4—471no—
675C23×C4—472no—
676C23×C4—471no—
677C23×C4—471no—
678C23×C4C22×D4712yes—
679C4⋊Q8—474no—
680C4⋊Q8—478no—
681C4⋊Q8—474no—
682C4⋊Q8—478no—
683C4⋊Q8—478no—
684C4⋊Q8—4716no—
685C4⋊Q8—4716no—
686C4⋊Q8—474no—
687C4⋊Q8—474no—
688C4⋊Q8—478no—
689C4⋊Q8—478no—
690C4⋊Q8—474no—
691C4⋊Q8—474no—
692C4⋊Q8—478no—
693C4⋊Q8—4716no—
694C4⋊Q8—4716no—
695C4⋊Q8—478no—
696C4⋊Q8—478no—
697C4⋊Q8—472no—
698C4⋊Q8—472no—
699C4⋊Q8—478no—
700C4⋊Q8C22×D4712yes—
701C4⋊Q8C22×D4712yes—
702C4⋊Q8C22×D4718yes—
703#125—478no—
704#125—478no—
705#125—4716no—
706#125—4716no—
707#125—4716no—
708#125—474no—
709#125—474no—
710#125—4716no—
711#125—4716no—
712#125—4716no—
713#125—4716no—
714#125—478no—
715#125—478no—
716#125—474no—
717#125—478no—
718#125C22×D4714yes—
719#125C22×D4718yes—
720C22⋊Q8—474no—
721C22⋊Q8—474no—
722C22⋊Q8—4716no—
723C22⋊Q8—474no—
724C22⋊Q8—478no—
725C22⋊Q8—474no—
726C22⋊Q8—478no—
727C22⋊Q8—478no—
728C22⋊Q8—4716no—
729C22⋊Q8—4716no—
730C22⋊Q8—478no—
731C22⋊Q8—474no—
732C22⋊Q8—478no—
733C22⋊Q8—474no—
734C22⋊Q8—4716no—
735C22⋊Q8—4716no—
736C22⋊Q8—4716no—
737C22⋊Q8—478no—
738C22⋊Q8—478no—
739C22⋊Q8—4716no—
740C22⋊Q8—4716no—
741C22⋊Q8—4716no—
742C22⋊Q8—4716no—
743C22⋊Q8—4716no—
744C22⋊Q8—4716no—
745C22⋊Q8—4716no—
746C22⋊Q8C22×D4714yes—
747C22⋊Q8C22×D4714yes—
748C22⋊Q8C22×D4718yes—
749C22⋊Q8C22×D4718yes—
750C22⋊Q8C22×D4718yes—
751C22⋊Q8C22×D47116yes—
752C22⋊Q8C22×D47116yes—
753C4×Q8—474no—
754C4×Q8—478no—
755C4×Q8—474no—
756C4×Q8—478no—
757C4×Q8—478no—
758C4×Q8—474no—
759C4×Q8—478no—
760C4×Q8—474no—
761C4×Q8—474no—
762C4×Q8—474no—
763C4×Q8—478no—
764C4×Q8—4716no—
765C4×Q8—478no—
766C4×Q8—4716no—
767C4×Q8—478no—
768C4×Q8—478no—
769C4×Q8—4716no—
770C4×Q8—478no—
771C4×Q8—478no—
772C4×Q8—474no—
773C4×Q8—474no—
774C4×Q8—478no—
775C4×Q8—474no—
776C4×Q8—478no—
777C4×Q8—474no—
778C4×Q8—478no—
779C4×Q8—478no—
780C4×Q8C22×D4714yes—
781C4×Q8C22×D4714yes—
782C4×D4—474no—
783C4×D4—474no—
784C4×D4—478no—
785C4×D4—478no—
786C4×D4—478no—
787C4×D4—478no—
788C4×D4—4716no—
789C4×D4—4716no—
790C4×D4—478no—
791C4×D4—478no—
792C4×D4—4716no—
793C4×D4—4716no—
794C4×D4C22×D4714yes—
795C4×D4C22×D4714yes—
796C4×D4C22×D4718yes—
797C4×D4C22×D4718yes—
798#117—474no—
799#117—474no—
800#117—474no—
801#117—474no—
802#117—474no—
803#117—478no—
804#117—478no—
805#117—4716no—
806#117—478no—
807#117—4716no—
808#117—4716no—
809#117—478no—
810#117C22×D4714yes—
811C2×C4⋊C4—472no—
812C2×C4⋊C4—472no—
813C2×C4⋊C4—471no—
814C2×C4⋊C4—478no—
815C2×C4⋊C4—478no—
816C2×C4⋊C4—478no—
817C2×C4⋊C4—478no—
818C2×C4⋊C4—478no—
819C2×C4⋊C4—478no—
820C2×C4⋊C4—474no—
821C2×C4⋊C4—474no—
822C2×C4⋊C4—474no—
823C2×C4⋊C4—478no—
824C2×C4⋊C4—478no—
825C2×C4⋊C4—474no—
826C2×C4⋊C4—474no—
827C2×C4⋊C4C22×D4711yescharacteristic
828C2×C4⋊C4C22×D4718yes—
829C2×C4⋊C4C22×D4714yes—
830C2×C22⋊C4—472no—
831C2×C22⋊C4—478no—
832C2×C22⋊C4—472no—
833C2×C22⋊C4—478no—
834C2×C22⋊C4C22×D4712yes—
835C2×C22⋊C4C22×D4718yes—
836C2×C42—472no—
837C2×C42—471no—
838C2×C42—478no—
839C2×C42—478no—
840C2×C42—472no—
841C2×C42—472no—
842C2×C42—471no—
843C2×C42—474no—
844C2×C42—474no—
845C2×C42—474no—
846C2×C42—474no—
847C2×C42—471no—
848C2×C42—478no—
849C2×C42—472no—
850C2×C42—472no—
851C2×C42—472no—
852C2×C42—472no—
853C2×C42C22×D4711yescharacteristic
854C24—471no—
855C24C23×D4712yes—
856#41—4732no—
857#41—4732no—
858C2×Q8—48no—
859C2×Q8—478no—
860C2×Q8—474no—
861C2×Q8—478no—
862C2×Q8—474no—
863C2×Q8—478no—
864C2×Q8—478no—
865C2×Q8—4716no—
866C2×Q8—474no—
867C2×Q8—1888no—
868C2×Q8—18816no—
869C2×Q8—1888no—
870C2×Q8—1888no—
871C2×Q8C23×D4714yes—
872C2×Q8C23×D4718yes—
873C2×Q8C23×D4714yes—
874C2×D4—4716no—
875C2×D4—478no—
876C2×D4Q8×D4718yescomplemented
877C2×D4C23×D4714yes—
878C22×C4—44no—
879C22×C4—4716no—
880C22×C4—474no—
881C22×C4—471no—
882C22×C4—474no—
883C22×C4—472no—
884C22×C4—478no—
885C22×C4—472no—
886C22×C4—472no—
887C22×C4—471no—
888C22×C4—474no—
889C22×C4—472no—
890C22×C4—471no—
891C22×C4—474no—
892C22×C4—478no—
893C22×C4—478no—
894C22×C4—472no—
895C22×C4—472no—
896C22×C4—472no—
897C22×C4—472no—
898C22×C4—478no—
899C22×C4—478no—
900C22×C4—1882no—
901C22×C4—1882no—
902C22×C4—1884no—
903C22×C4C23×D4711yescharacteristic
904C22×C4C23×D4714yes—
905C22×C4C23×D4712yes—
906C22×C4C23×D4714yes—
907C22×C4C23×D4711yescharacteristic
908C22×C4C23×D4718yes—
909C22×C4C23×D4718yes—
910C22×C4C23×D4711yescharacteristic
911C4⋊C4—478no—
912C4⋊C4—478no—
913C4⋊C4—478no—
914C4⋊C4—478no—
915C4⋊C4—478no—
916C4⋊C4—478no—
917C4⋊C4—4716no—
918C4⋊C4—4716no—
919C4⋊C4—478no—
920C4⋊C4—4716no—
921C4⋊C4—478no—
922C4⋊C4—4716no—
923C4⋊C4—478no—
924C4⋊C4—4716no—
925C4⋊C4—478no—
926C4⋊C4—478no—
927C4⋊C4—474no—
928C4⋊C4—474no—
929C4⋊C4—474no—
930C4⋊C4—474no—
931C4⋊C4—478no—
932C4⋊C4—4716no—
933C4⋊C4—478no—
934C4⋊C4—474no—
935C4⋊C4C23×D4718yes—
936C4⋊C4C23×D4714yes—
937C4⋊C4C23×D4714yes—
938C4⋊C4C23×D4714yes—
939C4⋊C4C23×D4714yes—
940C4⋊C4C23×D4718yes—
941C4⋊C4C23×D4714yes—
942C4⋊C4C23×D47116yes—
943C4⋊C4C23×D4718yes—
944C22⋊C4—478no—
945C22⋊C4—478no—
946C22⋊C4—4716no—
947C22⋊C4—478no—
948C22⋊C4—478no—
949C22⋊C4—478no—
950C22⋊C4C23×D4718yes—
951C22⋊C4C23×D4718yes—
952C22⋊C4C23×D47116yes—
953C42—471no—
954C42—471no—
955C42—471no—
956C42—471no—
957C42—474no—
958C42—478no—
959C42—478no—
960C42—472no—
961C42—474no—
962C42—472no—
963C42—474no—
964C42—474no—
965C42—472no—
966C42—474no—
967C42—474no—
968C42—472no—
969C42—4716no—
970C42—4716no—
971C42—478no—
972C42C23×D4712yes—
973C42C23×D4712yes—
974C42C23×D4718yes—
975C23—42no—
976C23—42no—
977C23—472no—
978C23—474no—
979C23—1881no—
980C23—1881no—
981C23C2×Q8×D4718yes—
982C23C24×D4711yescharacteristic
983C23C24×D4714yes—
984Q8—28no—
985Q8—48no—
986Q8—44no—
987Q8—4716no—
988Q8—9416no—
989Q8—948no—
990Q8—18816no—
991Q8—1884no—
992Q8—1888no—
993Q8—1888no—
994D4—4732no—
995D4C2×Q8×D47116yes—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—474no—
1004C2×C4—478no—
1005C2×C4—4716no—
1006C2×C4—4716no—
1007C2×C4—471no—
1008C2×C4—474no—
1009C2×C4—471no—
1010C2×C4—471no—
1011C2×C4—478no—
1012C2×C4—478no—
1013C2×C4—471no—
1014C2×C4—474no—
1015C2×C4—478no—
1016C2×C4—472no—
1017C2×C4—478no—
1018C2×C4—944no—
1019C2×C4—942no—
1020C2×C4—948no—
1021C2×C4—944no—
1022C2×C4—1882no—
1023C2×C4—1882no—
1024C2×C4—1888no—
1025C2×C4—1888no—
1026C2×C4—1884no—
1027C2×C4—1882no—
1028C2×C4—1881no—
1029C2×C4—1888no—
1030C2×C4—1888no—
1031C2×C4C2×Q8×D4714yes—
1032C2×C4C24×D4711yescharacteristic
1033C2×C4C24×D4714yes—
1034C2×C4C24×D4718yes—
1035C2×C4C24×D4718yes—
1036C2×C4C24×D4712yes—
1037C2×C4C24×D4712yes—
1038C2×C4C24×D4711yescharacteristic
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—474no—
1045C22—942no—
1046C22—942no—
1047C22—1884no—
1048C22C22×Q8×D4712yes—
1049C22C22×Q8×D4718yes—
1050C22C25×D4711yescharacteristic
1051C4—28no—
1052C4—22no—
1053C4—21no—
1054C4—24no—
1055C4—28no—
1056C4—472no—
1057C4—472no—
1058C4—478no—
1059C4—472no—
1060C4—941no—
1061C4—944no—
1062C4—948no—
1063C4—942no—
1064C4—948no—
1065C4C22×Q8×D4714yes—
1066C4#1568995812yes—
1067C2—22no—
1068C2—28no—
1069C2—944no—
1070C2C23×Q8×D4711yescharacteristic
1071C2#585×D4711yescharacteristic
1072C2C2×#1568995811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3501C2
prime radicalC22×#10625352C22
hypercenter#3501D47
hypocenterC47#62813
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #20257208C2semidirect
2. #20257202C2semidirect
3. #20257199C2semidirect
4. #20257196C2semidirect
5. #20257193C2semidirect
6. #20257191C2semidirect
7. #20257188C2semidirect
8. #20257186C2semidirect
9. #20257184C2semidirect
10. #20256967C2semidirect
11. #20256967C2semidirect
12. Q8×#10625352C2semidirect
13. #20256792C2semidirect
14. #20256790C2semidirect
15. C2×#15689675C2semidirect
16. #533×D47C2semidirect
19. C47×#3501C2semidirect
21. Q8×Dic94C22semidirect
22. #15689853C22semidirect
23. #15689853C22semidirect
24. #15689851C22semidirect
25. #15689851C22semidirect
26. #15689850C22semidirect
27. #15689850C22semidirect
28. #15689850C22semidirect
29. #15689848C22semidirect
30. #15689848C22semidirect
31. #15689832C22semidirect
32. #15689832C22semidirect
33. #15689832C22semidirect
34. #15689831C22semidirect
35. #15689831C22semidirect
36. #15689830C22semidirect
37. #15689830C22semidirect
38. #15689828C22semidirect
39. #15689828C22semidirect
40. #15689827C22semidirect
41. #15689827C22semidirect
42. #15689827C22semidirect
43. D4×Dic94C22semidirect
44. D4×Dic94C22semidirect
45. Q8×C22⋊D47C22semidirect
46. #15689786C22semidirect
47. #15689786C22semidirect
49. #15689753C22semidirect
52. #15689752C22semidirect
53. #15689752C22semidirect
55. #15689750C22semidirect
60. #15689679C22semidirect
61. #15689679C22semidirect
62. #15689678C22semidirect
63. #15689678C22semidirect
64. #15689678C22semidirect
65. #15689677C22semidirect
66. #15689677C22semidirect
73. #15689675C22semidirect
74. #15689675C22semidirect
75. #15689675C22semidirect
76. #15689675C22semidirect
77. #15689675C22semidirect
78. #15689675C22semidirect
79. C2×#13094023C22semidirect
80. C2×#13094022C22semidirect
81. C4⋊Q8×D47C22semidirect
82. C4⋊Q8×D47C22semidirect
83. C2×#13094014C22semidirect
84. #125×D47C22semidirect
100. C2×Q8×Dic47C22semidirect
103. C2×#13093989C22semidirect
104. C2×#13093989C22semidirect
105. C4×Q8×D47C22semidirect
106. C4×Q8×D47C22semidirect
116. C47×#554C22semidirect
117. C47×#554C22semidirect
118. D4×Q8×C47C22semidirect
125. C2×#10625352Q8semidirect
323. C2×D4×C47C2×Q8semidirect
334. C2×C22⋊D47C2×Q8semidirect
337. C22×Dic47C2×Q8semidirect
351. #10625352C2×Q8semidirect
352. #10625352C2×Q8semidirect
355. C2×C4×D47C2×Q8semidirect
366. C2×Dic94C2×Q8semidirect
540. #3501D47semidirect
579. #554C2×D47semidirect
580. #554C2×D47semidirect
586. D4×Q8C2×D47semidirect
661. C47#62813semidirect
876. C2×D4Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#202572082
#202572022
#202571992
#202571962
#202571932
#202571912
#202571882
#202571862
#202571842
#202569672
Q8×#106253522
#202567922
#202567902
C2×#156896752
#533×D472
#202565862
C2×C4×#106253522
C47×#35012
#6281347