Finite Group Databasebeta

← #26232505

Subgroups — #26232505

Order 12032.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689813C211yesmaximal, characteristic
2#20246317C211yesmaximal, characteristic
3#20244353C211yesmaximal, characteristic, complemented
4#20244343C211yesmaximal, characteristic, complemented
5#20243811C211yesmaximal, characteristic, complemented
6#20243811C211yesmaximal, characteristic, complemented
7#20243698C211yesmaximal, characteristic, complemented
8#20243693C211yesmaximal, characteristic, complemented
9#20243484C211yesmaximal, characteristic, complemented
10#20243475C211yesmaximal, characteristic, complemented
11#20243404C211yesmaximal, characteristic, complemented
12C4×#13093949C211yesmaximal, characteristic, complemented
13#20243105C211yesmaximal, characteristic, complemented
14C2×#15688886C211yesmaximal, characteristic, complemented
15C2×C8×D4×C47C211yesmaximal, characteristic
16#15689813—24no—
17#15689813C418yescomplemented
18C2×#13094017—21no—
19C2×#13094016C2211yescharacteristic
20C2×#13094014—21no—
21C2×#13094005—21no—
22C2×#13094003C2211yescharacteristic
23C2×#13094003C2211yescharacteristic
24C2×C4×Dic94C2211yescharacteristic
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2211yescharacteristic
27C2×#13093980—21no—
28C22×C4⋊Dic47C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30C2×#13093949C2211yescharacteristic
31C2×#13093949C2211yescharacteristic
32C2×#13093949C2211yescharacteristic
33C2×#13093949C2211yescharacteristic
34#15689016—21no—
35#15689009—21no—
36#15689003—21no—
37#15688989C2211yescharacteristic
38#15688983C2211yescharacteristic
39#15688983C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C22⋊C4×Dic47—21no—
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54C23×C8×C47C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C2×C4×D4×C47C2211yescharacteristic
57C8×D4×C47—24no—
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C22×Dic94C2311yescharacteristic
63C23×Dic47—21no—
64C23×Dic47—21no—
65#13094017—28no—
66#13094016—22no—
67#13094016C2×C414yescomplemented
68#13094014—28no—
69#13094005—28no—
70#13094003—22no—
71#13094003—22no—
72#13094003C2×C414yes—
73#13094003C2×C414yescomplemented
74C4×Dic94—22no—
75C4×Dic94C2×C414yescomplemented
76#13093983—22no—
77#13093983—22no—
78#13093983—41no—
79#13093983C2×C414yescomplemented
80#13093980—28no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—22no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—41no—
86C2×C4⋊Dic47C2×C414yes—
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2311yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×C22⋊Dic47—21no—
102C2×C22⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109#13093949—22no—
110#13093949—22no—
111#13093949—41no—
112#13093949—41no—
113C47⋊#95—21no—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C22×D4×C47D411yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C22×C8×C47—22no—
122C22×C8×C47—22no—
123C22×C8×C47—22no—
124C22×C8×C47—22no—
125C22×C8×C47—41no—
126C22×C8×C47—41no—
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C4×D4×C47C2×C414yes—
132C4×D4×C47D414yes—
133C2×C4⋊C4×C47D411yescharacteristic
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47—22no—
138C22⋊C8×C47—22no—
139C22⋊C8×C47—22no—
140C4×C8×C47—22no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47C22⋊C414yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—24no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—42no—
173C22×Dic47—42no—
174C22×Dic47—42no—
175C22×Dic47—42no—
176C22×Dic47—81no—
177C2×Dic94—21no—
178C2×Dic94—21no—
179C2×Dic94—21no—
180C2×Dic94—21no—
181C2×Dic94—21no—
182C2×Dic94C22×C412yes—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—44no—
195C2×C8×C47—44no—
196C2×C8×C47#4112yes—
197C4⋊C4×C47C22⋊C414yes—
198C22⋊C4×C47C22⋊C414yes—
199C22⋊C4×C47C22⋊C414yes—
200C42×C47C22×C412yes—
201C42×C47C2×D412yes—
202C22⋊Dic47—24no—
203C22⋊Dic47—24no—
204C22⋊Dic47—24no—
205C22⋊Dic47—42no—
206C22⋊Dic47—42no—
207C22⋊Dic47—81no—
208C4⋊Dic47—24no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—42no—
220C4⋊Dic47C22×C412yes—
221C4⋊Dic47C22×C412yes—
222C4⋊Dic47C22×C412yes—
223C4⋊Dic47#4112yes—
224Dic47⋊C4—24no—
225Dic47⋊C4—24no—
226Dic47⋊C4—24no—
227Dic47⋊C4—24no—
228Dic47⋊C4—24no—
229C4×Dic47—24no—
230C4×Dic47—24no—
231C4×Dic47—42no—
232C4×Dic47—81no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47C2×C22⋊C412yes—
244C23×C47C2×C22⋊C412yes—
245C23×C47#13512yes—
246C23×C47#13512yes—
247C23×C47C22×D411yescharacteristic
248D4×C47—28no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47C2×C22⋊C412yes—
266C2×C4×C47C2×C22⋊C412yes—
267C2×C4×C47C2×C22⋊C412yes—
268C2×C4×C47C2×C22⋊C412yes—
269C2×C4×C47C23×C411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47H(5,𝔽2)11yescharacteristic
274C2×C4×C472−1+411yescharacteristic
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—48no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—84no—
301Dic94—22no—
302Dic94—22no—
303Dic94—41no—
304Dic94—41no—
305C8×C47—22no—
306C8×C47—41no—
307C8×C47—41no—
308C8×C47—41no—
309#22486—471nomaximal, Sylow
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47#41614yes—
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47#54611yescharacteristic
326C22×C47#54711yescharacteristic
327C22×C47C2×#13511yescharacteristic
328C22×C47C2×#13511yescharacteristic
329C22×C47#57711yescharacteristic
330C22×C47#57811yescharacteristic
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47C4×#4111yescharacteristic
336C4×C47#52011yescharacteristic
337C4×C47#54611yescharacteristic
338C4×C47#54711yescharacteristic
339Dic47—42no—
340Dic47—42no—
341Dic47—42no—
342Dic47—42no—
343Dic47—42no—
344Dic47—81no—
345Dic47—81no—
346Dic47—81no—
347C2×#552—471no—
348C2×C8×D4D4711yescharacteristic
349#2352—471no—
350#1991—471no—
351#1989—471no—
352#1892—471no—
353#1892—471no—
354#1873—471no—
355#1872—471no—
356#1825—471no—
357#1823—471no—
358#1805—471no—
359C4×#103—471no—
360#1735—471no—
361C2×#340—471no—
362C2×C47—24no—
363C2×C47—42no—
364C2×C47#233911yescharacteristic
365C2×C47C2×#41611yescharacteristic
366C2×C47#289811yescharacteristic
367C2×C47#329611yescharacteristic
368C2×C47#330011yescharacteristic
369C2×C47#333611yescharacteristic
370C2×C47#333711yescharacteristic
371C23×C8C2×D4711yescharacteristic
372C23×C8C2×D4711yescharacteristic
373#552—478no—
374#552—944no—
375C2×#126—941no—
376C2×#125—471no—
377C2×#125—941no—
378C2×#123—941no—
379C2×C22⋊Q8—471no—
380C2×C22⋊Q8—471no—
381C2×C4×Q8—471no—
382C2×C4×D4C2×D4711yescharacteristic
383C2×#117—471no—
384C2×#117—471no—
385C2×#117—941no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C8×D4—24no—
389C2×C4⋊C8C2×D4711yescharacteristic
390C2×#103—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103—471no—
394C2×C22⋊C8C2×D4711yescharacteristic
395C2×C22⋊C8C2×D4711yescharacteristic
396C2×C4×C8C2×D4711yescharacteristic
397#388—941no—
398#387—941no—
399#386—941no—
400#382—471no—
401#380—471no—
402#380—471no—
403C4×C4⋊C4—471no—
404C4×C22⋊C4—941no—
405#340—471no—
406#340—471no—
407#340—471no—
408#340—471no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417C47#2248611yescharacteristic, complemented, Sylow
418C22×Q8—471no—
419C22×D4D18811yescharacteristic
420C23×C4—941no—
421C23×C4—941no—
422C23×C4C22×D4711yescharacteristic
423C23×C4C22×D4711yescharacteristic
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8—41no—
430C22×C8C22×D4711yescharacteristic
431C22×C8C22×D4711yescharacteristic
432C22×C8C22×D4711yescharacteristic
433C22×C8C22×D4711yescharacteristic
434#126—948no—
435#125—474no—
436#125—948no—
437#125—942no—
438#123—948no—
439C22⋊Q8—474no—
440C22⋊Q8—474no—
441C22⋊Q8—942no—
442C22⋊Q8—942no—
443C4×Q8—474no—
444C4×Q8—942no—
445C4×D4C4×D4714yes—
446C4×D4C22⋊D4714yes—
447#117—474no—
448#117—942no—
449#117—948no—
450#117—942no—
451#117—1881no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—942no—
461C2×C4⋊C4—941no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—1881no—
470C2×C4⋊C4D18811yescharacteristic
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4D18811yescharacteristic
478C2×C22⋊C4D18811yescharacteristic
479C2×C42—941no—
480C2×C42—941no—
481C2×C42—941no—
482C2×C42—941no—
483C2×C42C22×D4711yescharacteristic
484C4⋊C8—22no—
485#103—942no—
486#103—942no—
487#103—1881no—
488#103—1881no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C4×C8—22no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95—941no—
496#95—941no—
497C24C2×D18811yescharacteristic
498C24C2×D18811yescharacteristic
499C2×Q8—472no—
500C2×Q8—941no—
501C2×Q8—941no—
502C2×Q8—941no—
503C2×Q8—941no—
504C2×Q8—941no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4(C2×D47)⋊C414yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—944no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—941no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—3761no—
526C22×C4—1882no—
527C22×C4—1882no—
528C22×C4—1882no—
529C22×C4—1882no—
530C22×C4C2×C4×D4712yes—
531C22×C4C2×C4×D4712yes—
532C22×C4C2×D18811yescharacteristic
533C22×C4C2×D18811yescharacteristic
534C22×C4C2×D18811yescharacteristic
535C22×C4C2×D18811yescharacteristic
536C22×C4C2×C22⋊D4712yes—
537C22×C4C2×C22⋊D4712yes—
538C22×C4C23×D4711yescharacteristic
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—44no—
551C2×C8—44no—
552C2×C8#1062535212yes—
553C4⋊C4—472no—
554C4⋊C4—472no—
555C4⋊C4—472no—
556C4⋊C4—472no—
557C4⋊C4—944no—
558C4⋊C4—944no—
559C4⋊C4—944no—
560C4⋊C4—944no—
561C4⋊C4—944no—
562C4⋊C4—944no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—941no—
566C4⋊C4—941no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—941no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4—1882no—
574C4⋊C4(C2×D47)⋊C414yes—
575C22⋊C4—944no—
576C22⋊C4—944no—
577C22⋊C4—944no—
578C22⋊C4—3761no—
579C22⋊C4—1882no—
580C22⋊C4—1882no—
581C22⋊C4(C2×D47)⋊C414yes—
582C22⋊C4(C2×D47)⋊C414yes—
583C42—944no—
584C42—944no—
585C42—3761no—
586C42—1882no—
587C42C2×C4×D4712yes—
588C42C2×C22⋊D4712yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23C2×(C2×D47)⋊C412yes—
600C23C2×(C2×D47)⋊C412yes—
601C23#1309404612yes—
602C23#1309404612yes—
603C23C22×D18811yescharacteristic
604Q8—942no—
605Q8—942no—
606Q8—1881no—
607Q8—1881no—
608D4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—942no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—3764no—
631C2×C4—1881no—
632C2×C4—1881no—
633C2×C4—1881no—
634C2×C4—1881no—
635C2×C4—1881no—
636C2×C4—1881no—
637C2×C4—1881no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1888no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4C2×(C2×D47)⋊C412yes—
652C2×C4C2×(C2×D47)⋊C412yes—
653C2×C4C2×(C2×D47)⋊C412yes—
654C2×C4C2×(C2×D47)⋊C412yes—
655C2×C4C22×C4×D4711yescharacteristic
656C2×C4C22×C22⋊D4711yescharacteristic
657C2×C4#41×D4711yescharacteristic
658C2×C4C2×#1062535211yescharacteristic
659C2×C4#1309406911yescharacteristic
660C2×C4#1309407111yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22#1568912014yes—
679C22C22×(C2×D47)⋊C411yescharacteristic
680C22#1568976811yescharacteristic
681C22#1568977711yescharacteristic
682C22C2×#1309404611yescharacteristic
683C22C2×#1309404611yescharacteristic
684C22#1568993511yescharacteristic
685C22#1568994011yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—3761no—
691C4—3761no—
692C4—3761no—
693C4—1882no—
694C4—1882no—
695C4—1882no—
696C4—1882no—
697C4—1882no—
698C4C4×#1062535211yescharacteristic
699C4#1568960211yescharacteristic
700C4#1568976711yescharacteristic
701C4#1568977211yescharacteristic
702C2—24no—
703C2—42no—
704C2#2024621311yescharacteristic
705C2C2×#1568912011yescharacteristic
706C2#2025192211yescharacteristic
707C2#2025522511yescharacteristic
708C2#2025527711yescharacteristic
709C2#2025575711yescharacteristic
710C2#2025576911yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C8×D4×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
cosocleC22×C4×C47C24
hypercenterC2×C8×D4D47
hypocenterC47#22486
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
3. #20244353C2semidirect
4. #20244343C2semidirect
5. #20243811C2semidirect
6. #20243811C2semidirect
7. #20243698C2semidirect
8. #20243693C2semidirect
9. #20243484C2semidirect
10. #20243475C2semidirect
11. #20243404C2semidirect
12. C4×#13093949C2semidirect
13. #20243105C2semidirect
14. C2×#15688886C2semidirect
17. #15689813C4semidirect
67. #13094016C2×C4semidirect
73. #13094003C2×C4semidirect
75. C4×Dic94C2×C4semidirect
79. #13093983C2×C4semidirect
417. C47#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#156898132
#202463172
#202443532
#202443432
#202438112
#202436982
#202436932
#202434842
#202434752
#202434042
C4×#130939492
#202431052
C2×#156888862
C2×C8×D4×C472
#2248647