Finite Group Databasebeta

← #26232656

Subgroups — #26232656

Order 12032.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic
2#20246317C211yesmaximal, characteristic
3#20244362C211yesmaximal, characteristic, complemented
4#20244341C211yesmaximal, characteristic, complemented
5#20243822C211yesmaximal, characteristic, complemented
6#20243812C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic, complemented
8#20243696C211yesmaximal, characteristic, complemented
9#20243478C211yesmaximal, characteristic, complemented
10#20243474C211yesmaximal, characteristic, complemented
11#20243403C211yesmaximal, characteristic, complemented
12#20243218C211yesmaximal, characteristic, complemented
13#20243107C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15C2×C47×#554C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20#15689195—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29#15689016—21no—
30#15689009—21no—
31#15689003—21no—
32#15688989C2211yescharacteristic
33#15688983C2211yescharacteristic
34#15688983C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36C22⋊C4×Dic47—21no—
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C47×#554—24no—
50C47×#554C418yescomplemented
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×#125×C47—21no—
53C2×C22⋊Q8×C47—21no—
54C2×C22⋊Q8×C47—21no—
55C2×C22⋊Q8×C47C2211yescharacteristic
56C2×C22⋊Q8×C47C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×C4×D4×C47—21no—
59C2×C4×D4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—41no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—22no—
74#13093983—41no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—41no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C4⋊(C47⋊C8)—22no—
88#13093948—22no—
89#13093948—22no—
90#13093948—41no—
91#13093948—41no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—22no—
94#13093935—22no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47C2311yescharacteristic
102C22×D4×C47D411yescharacteristic
103C23×C4×C47—21no—
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C4⋊Q8×C47—22no—
108C4⋊Q8×C47C2×C414yescomplemented
109#125×C47—28no—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—28no—
113C22⋊Q8×C47—28no—
114C22⋊Q8×C47C2×C414yes—
115C22⋊Q8×C47C2×C414yescomplemented
116C4×Q8×C47—22no—
117C4×Q8×C47C2×C414yescomplemented
118C4×D4×C47—28no—
119C4×D4×C47C2×C414yes—
120C4×D4×C47D414yes—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47—22no—
124C2×C4⋊C4×C47—22no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47C2×C414yes—
130C2×C4⋊C4×C47C2×C414yescomplemented
131C2×C4⋊C4×C47D411yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C22⋊C4×C47D411yescharacteristic
139C2×C42×C47—21no—
140C2×C42×C47C2311yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C2×Q8×C47—24no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—81no—
150C2×Q8×C47—81no—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47C22⋊C414yes—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—24no—
168C22×C4×C47—24no—
169C22×C4×C47—81no—
170C22×C4×C47—81no—
171C22×C4×C47—81no—
172C22×C4×C47—81no—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C22×C412yes—
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D412yes—
180C22×C4×C47C2×D412yes—
181C22×C4×C47C2411yescharacteristic
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—42no—
187C22×Dic47—42no—
188C22×Dic47—81no—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—24no—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—24no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47C22⋊C414yes—
199C4⋊C4×C47C22×C412yes—
200C4⋊C4×C47C22×C412yes—
201C4⋊C4×C47C22×C412yes—
202C22⋊C4×C47—24no—
203C22⋊C4×C47—24no—
204C22⋊C4×C47C22⋊C414yes—
205C22⋊C4×C47C22⋊C414yes—
206C42×C47—24no—
207C42×C47C22×C412yes—
208C42×C47C2×D412yes—
209C22⋊Dic47—42no—
210C22⋊Dic47—42no—
211C22⋊Dic47—81no—
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⋊Dic47#4112yes—
221C4×Dic47—42no—
222C4×Dic47—81no—
223#10625329—44no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—44no—
236C2×C47⋊C8#4112yes—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C2×C22⋊C412yes—
248C23×C47C2×C22⋊C412yes—
249C23×C47#13712yes—
250C23×C47#13712yes—
251C23×C47C22×D411yescharacteristic
252Q8×C47—22no—
253Q8×C47—22no—
254Q8×C47—41no—
255Q8×C47—41no—
256Q8×C47—84no—
257D4×C47—28no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—84no—
287C2×C4×C47—84no—
288C2×C4×C47C2×C22⋊C412yes—
289C2×C4×C47C2×C22⋊C412yes—
290C2×C4×C47C2×C22⋊C412yes—
291C2×C4×C47C2×C22⋊C412yes—
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C47C2×#4111yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47H(5,𝔽2)11yescharacteristic
297C2×C4×C472−1+411yescharacteristic
298C2×Dic47—22no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—84no—
311C47⋊C8—22no—
312C47⋊C8—41no—
313C47⋊C8—41no—
314C47⋊C8—41no—
315#22497—471nomaximal, Sylow
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47#41914yes—
330C22×C47C22×C22⋊C411yescharacteristic
331C22×C47#54611yescharacteristic
332C22×C47#54711yescharacteristic
333C22×C47C2×#13711yescharacteristic
334C22×C47C2×#13711yescharacteristic
335C22×C47#57611yescharacteristic
336C22×C47#57711yescharacteristic
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47C4×#4111yescharacteristic
346C4×C47#52011yescharacteristic
347C4×C47#54611yescharacteristic
348C4×C47#54711yescharacteristic
349Dic47—42no—
350Dic47—81no—
351Dic47—81no—
352Dic47—81no—
353C2×#554D4711yescharacteristic
354C2×#435—471no—
355#2352—471no—
356#1993—471no—
357#1988—471no—
358#1894—471no—
359#1892—471no—
360#1873—471no—
361#1872—471no—
362#1824—471no—
363#1823—471no—
364#1805—471no—
365#1763—471no—
366#1736—471no—
367C2×#340—471no—
368C2×C47—24no—
369C2×C47—42no—
370C2×C47#233911yescharacteristic
371C2×C47C2×#41911yescharacteristic
372C2×C47#289711yescharacteristic
373C2×C47#331411yescharacteristic
374C2×C47#331611yescharacteristic
375C2×C47#334411yescharacteristic
376C2×C47#334611yescharacteristic
377C22×M16—471no—
378C23×C8—471no—
379#554—24no—
380#554Dic4718yescomplemented
381C2×C4⋊Q8C2×D4711yescharacteristic
382C2×#125—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8C2×D4711yescharacteristic
386C2×C22⋊Q8C2×D4711yescharacteristic
387C2×C4×Q8C2×D4711yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C2×D4711yescharacteristic
390C2×#117—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4C2×D4711yescharacteristic
393C22×C4⋊C4C2×D4711yescharacteristic
394#435—944no—
395C2×C4⋊C8—471no—
396C2×#103—471no—
397C2×#103—471no—
398C2×#103—471no—
399C2×#103—471no—
400C2×C22⋊C8—471no—
401C2×C22⋊C8—471no—
402C2×#97—471no—
403#388—941no—
404#387—941no—
405#386—941no—
406#382—471no—
407#380—471no—
408#380—471no—
409C4×C4⋊C4—471no—
410C4×C22⋊C4—941no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340—471no—
421#340—471no—
422#340—471no—
423C47#2249711yescharacteristic, complemented, Sylow
424C22×Q8—21no—
425C22×Q8C22×D4711yescharacteristic
426C22×D4C22⋊D4711yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—941no—
430C23×C4C22×D4711yescharacteristic
431C23×C4C22×D4711yescharacteristic
432C2×M16—942no—
433C2×M16—942no—
434C2×M16—1881no—
435C22×C8—471no—
436C22×C8—471no—
437C22×C8—471no—
438C22×C8—471no—
439C22×C8—942no—
440C22×C8—942no—
441C22×C8—1881no—
442C4⋊Q8—22no—
443C4⋊Q8C2×Dic4714yescomplemented
444#125—28no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8C2×Dic4714yes—
450C22⋊Q8C2×Dic4714yescomplemented
451C4×Q8—22no—
452C4×Q8C2×Dic4714yescomplemented
453C4×D4—28no—
454C4×D4C2×Dic4714yes—
455C4×D4C22⋊D4714yes—
456#117—942no—
457#117—1881no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—942no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—1881no—
473C2×C4⋊C4C2×Dic4714yes—
474C2×C4⋊C4C2×Dic4714yescomplemented
475C2×C4⋊C4C22⋊D4711yescharacteristic
476C2×C4⋊C4C22×D4711yescharacteristic
477C2×C4⋊C4C22×D4711yescharacteristic
478C2×C4⋊C4C22×D4711yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C22⋊C4C22⋊D4711yescharacteristic
485C2×C22⋊C4C22⋊D4711yescharacteristic
486C2×C42—21no—
487C2×C42—941no—
488C2×C42—941no—
489C2×C42C22×D4711yescharacteristic
490C4⋊C8—942no—
491#103—942no—
492#103—942no—
493#103—1881no—
494#103—1881no—
495C22⋊C8—942no—
496C22⋊C8—942no—
497#97—942no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503C24C2×C22⋊D4711yescharacteristic
504C24C2×C22⋊D4711yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—81no—
512C2×Q8—81no—
513C2×Q8C22×Dic4712yes—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4C22⋊Dic4714yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—3761no—
540C22×C4—1882no—
541C22×C4—1882no—
542C22×C4C22×Dic4712yes—
543C22×C4C22×Dic4712yes—
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C2×C22⋊D4711yescharacteristic
547C22×C4C2×C22⋊D4711yescharacteristic
548C22×C4C2×C22⋊D4712yes—
549C22×C4C2×C22⋊D4712yes—
550C22×C4C23×D4711yescharacteristic
551M16—1884no—
552C2×C8—472no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—1884no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—472no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—1882no—
583C4⋊C4C22⋊Dic4714yes—
584C4⋊C4C22×Dic4712yes—
585C4⋊C4C22×Dic4712yes—
586C4⋊C4C22×Dic4712yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—3761no—
590C22⋊C4—1882no—
591C22⋊C4—1882no—
592C22⋊C4C22⋊Dic4714yes—
593C22⋊C4C22⋊Dic4714yes—
594C42—24no—
595C42—3761no—
596C42—1882no—
597C42C22×Dic4712yes—
598C42C2×C22⋊D4712yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C22⋊Dic4712yes—
610C23C2×C22⋊Dic4712yes—
611C23#1309405512yes—
612C23#1309405512yes—
613C23C22×C22⋊D4711yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—942no—
651C2×C4—3764no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4C2×C22⋊Dic4712yes—
664C2×C4C2×C22⋊Dic4712yes—
665C2×C4C2×C22⋊Dic4712yes—
666C2×C4C2×C22⋊Dic4712yes—
667C2×C4C23×Dic4711yescharacteristic
668C2×C4C22×C22⋊D4711yescharacteristic
669C2×C4#41×D4711yescharacteristic
670C2×C4#41×D4711yescharacteristic
671C2×C4#1309407011yescharacteristic
672C2×C4#1309407111yescharacteristic
673C8—942no—
674C8—1881no—
675C8—1881no—
676C8—1881no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1568913214yes—
691C22C22×C22⋊Dic4711yescharacteristic
692C22#1568976111yescharacteristic
693C22#1568977211yescharacteristic
694C22C2×#1309405511yescharacteristic
695C22C2×#1309405511yescharacteristic
696C22#1568992611yescharacteristic
697C22#1568993411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—3761no—
707C4—3761no—
708C4—3761no—
709C4—1882no—
710C4#41×Dic4711yescharacteristic
711C4#1568960611yescharacteristic
712C4#1568976111yescharacteristic
713C4#1568977211yescharacteristic
714C2—24no—
715C2—42no—
716C2#2024621811yescharacteristic
717C2C2×#1568913211yescharacteristic
718C2#2025191411yescharacteristic
719C2#2025546311yescharacteristic
720C2#2025549311yescharacteristic
721C2#2025583711yescharacteristic
722C2#2025586711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#554C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
cosocleC22×C4×C47C24
hypercenterC2×#554D47
hypocenterC47#22497
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #20244362C2semidirect
4. #20244341C2semidirect
5. #20243822C2semidirect
6. #20243812C2semidirect
7. #20243701C2semidirect
8. #20243696C2semidirect
9. #20243478C2semidirect
10. #20243474C2semidirect
11. #20243403C2semidirect
12. #20243218C2semidirect
13. #20243107C2semidirect
14. C2×#15688885C2semidirect
50. C47×#554C4semidirect
108. C4⋊Q8×C47C2×C4semidirect
115. C22⋊Q8×C47C2×C4semidirect
117. C4×Q8×C47C2×C4semidirect
130. C2×C4⋊C4×C47C2×C4semidirect
380. #554Dic47semidirect
423. C47#22497semidirect
443. C4⋊Q8C2×Dic47semidirect
450. C22⋊Q8C2×Dic47semidirect
452. C4×Q8C2×Dic47semidirect
474. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
#202463172
#202443622
#202443412
#202438222
#202438122
#202437012
#202436962
#202434782
#202434742
#202434032
#202432182
#202431072
C2×#156888852
C2×C47×#5542
#2249747