Finite Group Databasebeta

← #26232786

Subgroups — #26232786

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#10625329C211yesmaximal, characteristic, complemented
2#20245853C211yesmaximal, characteristic, complemented
3#20244366C211yesmaximal, characteristic, complemented
4#20244333C211yesmaximal, characteristic, complemented
5#20243837C212yesmaximal, complemented
6#20243691C212yesmaximal, complemented
7#20243487C212yesmaximal, complemented
8#20243408C211yesmaximal, characteristic, complemented
9C4×#13093951C211yesmaximal, characteristic, complemented
10#20243097C212yesmaximal, complemented
11C47×#3475C211yesmaximal, characteristic
12C22×#10625329C2212yes—
13C2×#13093983C2212yes—
14#15689201—21no—
15#15689195—22no—
16D4×C47⋊C8—21no—
17#15689147C2211yescharacteristic
18C2×#13093951C2211yescharacteristic
19C2×#13093951C2211yescharacteristic
20C2×#13093951C2212yes—
21#15689087C2212yes—
22C4×#10625329C2211yescharacteristic
23#15689026—21no—
24#15689022—21no—
25#15689016—22no—
26C4×C4⋊Dic47C2211yescharacteristic
27C4×C22⋊Dic47C2212yes—
28C42×Dic47C2211yescharacteristic
29#15688882C2211yescharacteristic
30#15688882C2212yes—
31#15688882C2212yes—
32#15688882C2212yes—
33#15688882C2212yes—
34#15688882C2212yes—
35#15688882C2211yescharacteristic
36C47×#556C411yescharacteristic, complemented
37C47×#555C411yescharacteristic, complemented
38C47×#554C411yescharacteristic, complemented
39C47×#553C412yescomplemented
40C47×#552—21no—
41C47×#552C412yescomplemented
42C47×#551—22no—
43C47×#547C411yescharacteristic, complemented
44C47×#546—21no—
45C47×#533C2211yescharacteristic
46C47×#529—22no—
47C47×#529—21no—
48C47×#525C2212yes—
49C4×#41×C47—21no—
50C4×#41×C47C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C2×#117×C47C2212yes—
53C2×#10625329—22no—
54C2×#10625329—24no—
55C2×#10625329—42no—
56C2×#10625329C2311yescharacteristic
57C2×#10625329C2312yes—
58C2×#10625329C2311yescharacteristic
59C22×C47⋊C8—22no—
60#13093983—24no—
61#13093983—42no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—22no—
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47—22no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47C2311yescharacteristic
69C2×C4×Dic47C2312yes—
70C2×C4×Dic47C2311yescharacteristic
71C4⋊(C47⋊C8)—21no—
72C4⋊(C47⋊C8)—21no—
73#13093951—22no—
74#13093951—22no—
75#13093951—42no—
76C22⋊(C47⋊C8)—22no—
77C22⋊(C47⋊C8)—22no—
78#13093935—21no—
79C4×C47⋊C8—21no—
80C47⋊#95—22no—
81C47⋊#95—21no—
82C2×#41×C47—21no—
83C2×#41×C47C2311yescharacteristic
84C22×D4×C47D411yescharacteristic
85C23×C4×C47C2312yes—
86C4⋊Q8×C47C2×C411yescharacteristic
87C4⋊Q8×C47C2×C411yescharacteristic
88#126×C47—22no—
89#126×C47—22no—
90#126×C47—22no—
91#125×C47—22no—
92#125×C47—21no—
93#125×C47C2×C412yes—
94#124×C47—21no—
95#124×C47—22no—
96#123×C47—22no—
97#123×C47—22no—
98#123×C47—22no—
99#123×C47—22no—
100C22⋊Q8×C47—21no—
101C22⋊Q8×C47—21no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47—22no—
104C22⋊Q8×C47C2×C412yes—
105C22⋊Q8×C47C2×C412yes—
106#121×C47—22no—
107#121×C47—21no—
108#121×C47C2×C412yes—
109#121×C47C2×C412yes—
110#120×C47—22no—
111C4×Q8×C47—21no—
112C4×Q8×C47—21no—
113C4×Q8×C47—21no—
114C4×Q8×C47C2×C411yescharacteristic
115C4×Q8×C47C2×C411yescharacteristic
116C4×D4×C47—21no—
117C4×D4×C47—22no—
118C4×D4×C47—21no—
119C4×D4×C47—21no—
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47C2×C411yescharacteristic
123C4×D4×C47C2×C411yescharacteristic
124C4×D4×C47C2×C411yescharacteristic
125C4×D4×C47C2×C412yes—
126C4×D4×C47C2×C411yescharacteristic
127C4×D4×C47D411yescharacteristic
128C4×D4×C47D411yescharacteristic
129C4×D4×C47D412yes—
130#117×C47—22no—
131#117×C47—22no—
132#117×C47—21no—
133#117×C47—22no—
134#117×C47—21no—
135#117×C47C2×C412yes—
136#117×C47C2×C412yes—
137#117×C47C2311yescharacteristic
138#117×C47C2312yes—
139C2×C4⋊C4×C47C2×C412yes—
140C2×C4⋊C4×C47C2×C412yes—
141C2×C4⋊C4×C47D411yescharacteristic
142C2×C22⋊C4×C47—22no—
143C2×C22⋊C4×C47D412yes—
144C2×C42×C47—22no—
145C2×C42×C47—21no—
146C2×C42×C47C2311yescharacteristic
147C24×C47C2×D412yes—
148#41×C47—21no—
149#41×C47—21no—
150#41×C47—21no—
151#41×C47—21no—
152#41×C47—44no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47C22×C411yescharacteristic
156C2×D4×C47—22no—
157C2×D4×C47—21no—
158C2×D4×C47—22no—
159C2×D4×C47—42no—
160C2×D4×C47C22⋊C411yescharacteristic
161C2×D4×C47C22⋊C411yescharacteristic
162C2×D4×C47C22⋊C412yes—
163C2×D4×C47C22×C411yescharacteristic
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C22×C412yes—
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D412yes—
177C22×C4×C47C2×D412yes—
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2411yescharacteristic
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C4⋊C4×C47—22no—
185C4⋊C4×C47—22no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—22no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47C22⋊C411yescharacteristic
195C4⋊C4×C47C22⋊C411yescharacteristic
196C4⋊C4×C47C22⋊C412yes—
197C4⋊C4×C47C22×C411yescharacteristic
198C4⋊C4×C47C22×C411yescharacteristic
199C4⋊C4×C47C22×C412yes—
200C4⋊C4×C47C22×C412yes—
201C22⋊C4×C47—22no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—22no—
205C22⋊C4×C47—21no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—21no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47C22⋊C412yes—
212C22⋊C4×C47C22⋊C412yes—
213C22⋊C4×C47C22⋊C412yes—
214C22⋊C4×C47C22⋊C412yes—
215C42×C47—22no—
216C42×C47—21no—
217C42×C47—22no—
218C42×C47—21no—
219C42×C47—21no—
220C42×C47—22no—
221C42×C47C22×C411yescharacteristic
222C42×C47C22×C411yescharacteristic
223C42×C47C2×D411yescharacteristic
224C42×C47C2×D411yescharacteristic
225C22⋊Dic47—44no—
226C22⋊Dic47—44no—
227C4⋊Dic47—44no—
228C4⋊Dic47—42no—
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—22no—
232C4×Dic47—22no—
233C4×Dic47—21no—
234C4×Dic47—42no—
235C4×Dic47—42no—
236C4×Dic47#4112yescomplemented
237#10625329—21no—
238#10625329—21no—
239#10625329—22no—
240#10625329—22no—
241#10625329—21no—
242#10625329—44no—
243#10625329#4112yescomplemented
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—22no—
247C2×C47⋊C8—44no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—21no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47C2×C22⋊C412yes—
254C23×C47C2×C22⋊C412yes—
255C23×C47C22×D411yescharacteristic
256Q8×C47—21no—
257Q8×C47—21no—
258Q8×C47—42no—
259Q8×C47—81no—
260D4×C47—21no—
261D4×C47—21no—
262D4×C47—22no—
263D4×C47—22no—
264D4×C47—42no—
265D4×C47—44no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—82no—
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—22no—
279C2×C4×C47—22no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—41no—
286C2×C4×C47—44no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—42no—
290C2×C4×C47—81no—
291C2×C4×C47—82no—
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C411yescharacteristic
298C2×C4×C47C23×C411yescharacteristic
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C472−1+411yescharacteristic
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C47⋊C8—22no—
314C47⋊C8—42no—
315C47⋊C8—41no—
316#22507—471nomaximal, Sylow
317C22×C47—21no—
318C22×C47—21no—
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—82no—
329C22×C47—82no—
330C22×C47C22×C22⋊C411yescharacteristic
331C22×C47#54611yescharacteristic
332C22×C47#54711yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—21no—
336C4×C47—21no—
337C4×C47—21no—
338C4×C47—41no—
339C4×C47—41no—
340C4×C47—42no—
341C4×C47—41no—
342C4×C47—42no—
343C4×C47#42112yes—
344C4×C47C4×#4111yescharacteristic
345C4×C47#52011yescharacteristic
346C4×C47#54611yescharacteristic
347C4×C47#54711yescharacteristic
348Dic47—42no—
349Dic47—42no—
350Dic47—82no—
351#3475D4711yescharacteristic
352D4×M16—471no—
353#2293—471no—
354#1994—471no—
355#1986—471no—
356#1897—472no—
357#1871—472no—
358#1826—472no—
359#1806—471no—
360C4×#104—471no—
361#1733—472no—
362C2×C47—21no—
363C2×C47—21no—
364C2×C47—42no—
365C2×C47—42no—
366C2×C47—81no—
367C2×C47#233911yescharacteristic
368C2×C47C2×#42111yescharacteristic
369C2×C47#290111yescharacteristic
370C22×M16—472no—
371#556Dic4711yescharacteristic, complemented
372#555Dic4711yescharacteristic, complemented
373#554Dic4711yescharacteristic, complemented
374#553Dic4712yescomplemented
375#552—21no—
376#552Dic4712yescomplemented
377#551—22no—
378#547Dic4711yescharacteristic, complemented
379#546—21no—
380#533C2×D4711yescharacteristic
381#529—22no—
382#529—21no—
383#525C2×D4712yes—
384C4×#41—21no—
385C4×#41C2×D4711yescharacteristic
386C2×C4×D4C2×D4711yescharacteristic
387C2×#117—472no—
388C2×#117C2×D4712yes—
389#436—941no—
390#435—942no—
391C8×D4—941no—
392#423—471no—
393C2×#104—471no—
394C2×#104—471no—
395C2×#104—472no—
396#407—472no—
397C4×M16—471no—
398#390—941no—
399#389—941no—
400#388—942no—
401C4×C4⋊C4—471no—
402C4×C22⋊C4—472no—
403C43—471no—
404#339—472no—
405#339—471no—
406#339—472no—
407#339—472no—
408#339—472no—
409#339—472no—
410#339—471no—
411C47#2250711yescharacteristic, complemented, Sylow
412C2×#41—21no—
413C2×#41C22×D4711yescharacteristic
414C22×D4C22⋊D4711yescharacteristic
415C23×C4C22×D4712yes—
416C2×M16—471no—
417C2×M16—472no—
418C2×M16—471no—
419C2×M16—942no—
420C2×M16—944no—
421C2×M16—1882no—
422C22×C8—942no—
423C4⋊Q8C2×Dic4711yescharacteristic
424C4⋊Q8C2×Dic4711yescharacteristic
425#126—22no—
426#126—22no—
427#126—22no—
428#125—22no—
429#125—21no—
430#125C2×Dic4712yes—
431#124—21no—
432#124—22no—
433#123—22no—
434#123—22no—
435#123—22no—
436#123—22no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic4712yes—
442C22⋊Q8C2×Dic4712yes—
443#121—22no—
444#121—21no—
445#121C2×Dic4712yes—
446#121C2×Dic4712yes—
447#120—22no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8C2×Dic4711yescharacteristic
452C4×Q8C2×Dic4711yescharacteristic
453C4×D4—21no—
454C4×D4—22no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4C2×Dic4711yescharacteristic
460C4×D4C2×Dic4711yescharacteristic
461C4×D4C2×Dic4711yescharacteristic
462C4×D4C2×Dic4712yes—
463C4×D4C2×Dic4711yescharacteristic
464C4×D4C22⋊D4711yescharacteristic
465C4×D4C22⋊D4711yescharacteristic
466C4×D4C22⋊D4712yes—
467#117—22no—
468#117—22no—
469#117—21no—
470#117—22no—
471#117—21no—
472#117—944no—
473#117—1882no—
474#117C2×Dic4712yes—
475#117C2×Dic4712yes—
476#117C22×D4711yescharacteristic
477#117C22×D4712yes—
478C2×C4⋊C4—942no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4C2×Dic4712yes—
481C2×C4⋊C4C2×Dic4712yes—
482C2×C4⋊C4C22⋊D4711yescharacteristic
483C2×C22⋊C4—22no—
484C2×C22⋊C4—942no—
485C2×C22⋊C4—942no—
486C2×C22⋊C4C22⋊D4712yes—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42—471no—
490C2×C42—472no—
491C2×C42—471no—
492C2×C42—941no—
493C2×C42—941no—
494C2×C42C22×D4711yescharacteristic
495C4⋊C8—941no—
496C4⋊C8—941no—
497#104—942no—
498#104—942no—
499#104—1882no—
500C22⋊C8—942no—
501C22⋊C8—942no—
502#97—941no—
503C4×C8—941no—
504#95—942no—
505#95—941no—
506C24C2×C22⋊D4712yes—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—21no—
511#41—44no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C22×Dic4711yescharacteristic
515C2×D4—22no—
516C2×D4—21no—
517C2×D4—22no—
518C2×D4—42no—
519C2×D4C22⋊Dic4711yescharacteristic
520C2×D4C22⋊Dic4711yescharacteristic
521C2×D4C22⋊Dic4712yes—
522C2×D4C22×Dic4711yescharacteristic
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—942no—
535C22×C4C22×Dic4712yes—
536C22×C4C22×Dic4712yes—
537C22×C4C2×C22⋊D4712yes—
538C22×C4C2×C22⋊D4711yescharacteristic
539C22×C4C2×C22⋊D4712yes—
540C22×C4C2×C22⋊D4712yes—
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C23×D4711yescharacteristic
543M16—472no—
544M16—941no—
545M16—941no—
546M16—942no—
547M16—942no—
548M16—941no—
549M16—1884no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—942no—
553C2×C8—1884no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—1884no—
565C4⋊C4—1882no—
566C4⋊C4C22⋊Dic4711yescharacteristic
567C4⋊C4C22⋊Dic4711yescharacteristic
568C4⋊C4C22⋊Dic4712yes—
569C4⋊C4C22×Dic4711yescharacteristic
570C4⋊C4C22×Dic4711yescharacteristic
571C4⋊C4C22×Dic4712yes—
572C4⋊C4C22×Dic4712yes—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—21no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—22no—
583C22⋊C4—1884no—
584C22⋊C4—1884no—
585C22⋊C4C22⋊Dic4712yes—
586C22⋊C4C22⋊Dic4712yes—
587C22⋊C4C22⋊Dic4712yes—
588C22⋊C4C22⋊Dic4712yes—
589C42—22no—
590C42—21no—
591C42—22no—
592C42—21no—
593C42—21no—
594C42—22no—
595C42—472no—
596C42—941no—
597C42—941no—
598C42—942no—
599C42—942no—
600C42—941no—
601C42—1882no—
602C42—1882no—
603C42C22×Dic4711yescharacteristic
604C42C22×Dic4711yescharacteristic
605C42C2×C22⋊D4711yescharacteristic
606C42C2×C22⋊D4711yescharacteristic
607C23—22no—
608C23—22no—
609C23—21no—
610C23—42no—
611C23—42no—
612C23C2×C22⋊Dic4712yes—
613C23C2×C22⋊Dic4712yes—
614C23C22×C22⋊D4711yescharacteristic
615Q8—21no—
616Q8—21no—
617Q8—42no—
618Q8—81no—
619D4—21no—
620D4—21no—
621D4—22no—
622D4—22no—
623D4—42no—
624D4—44no—
625D4—41no—
626D4—41no—
627D4—82no—
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—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—41no—
645C2×C4—44no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—81no—
650C2×C4—82no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4C2×C22⋊Dic4712yes—
661C2×C4C2×C22⋊Dic4711yescharacteristic
662C2×C4C2×C22⋊Dic4711yescharacteristic
663C2×C4C2×C22⋊Dic4711yescharacteristic
664C2×C4C2×C22⋊Dic4712yes—
665C2×C4C2×C22⋊Dic4711yescharacteristic
666C2×C4C23×Dic4711yescharacteristic
667C2×C4C22×C22⋊D4711yescharacteristic
668C2×C4#41×D4711yescharacteristic
669C2×C4#41×D4711yescharacteristic
670C2×C4#1309407011yescharacteristic
671C2×C4#1309407111yescharacteristic
672C8—942no—
673C8—1882no—
674C8—1881no—
675C22—21no—
676C22—21no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—82no—
687C22—82no—
688C22C22×C22⋊Dic4711yescharacteristic
689C22#1568976111yescharacteristic
690C22#1568977211yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—22no—
695C4—22no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—42no—
700C4—41no—
701C4—3762no—
702C4—1882no—
703C4—1882no—
704C4#1568914012yes—
705C4#41×Dic4711yescharacteristic
706C4#1568960611yescharacteristic
707C4#1568976111yescharacteristic
708C4#1568977211yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—42no—
713C2—81no—
714C2#2024621811yescharacteristic
715C2C2×#1568914011yescharacteristic
716C2#2025193511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3475C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenter#3475D47
hypocenterC47#22507
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#10625329C2semidirect
2. #20245853C2semidirect
3. #20244366C2semidirect
4. #20244333C2semidirect
5. #20243837C2semidirect
6. #20243691C2semidirect
7. #20243487C2semidirect
8. #20243408C2semidirect
9. C4×#13093951C2semidirect
10. #20243097C2semidirect
36. C47×#556C4semidirect
37. C47×#555C4semidirect
38. C47×#554C4semidirect
39. C47×#553C4semidirect
41. C47×#552C4semidirect
43. C47×#547C4semidirect
236. C4×Dic47#41semidirect
243. #10625329#41semidirect
371. #556Dic47semidirect
372. #555Dic47semidirect
373. #554Dic47semidirect
374. #553Dic47semidirect
376. #552Dic47semidirect
378. #547Dic47semidirect
411. C47#22507semidirect

Maximal subgroups

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

subgroupindex
D4×#106253292
#202458532
#202443662
#202443332
#202438372
#202436912
#202434872
#202434082
C4×#130939512
#202430972
C47×#34752
#2250747