Finite Group Databasebeta

← #26232760

Subgroups — #26232760

Order 12032.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#10625329C211yesmaximal, characteristic, complemented
2C4×D4×Dic47C211yesmaximal, characteristic, complemented
3#20244366C211yesmaximal, characteristic, complemented
4#20244333C211yesmaximal, characteristic, complemented
5#20243832C212yesmaximal, complemented
6#20243691C212yesmaximal, complemented
7#20243487C212yesmaximal, complemented
8#20243408C211yesmaximal, characteristic, complemented
9C4×#13093951C211yesmaximal, characteristic, complemented
10C2×#15688882C212yesmaximal, complemented
11C47×#3475C211yesmaximal, characteristic
12C22×#10625329C2212yes—
13C2×D4×Dic47—21no—
14C22×C4×Dic47C2212yes—
15#15689201—21no—
16#15689195—22no—
17D4×C47⋊C8—21no—
18#15689147C2211yescharacteristic
19C2×#13093951C2211yescharacteristic
20C2×#13093951C2211yescharacteristic
21C2×#13093951C2212yes—
22#15689087C2212yes—
23C4×#10625329C2211yescharacteristic
24C4⋊C4×Dic47—21no—
25C4×C4⋊Dic47C2211yescharacteristic
26C22⋊C4×Dic47—22no—
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—
53C23×Dic47—22no—
54C2×#10625329—22no—
55C2×#10625329—24no—
56C2×#10625329—42no—
57C2×#10625329C2311yescharacteristic
58C2×#10625329C2312yes—
59C2×#10625329C2311yescharacteristic
60C22×C47⋊C8—22no—
61D4×Dic47—28no—
62C2×C4⋊Dic47—21no—
63C2×C22⋊Dic47—22no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—42no—
69C2×C4×Dic47C2311yescharacteristic
70C2×C4×Dic47C2312yes—
71C2×C4×Dic47C2311yescharacteristic
72C4⋊(C47⋊C8)—21no—
73C4⋊(C47⋊C8)—21no—
74#13093951—22no—
75#13093951—22no—
76#13093951—42no—
77C22⋊(C47⋊C8)—22no—
78C22⋊(C47⋊C8)—22no—
79#13093935—21no—
80C4×C47⋊C8—21no—
81C47⋊#95—22no—
82C47⋊#95—21no—
83C2×#41×C47—21no—
84C2×#41×C47C2311yescharacteristic
85C22×D4×C47D411yescharacteristic
86C23×C4×C47C2312yes—
87C4⋊Q8×C47C2×C411yescharacteristic, complemented
88C4⋊Q8×C47C2×C411yescharacteristic, complemented
89#126×C47—22no—
90#126×C47—22no—
91#126×C47—22no—
92#125×C47—22no—
93#125×C47—21no—
94#125×C47C2×C412yescomplemented
95#124×C47—21no—
96#124×C47—22no—
97#123×C47—22no—
98#123×C47—22no—
99#123×C47—22no—
100#123×C47—22no—
101C22⋊Q8×C47—21no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47C2×C412yescomplemented
106C22⋊Q8×C47C2×C412yescomplemented
107#121×C47—22no—
108#121×C47—21no—
109#121×C47C2×C412yescomplemented
110#121×C47C2×C412yescomplemented
111#120×C47—22no—
112C4×Q8×C47—21no—
113C4×Q8×C47—21no—
114C4×Q8×C47—21no—
115C4×Q8×C47C2×C411yescharacteristic, complemented
116C4×Q8×C47C2×C411yescharacteristic, complemented
117C4×D4×C47—21no—
118C4×D4×C47—22no—
119C4×D4×C47—21no—
120C4×D4×C47—21no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123C4×D4×C47C2×C411yescharacteristic
124C4×D4×C47C2×C412yes—
125C4×D4×C47C2×C411yescharacteristic
126C4×D4×C47C2×C411yescharacteristic, complemented
127C4×D4×C47C2×C411yescharacteristic, complemented
128C4×D4×C47D411yescharacteristic
129C4×D4×C47D412yes—
130C4×D4×C47D411yescharacteristic
131#117×C47—22no—
132#117×C47—22no—
133#117×C47—21no—
134#117×C47—22no—
135#117×C47—21no—
136#117×C47C2×C412yescomplemented
137#117×C47C2×C412yescomplemented
138#117×C47C2311yescharacteristic
139#117×C47C2312yes—
140C2×C4⋊C4×C47C2×C412yescomplemented
141C2×C4⋊C4×C47C2×C412yescomplemented
142C2×C4⋊C4×C47D411yescharacteristic
143C2×C22⋊C4×C47—22no—
144C2×C22⋊C4×C47D412yes—
145C2×C42×C47—22no—
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148C24×C47C2×D412yes—
149#41×C47—21no—
150#41×C47—21no—
151#41×C47—21no—
152#41×C47—21no—
153#41×C47—44no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47C22×C411yescharacteristic
157C2×D4×C47—24no—
158C2×D4×C47—22no—
159C2×D4×C47—21no—
160C2×D4×C47—22no—
161C2×D4×C47C22⋊C412yes—
162C2×D4×C47C22⋊C411yescharacteristic
163C2×D4×C47C22⋊C411yescharacteristic
164C2×D4×C47C22×C411yescharacteristic
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47C22×C412yes—
175C22×C4×C47C22×C412yes—
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D412yes—
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D412yes—
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2411yescharacteristic
182C22×Dic47—21no—
183C22×Dic47—28no—
184C22×Dic47—21no—
185C22×Dic47—22no—
186C22×Dic47—44no—
187C22×Dic47—44no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—22no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47C22⋊C411yescharacteristic
199C4⋊C4×C47C22⋊C411yescharacteristic
200C4⋊C4×C47C22⋊C412yes—
201C4⋊C4×C47C22×C411yescharacteristic
202C4⋊C4×C47C22×C411yescharacteristic
203C4⋊C4×C47C22×C412yes—
204C4⋊C4×C47C22×C412yes—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—21no—
213C22⋊C4×C47—21no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47C22⋊C412yes—
216C22⋊C4×C47C22⋊C412yes—
217C22⋊C4×C47C22⋊C412yes—
218C22⋊C4×C47C22⋊C412yes—
219C42×C47—22no—
220C42×C47—21no—
221C42×C47—22no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—22no—
225C42×C47C22×C411yescharacteristic
226C42×C47C22×C411yescharacteristic
227C42×C47C2×D411yescharacteristic
228C42×C47C2×D411yescharacteristic
229C22⋊Dic47—28no—
230C4⋊Dic47—24no—
231C4×Dic47—24no—
232C4×Dic47—21no—
233C4×Dic47—21no—
234C4×Dic47—22no—
235C4×Dic47—22no—
236C4×Dic47—21no—
237C4×Dic47—44no—
238C4×Dic47—42no—
239C4×Dic47#4112yescomplemented
240#10625329—21no—
241#10625329—21no—
242#10625329—22no—
243#10625329—22no—
244#10625329—21no—
245#10625329—44no—
246#10625329#4112yescomplemented
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—22no—
250C2×C47⋊C8—44no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—24no—
254C23×C47—21no—
255C23×C47—42no—
256C23×C47C2×C22⋊C412yes—
257C23×C47C2×C22⋊C412yes—
258C23×C47C22×D411yescharacteristic
259Q8×C47—21no—
260Q8×C47—21no—
261Q8×C47—42no—
262Q8×C47—81no—
263D4×C47—24no—
264D4×C47—21no—
265D4×C47—21no—
266D4×C47—22no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—44no—
270D4×C47—82no—
271D4×C47#10414yescomplemented
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—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—41no—
289C2×C4×C47—44no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—42no—
293C2×C4×C47—81no—
294C2×C4×C47—82no—
295C2×C4×C47C2×C22⋊C412yes—
296C2×C4×C47C2×C22⋊C411yescharacteristic
297C2×C4×C47C2×C22⋊C411yescharacteristic
298C2×C4×C47C2×C22⋊C411yescharacteristic
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C2×C22⋊C411yescharacteristic
301C2×C4×C47C23×C411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C2×C4×C472−1+411yescharacteristic
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—416no—
313C2×Dic47—41no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—41no—
317C47⋊C8—22no—
318C47⋊C8—42no—
319C47⋊C8—41no—
320#22505—471nomaximal, Sylow
321C22×C47—22no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—44no—
329C22×C47—44no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47C2×#10414yes—
334C22×C47C22×C22⋊C411yescharacteristic
335C22×C47#54611yescharacteristic
336C22×C47#54711yescharacteristic
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—21no—
340C4×C47—21no—
341C4×C47—21no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—42no—
345C4×C47—41no—
346C4×C47—42no—
347C4×C47C2×#10412yes—
348C4×C47C4×#4111yescharacteristic
349C4×C47#52011yescharacteristic
350C4×C47#54611yescharacteristic
351C4×C47#54711yescharacteristic
352Dic47—24no—
353Dic47—42no—
354Dic47—44no—
355#3475D4711yescharacteristic
356D4×M16—471no—
357C42×D4—471no—
358#1994—471no—
359#1986—471no—
360#1896—472no—
361#1871—472no—
362#1826—472no—
363#1806—471no—
364C4×#104—471no—
365C2×#339—472no—
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—24no—
369C2×C47—42no—
370C2×C47—81no—
371C2×C47#233911yescharacteristic
372C2×C47C22×#10411yescharacteristic
373C2×C47#290111yescharacteristic
374C22×M16—472no—
375#556Dic4711yescharacteristic, complemented
376#555Dic4711yescharacteristic, complemented
377#554Dic4711yescharacteristic, complemented
378#553Dic4712yescomplemented
379#552—21no—
380#552Dic4712yescomplemented
381#551—22no—
382#547Dic4711yescharacteristic, complemented
383#546—21no—
384#533C2×D4711yescharacteristic
385#529—22no—
386#529—21no—
387#525C2×D4712yes—
388C4×#41—21no—
389C4×#41C2×D4711yescharacteristic
390C2×C4×D4—941no—
391C2×C4×D4C2×D4711yescharacteristic
392C2×#117C2×D4712yes—
393C22×C42—472no—
394#436—941no—
395#435—942no—
396C8×D4—941no—
397#423—471no—
398C2×#104—471no—
399C2×#104—471no—
400C2×#104—472no—
401#407—472no—
402C4×M16—471no—
403C4×C4⋊C4—471no—
404C4×C4⋊C4—941no—
405C4×C22⋊C4—472no—
406C4×C22⋊C4—942no—
407C43—471no—
408#339—472no—
409#339—471no—
410#339—472no—
411#339—472no—
412#339—472no—
413#339—472no—
414#339—471no—
415C47#2250511yescharacteristic, complemented, Sylow
416C2×#41—21no—
417C2×#41C22×D4711yescharacteristic
418C22×D4C22⋊D4711yescharacteristic
419C23×C4—942no—
420C23×C4C22×D4712yes—
421C2×M16—471no—
422C2×M16—472no—
423C2×M16—471no—
424C2×M16—942no—
425C2×M16—944no—
426C2×M16—1882no—
427C22×C8—942no—
428C4⋊Q8C2×Dic4711yescharacteristic, complemented
429C4⋊Q8C2×Dic4711yescharacteristic, complemented
430#126—22no—
431#126—22no—
432#126—22no—
433#125—22no—
434#125—21no—
435#125C2×Dic4712yescomplemented
436#124—21no—
437#124—22no—
438#123—22no—
439#123—22no—
440#123—22no—
441#123—22no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—22no—
446C22⋊Q8C2×Dic4712yescomplemented
447C22⋊Q8C2×Dic4712yescomplemented
448#121—22no—
449#121—21no—
450#121C2×Dic4712yescomplemented
451#121C2×Dic4712yescomplemented
452#120—22no—
453C4×Q8—21no—
454C4×Q8—21no—
455C4×Q8—21no—
456C4×Q8C2×Dic4711yescharacteristic, complemented
457C4×Q8C2×Dic4711yescharacteristic, complemented
458C4×D4—21no—
459C4×D4—22no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—948no—
465C4×D4C2×Dic4711yescharacteristic
466C4×D4C2×Dic4712yes—
467C4×D4C2×Dic4711yescharacteristic
468C4×D4C2×Dic4711yescharacteristic, complemented
469C4×D4C2×Dic4711yescharacteristic, complemented
470C4×D4C22⋊D4711yescharacteristic
471C4×D4C22⋊D4712yes—
472C4×D4C22⋊D4711yescharacteristic
473#117—22no—
474#117—22no—
475#117—21no—
476#117—22no—
477#117—21no—
478#117C2×Dic4712yescomplemented
479#117C2×Dic4712yescomplemented
480#117C22×D4711yescharacteristic
481#117C22×D4712yes—
482C2×C4⋊C4—941no—
483C2×C4⋊C4C2×Dic4712yescomplemented
484C2×C4⋊C4C2×Dic4712yescomplemented
485C2×C4⋊C4C22⋊D4711yescharacteristic
486C2×C22⋊C4—22no—
487C2×C22⋊C4—942no—
488C2×C22⋊C4C22⋊D4712yes—
489C2×C42—22no—
490C2×C42—21no—
491C2×C42—471no—
492C2×C42—471no—
493C2×C42—472no—
494C2×C42—944no—
495C2×C42—941no—
496C2×C42—941no—
497C2×C42—942no—
498C2×C42—1882no—
499C2×C42C22×D4711yescharacteristic
500C4⋊C8—941no—
501C4⋊C8—941no—
502#104—942no—
503#104—942no—
504#104—1882no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507#97—941no—
508C4×C8—941no—
509#95—942no—
510#95—941no—
511C24C2×C22⋊D4712yes—
512#41—21no—
513#41—21no—
514#41—21no—
515#41—21no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8C22×Dic4711yescharacteristic
520C2×D4—24no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—22no—
524C2×D4C22⋊Dic4712yes—
525C2×D4C22⋊Dic4711yescharacteristic
526C2×D4C22⋊Dic4711yescharacteristic
527C2×D4C22×Dic4711yescharacteristic
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—941no—
538C22×C4—948no—
539C22×C4—941no—
540C22×C4—942no—
541C22×C4—1884no—
542C22×C4—1884no—
543C22×C4C22×Dic4712yes—
544C22×C4C22×Dic4712yes—
545C22×C4C2×C22⋊D4712yes—
546C22×C4C2×C22⋊D4711yescharacteristic
547C22×C4C2×C22⋊D4712yes—
548C22×C4C2×C22⋊D4712yes—
549C22×C4C2×C22⋊D4711yescharacteristic
550C22×C4C23×D4711yescharacteristic
551M16—472no—
552M16—941no—
553M16—941no—
554M16—942no—
555M16—942no—
556M16—941no—
557M16—1884no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—942no—
561C2×C8—1884no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—944no—
573C4⋊C4C22⋊Dic4711yescharacteristic
574C4⋊C4C22⋊Dic4711yescharacteristic
575C4⋊C4C22⋊Dic4712yes—
576C4⋊C4C22×Dic4711yescharacteristic
577C4⋊C4C22×Dic4711yescharacteristic
578C4⋊C4C22×Dic4712yes—
579C4⋊C4C22×Dic4712yes—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—21no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—22no—
590C22⋊C4—948no—
591C22⋊C4C22⋊Dic4712yes—
592C22⋊C4C22⋊Dic4712yes—
593C22⋊C4C22⋊Dic4712yes—
594C22⋊C4C22⋊Dic4712yes—
595C42—22no—
596C42—21no—
597C42—22no—
598C42—21no—
599C42—21no—
600C42—22no—
601C42—472no—
602C42—944no—
603C42—941no—
604C42—941no—
605C42—942no—
606C42—942no—
607C42—941no—
608C42—1884no—
609C42—1882no—
610C42C22×Dic4711yescharacteristic
611C42C22×Dic4711yescharacteristic
612C42C2×C22⋊D4711yescharacteristic
613C42C2×C22⋊D4711yescharacteristic
614C23—22no—
615C23—22no—
616C23—24no—
617C23—21no—
618C23—42no—
619C23C2×C22⋊Dic4712yes—
620C23C2×C22⋊Dic4712yes—
621C23C22×C22⋊D4711yescharacteristic
622Q8—21no—
623Q8—21no—
624Q8—42no—
625Q8—81no—
626D4—24no—
627D4—21no—
628D4—21no—
629D4—22no—
630D4—41no—
631D4—41no—
632D4—44no—
633D4—82no—
634D4#1309395114yescomplemented
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—44no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—81no—
657C2×C4—82no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—944no—
663C2×C4—18816no—
664C2×C4—1881no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1881no—
668C2×C4C2×C22⋊Dic4712yes—
669C2×C4C2×C22⋊Dic4711yescharacteristic
670C2×C4C2×C22⋊Dic4711yescharacteristic
671C2×C4C2×C22⋊Dic4711yescharacteristic
672C2×C4C2×C22⋊Dic4712yes—
673C2×C4C2×C22⋊Dic4711yescharacteristic
674C2×C4C23×Dic4711yescharacteristic
675C2×C4C22×C22⋊D4711yescharacteristic
676C2×C4#41×D4711yescharacteristic
677C2×C4#41×D4711yescharacteristic
678C2×C4#1309407011yescharacteristic
679C2×C4#1309407111yescharacteristic
680C8—942no—
681C8—1882no—
682C8—1881no—
683C22—21no—
684C22—21no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—44no—
691C22—44no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22C2×#1309395114yes—
696C22C22×C22⋊Dic4711yescharacteristic
697C22#1568976111yescharacteristic
698C22#1568977211yescharacteristic
699C4—21no—
700C4—21no—
701C4—21no—
702C4—22no—
703C4—22no—
704C4—41no—
705C4—42no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—944no—
710C4—1884no—
711C4—1882no—
712C4C2×#1309395112yes—
713C4#41×Dic4711yescharacteristic
714C4#1568960611yescharacteristic
715C4#1568976111yescharacteristic
716C4#1568977211yescharacteristic
717C2—21no—
718C2—21no—
719C2—24no—
720C2—42no—
721C2—81no—
722C2#2024621811yescharacteristic
723C2C22×#1309395111yescharacteristic
724C2#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#22505
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. C4×D4×Dic47C2semidirect
3. #20244366C2semidirect
4. #20244333C2semidirect
5. #20243832C2semidirect
6. #20243691C2semidirect
7. #20243487C2semidirect
8. #20243408C2semidirect
9. C4×#13093951C2semidirect
10. C2×#15688882C2semidirect
36. C47×#556C4semidirect
37. C47×#555C4semidirect
38. C47×#554C4semidirect
39. C47×#553C4semidirect
41. C47×#552C4semidirect
43. C47×#547C4semidirect
87. C4⋊Q8×C47C2×C4semidirect
88. C4⋊Q8×C47C2×C4semidirect
94. #125×C47C2×C4semidirect
105. C22⋊Q8×C47C2×C4semidirect
106. C22⋊Q8×C47C2×C4semidirect
109. #121×C47C2×C4semidirect
110. #121×C47C2×C4semidirect
115. C4×Q8×C47C2×C4semidirect
116. C4×Q8×C47C2×C4semidirect
126. C4×D4×C47C2×C4semidirect
127. C4×D4×C47C2×C4semidirect
136. #117×C47C2×C4semidirect
137. #117×C47C2×C4semidirect
140. C2×C4⋊C4×C47C2×C4semidirect
141. C2×C4⋊C4×C47C2×C4semidirect
239. C4×Dic47#41semidirect
246. #10625329#41semidirect
271. D4×C47#104semidirect
375. #556Dic47semidirect
376. #555Dic47semidirect
377. #554Dic47semidirect
378. #553Dic47semidirect
380. #552Dic47semidirect
382. #547Dic47semidirect
415. C47#22505semidirect
428. C4⋊Q8C2×Dic47semidirect
429. C4⋊Q8C2×Dic47semidirect
435. #125C2×Dic47semidirect
446. C22⋊Q8C2×Dic47semidirect
447. C22⋊Q8C2×Dic47semidirect
450. #121C2×Dic47semidirect
451. #121C2×Dic47semidirect
456. C4×Q8C2×Dic47semidirect
457. C4×Q8C2×Dic47semidirect
468. C4×D4C2×Dic47semidirect
469. C4×D4C2×Dic47semidirect
478. #117C2×Dic47semidirect
479. #117C2×Dic47semidirect
483. C2×C4⋊C4C2×Dic47semidirect
484. C2×C4⋊C4C2×Dic47semidirect
634. D4#13093951semidirect

Maximal subgroups

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

subgroupindex
D4×#106253292
C4×D4×Dic472
#202443662
#202443332
#202438322
#202436912
#202434872
#202434082
C4×#130939512
C2×#156888822
C47×#34752
#2250547