Finite Group Databasebeta

← #26183199

Subgroups — #26183199

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252355C211yesmaximal, characteristic, complemented
2#20252054C211yesmaximal, characteristic, complemented
3#20241861C211yesmaximal, characteristic, complemented
4#20241853C211yesmaximal, characteristic, complemented
5#20241848C211yesmaximal, characteristic, complemented
6#20241831C211yesmaximal, characteristic, complemented
7#20241827C211yesmaximal, characteristic, complemented
8#20241822C211yesmaximal, characteristic, complemented
9#20241809C211yesmaximal, characteristic, complemented
10#20241801C211yesmaximal, characteristic, complemented
11#20241796C211yesmaximal, characteristic, complemented
12#20241779C211yesmaximal, characteristic, complemented
13#20241775C211yesmaximal, characteristic, complemented
14#20241770C211yesmaximal, characteristic, complemented
15C47×#3475C211yesmaximal, characteristic
16#15689254—21no—
17#15689201—21no—
18#15689195—21no—
19#15689195—21no—
20#15689184—21no—
21#15689184—21no—
22#15689180C2211yescharacteristic
23#15689180C2211yescharacteristic, complemented
24#15689176C2211yescharacteristic
25#15689176C2211yescharacteristic
26#15689176C2211yescharacteristic, complemented
27#15689176C2211yescharacteristic, complemented
28#15689176C2211yescharacteristic, complemented
29#15689147C2211yescharacteristic, complemented
30C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
31#15689090—21no—
32#15689079—21no—
33C4×#10625329C2211yescharacteristic
34C4×#10625329C2211yescharacteristic, complemented
35C2×C4×C47⋊C8C2211yescharacteristic, complemented
36Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
37Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
38Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
39Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
40Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
41Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
42Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
43Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
44D4⋊(C47⋊C8)C2211yescharacteristic
45D4⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50D4⋊(C47⋊C8)C2211yescharacteristic
51D4⋊(C47⋊C8)C2211yescharacteristic
52C47×#556C411yescharacteristic
53C47×#555C411yescharacteristic
54C47×#554C411yescharacteristic
55C47×#553—21no—
56C47×#552—21no—
57C47×#552C411yescharacteristic
58C47×#552C411yescharacteristic
59C47×#551—21no—
60C47×#551—21no—
61C47×#547C411yescharacteristic
62C47×#546C411yescharacteristic
63C47×#546C411yescharacteristic
64C47×#533C2211yescharacteristic
65C47×#529—21no—
66C47×#529—21no—
67C47×#529C2211yescharacteristic
68C47×#529C2211yescharacteristic
69C47×#525—21no—
70C4×#41×C47C2211yescharacteristic
71C4×#41×C47C2211yescharacteristic
72C4×#41×C47C2211yescharacteristic
73C2×C4×D4×C47C2211yescharacteristic
74C2×#117×C47—21no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C4⋊(C47⋊C8)—21no—
81C4⋊(C47⋊C8)—21no—
82C4⋊(C47⋊C8)—21no—
83C4⋊(C47⋊C8)—21no—
84C4⋊(C47⋊C8)—21no—
85C4⋊(C47⋊C8)C2311yescharacteristic
86C4⋊(C47⋊C8)C2311yescharacteristic
87C4⋊(C47⋊C8)C2311yescharacteristic
88C4⋊(C47⋊C8)C2311yescharacteristic
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)—21no—
93C22⋊(C47⋊C8)—21no—
94C22⋊(C47⋊C8)—21no—
95C22⋊(C47⋊C8)—21no—
96#13093935—21no—
97#13093935—21no—
98#13093935—21no—
99#13093935—21no—
100C4×C47⋊C8—21no—
101C4×C47⋊C8—21no—
102C4×C47⋊C8—21no—
103C4×C47⋊C8C2311yescharacteristic
104C4×C47⋊C8C2311yescharacteristic
105C4×C47⋊C8C2311yescharacteristic
106C4×C47⋊C8C2311yescharacteristic
107C2×#41×C47C2×C411yescharacteristic
108C2×#41×C47C2×C411yescharacteristic
109C2×#41×C47D411yescharacteristic
110C22×D4×C47C2×C411yescharacteristic
111C23×C4×C47—21no—
112C4⋊Q8×C47C2×C411yescharacteristic
113C4⋊Q8×C47C2×C411yescharacteristic
114#126×C47—21no—
115#126×C47—21no—
116#126×C47—21no—
117#126×C47—21no—
118#126×C47—21no—
119#126×C47—21no—
120#125×C47—21no—
121#125×C47—21no—
122#125×C47—21no—
123#125×C47C2×C411yescharacteristic
124#125×C47C2×C411yescharacteristic
125#124×C47—21no—
126#124×C47—21no—
127#124×C47C2×C411yescharacteristic
128#124×C47C2×C411yescharacteristic
129#123×C47—21no—
130#123×C47—21no—
131#123×C47—21no—
132#123×C47—21no—
133#123×C47—21no—
134#123×C47—21no—
135#123×C47—21no—
136#123×C47—21no—
137C22⋊Q8×C47—21no—
138C22⋊Q8×C47—21no—
139C22⋊Q8×C47—21no—
140C22⋊Q8×C47—21no—
141C22⋊Q8×C47—21no—
142C22⋊Q8×C47C2×C411yescharacteristic
143C22⋊Q8×C47C2×C411yescharacteristic
144C22⋊Q8×C47C2×C411yescharacteristic
145C22⋊Q8×C47C2×C411yescharacteristic
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47—21no—
150#121×C47C2×C411yescharacteristic
151#121×C47C2×C411yescharacteristic
152#120×C47—21no—
153#120×C47—21no—
154C4×Q8×C47—21no—
155C4×Q8×C47C2×C411yescharacteristic
156C4×Q8×C47C2×C411yescharacteristic
157C4×Q8×C47C2×C411yescharacteristic
158C4×Q8×C47D411yescharacteristic
159C4×Q8×C47C2311yescharacteristic
160C4×Q8×C47C2311yescharacteristic
161C4×D4×C47—21no—
162C4×D4×C47—21no—
163C4×D4×C47—21no—
164C4×D4×C47—21no—
165C4×D4×C47—21no—
166C4×D4×C47—21no—
167C4×D4×C47—21no—
168C4×D4×C47—21no—
169C4×D4×C47C2×C411yescharacteristic
170C4×D4×C47C2×C411yescharacteristic
171C4×D4×C47C2×C411yescharacteristic
172C4×D4×C47C2×C411yescharacteristic
173C4×D4×C47C2×C411yescharacteristic
174C4×D4×C47C2×C411yescharacteristic
175C4×D4×C47C2×C411yescharacteristic
176C4×D4×C47D411yescharacteristic
177C4×D4×C47D411yescharacteristic
178C4×D4×C47D411yescharacteristic
179C4×D4×C47C2311yescharacteristic
180C4×D4×C47C2311yescharacteristic
181#117×C47—21no—
182#117×C47—21no—
183#117×C47—21no—
184#117×C47—21no—
185#117×C47—21no—
186#117×C47—21no—
187#117×C47—21no—
188#117×C47—21no—
189#117×C47—21no—
190#117×C47C2×C411yescharacteristic
191#117×C47C2×C411yescharacteristic
192#117×C47D411yescharacteristic
193#117×C47D411yescharacteristic
194#117×C47D411yescharacteristic
195C2×C4⋊C4×C47—21no—
196C2×C4⋊C4×C47—21no—
197C2×C4⋊C4×C47C2×C411yescharacteristic
198C2×C22⋊C4×C47—21no—
199C2×C22⋊C4×C47—21no—
200C2×C22⋊C4×C47—21no—
201C2×C42×C47—21no—
202C2×C42×C47—21no—
203C2×C42×C47C2311yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C24×C47—21no—
207#41×C47—22no—
208#41×C47—22no—
209#41×C47—41no—
210#41×C47—41no—
211#41×C47—41no—
212#41×C47—41no—
213C2×Q8×C47—21no—
214C2×Q8×C47C22⋊C411yescharacteristic
215C2×Q8×C47C22×C411yescharacteristic
216C2×Q8×C47C22×C411yescharacteristic
217C2×D4×C47—22no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—41no—
224C2×D4×C47C22⋊C411yescharacteristic
225C2×D4×C47C22⋊C411yescharacteristic
226C2×D4×C47C22⋊C411yescharacteristic
227C2×D4×C47C22×C411yescharacteristic
228C2×D4×C47C22×C411yescharacteristic
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—42no—
239C22×C4×C47—42no—
240C22×C4×C47C22×C411yescharacteristic
241C22×C4×C47C22×C411yescharacteristic
242C22×C4×C47C22×C411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47C22⋊C411yescharacteristic
266C4⋊C4×C47C22⋊C411yescharacteristic
267C4⋊C4×C47C22⋊C411yescharacteristic
268C4⋊C4×C47C22⋊C411yescharacteristic
269C4⋊C4×C47C22⋊C411yescharacteristic
270C4⋊C4×C47C22⋊C411yescharacteristic
271C4⋊C4×C47C22×C411yescharacteristic
272C4⋊C4×C47C22×C411yescharacteristic
273C4⋊C4×C47C22×C411yescharacteristic
274C4⋊C4×C47C22×C411yescharacteristic
275C22⋊C4×C47—21no—
276C22⋊C4×C47—21no—
277C22⋊C4×C47—21no—
278C22⋊C4×C47—21no—
279C22⋊C4×C47—21no—
280C22⋊C4×C47—21no—
281C22⋊C4×C47—21no—
282C22⋊C4×C47—21no—
283C22⋊C4×C47—21no—
284C22⋊C4×C47—21no—
285C22⋊C4×C47—21no—
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—21no—
292C22⋊C4×C47—21no—
293C22⋊C4×C47C22⋊C411yescharacteristic
294C22⋊C4×C47C22⋊C411yescharacteristic
295C22⋊C4×C47C22⋊C411yescharacteristic
296C22⋊C4×C47C22⋊C411yescharacteristic
297C22⋊C4×C47C22⋊C411yescharacteristic
298C22⋊C4×C47C22⋊C411yescharacteristic
299C42×C47—21no—
300C42×C47—21no—
301C42×C47—21no—
302C42×C47—21no—
303C42×C47—21no—
304C42×C47—21no—
305C42×C47C22×C411yescharacteristic
306C42×C47C22×C411yescharacteristic
307C42×C47C22×C411yescharacteristic
308C42×C47C2×D411yescharacteristic
309C42×C47C2×D411yescharacteristic
310C42×C47C2×D411yescharacteristic
311C42×C47C2×D411yescharacteristic
312C42×C47C2×D411yescharacteristic
313C42×C47C2×D411yescharacteristic
314C42×C47C2411yescharacteristic
315#10625329—42no—
316#10625329—42no—
317#10625329—42no—
318C2×C47⋊C8—21no—
319C2×C47⋊C8—21no—
320C2×C47⋊C8—21no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—21no—
326C2×C47⋊C8—42no—
327C2×C47⋊C8—42no—
328C23×C47—21no—
329C23×C47—21no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47—81no—
333C23×C47C2×C22⋊C411yescharacteristic
334C23×C47C2×C22⋊C411yescharacteristic
335C23×C47C2×C22⋊C411yescharacteristic
336Q8×C47—21no—
337Q8×C47—21no—
338Q8×C47—21no—
339Q8×C47—21no—
340Q8×C47—41no—
341Q8×C47—81no—
342D4×C47—21no—
343D4×C47—21no—
344D4×C47—21no—
345D4×C47—41no—
346D4×C47—41no—
347D4×C47—41no—
348D4×C47—42no—
349D4×C47—42no—
350D4×C47—42no—
351D4×C47—81no—
352D4×C47—81no—
353D4×C47#13112yes—
354C2×C4×C47—21no—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—21no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—42no—
376C2×C4×C47—42no—
377C2×C4×C47—42no—
378C2×C4×C47—42no—
379C2×C4×C47—42no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—81no—
385C2×C4×C47—81no—
386C2×C4×C47C2×C22⋊C411yescharacteristic
387C2×C4×C47C2×C22⋊C411yescharacteristic
388C2×C4×C47C2×C22⋊C411yescharacteristic
389C2×C4×C47C2×C22⋊C411yescharacteristic
390C2×C4×C47C2×C22⋊C411yescharacteristic
391C2×C4×C47C2×C22⋊C411yescharacteristic
392C2×C4×C47C2×C22⋊C411yescharacteristic
393C2×C4×C47C2×C22⋊C411yescharacteristic
394C2×C4×C47C2×C22⋊C411yescharacteristic
395C2×C4×C47C23×C411yescharacteristic
396C2×C4×C47C22×D411yescharacteristic
397C2×C4×C47C22×D411yescharacteristic
398C47⋊C8—22no—
399C47⋊C8—41no—
400C47⋊C8—41no—
401C47⋊C8—41no—
402C47⋊C8—41no—
403C47⋊C8—41no—
404C47⋊C8—41no—
405C47⋊C8—41no—
406#17513—471nomaximal, Sylow
407C22×C47—21no—
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—22no—
411C22×C47—21no—
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—21no—
416C22×C47—21no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—41no—
422C22×C47—84no—
423C22×C47C22×C22⋊C411yescharacteristic
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47—21no—
432C4×C47—21no—
433C4×C47—21no—
434C4×C47—41no—
435C4×C47—41no—
436C4×C47—41no—
437C4×C47—41no—
438C4×C47—41no—
439C4×C47—41no—
440C4×C47C2×#13111yescharacteristic
441C4×C47#56811yescharacteristic
442C4×C47#57511yescharacteristic
443C4×C47#57511yescharacteristic
444#3475D4711yescharacteristic
445#2965—471no—
446#2925—471no—
447#1497—471no—
448#1495—471no—
449#1494—471no—
450#1490—471no—
451#1489—471no—
452#1488—471no—
453#1485—471no—
454#1483—471no—
455#1482—471no—
456#1478—471no—
457#1477—471no—
458#1476—471no—
459C2×C47—41no—
460C2×C47—41no—
461C2×C47—41no—
462C2×C47—42no—
463C2×C47—81no—
464C2×C47#288011yescharacteristic
465C2×C47#289611yescharacteristic
466C2×C47#290111yescharacteristic
467#556Dic4711yescharacteristic
468#555Dic4711yescharacteristic
469#554Dic4711yescharacteristic
470#553—21no—
471#552—21no—
472#552Dic4711yescharacteristic
473#552Dic4711yescharacteristic
474#551—21no—
475#551—21no—
476#547Dic4711yescharacteristic
477#546Dic4711yescharacteristic
478#546Dic4711yescharacteristic
479#533C2×D4711yescharacteristic
480#529—21no—
481#529—21no—
482#529C2×D4711yescharacteristic
483#529C2×D4711yescharacteristic
484#525—21no—
485C4×#41C2×D4711yescharacteristic
486C4×#41C2×D4711yescharacteristic
487C4×#41C2×D4711yescharacteristic
488C2×C4×D4C2×D4711yescharacteristic
489C2×#117—21no—
490#446—941no—
491#436—941no—
492#435—941no—
493#435—941no—
494#433—941no—
495#433—941no—
496#432—471no—
497#432—471no—
498#431—471no—
499#431—471no—
500#431—471no—
501#431—471no—
502#431—471no—
503#423—471no—
504C2×C4⋊C8—471no—
505#408—941no—
506#405—941no—
507C4×M16—471no—
508C4×M16—471no—
509C2×C4×C8—471no—
510Q8⋊C8—471no—
511Q8⋊C8—471no—
512Q8⋊C8—471no—
513Q8⋊C8—471no—
514Q8⋊C8—471no—
515Q8⋊C8—471no—
516Q8⋊C8—471no—
517Q8⋊C8—471no—
518D4⋊C8—471no—
519D4⋊C8—471no—
520D4⋊C8—471no—
521D4⋊C8—471no—
522D4⋊C8—471no—
523D4⋊C8—471no—
524D4⋊C8—471no—
525D4⋊C8—471no—
526C47#1751311yescharacteristic, complemented, Sylow
527C2×#41C2×Dic4711yescharacteristic
528C2×#41C2×Dic4711yescharacteristic
529C2×#41C22⋊D4711yescharacteristic
530C22×D4C2×Dic4711yescharacteristic
531C23×C4—21no—
532C2×M16—941no—
533C2×M16—941no—
534C2×M16—941no—
535C22×C8—941no—
536C22×C8—941no—
537C4⋊Q8C2×Dic4711yescharacteristic
538C4⋊Q8C2×Dic4711yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125C2×Dic4711yescharacteristic
549#125C2×Dic4711yescharacteristic
550#124—21no—
551#124—21no—
552#124C2×Dic4711yescharacteristic
553#124C2×Dic4711yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C2×Dic4711yescharacteristic
568C22⋊Q8C2×Dic4711yescharacteristic
569C22⋊Q8C2×Dic4711yescharacteristic
570C22⋊Q8C2×Dic4711yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121C2×Dic4711yescharacteristic
576#121C2×Dic4711yescharacteristic
577#120—21no—
578#120—21no—
579C4×Q8—21no—
580C4×Q8C2×Dic4711yescharacteristic
581C4×Q8C2×Dic4711yescharacteristic
582C4×Q8C2×Dic4711yescharacteristic
583C4×Q8C22⋊D4711yescharacteristic
584C4×Q8C22×D4711yescharacteristic
585C4×Q8C22×D4711yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×Dic4711yescharacteristic
595C4×D4C2×Dic4711yescharacteristic
596C4×D4C2×Dic4711yescharacteristic
597C4×D4C2×Dic4711yescharacteristic
598C4×D4C2×Dic4711yescharacteristic
599C4×D4C2×Dic4711yescharacteristic
600C4×D4C2×Dic4711yescharacteristic
601C4×D4C22⋊D4711yescharacteristic
602C4×D4C22⋊D4711yescharacteristic
603C4×D4C22⋊D4711yescharacteristic
604C4×D4C22×D4711yescharacteristic
605C4×D4C22×D4711yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C2×Dic4711yescharacteristic
616#117C2×Dic4711yescharacteristic
617#117C22⋊D4711yescharacteristic
618#117C22⋊D4711yescharacteristic
619#117C22⋊D4711yescharacteristic
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×Dic4711yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C22×D4711yescharacteristic
629C2×C42C22×D4711yescharacteristic
630C2×C42C22×D4711yescharacteristic
631C4⋊C8—471no—
632C4⋊C8—471no—
633C4⋊C8—471no—
634C4⋊C8—471no—
635C4⋊C8—941no—
636C4⋊C8—941no—
637C4⋊C8—941no—
638C4⋊C8—941no—
639C4⋊C8—941no—
640C22⋊C8—941no—
641C22⋊C8—941no—
642C22⋊C8—941no—
643C22⋊C8—941no—
644C22⋊C8—941no—
645C22⋊C8—941no—
646C22⋊C8—941no—
647#97—941no—
648#97—941no—
649#97—941no—
650#97—941no—
651C4×C8—471no—
652C4×C8—471no—
653C4×C8—471no—
654C4×C8—471no—
655C4×C8—941no—
656C4×C8—941no—
657C4×C8—941no—
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊Dic4711yescharacteristic
667C2×Q8C22×Dic4711yescharacteristic
668C2×Q8C22×Dic4711yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊Dic4711yescharacteristic
677C2×D4C22⋊Dic4711yescharacteristic
678C2×D4C22⋊Dic4711yescharacteristic
679C2×D4C22×Dic4711yescharacteristic
680C2×D4C22×Dic4711yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×Dic4711yescharacteristic
693C22×C4C22×Dic4711yescharacteristic
694C22×C4C22×Dic4711yescharacteristic
695C22×C4C2×C22⋊D4711yescharacteristic
696C22×C4C2×C22⋊D4711yescharacteristic
697C22×C4C2×C22⋊D4711yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701M16—1882no—
702M16—1882no—
703M16—1882no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—941no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—1882no—
713C2×C8—1882no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊Dic4711yescharacteristic
731C4⋊C4C22⋊Dic4711yescharacteristic
732C4⋊C4C22⋊Dic4711yescharacteristic
733C4⋊C4C22⋊Dic4711yescharacteristic
734C4⋊C4C22⋊Dic4711yescharacteristic
735C4⋊C4C22⋊Dic4711yescharacteristic
736C4⋊C4C22×Dic4711yescharacteristic
737C4⋊C4C22×Dic4711yescharacteristic
738C4⋊C4C22×Dic4711yescharacteristic
739C4⋊C4C22×Dic4711yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4C22⋊Dic4711yescharacteristic
759C22⋊C4C22⋊Dic4711yescharacteristic
760C22⋊C4C22⋊Dic4711yescharacteristic
761C22⋊C4C22⋊Dic4711yescharacteristic
762C22⋊C4C22⋊Dic4711yescharacteristic
763C22⋊C4C22⋊Dic4711yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×Dic4711yescharacteristic
771C42C22×Dic4711yescharacteristic
772C42C22×Dic4711yescharacteristic
773C42C2×C22⋊D4711yescharacteristic
774C42C2×C22⋊D4711yescharacteristic
775C42C2×C22⋊D4711yescharacteristic
776C42C2×C22⋊D4711yescharacteristic
777C42C2×C22⋊D4711yescharacteristic
778C42C2×C22⋊D4711yescharacteristic
779C42C23×D4711yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊Dic4711yescharacteristic
786C23C2×C22⋊Dic4711yescharacteristic
787C23C2×C22⋊Dic4711yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4#1309403112yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊Dic4711yescharacteristic
839C2×C4C2×C22⋊Dic4711yescharacteristic
840C2×C4C2×C22⋊Dic4711yescharacteristic
841C2×C4C2×C22⋊Dic4711yescharacteristic
842C2×C4C2×C22⋊Dic4711yescharacteristic
843C2×C4C2×C22⋊Dic4711yescharacteristic
844C2×C4C2×C22⋊Dic4711yescharacteristic
845C2×C4C2×C22⋊Dic4711yescharacteristic
846C2×C4C2×C22⋊Dic4711yescharacteristic
847C2×C4C23×Dic4711yescharacteristic
848C2×C4C22×C22⋊D4711yescharacteristic
849C2×C4C22×C22⋊D4711yescharacteristic
850C8—942no—
851C8—1881no—
852C8—1881no—
853C8—1881no—
854C8—1881no—
855C8—1881no—
856C8—1881no—
857C8—1881no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—22no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊Dic4711yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×#1309403111yescharacteristic
892C4#1568989011yescharacteristic
893C4#1568992111yescharacteristic
894C4#1568992111yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2#2025183711yescharacteristic
901C2#2025190711yescharacteristic
902C2#2025193511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
Fitting, prime radicalC47×#3475C2
socleC22×C47C22×C22⋊C4
cosocleC42×C47C24
hypercenter#3475D47
hypocenterC47#17513
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #20252355C2semidirect
2. #20252054C2semidirect
3. #20241861C2semidirect
4. #20241853C2semidirect
5. #20241848C2semidirect
6. #20241831C2semidirect
7. #20241827C2semidirect
8. #20241822C2semidirect
9. #20241809C2semidirect
10. #20241801C2semidirect
11. #20241796C2semidirect
12. #20241779C2semidirect
13. #20241775C2semidirect
14. #20241770C2semidirect
23. #15689180C22semidirect
26. #15689176C22semidirect
27. #15689176C22semidirect
28. #15689176C22semidirect
29. #15689147C22semidirect
30. C2×C4⋊(C47⋊C8)C22semidirect
34. C4×#10625329C22semidirect
35. C2×C4×C47⋊C8C22semidirect
36. Q8⋊(C47⋊C8)C22semidirect
37. Q8⋊(C47⋊C8)C22semidirect
38. Q8⋊(C47⋊C8)C22semidirect
39. Q8⋊(C47⋊C8)C22semidirect
40. Q8⋊(C47⋊C8)C22semidirect
41. Q8⋊(C47⋊C8)C22semidirect
42. Q8⋊(C47⋊C8)C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
526. C47#17513semidirect

Maximal subgroups

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

subgroupindex
#202523552
#202520542
#202418612
#202418532
#202418482
#202418312
#202418272
#202418222
#202418092
#202418012
#202417962
#202417792
#202417752
#202417702
C47×#34752
#1751347