Finite Group Databasebeta

← #26183324

Subgroups — #26183324

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252513C211yesmaximal, characteristic, complemented
2#20252032C211yesmaximal, characteristic, complemented
3#20241861C211yesmaximal, characteristic, complemented
4#20241853C211yesmaximal, characteristic, complemented
5#20241848C211yesmaximal, characteristic, complemented
6#20241835C211yesmaximal, characteristic, complemented
7#20241822C211yesmaximal, characteristic, complemented
8#20241817C211yesmaximal, characteristic, complemented
9#20241801C211yesmaximal, characteristic, complemented
10#20241796C211yesmaximal, characteristic, complemented
11#20241791C211yesmaximal, characteristic, complemented
12#20241783C211yesmaximal, characteristic, complemented
13#20241775C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C47×#3482C211yesmaximal, characteristic
16#15689254—21no—
17#15689195—21no—
18#15689195—21no—
19D4×C47⋊C8—21no—
20#15689184—21no—
21#15689184—21no—
22#15689180C2211yescharacteristic
23#15689180C2211yescharacteristic
24#15689176C2211yescharacteristic
25#15689176C2211yescharacteristic
26#15689176C2211yescharacteristic
27#15689176C2211yescharacteristic
28#15689176C2211yescharacteristic
29#15689150—21no—
30#15689147C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×C4⋊(C47⋊C8)C2211yescharacteristic
33#15689090—21no—
34C4×#10625329C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36Q8⋊(C47⋊C8)C2211yescharacteristic
37Q8⋊(C47⋊C8)C2211yescharacteristic
38Q8⋊(C47⋊C8)C2211yescharacteristic
39Q8⋊(C47⋊C8)C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42Q8⋊(C47⋊C8)C2211yescharacteristic
43Q8⋊(C47⋊C8)C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46Q8⋊(C47⋊C8)C2211yescharacteristic
47Q8⋊(C47⋊C8)C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50D4⋊(C47⋊C8)C2211yescharacteristic
51D4⋊(C47⋊C8)C2211yescharacteristic
52C47×#557C411yescharacteristic
53C47×#556—21no—
54C47×#556C411yescharacteristic
55C47×#552—21no—
56C47×#552—21no—
57C47×#552C411yescharacteristic
58C47×#552C411yescharacteristic
59D4×Q8×C47C411yescharacteristic
60C47×#548C411yescharacteristic
61C47×#548C411yescharacteristic
62C47×#547—21no—
63C47×#547C411yescharacteristic
64C47×#533—21no—
65C47×#533C2211yescharacteristic
66C47×#529—21no—
67C47×#529—21no—
68C47×#529C2211yescharacteristic
69C47×#529C2211yescharacteristic
70C4×#41×C47—21no—
71C4×#41×C47C2211yescharacteristic
72C4×#41×C47C2211yescharacteristic
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×#10625329—21no—
76C2×#10625329—21no—
77C22×C47⋊C8—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)—21no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)C2311yescharacteristic
88C4⋊(C47⋊C8)C2311yescharacteristic
89C4⋊(C47⋊C8)C2311yescharacteristic
90C4⋊(C47⋊C8)C2311yescharacteristic
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)—21no—
93C22⋊(C47⋊C8)—21no—
94C22⋊(C47⋊C8)—21no—
95C22⋊(C47⋊C8)—21no—
96C22⋊(C47⋊C8)—21no—
97C22⋊(C47⋊C8)—21no—
98#13093935—21no—
99#13093935—21no—
100#13093935—21no—
101C4×C47⋊C8—21no—
102C4×C47⋊C8—21no—
103C4×C47⋊C8C2311yescharacteristic
104C4×C47⋊C8C2311yescharacteristic
105C4×C47⋊C8C2311yescharacteristic
106C4×C47⋊C8C2311yescharacteristic
107C2×#41×C47—21no—
108C2×#41×C47C2×C411yescharacteristic
109C2×#41×C47D411yescharacteristic
110C22×Q8×C47C2×C411yescharacteristic
111C22×Q8×C47C2×C411yescharacteristic
112C4⋊Q8×C47—21no—
113C4⋊Q8×C47—21no—
114C4⋊Q8×C47C2×C411yescharacteristic
115C4⋊Q8×C47C2×C411yescharacteristic
116#126×C47—21no—
117#126×C47—21no—
118#126×C47—21no—
119#126×C47—21no—
120#126×C47—21no—
121#126×C47—21no—
122#125×C47—21no—
123#125×C47—21no—
124#125×C47—21no—
125#125×C47—21no—
126#125×C47—21no—
127#125×C47C2×C411yescharacteristic
128#125×C47C2×C411yescharacteristic
129#124×C47—21no—
130#124×C47—21no—
131#124×C47C2×C411yescharacteristic
132#124×C47C2×C411yescharacteristic
133#123×C47—21no—
134#123×C47—21no—
135#123×C47—21no—
136#123×C47—21no—
137#123×C47—21no—
138#123×C47—21no—
139C22⋊Q8×C47—21no—
140C22⋊Q8×C47—21no—
141C22⋊Q8×C47—21no—
142C22⋊Q8×C47—21no—
143C22⋊Q8×C47—21no—
144C22⋊Q8×C47—21no—
145C22⋊Q8×C47—21no—
146C22⋊Q8×C47C2×C411yescharacteristic
147C22⋊Q8×C47C2×C411yescharacteristic
148C22⋊Q8×C47C2×C411yescharacteristic
149C22⋊Q8×C47C2×C411yescharacteristic
150#121×C47—21no—
151#121×C47—21no—
152#121×C47C2×C411yescharacteristic
153#121×C47C2×C411yescharacteristic
154C4×Q8×C47—21no—
155C4×Q8×C47—21no—
156C4×Q8×C47—21no—
157C4×Q8×C47—21no—
158C4×Q8×C47—21no—
159C4×Q8×C47—21no—
160C4×Q8×C47C2×C411yescharacteristic
161C4×Q8×C47C2×C411yescharacteristic
162C4×Q8×C47C2×C411yescharacteristic
163C4×Q8×C47C2×C411yescharacteristic
164C4×Q8×C47C2×C411yescharacteristic
165C4×Q8×C47C2×C411yescharacteristic
166C4×Q8×C47D411yescharacteristic
167C4×Q8×C47C2311yescharacteristic
168C4×Q8×C47C2311yescharacteristic
169C4×Q8×C47C2311yescharacteristic
170C4×D4×C47—21no—
171C4×D4×C47—21no—
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47—21no—
175C4×D4×C47—21no—
176C4×D4×C47—21no—
177C4×D4×C47C2×C411yescharacteristic
178C4×D4×C47C2×C411yescharacteristic
179C4×D4×C47C2×C411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47D411yescharacteristic
182C4×D4×C47D411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47C2311yescharacteristic
185#117×C47—21no—
186#117×C47—21no—
187#117×C47—21no—
188#117×C47—21no—
189#117×C47—21no—
190#117×C47—21no—
191#117×C47—21no—
192#117×C47C2×C411yescharacteristic
193#117×C47D411yescharacteristic
194#117×C47D411yescharacteristic
195#117×C47D411yescharacteristic
196C2×C4⋊C4×C47—21no—
197C2×C4⋊C4×C47—21no—
198C2×C4⋊C4×C47C2×C411yescharacteristic
199C2×C4⋊C4×C47C2×C411yescharacteristic
200C2×C42×C47—21no—
201C2×C42×C47—21no—
202C2×C42×C47—21no—
203C2×C42×C47C2311yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206#41×C47—22no—
207#41×C47—42no—
208#41×C47—41no—
209#41×C47—44no—
210C2×Q8×C47—21no—
211C2×Q8×C47—21no—
212C2×Q8×C47—21no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—41no—
216C2×Q8×C47—41no—
217C2×Q8×C47C22⋊C411yescharacteristic
218C2×Q8×C47C22×C411yescharacteristic
219C2×Q8×C47C22×C411yescharacteristic
220C2×Q8×C47C22×C411yescharacteristic
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47C22⋊C411yescharacteristic
225C2×D4×C47C22⋊C411yescharacteristic
226C2×D4×C47C22⋊C411yescharacteristic
227C2×D4×C47C22×C411yescharacteristic
228C22×C4×C47—21no—
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×C47C22×C411yescharacteristic
236C22×C4×C47C22×C411yescharacteristic
237C22×C4×C47C22×C411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
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×C47C22⋊C411yescharacteristic
289C22⋊C4×C47C22⋊C411yescharacteristic
290C22⋊C4×C47C22⋊C411yescharacteristic
291C22⋊C4×C47C22⋊C411yescharacteristic
292C22⋊C4×C47C22⋊C411yescharacteristic
293C22⋊C4×C47C22⋊C411yescharacteristic
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C42×C47—21no—
298C42×C47—21no—
299C42×C47—21no—
300C42×C47—21no—
301C42×C47—21no—
302C42×C47—21no—
303C42×C47C22×C411yescharacteristic
304C42×C47C22×C411yescharacteristic
305C42×C47C22×C411yescharacteristic
306C42×C47C2×D411yescharacteristic
307C42×C47C2×D411yescharacteristic
308C42×C47C2×D411yescharacteristic
309C42×C47C2×D411yescharacteristic
310C42×C47C2×D411yescharacteristic
311C42×C47C2×D411yescharacteristic
312C42×C47C2411yescharacteristic
313#10625329—42no—
314#10625329—81no—
315C2×C47⋊C8—21no—
316C2×C47⋊C8—21no—
317C2×C47⋊C8—21no—
318C2×C47⋊C8—21no—
319C2×C47⋊C8—21no—
320C2×C47⋊C8—21no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—42no—
324C2×C47⋊C8—81no—
325C2×C47⋊C8—81no—
326C23×C47—21no—
327C23×C47C2×C22⋊C411yescharacteristic
328C23×C47C2×C22⋊C411yescharacteristic
329C23×C47C2×C22⋊C411yescharacteristic
330Q8×C47—21no—
331Q8×C47—21no—
332Q8×C47—21no—
333Q8×C47—21no—
334Q8×C47—21no—
335Q8×C47—41no—
336Q8×C47—42no—
337Q8×C47—42no—
338Q8×C47—42no—
339Q8×C47#13112yes—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—21no—
343D4×C47—21no—
344D4×C47—41no—
345D4×C47—42no—
346D4×C47—42no—
347D4×C47—42no—
348C2×C4×C47—21no—
349C2×C4×C47—22no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
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—41no—
369C2×C4×C47—41no—
370C2×C4×C47—42no—
371C2×C4×C47—42no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47—42no—
375C2×C4×C47—42no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47C2×C22⋊C411yescharacteristic
379C2×C4×C47C2×C22⋊C411yescharacteristic
380C2×C4×C47C2×C22⋊C411yescharacteristic
381C2×C4×C47C2×C22⋊C411yescharacteristic
382C2×C4×C47C2×C22⋊C411yescharacteristic
383C2×C4×C47C2×C22⋊C411yescharacteristic
384C2×C4×C47C2×C22⋊C411yescharacteristic
385C2×C4×C47C2×C22⋊C411yescharacteristic
386C2×C4×C47C2×C22⋊C411yescharacteristic
387C2×C4×C47C23×C411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C22×D411yescharacteristic
390C47⋊C8—41no—
391C47⋊C8—41no—
392C47⋊C8—41no—
393C47⋊C8—41no—
394C47⋊C8—41no—
395C47⋊C8—41no—
396C47⋊C8—41no—
397C47⋊C8—41no—
398#17524—471nomaximal, Sylow
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—21no—
405C22×C47—21no—
406C22×C47—21no—
407C22×C47—41no—
408C22×C47—41no—
409C22×C47—41no—
410C22×C47#42112yes—
411C22×C47C22×C22⋊C411yescharacteristic
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—22no—
416C4×C47—21no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47—21no—
423C4×C47—41no—
424C4×C47—41no—
425C4×C47—41no—
426C4×C47—41no—
427C4×C47—41no—
428C4×C47—41no—
429C4×C47C2×#13111yescharacteristic
430C4×C47#56811yescharacteristic
431C4×C47#57711yescharacteristic
432C4×C47#57811yescharacteristic
433#3482D4711yescharacteristic
434#2990—471no—
435#2922—471no—
436#1497—471no—
437#1495—471no—
438#1494—471no—
439#1491—471no—
440#1488—471no—
441#1487—471no—
442#1483—471no—
443#1482—471no—
444#1481—471no—
445#1479—471no—
446#1477—471no—
447C2×Q8⋊C8—471no—
448C2×C47—22no—
449C2×C47—41no—
450C2×C47—41no—
451C2×C47—81no—
452C2×C47#288011yescharacteristic
453C2×C47#289811yescharacteristic
454C2×C47C2×#42111yescharacteristic
455#557Dic4711yescharacteristic
456#556—21no—
457#556Dic4711yescharacteristic
458#552—21no—
459#552—21no—
460#552Dic4711yescharacteristic
461#552Dic4711yescharacteristic
462D4×Q8Dic4711yescharacteristic
463#548Dic4711yescharacteristic
464#548Dic4711yescharacteristic
465#547—21no—
466#547Dic4711yescharacteristic
467#533—21no—
468#533C2×D4711yescharacteristic
469#529—21no—
470#529—21no—
471#529C2×D4711yescharacteristic
472#529C2×D4711yescharacteristic
473C4×#41—21no—
474C4×#41C2×D4711yescharacteristic
475C4×#41C2×D4711yescharacteristic
476C2×C4×Q8C2×D4711yescharacteristic
477C2×C4×Q8C2×D4711yescharacteristic
478#446—941no—
479#435—941no—
480#435—941no—
481C8×D4—941no—
482#433—941no—
483#433—941no—
484#432—471no—
485#432—471no—
486#431—471no—
487#431—471no—
488#431—471no—
489#431—471no—
490#431—471no—
491#424—941no—
492#423—471no—
493C2×C4⋊C8—471no—
494C2×C4⋊C8—471no—
495#408—941no—
496C4×M16—471no—
497C2×C4×C8—471no—
498Q8⋊C8—471no—
499Q8⋊C8—471no—
500Q8⋊C8—471no—
501Q8⋊C8—471no—
502Q8⋊C8—471no—
503Q8⋊C8—471no—
504Q8⋊C8—471no—
505Q8⋊C8—471no—
506Q8⋊C8—471no—
507Q8⋊C8—471no—
508Q8⋊C8—471no—
509Q8⋊C8—471no—
510D4⋊C8—471no—
511D4⋊C8—471no—
512D4⋊C8—471no—
513D4⋊C8—471no—
514C47#1752411yescharacteristic, complemented, Sylow
515C2×#41—21no—
516C2×#41C2×Dic4711yescharacteristic
517C2×#41C22⋊D4711yescharacteristic
518C22×Q8C2×Dic4711yescharacteristic
519C22×Q8C2×Dic4711yescharacteristic
520C2×M16—941no—
521C2×M16—941no—
522C22×C8—941no—
523C22×C8—941no—
524C22×C8—941no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×Dic4711yescharacteristic
528C4⋊Q8C2×Dic4711yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×Dic4711yescharacteristic
541#125C2×Dic4711yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×Dic4711yescharacteristic
545#124C2×Dic4711yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×Dic4711yescharacteristic
560C22⋊Q8C2×Dic4711yescharacteristic
561C22⋊Q8C2×Dic4711yescharacteristic
562C22⋊Q8C2×Dic4711yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×Dic4711yescharacteristic
566#121C2×Dic4711yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×Dic4711yescharacteristic
574C4×Q8C2×Dic4711yescharacteristic
575C4×Q8C2×Dic4711yescharacteristic
576C4×Q8C2×Dic4711yescharacteristic
577C4×Q8C2×Dic4711yescharacteristic
578C4×Q8C2×Dic4711yescharacteristic
579C4×Q8C22⋊D4711yescharacteristic
580C4×Q8C22×D4711yescharacteristic
581C4×Q8C22×D4711yescharacteristic
582C4×Q8C22×D4711yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×Dic4711yescharacteristic
591C4×D4C2×Dic4711yescharacteristic
592C4×D4C2×Dic4711yescharacteristic
593C4×D4C2×Dic4711yescharacteristic
594C4×D4C22⋊D4711yescharacteristic
595C4×D4C22⋊D4711yescharacteristic
596C4×D4C22⋊D4711yescharacteristic
597C4×D4C22×D4711yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×Dic4711yescharacteristic
606#117C22⋊D4711yescharacteristic
607#117C22⋊D4711yescharacteristic
608#117C22⋊D4711yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×Dic4711yescharacteristic
612C2×C4⋊C4C2×Dic4711yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C22×D4711yescharacteristic
617C2×C42C22×D4711yescharacteristic
618C2×C42C22×D4711yescharacteristic
619C4⋊C8—471no—
620C4⋊C8—471no—
621C4⋊C8—471no—
622C4⋊C8—471no—
623C4⋊C8—941no—
624C4⋊C8—941no—
625C4⋊C8—941no—
626C4⋊C8—941no—
627C4⋊C8—941no—
628C4⋊C8—941no—
629C4⋊C8—941no—
630C22⋊C8—941no—
631C22⋊C8—941no—
632C22⋊C8—941no—
633C22⋊C8—941no—
634C22⋊C8—941no—
635C22⋊C8—941no—
636C22⋊C8—941no—
637#97—941no—
638#97—941no—
639#97—941no—
640C4×C8—471no—
641C4×C8—471no—
642C4×C8—471no—
643C4×C8—471no—
644C4×C8—941no—
645C4×C8—941no—
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊Dic4711yescharacteristic
658C2×Q8C22×Dic4711yescharacteristic
659C2×Q8C22×Dic4711yescharacteristic
660C2×Q8C22×Dic4711yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊Dic4711yescharacteristic
665C2×D4C22⋊Dic4711yescharacteristic
666C2×D4C22⋊Dic4711yescharacteristic
667C2×D4C22×Dic4711yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×Dic4711yescharacteristic
676C22×C4C22×Dic4711yescharacteristic
677C22×C4C22×Dic4711yescharacteristic
678C22×C4C2×C22⋊D4711yescharacteristic
679C22×C4C2×C22⋊D4711yescharacteristic
680C22×C4C2×C22⋊D4711yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684M16—3761no—
685M16—1882no—
686C2×C8—941no—
687C2×C8—941no—
688C2×C8—941no—
689C2×C8—941no—
690C2×C8—941no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—941no—
694C2×C8—3761no—
695C2×C8—3761no—
696C2×C8—1882no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊Dic4711yescharacteristic
719C4⋊C4C22⋊Dic4711yescharacteristic
720C4⋊C4C22⋊Dic4711yescharacteristic
721C4⋊C4C22⋊Dic4711yescharacteristic
722C4⋊C4C22⋊Dic4711yescharacteristic
723C4⋊C4C22⋊Dic4711yescharacteristic
724C4⋊C4C22×Dic4711yescharacteristic
725C4⋊C4C22×Dic4711yescharacteristic
726C4⋊C4C22×Dic4711yescharacteristic
727C4⋊C4C22×Dic4711yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4C22⋊Dic4711yescharacteristic
742C22⋊C4C22⋊Dic4711yescharacteristic
743C22⋊C4C22⋊Dic4711yescharacteristic
744C22⋊C4C22⋊Dic4711yescharacteristic
745C22⋊C4C22⋊Dic4711yescharacteristic
746C22⋊C4C22⋊Dic4711yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×Dic4711yescharacteristic
757C42C22×Dic4711yescharacteristic
758C42C22×Dic4711yescharacteristic
759C42C2×C22⋊D4711yescharacteristic
760C42C2×C22⋊D4711yescharacteristic
761C42C2×C22⋊D4711yescharacteristic
762C42C2×C22⋊D4711yescharacteristic
763C42C2×C22⋊D4711yescharacteristic
764C42C2×C22⋊D4711yescharacteristic
765C42C23×D4711yescharacteristic
766C23—21no—
767C23C2×C22⋊Dic4711yescharacteristic
768C23C2×C22⋊Dic4711yescharacteristic
769C23C2×C22⋊Dic4711yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#1309403112yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊Dic4711yescharacteristic
819C2×C4C2×C22⋊Dic4711yescharacteristic
820C2×C4C2×C22⋊Dic4711yescharacteristic
821C2×C4C2×C22⋊Dic4711yescharacteristic
822C2×C4C2×C22⋊Dic4711yescharacteristic
823C2×C4C2×C22⋊Dic4711yescharacteristic
824C2×C4C2×C22⋊Dic4711yescharacteristic
825C2×C4C2×C22⋊Dic4711yescharacteristic
826C2×C4C2×C22⋊Dic4711yescharacteristic
827C2×C4C23×Dic4711yescharacteristic
828C2×C4C22×C22⋊D4711yescharacteristic
829C2×C4C22×C22⋊D4711yescharacteristic
830C8—1881no—
831C8—1881no—
832C8—1881no—
833C8—1881no—
834C8—1881no—
835C8—1881no—
836C8—1881no—
837C8—1881no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#1568914012yes—
850C22C22×C22⋊Dic4711yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#1309403111yescharacteristic
869C4#1568989011yescharacteristic
870C4#1568993111yescharacteristic
871C4#1568993811yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2#2025183711yescharacteristic
877C2#2025192111yescharacteristic
878C2C2×#1568914011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
Fitting, prime radicalC47×#3482C2
socleC22×C47C22×C22⋊C4
cosocleC42×C47C24
hypercenter#3482D47
hypocenterC47#17524
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #20252513C2semidirect
2. #20252032C2semidirect
3. #20241861C2semidirect
4. #20241853C2semidirect
5. #20241848C2semidirect
6. #20241835C2semidirect
7. #20241822C2semidirect
8. #20241817C2semidirect
9. #20241801C2semidirect
10. #20241796C2semidirect
11. #20241791C2semidirect
12. #20241783C2semidirect
13. #20241775C2semidirect
14. C2×Q8⋊(C47⋊C8)C2semidirect
514. C47#17524semidirect

Maximal subgroups

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

subgroupindex
#202525132
#202520322
#202418612
#202418532
#202418482
#202418352
#202418222
#202418172
#202418012
#202417962
#202417912
#202417832
#202417752
C2×Q8⋊(C47⋊C8)2
C47×#34822
#1752447