Finite Group Databasebeta

← #26183126

Subgroups — #26183126

Order 12032.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252505C211yesmaximal, characteristic, complemented
2#20252355C211yesmaximal, characteristic, complemented
3#20241861C211yesmaximal, characteristic, complemented
4#20241853C211yesmaximal, characteristic, complemented
5#20241848C211yesmaximal, characteristic, complemented
6#20241843C211yesmaximal, characteristic, complemented
7#20241835C211yesmaximal, characteristic, complemented
8#20241827C211yesmaximal, characteristic, complemented
9#20241822C211yesmaximal, characteristic, complemented
10#20241817C211yesmaximal, characteristic, complemented
11#20241809C211yesmaximal, characteristic, complemented
12#20241801C211yesmaximal, characteristic, complemented
13#20241796C211yesmaximal, characteristic, complemented
14#20241791C211yesmaximal, characteristic, complemented
15C47×#3461C211yesmaximal, characteristic
16#15689254—21no—
17#15689254—21no—
18#15689201—21no—
19#15689201—21no—
20#15689195—21no—
21#15689195—21no—
22#15689195—21no—
23#15689195—21no—
24#15689180C2211yescharacteristic
25#15689180C2211yescharacteristic
26#15689176C2211yescharacteristic
27#15689176C2211yescharacteristic
28#15689176C2211yescharacteristic
29#15689176C2211yescharacteristic
30#15689147C2211yescharacteristic
31#15689147C2211yescharacteristic
32C2×C4⋊(C47⋊C8)C2211yescharacteristic
33C4×#10625329C2211yescharacteristic
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×#544C411yescharacteristic
53C47×#542—21no—
54C47×#542C411yescharacteristic
55C47×#542C411yescharacteristic
56C47×#541—21no—
57C47×#541C411yescharacteristic
58C47×#541C411yescharacteristic
59C47×#539—21no—
60C47×#539—21no—
61C47×#537C411yescharacteristic
62C47×#536C411yescharacteristic
63C47×#536C411yescharacteristic
64C47×#533—21no—
65C47×#533C2211yescharacteristic
66C47×#533C2211yescharacteristic
67C47×#529—21no—
68C47×#529—21no—
69C47×#529—21no—
70C47×#529C2211yescharacteristic
71C47×#529C2211yescharacteristic
72C4×#41×C47C2211yescharacteristic
73C4×#41×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C22×C47⋊C8—21no—
80C22×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—
97#13093935—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×C47C2×C411yescharacteristic
108C2×#41×C47C2×C411yescharacteristic
109C22×Q8×C47C2×C411yescharacteristic
110C4⋊Q8×C47—21no—
111C4⋊Q8×C47—21no—
112C4⋊Q8×C47C2×C411yescharacteristic
113C4⋊Q8×C47C2×C411yescharacteristic
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#126×C47—21no—
123#126×C47—21no—
124#125×C47—21no—
125#125×C47—21no—
126#125×C47—21no—
127#125×C47—21no—
128#125×C47—21no—
129#125×C47—21no—
130#125×C47—21no—
131#125×C47C2×C411yescharacteristic
132#125×C47C2×C411yescharacteristic
133#124×C47—21no—
134#124×C47—21no—
135#124×C47—21no—
136#124×C47C2×C411yescharacteristic
137#124×C47C2×C411yescharacteristic
138#123×C47—21no—
139#123×C47—21no—
140#123×C47—21no—
141#123×C47—21no—
142#123×C47—21no—
143#123×C47—21no—
144#123×C47—21no—
145#123×C47—21no—
146C22⋊Q8×C47—21no—
147C22⋊Q8×C47—21no—
148C22⋊Q8×C47—21no—
149C22⋊Q8×C47—21no—
150C22⋊Q8×C47—21no—
151C22⋊Q8×C47—21no—
152C22⋊Q8×C47—21no—
153C22⋊Q8×C47—21no—
154C22⋊Q8×C47—21no—
155C22⋊Q8×C47C2×C411yescharacteristic
156C22⋊Q8×C47C2×C411yescharacteristic
157C22⋊Q8×C47C2×C411yescharacteristic
158C22⋊Q8×C47C2×C411yescharacteristic
159C22⋊Q8×C47C2×C411yescharacteristic
160C22⋊Q8×C47C2×C411yescharacteristic
161#121×C47—21no—
162#121×C47—21no—
163#121×C47—21no—
164#121×C47C2×C411yescharacteristic
165#121×C47C2×C411yescharacteristic
166C4×Q8×C47—21no—
167C4×Q8×C47—21no—
168C4×Q8×C47—21no—
169C4×Q8×C47—21no—
170C4×Q8×C47C2×C411yescharacteristic
171C4×Q8×C47C2×C411yescharacteristic
172C4×Q8×C47C2×C411yescharacteristic
173C4×Q8×C47D411yescharacteristic
174C4×Q8×C47D411yescharacteristic
175C4×Q8×C47C2311yescharacteristic
176C4×Q8×C47C2311yescharacteristic
177C4×Q8×C47C2311yescharacteristic
178C4×D4×C47—21no—
179C4×D4×C47—21no—
180C4×D4×C47—21no—
181C4×D4×C47—21no—
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187C4×D4×C47D411yescharacteristic
188C4×D4×C47D411yescharacteristic
189C4×D4×C47C2311yescharacteristic
190#117×C47—21no—
191#117×C47—21no—
192#117×C47—21no—
193#117×C47—21no—
194#117×C47—21no—
195#117×C47C2×C411yescharacteristic
196#117×C47C2×C411yescharacteristic
197#117×C47C2×C411yescharacteristic
198#117×C47C2×C411yescharacteristic
199C2×C4⋊C4×C47—21no—
200C2×C4⋊C4×C47C2×C411yescharacteristic
201C2×C42×C47—21no—
202C2×C42×C47—21no—
203C2×C42×C47C2311yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206#41×C47—42no—
207#41×C47—42no—
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47—21no—
211C2×Q8×C47—42no—
212C2×Q8×C47C22⋊C411yescharacteristic
213C2×Q8×C47C22×C411yescharacteristic
214C2×Q8×C47C22×C411yescharacteristic
215C2×Q8×C47C22×C411yescharacteristic
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47C22⋊C411yescharacteristic
220C2×D4×C47C22⋊C411yescharacteristic
221C2×D4×C47C22⋊C411yescharacteristic
222C2×D4×C47C22×C411yescharacteristic
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47C22×C411yescharacteristic
229C22×C4×C47C22×C411yescharacteristic
230C22×C4×C47C22×C411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
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×C47C22⋊C411yescharacteristic
261C4⋊C4×C47C22⋊C411yescharacteristic
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C4⋊C4×C47C22⋊C411yescharacteristic
266C4⋊C4×C47C22×C411yescharacteristic
267C4⋊C4×C47C22×C411yescharacteristic
268C4⋊C4×C47C22×C411yescharacteristic
269C4⋊C4×C47C22×C411yescharacteristic
270C22⋊C4×C47—21no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—21no—
273C22⋊C4×C47—21no—
274C22⋊C4×C47—21no—
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×C47C22⋊C411yescharacteristic
286C22⋊C4×C47C22⋊C411yescharacteristic
287C22⋊C4×C47C22⋊C411yescharacteristic
288C22⋊C4×C47C22⋊C411yescharacteristic
289C22⋊C4×C47C22⋊C411yescharacteristic
290C22⋊C4×C47C22⋊C411yescharacteristic
291C42×C47—21no—
292C42×C47—21no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C42×C47—21no—
298C42×C47C22×C411yescharacteristic
299C42×C47C22×C411yescharacteristic
300C42×C47C22×C411yescharacteristic
301C42×C47C2×D411yescharacteristic
302C42×C47C2×D411yescharacteristic
303C42×C47C2×D411yescharacteristic
304C42×C47C2×D411yescharacteristic
305C42×C47C2×D411yescharacteristic
306C42×C47C2×D411yescharacteristic
307C42×C47C2411yescharacteristic
308#10625329—42no—
309#10625329—42no—
310#10625329—81no—
311#10625329—81no—
312C2×C47⋊C8—21no—
313C2×C47⋊C8—21no—
314C2×C47⋊C8—21no—
315C2×C47⋊C8—21no—
316C2×C47⋊C8—21no—
317C2×C47⋊C8—21no—
318C2×C47⋊C8—21no—
319C2×C47⋊C8—21no—
320C2×C47⋊C8—42no—
321C2×C47⋊C8—81no—
322C23×C47—21no—
323C23×C47C2×C22⋊C411yescharacteristic
324C23×C47C2×C22⋊C411yescharacteristic
325C23×C47C2×C22⋊C411yescharacteristic
326Q8×C47—22no—
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—41no—
330Q8×C47—42no—
331Q8×C47—81no—
332Q8×C47—81no—
333D4×C47—22no—
334D4×C47—41no—
335D4×C47—41no—
336D4×C47—41no—
337D4×C47—42no—
338D4×C47—81no—
339D4×C47—81no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
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—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—42no—
360C2×C4×C47—42no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—81no—
364C2×C4×C47—81no—
365C2×C4×C47C2×C22⋊C411yescharacteristic
366C2×C4×C47C2×C22⋊C411yescharacteristic
367C2×C4×C47C2×C22⋊C411yescharacteristic
368C2×C4×C47C2×C22⋊C411yescharacteristic
369C2×C4×C47C2×C22⋊C411yescharacteristic
370C2×C4×C47C2×C22⋊C411yescharacteristic
371C2×C4×C47C2×C22⋊C411yescharacteristic
372C2×C4×C47C2×C22⋊C411yescharacteristic
373C2×C4×C47C2×C22⋊C411yescharacteristic
374C2×C4×C47C23×C411yescharacteristic
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C22×D411yescharacteristic
377C47⋊C8—22no—
378C47⋊C8—41no—
379C47⋊C8—41no—
380C47⋊C8—41no—
381C47⋊C8—41no—
382C47⋊C8—41no—
383C47⋊C8—41no—
384C47⋊C8—41no—
385#17506—471nomaximal, Sylow
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47C22×C22⋊C411yescharacteristic
399C4×C47—21no—
400C4×C47—21no—
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—21no—
404C4×C47—21no—
405C4×C47—21no—
406C4×C47—21no—
407C4×C47—21no—
408C4×C47—21no—
409C4×C47—41no—
410C4×C47—41no—
411C4×C47—41no—
412C4×C47—41no—
413C4×C47—41no—
414C4×C47—41no—
415C4×C47—41no—
416C4×C47#56812yes—
417C4×C47#57711yescharacteristic
418C4×C47#57811yescharacteristic
419#3461D4711yescharacteristic
420#2989—471no—
421#2965—471no—
422#1497—471no—
423#1495—471no—
424#1494—471no—
425#1493—471no—
426#1491—471no—
427#1489—471no—
428#1488—471no—
429#1487—471no—
430#1485—471no—
431#1483—471no—
432#1482—471no—
433#1481—471no—
434C2×C47—41no—
435C2×C47—41no—
436C2×C47—41no—
437C2×C47—81no—
438C2×C47#287911yescharacteristic
439C2×C47#289811yescharacteristic
440C2×C47#290111yescharacteristic
441#544Dic4711yescharacteristic
442#542—21no—
443#542Dic4711yescharacteristic
444#542Dic4711yescharacteristic
445#541—21no—
446#541Dic4711yescharacteristic
447#541Dic4711yescharacteristic
448#539—21no—
449#539—21no—
450#537Dic4711yescharacteristic
451#536Dic4711yescharacteristic
452#536Dic4711yescharacteristic
453#533—21no—
454#533C2×D4711yescharacteristic
455#533C2×D4711yescharacteristic
456#529—21no—
457#529—21no—
458#529—21no—
459#529C2×D4711yescharacteristic
460#529C2×D4711yescharacteristic
461C4×#41C2×D4711yescharacteristic
462C4×#41C2×D4711yescharacteristic
463C2×C4×Q8C2×D4711yescharacteristic
464#446—941no—
465#446—941no—
466#436—941no—
467#436—941no—
468#435—941no—
469#435—941no—
470#435—941no—
471#435—941no—
472#432—471no—
473#432—471no—
474#431—471no—
475#431—471no—
476#431—471no—
477#431—471no—
478#423—471no—
479#423—471no—
480C2×C4⋊C8—471no—
481C4×M16—471no—
482C4×M16—471no—
483C2×C4×C8—471no—
484Q8⋊C8—471no—
485Q8⋊C8—471no—
486Q8⋊C8—471no—
487Q8⋊C8—471no—
488Q8⋊C8—471no—
489Q8⋊C8—471no—
490Q8⋊C8—471no—
491Q8⋊C8—471no—
492Q8⋊C8—471no—
493Q8⋊C8—471no—
494Q8⋊C8—471no—
495Q8⋊C8—471no—
496D4⋊C8—471no—
497D4⋊C8—471no—
498D4⋊C8—471no—
499D4⋊C8—471no—
500C47#1750611yescharacteristic, complemented, Sylow
501C2×#41C2×Dic4711yescharacteristic
502C2×#41C2×Dic4711yescharacteristic
503C22×Q8C2×Dic4711yescharacteristic
504C2×M16—941no—
505C2×M16—941no—
506C2×M16—941no—
507C2×M16—941no—
508C22×C8—941no—
509C22×C8—941no—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8C2×Dic4711yescharacteristic
513C4⋊Q8C2×Dic4711yescharacteristic
514C4⋊Q8C2×Dic4711yescharacteristic
515C4⋊Q8C2×Dic4711yescharacteristic
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#125—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125C2×Dic4711yescharacteristic
532#125C2×Dic4711yescharacteristic
533#124—21no—
534#124—21no—
535#124—21no—
536#124C2×Dic4711yescharacteristic
537#124C2×Dic4711yescharacteristic
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8C2×Dic4711yescharacteristic
556C22⋊Q8C2×Dic4711yescharacteristic
557C22⋊Q8C2×Dic4711yescharacteristic
558C22⋊Q8C2×Dic4711yescharacteristic
559C22⋊Q8C2×Dic4711yescharacteristic
560C22⋊Q8C2×Dic4711yescharacteristic
561#121—21no—
562#121—21no—
563#121—21no—
564#121C2×Dic4711yescharacteristic
565#121C2×Dic4711yescharacteristic
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8C2×Dic4711yescharacteristic
571C4×Q8C2×Dic4711yescharacteristic
572C4×Q8C2×Dic4711yescharacteristic
573C4×Q8C22⋊D4711yescharacteristic
574C4×Q8C22⋊D4711yescharacteristic
575C4×Q8C22×D4711yescharacteristic
576C4×Q8C22×D4711yescharacteristic
577C4×Q8C22×D4711yescharacteristic
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4C2×Dic4711yescharacteristic
583C4×D4C22⋊D4711yescharacteristic
584C4×D4C22⋊D4711yescharacteristic
585C4×D4C22⋊D4711yescharacteristic
586C4×D4C22⋊D4711yescharacteristic
587C4×D4C22⋊D4711yescharacteristic
588C4×D4C22⋊D4711yescharacteristic
589C4×D4C22×D4711yescharacteristic
590#117—21no—
591#117—21no—
592#117—21no—
593#117—21no—
594#117—21no—
595#117C2×Dic4711yescharacteristic
596#117C2×Dic4711yescharacteristic
597#117C2×Dic4711yescharacteristic
598#117C2×Dic4711yescharacteristic
599C2×C4⋊C4—21no—
600C2×C4⋊C4C2×Dic4711yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C22×D4711yescharacteristic
604C2×C42C22×D4711yescharacteristic
605C2×C42C22×D4711yescharacteristic
606C4⋊C8—471no—
607C4⋊C8—471no—
608C4⋊C8—471no—
609C4⋊C8—471no—
610C4⋊C8—941no—
611C4⋊C8—941no—
612C4⋊C8—941no—
613C4⋊C8—941no—
614C4⋊C8—941no—
615C4⋊C8—941no—
616C22⋊C8—941no—
617C22⋊C8—941no—
618C22⋊C8—941no—
619C22⋊C8—941no—
620C22⋊C8—941no—
621C22⋊C8—941no—
622#97—941no—
623#97—941no—
624#97—941no—
625#97—941no—
626C4×C8—471no—
627C4×C8—471no—
628C4×C8—471no—
629C4×C8—471no—
630C4×C8—941no—
631C4×C8—941no—
632#41—42no—
633#41—42no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—42no—
638C2×Q8C22⋊Dic4711yescharacteristic
639C2×Q8C22×Dic4711yescharacteristic
640C2×Q8C22×Dic4711yescharacteristic
641C2×Q8C22×Dic4711yescharacteristic
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4C22⋊Dic4711yescharacteristic
646C2×D4C22⋊Dic4711yescharacteristic
647C2×D4C22⋊Dic4711yescharacteristic
648C2×D4C22×Dic4711yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4C22×Dic4711yescharacteristic
655C22×C4C22×Dic4711yescharacteristic
656C22×C4C22×Dic4711yescharacteristic
657C22×C4C2×C22⋊D4711yescharacteristic
658C22×C4C2×C22⋊D4711yescharacteristic
659C22×C4C2×C22⋊D4711yescharacteristic
660C22×C4C2×C22⋊D4711yescharacteristic
661C22×C4C2×C22⋊D4711yescharacteristic
662C22×C4C2×C22⋊D4711yescharacteristic
663M16—3761no—
664M16—3761no—
665M16—1882no—
666M16—1882no—
667C2×C8—941no—
668C2×C8—941no—
669C2×C8—941no—
670C2×C8—941no—
671C2×C8—941no—
672C2×C8—941no—
673C2×C8—941no—
674C2×C8—941no—
675C2×C8—3761no—
676C2×C8—1882no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C22⋊Dic4711yescharacteristic
701C4⋊C4C22⋊Dic4711yescharacteristic
702C4⋊C4C22⋊Dic4711yescharacteristic
703C4⋊C4C22⋊Dic4711yescharacteristic
704C4⋊C4C22⋊Dic4711yescharacteristic
705C4⋊C4C22⋊Dic4711yescharacteristic
706C4⋊C4C22×Dic4711yescharacteristic
707C4⋊C4C22×Dic4711yescharacteristic
708C4⋊C4C22×Dic4711yescharacteristic
709C4⋊C4C22×Dic4711yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4C22⋊Dic4711yescharacteristic
726C22⋊C4C22⋊Dic4711yescharacteristic
727C22⋊C4C22⋊Dic4711yescharacteristic
728C22⋊C4C22⋊Dic4711yescharacteristic
729C22⋊C4C22⋊Dic4711yescharacteristic
730C22⋊C4C22⋊Dic4711yescharacteristic
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42C22×Dic4711yescharacteristic
739C42C22×Dic4711yescharacteristic
740C42C22×Dic4711yescharacteristic
741C42C2×C22⋊D4711yescharacteristic
742C42C2×C22⋊D4711yescharacteristic
743C42C2×C22⋊D4711yescharacteristic
744C42C2×C22⋊D4711yescharacteristic
745C42C2×C22⋊D4711yescharacteristic
746C42C2×C22⋊D4711yescharacteristic
747C42C23×D4711yescharacteristic
748C23—21no—
749C23C2×C22⋊Dic4711yescharacteristic
750C23C2×C22⋊Dic4711yescharacteristic
751C23C2×C22⋊Dic4711yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—41no—
756Q8—42no—
757Q8—81no—
758Q8—81no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—42no—
764D4—81no—
765D4—81no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C2×C22⋊Dic4711yescharacteristic
792C2×C4C2×C22⋊Dic4711yescharacteristic
793C2×C4C2×C22⋊Dic4711yescharacteristic
794C2×C4C2×C22⋊Dic4711yescharacteristic
795C2×C4C2×C22⋊Dic4711yescharacteristic
796C2×C4C2×C22⋊Dic4711yescharacteristic
797C2×C4C2×C22⋊Dic4711yescharacteristic
798C2×C4C2×C22⋊Dic4711yescharacteristic
799C2×C4C2×C22⋊Dic4711yescharacteristic
800C2×C4C23×Dic4711yescharacteristic
801C2×C4C22×C22⋊D4711yescharacteristic
802C2×C4C22×C22⋊D4711yescharacteristic
803C8—942no—
804C8—1881no—
805C8—1881no—
806C8—1881no—
807C8—1881no—
808C8—1881no—
809C8—1881no—
810C8—1881no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22C22×C22⋊Dic4711yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4#1568989012yes—
842C4#1568993111yescharacteristic
843C4#1568993811yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—81no—
848C2#2025183311yescharacteristic
849C2#2025192111yescharacteristic
850C2#2025193511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#3461C2
socleC22×C47C22×C22⋊C4
prime radicalC47×#537C4
cosocleC42×C47C24
hypercenter#3461D47
hypocenterC47#17506
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #20252505C2semidirect
2. #20252355C2semidirect
3. #20241861C2semidirect
4. #20241853C2semidirect
5. #20241848C2semidirect
6. #20241843C2semidirect
7. #20241835C2semidirect
8. #20241827C2semidirect
9. #20241822C2semidirect
10. #20241817C2semidirect
11. #20241809C2semidirect
12. #20241801C2semidirect
13. #20241796C2semidirect
14. #20241791C2semidirect
500. C47#17506semidirect

Maximal subgroups

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

subgroupindex
#202525052
#202523552
#202418612
#202418532
#202418482
#202418432
#202418352
#202418272
#202418222
#202418172
#202418092
#202418012
#202417962
#202417912
C47×#34612
#1750647