Finite Group Databasebeta

← #37583383

Subgroups — #37583383

Order 24448.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133230C211yesmaximal, characteristic, complemented
2#27133229C211yesmaximal, characteristic, complemented
3#27132988C211yesmaximal, characteristic, complemented
4#27132986C211yesmaximal, characteristic, complemented
5#27132985C211yesmaximal, characteristic, complemented
6#27132984C211yesmaximal, characteristic, complemented
7#27132915C211yesmaximal, characteristic, complemented
8#27132913C211yesmaximal, characteristic, complemented
9#27132898C211yesmaximal, characteristic, complemented
10#27132896C211yesmaximal, characteristic, complemented
11#27132797C211yesmaximal, characteristic, complemented
12#27132795C211yesmaximal, characteristic, complemented
13#27132795C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#447×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×D4×D191C2211yescharacteristic, complemented
18C2×#15690272C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690270C2211yescharacteristic, complemented
21C2×C8×D191C2211yescharacteristic, complemented
22#20259318—21no—
23#20259318—21no—
24#20259309—21no—
25#20259308—21no—
26#20259297C2211yescharacteristic, complemented
27#20259296C2211yescharacteristic
28#20259293C2211yescharacteristic
29#20259293C2211yescharacteristic
30#20259293C2211yescharacteristic, complemented
31#20259293C2211yescharacteristic, complemented
32#20259293C2211yescharacteristic, complemented
33#20259292—21no—
34#20259291—21no—
35#20259291—21no—
36#20259290—21no—
37#20259281C2211yescharacteristic, complemented
38#20259280C2211yescharacteristic, complemented
39#20259256C2211yescharacteristic, complemented
40#20259255C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic, complemented
45#20259243C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic, complemented
47#20259243C2211yescharacteristic, complemented
48#20259243C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic, complemented
50(C2×D191)⋊C8C2211yescharacteristic, complemented
51(C2×D191)⋊C8C2211yescharacteristic, complemented
52C22×D4×C191C2211yescharacteristic, complemented
53C2×D8×C191C2211yescharacteristic
54C2×D8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#102×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60#15690287—41no—
61#15690287—41no—
62C2×Dic382D411yescharacteristic
63C2×D764—21no—
64C2×D764D411yescharacteristic
65C2×D764C2311yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C2×C22⋊D191—21no—
73C2×C22⋊D191D411yescharacteristic
74C2×C22⋊D191D411yescharacteristic
75D4×D191—41no—
76D4×D191—41no—
77C2×C4×D191C2311yescharacteristic
78C2×C4×D191C2311yescharacteristic
79#15690272—41no—
80#15690272—41no—
81#15690270—41no—
82C2×C191⋊C8C2311yescharacteristic
83C2×C191⋊C8C2311yescharacteristic
84C8×D191—41no—
85C4⋊Dic191C2311yescharacteristic
86C4⋊Dic191C2311yescharacteristic
87C4⋊Dic191C2311yescharacteristic
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90C22⋊Dic191—21no—
91C22⋊Dic191—21no—
92C22⋊Dic191—21no—
93C22⋊Dic191—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97C4×Dic191—21no—
98C4×Dic191—21no—
99C24×C191—21no—
100C2×D4×C191—21no—
101C2×D4×C191—21no—
102C2×D4×C191—41no—
103C2×D4×C191—41no—
104C2×D4×C191C2311yescharacteristic
105C2×D4×C191C2311yescharacteristic
106C2×D4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108D8×C191—41no—
109D8×C191—41no—
110C2×C8×C191C2311yescharacteristic
111C2×C8×C191C2311yescharacteristic
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191—21no—
115C22×D191—42no—
116C22×D191—81no—
117C22×D191—81no—
118C22×D191C2×D411yescharacteristic
119C22×D191C2×D411yescharacteristic
120Dic382—41no—
121D764—21no—
122D764—21no—
123D764—41no—
124D764—81no—
125C22⋊D191—41no—
126C22⋊D191—41no—
127C22⋊D191—42no—
128C22⋊D191—81no—
129C22⋊D191—81no—
130C22⋊D191—81no—
131C22⋊D191—81no—
132C22⋊D191—81no—
133C22⋊D191—81no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191C2×D411yescharacteristic
138C2×Dic191C2×D411yescharacteristic
139C4×D191—21no—
140C4×D191—21no—
141C4×D191—21no—
142C4×D191—21no—
143C191⋊C8—21no—
144C191⋊C8—21no—
145C23×C191—21no—
146C23×C191—21no—
147C23×C191—21no—
148C23×C191—42no—
149C23×C191—81no—
150C23×C191—81no—
151C23×C191C2×D411yescharacteristic
152D4×C191—21no—
153D4×C191—21no—
154D4×C191—21no—
155D4×C191—21no—
156D4×C191—21no—
157D4×C191—21no—
158D4×C191—42no—
159D4×C191—81no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2411yescharacteristic
165C8×C191—21no—
166C8×C191—21no—
167C22×C191—21no—
168C22×C191—21no—
169C22×C191—21no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191—41no—
173C22×C191—41no—
174C22×C191—41no—
175C22×C191—41no—
176C22×C191—41no—
177C22×C191—41no—
178C22×C191—41no—
179C22×C191—84no—
180C22×C191C22×D411yescharacteristic
181C2×D191—21no—
182C2×D191—21no—
183C2×D191—21no—
184C2×D191—21no—
185C2×D191—21no—
186C2×D191—21no—
187C2×D191—41no—
188C2×D191—41no—
189C2×D191—41no—
190C2×D191—84no—
191C4×C191—21no—
192C4×C191—41no—
193C4×C191H(5,𝔽2)11yescharacteristic
194C4×C191H(5,𝔽2)11yescharacteristic
195Dic191—21no—
196Dic191—21no—
197Dic191—41no—
198Dic191—41no—
199Dic191—41no—
200C2×C191—41no—
201C2×C191—81no—
202C2×C191—81no—
203C2×C191—81no—
204C2×C191#53411yescharacteristic
205C2×C191#57611yescharacteristic
206C2×C191#57611yescharacteristic
207D191—41no—
208D191—41no—
209D191—81no—
210C191#319911yescharacteristic, complemented, Sylow
211#3199—1911nomaximal, Sylow
212#535—1911no—
213#535—1911no—
214#482—1911no—
215#482—1911no—
216#482—1911no—
217#482—1911no—
218#469—1911no—
219#469—1911no—
220#466—1911no—
221#466—1911no—
222#447—1911no—
223#447—1911no—
224#447—1911no—
225#447D19111yescharacteristic, complemented
226#408—1911no—
227C2×#41—1911no—
228C22×D4—1911no—
229C22×D4C2×D19111yescharacteristic, complemented
230C2×D8—1911no—
231C2×D8—1911no—
232C2×D8C2×D19111yescharacteristic
233C2×D8C2×D19111yescharacteristic
234C2×M16—1911no—
235C22×C8—1911no—
236#127—3821no—
237#127—3821no—
238#124—3821no—
239#124—3821no—
240#121—1911no—
241#121—1911no—
242#121—1911no—
243#121—1911no—
244#121—1911no—
245#121—1911no—
246#121—1911no—
247#121C2×D19111yescharacteristic
248#120—3821no—
249#120—3821no—
250#120—3821no—
251#120—3821no—
252#117—1911no—
253#117—1911no—
254#107—1911no—
255#107—1911no—
256#106—1911no—
257#106—1911no—
258#102—1911no—
259#102—1911no—
260#102—1911no—
261#102—1911no—
262#102—1911no—
263#102—1911no—
264#102C2×D19111yescharacteristic, complemented
265#102C2×D19111yescharacteristic, complemented
266C22⋊C8—1911no—
267C22⋊C8—1911no—
268C22⋊C8—1911no—
269C22⋊C8C2×D19111yescharacteristic, complemented
270C24—21no—
271C24—3821no—
272#41—7641no—
273#41—7641no—
274C2×Q8—1911no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—3821no—
280C2×D4—3821no—
281C2×D4—3821no—
282C2×D4—3821no—
283C2×D4—3821no—
284C2×D4—3821no—
285C2×D4—3821no—
286C2×D4—3821no—
287C2×D4—1911no—
288C2×D4—1911no—
289C2×D4—1911no—
290C2×D4—1911no—
291C2×D4—7641no—
292C2×D4—7641no—
293C2×D4C22×D19111yescharacteristic
294C2×D4C22×D19111yescharacteristic
295C2×D4C22×D19111yescharacteristic
296C22×C4—1911no—
297C22×C4—1911no—
298C22×C4C22×D19111yescharacteristic
299D8—41no—
300D8—41no—
301D8—7641no—
302D8—7641no—
303M16—7641no—
304C2×C8—1911no—
305C2×C8—1911no—
306C2×C8—7641no—
307C2×C8C22×D19111yescharacteristic
308C2×C8C22×D19111yescharacteristic
309C4⋊C4—1911no—
310C4⋊C4—1911no—
311C4⋊C4—1911no—
312C4⋊C4C22×D19111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C22⋊C4—3821no—
318C22⋊C4—3821no—
319C22⋊C4—3821no—
320C22⋊C4—3821no—
321C22⋊C4—3821no—
322C22⋊C4—3821no—
323C42—3821no—
324C42—3821no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—3821no—
332C23—1911no—
333C23—1911no—
334C23—15281no—
335C23—15281no—
336C23—7642no—
337C23D4×D19111yescharacteristic
338Q8—7641no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—3821no—
348D4—3821no—
349D4—15281no—
350D4—15281no—
351D4—15281no—
352D4—15281no—
353D4—15281no—
354D4—15281no—
355D4—15281no—
356D4—7641no—
357D4—7641no—
358D4—7641no—
359D4—7642no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3821no—
364C2×C4—3821no—
365C2×C4—3821no—
366C2×C4—3821no—
367C2×C4—3821no—
368C2×C4—3821no—
369C2×C4—3821no—
370C2×C4—1911no—
371C2×C4—1911no—
372C2×C4D4×D19111yescharacteristic
373C2×C4C23×D19111yescharacteristic
374C8—21no—
375C8—21no—
376C8—3821no—
377C8—3821no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—3821no—
392C22—3821no—
393C22—3821no—
394C22—3821no—
395C22—3821no—
396C22—3821no—
397C22—15284no—
398C22—7641no—
399C22—7641no—
400C22—7641no—
401C22C2×D4×D19111yescharacteristic
402C4—21no—
403C4—41no—
404C4—3821no—
405C4—3821no—
406C4—7641no—
407C4—7641no—
408C4—7641no—
409C4#2025936711yescharacteristic
410C4#2025936711yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—15281no—
416C2—7641no—
417C2—7641no—
418C2#2713322311yescharacteristic
419C2#2713346411yescharacteristic
420C2#2713346711yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#447×C191C2
socleC22×C191C22×D4
hypercenter#447D191
hypocenterC191#3199
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #27133230C2semidirect
2. #27133229C2semidirect
3. #27132988C2semidirect
4. #27132986C2semidirect
5. #27132985C2semidirect
6. #27132984C2semidirect
7. #27132915C2semidirect
8. #27132913C2semidirect
9. #27132898C2semidirect
10. #27132896C2semidirect
11. #27132797C2semidirect
12. #27132795C2semidirect
13. #27132795C2semidirect
14. #27132628C2semidirect
15. #447×C191C2semidirect
17. C2×D4×D191C22semidirect
20. C2×#15690270C22semidirect
21. C2×C8×D191C22semidirect
26. #20259297C22semidirect
30. #20259293C22semidirect
31. #20259293C22semidirect
32. #20259293C22semidirect
37. #20259281C22semidirect
38. #20259280C22semidirect
39. #20259256C22semidirect
40. #20259255C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
43. #20259244C22semidirect
44. #20259244C22semidirect
45. #20259243C22semidirect
46. #20259243C22semidirect
47. #20259243C22semidirect
48. #20259243C22semidirect
49. C22⋊(C191⋊C8)C22semidirect
50. (C2×D191)⋊C8C22semidirect
51. (C2×D191)⋊C8C22semidirect
52. C22×D4×C191C22semidirect
56. #102×C191C22semidirect
57. #102×C191C22semidirect
58. C22⋊C8×C191C22semidirect
210. C191#3199semidirect
225. #447D191semidirect
229. C22×D4C2×D191semidirect
264. #102C2×D191semidirect
265. #102C2×D191semidirect
269. C22⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332302
#271332292
#271329882
#271329862
#271329852
#271329842
#271329152
#271329132
#271328982
#271328962
#271327972
#271327952
#271326282
#447×C1912
#3199191