Finite Group Databasebeta

← #37583384

Subgroups — #37583384

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#27133232C211yesmaximal, characteristic, complemented
2#27133229C211yesmaximal, characteristic, complemented
3#27132990C211yesmaximal, characteristic, complemented
4#27132989C211yesmaximal, characteristic, complemented
5#27132987C211yesmaximal, characteristic, complemented
6#27132917C211yesmaximal, characteristic, complemented
7#27132915C211yesmaximal, characteristic, complemented
8#27132900C211yesmaximal, characteristic, complemented
9#27132898C211yesmaximal, characteristic, complemented
10#27132799C211yesmaximal, characteristic, complemented
11#27132798C211yesmaximal, characteristic, complemented
12#27132798C211yesmaximal, characteristic, complemented
13#27132796C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#482×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C22×D764C2211yescharacteristic, complemented
18C2×D4×D191C2211yescharacteristic, complemented
19C2×D1528C2211yescharacteristic
20C2×D1528C2211yescharacteristic
21C2×#15690272C2211yescharacteristic
22C2×#15690272C2211yescharacteristic
23C2×#15690270C2211yescharacteristic, complemented
24C2×C8×D191C2211yescharacteristic, complemented
25#20259319—21no—
26#20259318—21no—
27#20259310—21no—
28#20259308—21no—
29#20259297C2211yescharacteristic
30#20259297C2211yescharacteristic
31#20259297C2211yescharacteristic, complemented
32#20259297C2211yescharacteristic, complemented
33#20259297C2211yescharacteristic, complemented
34#20259296C2211yescharacteristic
35#20259293C2211yescharacteristic, complemented
36#20259292—21no—
37#20259292—21no—
38#20259292—21no—
39#20259290—21no—
40#20259280C2211yescharacteristic, complemented
41#20259255C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic, complemented
45#20259242C2211yescharacteristic, complemented
46#20259242C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic, complemented
48#20259242C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic, complemented
50(C2×D191)⋊C8C2211yescharacteristic, complemented
51(C2×D191)⋊C8C2211yescharacteristic, complemented
52#121×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic, complemented
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#102×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C23×D191—21no—
61#15690287—41no—
62#15690287—41no—
63C2×Dic382D411yescharacteristic
64C2×D764—21no—
65C2×D764—21no—
66C2×D764—21no—
67C2×D764—21no—
68C2×D764—21no—
69C2×D764—21no—
70C2×D764—41no—
71C2×D764—41no—
72C2×D764D411yescharacteristic
73C2×D764C2311yescharacteristic
74C2×D764C2311yescharacteristic
75C2×D764C2311yescharacteristic
76C2×C22⋊D191—21no—
77C2×C22⋊D191—21no—
78C2×C22⋊D191—21no—
79C2×C22⋊D191D411yescharacteristic
80C2×C22⋊D191D411yescharacteristic
81D4×D191—41no—
82D4×D191—41no—
83C2×C4×D191C2311yescharacteristic
84C2×C4×D191C2311yescharacteristic
85D1528—41no—
86D1528—41no—
87#15690272—41no—
88#15690272—41no—
89#15690270—41no—
90C2×C191⋊C8C2311yescharacteristic
91C2×C191⋊C8C2311yescharacteristic
92C8×D191—41no—
93C4⋊Dic191C2311yescharacteristic
94C22⋊Dic191—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99(C2×D191)⋊C4—21no—
100(C2×D191)⋊C4—21no—
101(C2×D191)⋊C4—21no—
102C4×Dic191—21no—
103C2×D4×C191—21no—
104C2×D4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C2×C8×C191C2311yescharacteristic
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C4⋊C4×C191C2311yescharacteristic
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C42×C191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—42no—
118C22×D191—42no—
119C22×D191—81no—
120C22×D191—81no—
121C22×D191—81no—
122C22×D191—81no—
123C22×D191C2×D411yescharacteristic
124C22×D191C2×D411yescharacteristic
125Dic382—41no—
126D764—21no—
127D764—21no—
128D764—21no—
129D764—21no—
130D764—21no—
131D764—21no—
132D764—41no—
133D764—42no—
134D764—81no—
135D764—81no—
136D764—81no—
137D764—81no—
138D764—81no—
139C22⋊D191—41no—
140C22⋊D191—41no—
141C22⋊D191—42no—
142C22⋊D191—81no—
143C22⋊D191—81no—
144C2×Dic191—21no—
145C2×Dic191C2×D411yescharacteristic
146C2×Dic191C2×D411yescharacteristic
147C4×D191—21no—
148C4×D191—21no—
149C4×D191—21no—
150C4×D191—21no—
151C191⋊C8—21no—
152C191⋊C8—21no—
153C23×C191—21no—
154C23×C191C2×D411yescharacteristic
155D4×C191—21no—
156D4×C191—21no—
157D4×C191—81no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
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×C191C22×D411yescharacteristic
174C2×D191—21no—
175C2×D191—21no—
176C2×D191—21no—
177C2×D191—21no—
178C2×D191—21no—
179C2×D191—21no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191—41no—
183C2×D191—41no—
184C2×D191—41no—
185C2×D191—41no—
186C2×D191—41no—
187C2×D191—41no—
188C2×D191—41no—
189C2×D191—84no—
190C2×D191—84no—
191C4×C191—21no—
192C4×C191—41no—
193C4×C191—41no—
194C4×C191—41no—
195C4×C191H(5,𝔽2)11yescharacteristic
196C4×C191H(5,𝔽2)11yescharacteristic
197Dic191—21no—
198Dic191—21no—
199Dic191—41no—
200C2×C191—41no—
201C2×C191—81no—
202C2×C191#53411yescharacteristic
203C2×C191#57611yescharacteristic
204C2×C191#57611yescharacteristic
205D191—41no—
206D191—41no—
207D191—81no—
208D191—81no—
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#482D19111yescharacteristic, complemented
218#469—1911no—
219#469—1911no—
220#466—1911no—
221#466—1911no—
222#447—1911no—
223#447—1911no—
224#447—1911no—
225#447—1911no—
226#408—1911no—
227C2×#41—1911no—
228C22×D4—1911no—
229C22×D4—1911no—
230C2×D8—1911no—
231C2×D8—1911no—
232C2×D8—1911no—
233C2×D8—1911no—
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#117C2×D19111yescharacteristic, complemented
254#107—1911no—
255#107C2×D19111yescharacteristic, complemented
256#106—1911no—
257#106C2×D19111yescharacteristic, complemented
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—3821no—
271C24—3821no—
272#41—7641no—
273#41—7641no—
274C2×Q8—1911no—
275C2×D4—21no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3821no—
279C2×D4—3821no—
280C2×D4—3821no—
281C2×D4—3821no—
282C2×D4—3821no—
283C2×D4—3821no—
284C2×D4—3821no—
285C2×D4—1911no—
286C2×D4—1911no—
287C2×D4—1911no—
288C2×D4—1911no—
289C2×D4—1911no—
290C2×D4—1911no—
291C2×D4—7641no—
292C2×D4—7641no—
293C2×D4—7641no—
294C2×D4—7641no—
295C2×D4C22×D19111yescharacteristic
296C22×C4—1911no—
297C22×C4—1911no—
298C22×C4C22×D19111yescharacteristic
299D8—7641no—
300D8—7641no—
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⋊C4C22×D19111yescharacteristic
311C4⋊C4C22×D19111yescharacteristic
312C4⋊C4C22×D19111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
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—21no—
324C42—3821no—
325C23—21no—
326C23—3821no—
327C23—3821no—
328C23—3821no—
329C23—1911no—
330C23—1911no—
331C23—15281no—
332C23—15281no—
333C23—15281no—
334C23—15281no—
335C23—7642no—
336C23—7642no—
337C23D4×D19111yescharacteristic
338Q8—7641no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—3821no—
343D4—3821no—
344D4—3821no—
345D4—3821no—
346D4—3821no—
347D4—3821no—
348D4—15281no—
349D4—15281no—
350D4—15281no—
351D4—15281no—
352D4—15281no—
353D4—15281no—
354D4—15281no—
355D4—7641no—
356D4—7642no—
357D4—7641no—
358D4—7641no—
359D4—7642no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
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—3821no—
385C22—3821no—
386C22—3821no—
387C22—3821no—
388C22—3821no—
389C22—3821no—
390C22—15284no—
391C22—15284no—
392C22—7641no—
393C22—7641no—
394C22—7641no—
395C22—7641no—
396C22—7641no—
397C22—7641no—
398C22—7641no—
399C22—7641no—
400C22—7641no—
401C22C2×D4×D19111yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3821no—
407C4—3821no—
408C4—7641no—
409C4#2025936811yescharacteristic
410C4#2025936811yescharacteristic
411C2—41no—
412C2—81no—
413C2—15281no—
414C2—15281no—
415C2—15281no—
416C2—7641no—
417C2—7641no—
418C2#2713322411yescharacteristic
419C2#2713346511yescharacteristic
420C2#2713346711yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#482×C191C2
socleC22×C191C22×D4
hypercenter#482D191
hypocenterC191#3199
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #27133232C2semidirect
2. #27133229C2semidirect
3. #27132990C2semidirect
4. #27132989C2semidirect
5. #27132987C2semidirect
6. #27132917C2semidirect
7. #27132915C2semidirect
8. #27132900C2semidirect
9. #27132898C2semidirect
10. #27132799C2semidirect
11. #27132798C2semidirect
12. #27132798C2semidirect
13. #27132796C2semidirect
14. #27132628C2semidirect
15. #482×C191C2semidirect
17. C22×D764C22semidirect
18. C2×D4×D191C22semidirect
23. C2×#15690270C22semidirect
24. C2×C8×D191C22semidirect
31. #20259297C22semidirect
32. #20259297C22semidirect
33. #20259297C22semidirect
35. #20259293C22semidirect
40. #20259280C22semidirect
41. #20259255C22semidirect
42. #20259253C22semidirect
43. #20259244C22semidirect
44. #20259244C22semidirect
45. #20259242C22semidirect
46. #20259242C22semidirect
47. #20259242C22semidirect
48. #20259242C22semidirect
49. C22⋊(C191⋊C8)C22semidirect
50. (C2×D191)⋊C8C22semidirect
51. (C2×D191)⋊C8C22semidirect
53. #117×C191C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #102×C191C22semidirect
57. #102×C191C22semidirect
58. C22⋊C8×C191C22semidirect
210. C191#3199semidirect
217. #482D191semidirect
253. #117C2×D191semidirect
255. #107C2×D191semidirect
257. #106C2×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
#271332322
#271332292
#271329902
#271329892
#271329872
#271329172
#271329152
#271329002
#271328982
#271327992
#271327982
#271327962
#271326282
#482×C1912
#3199191