Finite Group Databasebeta

← #37582452

Subgroups — #37582452

Order 24448.

414 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133176C211yesmaximal, characteristic
2#117×D191C211yesmaximal, characteristic, complemented
3#27133003C211yesmaximal, characteristic, complemented
4#27133002C211yesmaximal, characteristic, complemented
5#27133001C211yesmaximal, characteristic, complemented
6#27132990C211yesmaximal, characteristic, complemented
7#27132989C211yesmaximal, characteristic, complemented
8#27132988C211yesmaximal, characteristic, complemented
9#27132987C211yesmaximal, characteristic, complemented
10#27132704C211yesmaximal, characteristic, complemented
11#27132702C211yesmaximal, characteristic, complemented
12#27132663C211yesmaximal, characteristic, complemented
13#27132663C211yesmaximal, characteristic, complemented
14#27132625C211yesmaximal, characteristic, complemented
15#485×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C22×C4×D191C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×#15690270C2211yescharacteristic
20#20259307—21no—
21#20259298C2211yescharacteristic
22#20259297C2211yescharacteristic
23#20259296C2211yescharacteristic
24#20259292—21no—
25#20259284—21no—
26(C22⋊D191)⋊C4—21no—
27#20259281C2211yescharacteristic
28#20259280C2211yescharacteristic
29#20259280C2211yescharacteristic
30#20259280C2211yescharacteristic
31#20259279—21no—
32#20259278—21no—
33C4⋊C4×D191C2211yescharacteristic
34C4⋊C4×D191C2211yescharacteristic
35C22⋊C4×D191—21no—
36C42×D191—21no—
37#20259256C2211yescharacteristic, complemented
38#20259255C2211yescharacteristic, complemented
39#20259255C2211yescharacteristic, complemented
40#20259254C2211yescharacteristic, complemented
41#20259253C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259246C2211yescharacteristic, complemented
44#20259246C2211yescharacteristic, complemented
45#20259244C2211yescharacteristic, complemented
46#20259244C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic, complemented
48#20259242C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22⋊Q8×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#103×C191C2211yescharacteristic, complemented
57#103×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C23×D191D411yescharacteristic
60#15690288—22no—
61#15690288—22no—
62C2×D764—21no—
63C2×D764—21no—
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C22×Dic191D411yescharacteristic
67C2×C4×D191—22no—
68C2×C4×D191—22no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191D411yescharacteristic
73C2×C4×D191D411yescharacteristic
74C2×C4×D191C2311yescharacteristic
75C2×C4×D191C2311yescharacteristic
76#15690270—22no—
77#15690270—22no—
78C2×C191⋊C8C2311yescharacteristic
79C2×C191⋊C8C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86C22⋊Dic191—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93C4×Dic191—21no—
94C4×Dic191—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C2×Q8×C191C2311yescharacteristic
98C22×C4×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C4⋊C4×C191—21no—
102C4⋊C4×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C22×D191—22no—
109C22×D191—21no—
110C22×D191—41no—
111C22×D191—41no—
112C22×D191C2×D411yescharacteristic
113C22×D191C2×D411yescharacteristic
114D764—21no—
115D764—21no—
116D764—42no—
117D764—42no—
118C22⋊D191—42no—
119C2×Dic191—22no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C4×D191—22no—
126C4×D191—21no—
127C4×D191—21no—
128C4×D191—22no—
129C4×D191—42no—
130C4×D191—42no—
131C4×D191—42no—
132C4×D191#4112yes—
133C4×D191#4112yes—
134C191⋊C8—21no—
135C191⋊C8—21no—
136C23×C191C2×D411yescharacteristic
137Q8×C191—21no—
138Q8×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191—21no—
152C22×C191C22×D411yescharacteristic
153C2×D191—21no—
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—21no—
157C2×D191—21no—
158C2×D191—44no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—41no—
162C2×D191#12312yes—
163C4×C191—21no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191—41no—
167C4×C191—41no—
168C4×C191C2×#4111yescharacteristic
169C4×C191C2×#4111yescharacteristic
170Dic191—21no—
171Dic191—41no—
172Dic191—41no—
173Dic191—41no—
174Dic191#12312yes—
175C2×C191—41no—
176C2×C191C2×#12311yescharacteristic
177C2×C191#57511yescharacteristic
178C2×C191#57511yescharacteristic
179D191—22no—
180D191—41no—
181D191—81no—
182C191#309311yescharacteristic, complemented, Sylow
183#3093—1911nomaximal, Sylow
184#525—1911no—
185C2×#117—1911no—
186#485—1911no—
187#485—1911no—
188#485—1911no—
189#485D19111yescharacteristic, complemented
190#482—1911no—
191#482—1911no—
192#482—1911no—
193#482—1911no—
194#428—1911no—
195#428—1911no—
196#417—1911no—
197#417—1911no—
198#407—1911no—
199C2×#41—1911no—
200C23×C4—1911no—
201C2×M16—1911no—
202C2×M16—1911no—
203#123—3821no—
204C22⋊Q8—1911no—
205C22⋊Q8C2×D19111yescharacteristic
206#121—1911no—
207#121—1911no—
208#120—3821no—
209C4×D4—3821no—
210C4×D4—3821no—
211#117—3821no—
212#117—3821no—
213#117—1911no—
214#117—1911no—
215#117—1911no—
216#117—1911no—
217#117C2×D19111yescharacteristic
218C2×C4⋊C4—1911no—
219C2×C4⋊C4—1911no—
220C2×C22⋊C4—3821no—
221C2×C42—3821no—
222#107—1911no—
223#107—1911no—
224#107—1911no—
225#107C2×D19111yescharacteristic, complemented
226#106—1911no—
227#106—1911no—
228#106—1911no—
229#106C2×D19111yescharacteristic, complemented
230#103—1911no—
231#103—1911no—
232#103C2×D19111yescharacteristic, complemented
233#103C2×D19111yescharacteristic, complemented
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238C22⋊C8—1911no—
239C22⋊C8—1911no—
240C22⋊C8—1911no—
241C22⋊C8C2×D19111yescharacteristic
242C24—1911no—
243#41—3822no—
244#41—3822no—
245C2×Q8C22×D19111yescharacteristic
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4—1911no—
250C22×C4—3822no—
251C22×C4—3822no—
252C22×C4—3821no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—1911no—
256C22×C4—1911no—
257C22×C4—1911no—
258C22×C4—1911no—
259C22×C4—1911no—
260C22×C4C22×D19111yescharacteristic
261M16—3822no—
262M16—3822no—
263C2×C8—1911no—
264C2×C8—1911no—
265C2×C8C22×D19111yescharacteristic
266C2×C8C22×D19111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—3821no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—1911no—
272C4⋊C4—1911no—
273C4⋊C4—1911no—
274C4⋊C4C22×D19111yescharacteristic
275C4⋊C4C22×D19111yescharacteristic
276C4⋊C4C22×D19111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C42—21no—
287C42—3821no—
288C42—3821no—
289C42—3821no—
290C42—3821no—
291C23—3822no—
292C23—3821no—
293C23—1911no—
294C23—1911no—
295C23—7641no—
296C23—7641no—
297C23D4×D19111yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—3821no—
301D4—3821no—
302D4—7642no—
303D4—7642no—
304D4—7642no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3822no—
312C2×C4—3822no—
313C2×C4—3822no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—1911no—
320C2×C4—1911no—
321C2×C4—1912no—
322C2×C4—1912no—
323C2×C4—7642no—
324C2×C4—7642no—
325C2×C4—7642no—
326C2×C4D4×D19111yescharacteristic
327C2×C4C23×D19111yescharacteristic
328C8—21no—
329C8—21no—
330C8—3821no—
331C8—3821no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—3821no—
336C22—3821no—
337C22—3821no—
338C22—3821no—
339C22—3821no—
340C22—1912no—
341C22—7644no—
342C22—7641no—
343C22—7641no—
344C22—7641no—
345C22C2×D4×D19111yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—3821no—
352C4—1912no—
353C4—7641no—
354C4—7641no—
355C4—7641no—
356C4#41×D19111yescharacteristic
357C4#41×D19111yescharacteristic
358C2—41no—
359C2—3822no—
360C2—15281no—
361C2—7641no—
362C2#123×D19111yescharacteristic
363C2#2713346011yescharacteristic
364C2#2713346211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#485×C191C2
socleC22×C191C22×D4
prime radical#27133176C2
hypercenter#485D191
hypocenterC191#3093
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #117×D191C2semidirect
3. #27133003C2semidirect
4. #27133002C2semidirect
5. #27133001C2semidirect
6. #27132990C2semidirect
7. #27132989C2semidirect
8. #27132988C2semidirect
9. #27132987C2semidirect
10. #27132704C2semidirect
11. #27132702C2semidirect
12. #27132663C2semidirect
13. #27132663C2semidirect
14. #27132625C2semidirect
15. #485×C191C2semidirect
37. #20259256C22semidirect
38. #20259255C22semidirect
39. #20259255C22semidirect
40. #20259254C22semidirect
41. #20259253C22semidirect
42. #20259253C22semidirect
43. #20259246C22semidirect
44. #20259246C22semidirect
45. #20259244C22semidirect
46. #20259244C22semidirect
47. #20259242C22semidirect
48. #20259242C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #103×C191C22semidirect
57. #103×C191C22semidirect
182. C191#3093semidirect
189. #485D191semidirect
225. #107C2×D191semidirect
229. #106C2×D191semidirect
232. #103C2×D191semidirect
233. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331762
#117×D1912
#271330032
#271330022
#271330012
#271329902
#271329892
#271329882
#271329872
#271327042
#271327022
#271326632
#271326252
#485×C1912
#3093191