Finite Group Databasebeta

← #485×D191 #37582408

Subgroups — #485×D191 #37582408

Order 24448.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D191C211yesmaximal, characteristic
2#117×D191C211yesmaximal, characteristic
3#27133007C211yesmaximal, characteristic, complemented
4#27133006C211yesmaximal, characteristic, complemented
5#27133005C211yesmaximal, characteristic, complemented
6#27133004C211yesmaximal, characteristic, complemented
7#27133003C211yesmaximal, characteristic, complemented
8#27133002C211yesmaximal, characteristic, complemented
9#27133001C211yesmaximal, characteristic, complemented
10#107×D191C211yesmaximal, characteristic, complemented
11#106×D191C211yesmaximal, characteristic, complemented
12#103×D191C211yesmaximal, characteristic, complemented
13#103×D191C211yesmaximal, characteristic, complemented
14C22⋊C8×D191C211yesmaximal, characteristic
15#485×C191C211yesmaximal, characteristic, complemented
16C2×Q8×D191C2211yescharacteristic
17C22×C4×D191C2211yescharacteristic
18C2×C8×D191C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259302C2211yescharacteristic
21#20259301C2211yescharacteristic
22#20259300—21no—
23#20259299—21no—
24#20259298C2211yescharacteristic
25#20259281C2211yescharacteristic
26#20259280C2211yescharacteristic
27#20259280C2211yescharacteristic
28#20259279—21no—
29#20259278—21no—
30C4⋊C4×D191—21no—
31C4⋊C4×D191C2211yescharacteristic
32C4⋊C4×D191C2211yescharacteristic
33C4⋊C4×D191C2211yescharacteristic
34C22⋊C4×D191—21no—
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#20259247C2211yescharacteristic, complemented
44#20259247C2211yescharacteristic, complemented
45#20259246C2211yescharacteristic, complemented
46#20259246C2211yescharacteristic, complemented
47#20259245C2211yescharacteristic, complemented
48#20259245C2211yescharacteristic, 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
60C2×Dic382—21no—
61C2×Dic382C2311yescharacteristic
62Q8×D191—22no—
63Q8×D191—22no—
64C22×Dic191D411yescharacteristic
65C2×C4×D191—22no—
66C2×C4×D191—22no—
67C2×C4×D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191D411yescharacteristic
72C2×C4×D191D411yescharacteristic
73C2×C4×D191C2311yescharacteristic
74C2×C4×D191C2311yescharacteristic
75C2×C191⋊C8C2311yescharacteristic
76C2×C191⋊C8C2311yescharacteristic
77C8×D191—22no—
78C8×D191—22no—
79C4⋊Dic191—21no—
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—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—22no—
110C22×D191—22no—
111C22×D191C2×D411yescharacteristic
112C22×D191C2×D411yescharacteristic
113Dic382—21no—
114Dic382—21no—
115Dic382—42no—
116C2×Dic191—22no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191C2×D411yescharacteristic
122C2×Dic191C2×D411yescharacteristic
123C4×D191—22no—
124C4×D191—21no—
125C4×D191—21no—
126C4×D191—22no—
127C4×D191—42no—
128C4×D191—42no—
129C4×D191—42no—
130C4×D191—42no—
131C4×D191#4112yes—
132C4×D191#4112yes—
133C191⋊C8—21no—
134C191⋊C8—21no—
135C23×C191C2×D411yescharacteristic
136Q8×C191—21no—
137Q8×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C8×C191—21no—
147C8×C191—21no—
148C22×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191C22×D411yescharacteristic
152C2×D191—21no—
153C2×D191—21no—
154C2×D191—21no—
155C2×D191—44no—
156C2×D191#12312yes—
157C2×D191#13512yes—
158C2×D191#13712yes—
159C4×C191—21no—
160C4×C191—41no—
161C4×C191—41no—
162C4×C191—41no—
163C4×C191—41no—
164C4×C191C2×#4111yescharacteristic
165C4×C191C2×#4111yescharacteristic
166Dic191—21no—
167Dic191—41no—
168Dic191—41no—
169Dic191—41no—
170Dic191—41no—
171Dic191#12312yes—
172C2×C191—41no—
173C2×C191C2×#12311yescharacteristic
174C2×C191C2×#13511yescharacteristic
175C2×C191C2×#13711yescharacteristic
176D191—41no—
177D191#48514yesdirect product factor
178C191C2×#48511yescharacteristic, complemented, Sylow
179C2×#485—1911nomaximal, Sylow
180C2×C22⋊Q8—1911no—
181C2×#117—1911no—
182#485—1911no—
183#485—1911no—
184#485—1911no—
185#485—1911no—
186#485—1911no—
187#485—1911no—
188#485—1911no—
189#485D19111yescharacteristic, direct product factor
190C2×#107—1911no—
191C2×#106—1911no—
192C2×#103—1911no—
193C2×#103—1911no—
194C2×C22⋊C8—1911no—
195C22×Q8—1911no—
196C23×C4—1911no—
197C22×C8—1911no—
198C22×C8—1911no—
199C22⋊Q8—3821no—
200C22⋊Q8—3821no—
201C22⋊Q8—1911no—
202C22⋊Q8—1911no—
203C22⋊Q8—1911no—
204C22⋊Q8C2×D19111yescharacteristic
205#117—3821no—
206#117—3821no—
207#117—1911no—
208#117—1911no—
209#117—1911no—
210#117C2×D19111yescharacteristic
211C2×C4⋊C4—3821no—
212C2×C4⋊C4—1911no—
213C2×C4⋊C4—1911no—
214C2×C4⋊C4—1911no—
215C2×C22⋊C4—3821no—
216C2×C22⋊C4—3821no—
217C2×C42—3821no—
218#107—1911no—
219#107—1911no—
220#107—1911no—
221#107C2×D19111yescharacteristic, complemented
222#106—1911no—
223#106—1911no—
224#106—1911no—
225#106C2×D19111yescharacteristic, complemented
226#103—1911no—
227#103—1911no—
228#103—1911no—
229#103—1911no—
230#103—1911no—
231#103—1911no—
232#103C2×D19111yescharacteristic, complemented
233#103C2×D19111yescharacteristic, complemented
234C22⋊C8—1911no—
235C22⋊C8—1911no—
236C22⋊C8—1911no—
237C22⋊C8C2×D19111yescharacteristic
238C24—1911no—
239C2×Q8—3821no—
240C2×Q8—3822no—
241C2×Q8—3822no—
242C2×Q8—1911no—
243C2×Q8C22×D19111yescharacteristic
244C22×C4—3822no—
245C22×C4—3822no—
246C22×C4—3821no—
247C22×C4—3821no—
248C22×C4—3821no—
249C22×C4—3821no—
250C22×C4—1911no—
251C22×C4—1911no—
252C22×C4—1911no—
253C22×C4—1911no—
254C22×C4—1911no—
255C22×C4C22×D19111yescharacteristic
256C2×C8—3822no—
257C2×C8—3822no—
258C2×C8—1911no—
259C2×C8—1911no—
260C2×C8C22×D19111yescharacteristic
261C2×C8C22×D19111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3821no—
264C4⋊C4—3821no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—3821no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4—1911no—
272C4⋊C4C22×D19111yescharacteristic
273C4⋊C4C22×D19111yescharacteristic
274C4⋊C4C22×D19111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C42—21no—
284C42—3821no—
285C42—3821no—
286C42—3821no—
287C23—3822no—
288C23—3822no—
289C23—3822no—
290C23—1911no—
291C23—1911no—
292C23D4×D19111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3821no—
296Q8—3821no—
297Q8—7642no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—3822no—
305C2×C4—3822no—
306C2×C4—3822no—
307C2×C4—3821no—
308C2×C4—3821no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—1911no—
314C2×C4—1911no—
315C2×C4—1912no—
316C2×C4—1912no—
317C2×C4—7642no—
318C2×C4—7642no—
319C2×C4—7642no—
320C2×C4—7642no—
321C2×C4D4×D19111yescharacteristic
322C2×C4C23×D19111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3821no—
326C8—3821no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—3821no—
331C22—3821no—
332C22—3821no—
333C22—1912no—
334C22—1912no—
335C22—1912no—
336C22—7644no—
337C22C2×D4×D19111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3821no—
344C4—1912no—
345C4—7641no—
346C4—7641no—
347C4—7641no—
348C4—7641no—
349C4#41×D19111yescharacteristic
350C4#41×D19111yescharacteristic
351C2—41no—
352C2—1914no—
353C2—7641no—
354C2#123×D19111yescharacteristic
355C2#135×D19111yescharacteristic
356C2#137×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#485×C191C2
socleC22×C191C22×D4
prime radicalC23×D191D4
hypercenter#485D191
hypocenterC191C2×#485
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
3. #27133007C2semidirect
4. #27133006C2semidirect
5. #27133005C2semidirect
6. #27133004C2semidirect
7. #27133003C2semidirect
8. #27133002C2semidirect
9. #27133001C2semidirect
10. #107×D191C2semidirect
11. #106×D191C2semidirect
12. #103×D191C2semidirect
13. #103×D191C2semidirect
15. #485×C191C2semidirect
37. #20259256C22semidirect
38. #20259255C22semidirect
39. #20259255C22semidirect
40. #20259254C22semidirect
41. #20259253C22semidirect
42. #20259253C22semidirect
43. #20259247C22semidirect
44. #20259247C22semidirect
45. #20259246C22semidirect
46. #20259246C22semidirect
47. #20259245C22semidirect
48. #20259245C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #103×C191C22semidirect
57. #103×C191C22semidirect
177. D191#485direct (N × H)
178. C191C2×#485semidirect
189. #485D191direct (N × H)
221. #107C2×D191semidirect
225. #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
C22⋊Q8×D1912
#117×D1912
#271330072
#271330062
#271330052
#271330042
#271330032
#271330022
#271330012
#107×D1912
#106×D1912
#103×D1912
C22⋊C8×D1912
#485×C1912
C2×#485191