Finite Group Databasebeta

← #37582431

Subgroups — #37582431

Order 24448.

420 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#27133170C211yesmaximal, characteristic
2#117×D191C211yesmaximal, characteristic, complemented
3#27133003C211yesmaximal, characteristic, complemented
4#27133002C211yesmaximal, characteristic, complemented
5#27132997C211yesmaximal, characteristic, complemented
6#27132992C211yesmaximal, characteristic, complemented
7#27132986C211yesmaximal, characteristic, complemented
8#27132985C211yesmaximal, characteristic, complemented
9#27132980C211yesmaximal, characteristic, complemented
10#27132975C211yesmaximal, characteristic, complemented
11#27132701C211yesmaximal, characteristic, complemented
12#27132699C211yesmaximal, characteristic, complemented
13#27132659C211yesmaximal, characteristic, complemented
14C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
15#416×C191C211yesmaximal, characteristic, complemented
16C22×C4×D191C2211yescharacteristic
17C22×C191⋊C8C2211yescharacteristic
18#20259303—21no—
19#20259298C2211yescharacteristic
20#20259298C2211yescharacteristic
21#20259293C2211yescharacteristic
22#20259293C2211yescharacteristic
23#20259290—21no—
24C4×C22⋊D191—21no—
25C4×C22⋊D191—21no—
26#20259281C2211yescharacteristic
27#20259281C2211yescharacteristic
28#20259280C2211yescharacteristic
29#20259280C2211yescharacteristic
30#20259279—21no—
31#20259278—21no—
32C4⋊C4×D191C2211yescharacteristic
33C4⋊C4×D191C2211yescharacteristic
34C22⋊C4×D191—21no—
35C42×D191—21no—
36#20259256C2211yescharacteristic, complemented
37#20259256C2211yescharacteristic, complemented
38#20259255C2211yescharacteristic, complemented
39#20259255C2211yescharacteristic, complemented
40#20259254C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259253C2211yescharacteristic, complemented
44#20259246C2211yescharacteristic, complemented
45#20259246C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic, complemented
47#20259243C2211yescharacteristic, complemented
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic
53C22×C8×C191C2211yescharacteristic
54#117×C191C2211yescharacteristic
55#103×C191C2211yescharacteristic, complemented
56#103×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58#102×C191C2211yescharacteristic, complemented
59C23×D191D411yescharacteristic
60C2×C22⋊D191—21no—
61C2×C22⋊D191—21no—
62C22×Dic191D411yescharacteristic
63C2×C4×D191—21no—
64C2×C4×D191—21no—
65C2×C4×D191—22no—
66C2×C4×D191—22no—
67C2×C4×D191D411yescharacteristic
68C2×C4×D191D411yescharacteristic
69C2×C4×D191C2311yescharacteristic
70C2×C4×D191C2311yescharacteristic
71C2×C191⋊C8—22no—
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C4⋊Dic191C2311yescharacteristic
75C4⋊Dic191C2311yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77C4⋊Dic191C2311yescharacteristic
78Dic191⋊C4—21no—
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82C22⋊Dic191—21no—
83C22⋊Dic191—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90C4×Dic191—21no—
91C4×Dic191—21no—
92C4×Dic191—21no—
93C4×Dic191—21no—
94#41×C191—22no—
95#41×C191—22no—
96C2×Q8×C191C2311yescharacteristic
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100C22×C4×C191C2311yescharacteristic
101C2×C8×C191—22no—
102C2×C8×C191C2311yescharacteristic
103C2×C8×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C22×D191—22no—
109C22×D191—22no—
110C22×D191—41no—
111C22×D191C2×D411yescharacteristic
112C22×D191C2×D411yescharacteristic
113C22⋊D191—42no—
114C22⋊D191—42no—
115C2×Dic191—22no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191C2×D411yescharacteristic
121C2×Dic191C2×D411yescharacteristic
122C4×D191—22no—
123C4×D191—22no—
124C4×D191—21no—
125C4×D191—21no—
126C4×D191—21no—
127C4×D191—21no—
128C4×D191—42no—
129C4×D191—42no—
130C191⋊C8—21no—
131C191⋊C8—21no—
132C23×C191—21no—
133C23×C191C2×D411yescharacteristic
134Q8×C191—21no—
135Q8×C191—21no—
136D4×C191—21no—
137D4×C191—21no—
138D4×C191—42no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—42no—
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191#4112yes—
145C2×C4×C191#4112yes—
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191#12312yes—
155C22×C191C22×D411yescharacteristic
156C2×D191—21no—
157C2×D191—21no—
158C2×D191—21no—
159C2×D191—21no—
160C2×D191—21no—
161C2×D191—44no—
162C2×D191#13512yes—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191#12312yes—
167C4×C191C2×#4111yescharacteristic
168C4×C191C2×#4111yescharacteristic
169Dic191—21no—
170Dic191—21no—
171Dic191—41no—
172Dic191—41no—
173Dic191—41no—
174Dic191—41no—
175C2×C191—22no—
176C2×C191—81no—
177C2×C191C2×#12311yescharacteristic
178C2×C191C2×#13511yescharacteristic
179C2×C191#57511yescharacteristic
180D191—22no—
181D191—41no—
182C191#309111yescharacteristic, complemented, Sylow
183#3091—1911nomaximal, Sylow
184#525—1911no—
185C2×#117—1911no—
186#485—1911no—
187#485—1911no—
188#484—1911no—
189#483—1911no—
190#482—1911no—
191#482—1911no—
192#481—1911no—
193#480—1911no—
194#427—1911no—
195#427—1911no—
196#416—1911no—
197#416D19111yescharacteristic, complemented
198C2×C22⋊C8—1911no—
199C2×#41C2×D19111yescharacteristic
200C23×C4—1911no—
201C22×C8—1911no—
202C22×C8C2×D19111yescharacteristic
203#123—3821no—
204C22⋊Q8—1911no—
205C22⋊Q8—1911no—
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#107—1911no—
226#106—1911no—
227#106—1911no—
228#106—1911no—
229#106—1911no—
230#103—1911no—
231#103—1911no—
232#103C2×D19111yescharacteristic, complemented
233#103C2×D19111yescharacteristic, complemented
234#102—1911no—
235#102—1911no—
236#102C2×D19111yescharacteristic, complemented
237#102C2×D19111yescharacteristic, complemented
238C22⋊C8—1911no—
239C22⋊C8—1911no—
240C22⋊C8—1911no—
241C22⋊C8—1911no—
242C24—1911no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D19111yescharacteristic
246C2×D4—21no—
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4C22×D19111yescharacteristic
250C22×C4—21no—
251C22×C4—3821no—
252C22×C4—3821no—
253C22×C4—3822no—
254C22×C4—3822no—
255C22×C4—1911no—
256C22×C4—1911no—
257C22×C4—1911no—
258C22×C4—1911no—
259C22×C4—1911no—
260C22×C4C22×D19111yescharacteristic
261C2×C8—22no—
262C2×C8—3822no—
263C2×C8—1911no—
264C2×C8—1911no—
265C2×C8C22×D19111yescharacteristic
266C2×C8C22×D19111yescharacteristic
267C4⋊C4—3821no—
268C4⋊C4—3821no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—1911no—
272C4⋊C4—1911no—
273C4⋊C4—1911no—
274C4⋊C4—1911no—
275C4⋊C4C22×D19111yescharacteristic
276C4⋊C4C22×D19111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3821no—
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—21no—
292C23—3822no—
293C23—3822no—
294C23—1911no—
295C23—1911no—
296C23—7641no—
297C23D4×D19111yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—7642no—
304D4—7642no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—3822no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3822no—
315C2×C4—3822no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—1911no—
321C2×C4—1911no—
322C2×C4—7642no—
323C2×C4—7642no—
324C2×C4D4×D19111yescharacteristic
325C2×C4#1569028612yes—
326C2×C4#1569028712yes—
327C2×C4C23×D19111yescharacteristic
328C8—21no—
329C8—21no—
330C8—3821no—
331C8—3821no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3821no—
338C22—3821no—
339C22—3821no—
340C22—3821no—
341C22—3821no—
342C22—1912no—
343C22—7644no—
344C22#2025930412yes—
345C22C2×D4×D19111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3821no—
350C4—3821no—
351C4—7641no—
352C4—7641no—
353C4—7641no—
354C4—7641no—
355C4#2025930412yes—
356C4C2×#1569028611yescharacteristic
357C4C2×#1569028711yescharacteristic
358C2—22no—
359C2—81no—
360C2—3822no—
361C2—7641no—
362C2C2×#2025930411yescharacteristic
363C2#135×D19111yescharacteristic
364C2#2713346011yescharacteristic
subgroupG/H
centerC2×C4D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#416×C191C2
socleC22×C191C22×D4
prime radical#27133170C2
hypercenter#416D191
hypocenterC191#3091
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D191C2semidirect
3. #27133003C2semidirect
4. #27133002C2semidirect
5. #27132997C2semidirect
6. #27132992C2semidirect
7. #27132986C2semidirect
8. #27132985C2semidirect
9. #27132980C2semidirect
10. #27132975C2semidirect
11. #27132701C2semidirect
12. #27132699C2semidirect
13. #27132659C2semidirect
14. C2×(C2×D191)⋊C8C2semidirect
15. #416×C191C2semidirect
36. #20259256C22semidirect
37. #20259256C22semidirect
38. #20259255C22semidirect
39. #20259255C22semidirect
40. #20259254C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
43. #20259253C22semidirect
44. #20259246C22semidirect
45. #20259246C22semidirect
46. #20259243C22semidirect
47. #20259243C22semidirect
55. #103×C191C22semidirect
56. #103×C191C22semidirect
57. #102×C191C22semidirect
58. #102×C191C22semidirect
182. C191#3091semidirect
197. #416D191semidirect
232. #103C2×D191semidirect
233. #103C2×D191semidirect
236. #102C2×D191semidirect
237. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331702
#117×D1912
#271330032
#271330022
#271329972
#271329922
#271329862
#271329852
#271329802
#271329752
#271327012
#271326992
#271326592
C2×(C2×D191)⋊C82
#416×C1912
#3091191