Finite Group Databasebeta

← #37582661

Subgroups — #37582661

Order 24448.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133199C211yesmaximal, characteristic, complemented
2C2×#20259284C211yesmaximal, characteristic, complemented
3#27132976C211yesmaximal, characteristic, complemented
4#27132962C212yesmaximal, complemented
5#27132881C212yesmaximal, complemented
6#27132813C211yesmaximal, characteristic, complemented
7#27132799C211yesmaximal, characteristic
8#27132774C212yesmaximal, complemented
9#27132766C212yesmaximal, complemented
10#27132717C211yesmaximal, characteristic, complemented
11#483×C191C211yesmaximal, characteristic, complemented
12C22×D764C2211yescharacteristic
13C22×C4×D191—21no—
14C2×#15690274C2212yes—
15C2×D1528C2212yes—
16#20259317—21no—
17#20259313C2211yescharacteristic, complemented
18#20259311C2211yescharacteristic, complemented
19#20259306—21no—
20#20259296C2211yescharacteristic
21Q8×Dic191C2211yescharacteristic, complemented
22#20259284—21no—
23#20259284—21no—
24#20259284C2212yes—
25#20259284C2212yes—
26#20259284C2211yescharacteristic, complemented
27(C22⋊D191)⋊C4—21no—
28#20259280—21no—
29C2×(C2×D191)⋊C4—21no—
30C2×C4×Dic191C2211yescharacteristic
31#20259255C2212yescomplemented
32Dic191⋊C8C2212yescomplemented
33#20259244C2212yes—
34#20259242C2212yes—
35#20259242C2212yescomplemented
36C22⋊(C191⋊C8)C2211yescharacteristic
37#20259232C2212yescomplemented
38C22⋊Q8×C191C2211yescharacteristic
39C2×C4⋊C4×C191C2211yescharacteristic
40#106×C191C2212yescomplemented
41#103×C191C2212yescomplemented
42C22⋊C8×C191C2211yescharacteristic
43C23×D191—21no—
44C2×D764—24no—
45C2×D764—21no—
46C2×D764C2311yescharacteristic
47C2×D764C2312yes—
48C2×C22⋊D191—21no—
49C22×Dic191D411yescharacteristic
50C22×Dic191D411yescharacteristic
51C2×C4×D191—22no—
52C2×C4×D191—22no—
53C2×C4×D191—21no—
54C2×C4×D191—44no—
55#15690274—24no—
56D1528—24no—
57C2×C191⋊C8C2312yes—
58C4⋊Dic191—21no—
59C4⋊Dic191—21no—
60C4⋊Dic191C2311yescharacteristic
61Dic191⋊C4—21no—
62(C2×D191)⋊C4—22no—
63(C2×D191)⋊C4—22no—
64(C2×D191)⋊C4—21no—
65(C2×D191)⋊C4—21no—
66(C2×D191)⋊C4—21no—
67(C2×D191)⋊C4—21no—
68C4×Dic191—21no—
69C4×Dic191D411yescharacteristic
70C4×Dic191D411yescharacteristic
71C4×Dic191C2311yescharacteristic
72C4×Dic191C2311yescharacteristic
73C2×Q8×C191C2311yescharacteristic
74C22×C4×C191—21no—
75C22×C4×C191C2311yescharacteristic
76C2×C8×C191C2312yes—
77C4⋊C4×C191—21no—
78C4⋊C4×C191—21no—
79C4⋊C4×C191C2312yes—
80C4⋊C4×C191C2311yescharacteristic
81C22⋊C4×C191—21no—
82C22×D191—24no—
83C22×D191—22no—
84C22×D191—21no—
85C22×D191—42no—
86C22×D191—42no—
87D764—24no—
88D764—22no—
89D764—22no—
90D764#4114yes—
91C22⋊D191—42no—
92C2×Dic191—22no—
93C2×Dic191—21no—
94C2×Dic191—41no—
95C2×Dic191C2×D411yescharacteristic
96C2×Dic191C2×D411yescharacteristic
97C2×Dic191C2×D411yescharacteristic
98C2×Dic191C2×D411yescharacteristic
99C4×D191—42no—
100C4×D191—44no—
101C4×D191—44no—
102C191⋊C8—22no—
103C23×C191C2×D411yescharacteristic
104Q8×C191—22no—
105C2×C4×C191—22no—
106C2×C4×C191—21no—
107C2×C4×C191—21no—
108C2×C4×C191—22no—
109C2×C4×C191—42no—
110C2×C4×C191C2×D411yescharacteristic
111C2×C4×C191C2411yescharacteristic
112C8×C191—22no—
113C22×C191—21no—
114C22×C191—21no—
115C22×C191AGL(1,ℤ/8)12yes—
116C22×C191C22×D411yescharacteristic
117C2×D191—24no—
118C2×D191—48no—
119C2×D191—42no—
120C2×D191—42no—
121C2×D191—41no—
122C2×D191—41no—
123C2×D191—41no—
124C4×C191—21no—
125C4×C191—41no—
126C4×C191—42no—
127C4×C191—41no—
128C4×C191C2×#4112yes—
129Dic191—21no—
130Dic191—21no—
131Dic191—21no—
132Dic191—21no—
133Dic191—41no—
134C2×C191—22no—
135C2×C191#52511yescharacteristic
136C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C191#57511yescharacteristic
138D191—44no—
139D191—81no—
140C191#311411yescharacteristic, complemented, Sylow
141#3114—1911nomaximal, Sylow
142#529—1911no—
143C2×C4×D4—1911no—
144#483D19111yescharacteristic, complemented
145#480—1911no—
146#478—1912no—
147#463—1912no—
148#450—1911no—
149#447—1911no—
150#442—1912no—
151#440—1912no—
152#432—1911no—
153C22×D4—1911no—
154C23×C4—3821no—
155C2×SD16—1912no—
156C2×D8—1912no—
157#126—3821no—
158#125—1911no—
159#124—1911no—
160#123—3821no—
161C22⋊Q8C2×D19111yescharacteristic
162#121—1911no—
163C4×Q8—1911no—
164C4×D4—3821no—
165C4×D4—3821no—
166C4×D4—3821no—
167C4×D4—1912no—
168C4×D4—1912no—
169C4×D4—1911no—
170#117—3821no—
171C2×C4⋊C4C2×D19111yescharacteristic
172C2×C22⋊C4—3821no—
173C2×C42—1911no—
174#107—1912no—
175#106C2×D19112yescomplemented
176C4⋊C8—1912no—
177#103C2×D19112yescomplemented
178#102—1912no—
179#102—1912no—
180#102—1912no—
181C22⋊C8—1911no—
182C22⋊C8C2×D19111yescharacteristic
183#97—1912no—
184C24—3821no—
185C2×Q8C22×D19111yescharacteristic
186C2×D4—3824no—
187C2×D4—3821no—
188C2×D4—3821no—
189C2×D4—1911no—
190C2×D4—1912no—
191C22×C4—21no—
192C22×C4—3821no—
193C22×C4—3822no—
194C22×C4—3822no—
195C22×C4—1911no—
196C22×C4—1911no—
197C22×C4—7644no—
198C22×C4C22×D19111yescharacteristic
199SD16—3824no—
200D8—3824no—
201C2×C8—1912no—
202C2×C8C22×D19112yes—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—3821no—
206C4⋊C4—3821no—
207C4⋊C4—3821no—
208C4⋊C4—1911no—
209C4⋊C4C22×D19111yescharacteristic
210C4⋊C4C22×D19112yes—
211C22⋊C4—21no—
212C22⋊C4—3822no—
213C22⋊C4—3822no—
214C22⋊C4—3821no—
215C22⋊C4—3821no—
216C22⋊C4—3821no—
217C22⋊C4—3821no—
218C42—3821no—
219C42—1911no—
220C42—1911no—
221C42—1911no—
222C42—1911no—
223C23—3824no—
224C23—3822no—
225C23—3821no—
226C23—7642no—
227C23—7642no—
228C23D4×D19111yescharacteristic
229Q8—22no—
230D4—3824no—
231D4—3822no—
232D4—3822no—
233D4—1914no—
234D4—7642no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—3822no—
241C2×C4—3821no—
242C2×C4—1911no—
243C2×C4—1911no—
244C2×C4—1911no—
245C2×C4—1911no—
246C2×C4—7644no—
247C2×C4—7644no—
248C2×C4—7642no—
249C2×C4—7641no—
250C2×C4D4×D19111yescharacteristic
251C2×C4C23×D19111yescharacteristic
252C8—22no—
253C8—3822no—
254C22—21no—
255C22—21no—
256C22—3824no—
257C22—7648no—
258C22—7641no—
259C22—7641no—
260C22—7641no—
261C22—7642no—
262C22—7642no—
263C22#2025934912yes—
264C22C2×D4×D19111yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—41no—
269C4—3821no—
270C4—3821no—
271C4—3821no—
272C4—3821no—
273C4—7641no—
274C4#41×D19112yes—
275C2—22no—
276C2—15281no—
277C2—7644no—
278C2#2713317111yescharacteristic
279C2C2×#2025934911yescharacteristic
280C2#2713346211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#483×C191C2
socleC22×C191C22×D4
prime radical#27132799C2
hypercenter#483D191
hypocenterC191#3114
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #27133199C2semidirect
2. C2×#20259284C2semidirect
3. #27132976C2semidirect
4. #27132962C2semidirect
5. #27132881C2semidirect
6. #27132813C2semidirect
8. #27132774C2semidirect
9. #27132766C2semidirect
10. #27132717C2semidirect
11. #483×C191C2semidirect
17. #20259313C22semidirect
18. #20259311C22semidirect
21. Q8×Dic191C22semidirect
26. #20259284C22semidirect
31. #20259255C22semidirect
32. Dic191⋊C8C22semidirect
35. #20259242C22semidirect
37. #20259232C22semidirect
40. #106×C191C22semidirect
41. #103×C191C22semidirect
140. C191#3114semidirect
144. #483D191semidirect
175. #106C2×D191semidirect
177. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331992
C2×#202592842
#271329762
#271329622
#271328812
#271328132
#271327992
#271327742
#271327662
#271327172
#483×C1912
#3114191