Finite Group Databasebeta

← #11802896

Subgroups — #11802896

Order 1152.

1490 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1490 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C22×C22⋊#157C212yesmaximal
2C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
3#10593812C214yesmaximal, complemented
4#10593746C218yesmaximal, complemented
5C24×C3⋊D3C2211yescharacteristic
6C23×#157C2214yes—
7C22×C4×C3⋊D3C2212yes—
8C2×C22⋊#157—28no—
9C2×C22⋊#157C2214yes—
10C2×C22⋊#157C2214yes—
11C2×C4⋊#157C2218yescomplemented
12C2×C32×C22⋊C4C411yescharacteristic, complemented
13C2×#3757C411yescharacteristic, complemented
14C2×#3752C412yescomplemented
15C22⋊C4×C3⋊D3C414yescomplemented
16C22⋊C4×C3⋊D3C2214yes—
17#63781C2218yescomplemented
18C2×D3×C22⋊C4—62no—
19C24×C32C2×C411yescharacteristic
20C23×C3⋊D3—44no—
21C23×C3⋊D3C2×C412yes—
22C23×C3⋊D3C2×C411yescharacteristic
23C23×C3⋊D3D414yes—
24C23×C3⋊D3Q814yes—
25C23×C3⋊D3C2311yescharacteristic
26C23×C3⋊D3C2312yes—
27C22×#157—28no—
28C22×#157—48no—
29C22×#157C2318yes—
30C22×C32×C4C2×C412yescomplemented
31C22×C3⋊Dic3C2×C412yescomplemented
32C2×C4×C3⋊D3—44no—
33C2×C4×C3⋊D3C2×C414yescomplemented
34C2×C4×C3⋊D3C2314yes—
35C22⋊#157—28no—
36C22⋊#157—28no—
37C4⋊#157—48no—
38C32×C22⋊C4C2×C414yescomplemented
39#3757C2×C414yescomplemented
40#3752C2×C418yescomplemented
41#2315—91nomaximal, Sylow
42C24×D3—62no—
43C22×C4×D3—64no—
44C2×C3×C22⋊C4—22no—
45C2×#217—62no—
46C2×(C2×D3)⋊C4—64no—
47D3×C22⋊C4—68no—
48D3×C22⋊C4—68no—
49C23×C32—42no—
50C23×C32C4⋊C414yescomplemented
51C23×C32C22×C412yes—
52C23×C32C22×C411yescharacteristic
53C22×C3⋊D3—24no—
54C22×C3⋊D3—28no—
55C22×C3⋊D3—48no—
56C22×C3⋊D3—48no—
57C22×C3⋊D3—44no—
58C22×C3⋊D3—42no—
59C22×C3⋊D3C4⋊C418yescomplemented
60C22×C3⋊D3C4⋊C414yescomplemented
61C22×C3⋊D3C22×C412yes—
62C22×C3⋊D3C22×C411yescharacteristic
63C22×C3⋊D3C2×D414yes—
64C22×C3⋊D3C2×D412yes—
65C22×C3⋊D3C2×Q812yes—
66C22×C3⋊D3C2×Q814yes—
67C22×C3⋊D3C2411yescharacteristic
68C2×#157—28no—
69C2×#157—216no—
70C2×#157—416no—
71C2×C32×C4—42no—
72C2×C32×C4C22×C414yes—
73C2×C3⋊Dic3—42no—
74C2×C3⋊Dic3C22×C414yes—
75C4×C3⋊D3—28no—
76C4×C3⋊D3—44no—
77C22×C22⋊C4—91no—
78C22×C22⋊C4—92no—
79#385—98no—
80#380—94no—
81C24×C3—22no—
82C23×D3—62no—
83C23×D3—64no—
84C23×D3—62no—
85C23×D3—68no—
86C23×D3—68no—
87C23×D3—64no—
88C23×D3—1216no—
89C22×C3×C4—24no—
90C22×Dic3—64no—
91C2×C4×D3—68no—
92C2×C4×D3—68no—
93C2×C4×D3—1216no—
94C3×C22⋊C4—28no—
95#217—68no—
96(C2×D3)⋊C4—616no—
97C22×C32—22no—
98C22×C32—24no—
99C22×C32—44no—
100C22×C32C2×C4⋊C412yes—
101C22×C32C2×C4⋊C414yes—
102C22×C32C23×C411yescharacteristic
103C2×C3⋊D3—22no—
104C2×C3⋊D3—24no—
105C2×C3⋊D3—24no—
106C2×C3⋊D3—24no—
107C2×C3⋊D3—28no—
108C2×C3⋊D3—28no—
109C2×C3⋊D3—48no—
110C2×C3⋊D3—44no—
111C2×C3⋊D3C2×C4⋊C412yes—
112C2×C3⋊D3C2×C4⋊C414yes—
113C2×C3⋊D3C22×D411yescharacteristic
114C2×C3⋊D3C22×Q811yescharacteristic
115C2×C3⋊D3H(5,𝔽2)14yes—
116#157—48no—
117C32×C4—24no—
118C3⋊Dic3—24no—
119C25—91no—
120C23×C4—92no—
121C23×C4—94no—
122C2×C4⋊C4—98no—
123C2×C22⋊C4—91no—
124C2×C22⋊C4—92no—
125C2×C22⋊C4—94no—
126C2×C22⋊C4—94no—
127C2×C22⋊C4—94no—
128C2×C22⋊C4—94no—
129C2×C22⋊C4—188no—
130C2×C22⋊C4#15711yescharacteristic, complemented
131#95—98no—
132C23×C3—22no—
133C23×C3—24no—
134C23×C3—28no—
135C23×C3—48no—
136C22×D3—62no—
137C22×D3—64no—
138C22×D3—64no—
139C22×D3—62no—
140C22×D3—616no—
141C22×D3—68no—
142C22×D3—64no—
143C22×D3—68no—
144C22×D3—68no—
145C22×D3—616no—
146C22×D3—1216no—
147C22×D3—1216no—
148C22×D3—1232no—
149C22×D3—1232no—
150C22×D3—128no—
151C2×C3×C4—28no—
152C2×C3×C4—48no—
153C2×Dic3—68no—
154C2×Dic3—128no—
155C4×D3—1216no—
156C4×D3—1216no—
157C2×C32—22no—
158C2×C32—24no—
159C2×C32C22×C4⋊C411yescharacteristic
160C2×C32#51812yes—
161C3⋊D3—22no—
162C3⋊D3—24no—
163C3⋊D3#53412yes—
164C3⋊D3#54312yes—
165C24—91no—
166C24—92no—
167C24—91no—
168C24—92no—
169C24—94no—
170C24—94no—
171C24—364no—
172C24C2×#15711yescharacteristic
173C22×C4—92no—
174C22×C4—94no—
175C22×C4—94no—
176C22×C4—98no—
177C22×C4—188no—
178C22×C4—364no—
179C22×C4—368no—
180C22×C4C2×#15712yescomplemented
181C4⋊C4—368no—
182C22⋊C4—94no—
183C22⋊C4—98no—
184C22⋊C4—188no—
185C22⋊C4—188no—
186C22⋊C4C2×#15714yescomplemented
187C22×C3—28no—
188C22×C3—24no—
189C22×C3—28no—
190C22×C3—22no—
191C22×C3—48no—
192C22×C3—416no—
193C2×D3—68no—
194C2×D3—64no—
195C2×D3—62no—
196C2×D3—62no—
197C2×D3—68no—
198C2×D3—68no—
199C2×D3—616no—
200C2×D3—616no—
201C2×D3—1216no—
202C2×D3—1216no—
203C2×D3—128no—
204C2×D3—1232no—
205C2×D3—1216no—
206C3×C4—48no—
207Dic3—128no—
208C32#231511yescharacteristic, complemented, Sylow
209C23—42no—
210C23—91no—
211C23—92no—
212C23—94no—
213C23—92no—
214C23—94no—
215C23—92no—
216C23—91no—
217C23—98no—
218C23—94no—
219C23—184no—
220C23—188no—
221C23—362no—
222C23—364no—
223C23—368no—
224C23—368no—
225C23C4⋊#15714yescomplemented
226C23C22×#15712yes—
227C23C22×#15711yescharacteristic
228C2×C4—42no—
229C2×C4—94no—
230C2×C4—188no—
231C2×C4—188no—
232C2×C4—1816no—
233C2×C4—364no—
234C2×C4—362no—
235C2×C4—3616no—
236C2×C4C22×#15714yes—
237C2×C3—28no—
238C2×C3—22no—
239C2×C3—24no—
240C2×C3—48no—
241D3—64no—
242D3—64no—
243D3—68no—
244D3—128no—
245C22—22no—
246C22—24no—
247C22—44no—
248C22—91no—
249C22—91no—
250C22—94no—
251C22—92no—
252C22—94no—
253C22—188no—
254C22—184no—
255C22—184no—
256C22—188no—
257C22—182no—
258C22—184no—
259C22—364no—
260C22—368no—
261C22C2×C4⋊#15712yes—
262C22C2×C4⋊#15714yes—
263C22C23×#15711yescharacteristic
264C4—24no—
265C4—184no—
266C4—368no—
267C3—22no—
268C2—22no—
269C2—24no—
270C2—92no—
271C2—92no—
272C2—182no—
273C2—184no—
274C2C22×C4⋊#15711yescharacteristic
275C2#1059664212yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C22⋊C4C4
prime radicalC24×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC2×C22⋊C4#157
hypocenterC32#2315
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10593812C2semidirect
4. #10593746C2semidirect
11. C2×C4⋊#157C22semidirect
12. C2×C32×C22⋊C4C4semidirect
13. C2×#3757C4semidirect
14. C2×#3752C4semidirect
15. C22⋊C4×C3⋊D3C4semidirect
17. #63781C22semidirect
30. C22×C32×C4C2×C4semidirect
31. C22×C3⋊Dic3C2×C4semidirect
33. C2×C4×C3⋊D3C2×C4semidirect
38. C32×C22⋊C4C2×C4semidirect
39. #3757C2×C4semidirect
40. #3752C2×C4semidirect
50. C23×C32C4⋊C4semidirect
59. C22×C3⋊D3C4⋊C4semidirect
60. C22×C3⋊D3C4⋊C4semidirect
130. C2×C22⋊C4#157semidirect
180. C22×C4C2×#157semidirect
186. C22⋊C4C2×#157semidirect
208. C32#2315semidirect
225. C23C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#1572
C2×C22⋊C4×C3⋊D32
#105938122
#105937462
#23159