Finite Group Databasebeta

← #11803856

Subgroups — #11803856

Order 1152.

1238 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 170 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
1C2×D4×#157C212yesmaximal, complemented
2C3⋊D3×#127C211yesmaximal, characteristic
3#10593827C212yesmaximal, complemented
4#10593826C218yesmaximal, complemented
5#10593736C211yesmaximal, characteristic, complemented
6#10593733C211yesmaximal, characteristic, complemented
7C23×#157C2214yes—
8C2×D4×C3⋊D3C2212yes—
9C2×D4×C3⋊D3C2214yes—
10C2×C22⋊#157C2214yes—
11C2×C22⋊#157C2218yes—
12D4×#157—28no—
13C2×C4⋊#157C2212yes—
14C2×C4×#157C2211yescharacteristic
15C2×C4×#157C2211yescharacteristic
16C32×#127C411yescharacteristic, complemented
17#64149C412yescomplemented
18#64149C414yescomplemented
19#64083C411yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21#63781C2214yes—
22#63781C2214yes—
23D3×#127—62no—
24C23×C3⋊D3C2314yes—
25C22×#157—28no—
26C22×#157—48no—
27C22×#157C2312yes—
28C22×#157C2314yes—
29C22×#157C2312yes—
30C2×C32×D4C2×C412yescomplemented
31C2×C32×D4C2×C414yescomplemented
32C2×#638C2×C414yescomplemented
33C2×#638C2×C418yescomplemented
34D4×C3⋊D3—24no—
35D4×C3⋊D3—24no—
36D4×C3⋊D3—48no—
37C2×C4⋊(C3⋊D3)C2×C412yescomplemented
38C2×C4⋊(C3⋊D3)C2×C414yescomplemented
39C2×C4×C3⋊D3C2312yes—
40C2×C4×C3⋊D3C2311yescharacteristic
41C22⋊#157—28no—
42C22⋊#157—48no—
43C4⋊#157—24no—
44C4×#157—22no—
45C4×#157D414yescomplemented
46C32×C42C2×C411yescharacteristic, complemented
47C4×C3⋊Dic3C2×C411yescharacteristic, complemented
48C4×C3⋊Dic3C2×C412yescomplemented
49#2328—91nomaximal, Sylow
50C2×D3×D4—64no—
51C2×D3×D4—68no—
52C3×#127—22no—
53#940—68no—
54#940—64no—
55#874—62no—
56C42×D3—62no—
57C23×C32C22×C414yes—
58C22×C3⋊D3—24no—
59C22×C3⋊D3—24no—
60C22×C3⋊D3—28no—
61C22×C3⋊D3—28no—
62C22×C3⋊D3C22×C414yes—
63C22×C3⋊D3C2411yescharacteristic
64C2×#157—24no—
65C2×#157—24no—
66C2×#157—22no—
67C2×#157—28no—
68C2×#157—24no—
69C2×#157—416no—
70C2×#157C2×D414yes—
71C32×D4—24no—
72C32×D4—44no—
73C2×C32×C4C22×C412yes—
74C2×C32×C4C22×C411yescharacteristic
75#638—28no—
76#638—48no—
77C2×C3⋊Dic3C22×C412yes—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C4⋊(C3⋊D3)—24no—
80C4⋊(C3⋊D3)—44no—
81C4×C3⋊D3—24no—
82C4×C3⋊D3C2×D412yes—
83C4×C3⋊D3#4112yes—
84C2×#127—91no—
85C2×C4×D4—92no—
86#390—92no—
87#386—98no—
88#382—91no—
89#376—91no—
90C23×D3—68no—
91C2×C3×D4—24no—
92C2×C3×D4—28no—
93C2×#67—68no—
94C2×#67—616no—
95D3×D4—128no—
96D3×D4—128no—
97D3×D4—1232no—
98C2×D12—64no—
99C2×D12—68no—
100C2×C4×D3—62no—
101C2×C4×D3—64no—
102C3×C42—22no—
103C4×Dic3—64no—
104C4×Dic3—62no—
105C22×C32—24no—
106C22×C32—28no—
107C22×C32C23×C411yescharacteristic
108C2×C3⋊D3—24no—
109C2×C3⋊D3—28no—
110C2×C3⋊D3—44no—
111C2×C3⋊D3—44no—
112C2×C3⋊D3—48no—
113C2×C3⋊D3C22×D411yescharacteristic
114C2×C3⋊D3C2×#4111yescharacteristic
115C2×C3⋊D3H(5,𝔽2)14yes—
116#157—24no—
117#157—44no—
118#157—42no—
119C32×C4—22no—
120C32×C4C4×D412yes—
121C3⋊Dic3—22no—
122C3⋊Dic3C4×D412yes—
123C22×D4—92no—
124C22×D4—94no—
125C23×C4—94no—
126#127—94no—
127#127—92no—
128#127—91no—
129#127#15711yescharacteristic, complemented
130C4×D4—188no—
131C2×C4⋊C4—92no—
132C2×C22⋊C4—94no—
133C2×C22⋊C4—98no—
134C2×C42—91no—
135C2×C42—91no—
136C2×C42—91no—
137#95—94no—
138#95—94no—
139C23×C3—28no—
140C22×D3—62no—
141C22×D3—68no—
142C22×D3—128no—
143C22×D3—1216no—
144C22×D3—1216no—
145C22×D3—128no—
146C3×D4—48no—
147C3×D4—416no—
148C2×C3×C4—24no—
149C2×C3×C4—22no—
150#67—1216no—
151#67—1232no—
152C2×Dic3—62no—
153C2×Dic3—64no—
154D12—128no—
155D12—1216no—
156C4×D3—64no—
157C4×D3—64no—
158C4×D3—616no—
159C2×C32—44no—
160C2×C32C2×C4×D411yescharacteristic
161C2×C32#51812yes—
162C3⋊D3—44no—
163C3⋊D3#53512yes—
164C3⋊D3#54012yes—
165C24—94no—
166C2×D4—94no—
167C2×D4—98no—
168C2×D4—92no—
169C2×D4—94no—
170C2×D4—184no—
171C2×D4—184no—
172C2×D4—368no—
173C2×D4C2×#15712yescomplemented
174C2×D4C2×#15714yescomplemented
175C22×C4—91no—
176C22×C4—92no—
177C22×C4—92no—
178C22×C4—92no—
179C22×C4—94no—
180C22×C4—188no—
181C22×C4—368no—
182C4⋊C4—184no—
183C22⋊C4—188no—
184C22⋊C4—368no—
185C42—94no—
186C42—92no—
187C42—91no—
188C42—182no—
189C42C2×#15711yescharacteristic, complemented
190C22×C3—22no—
191C22×C3—48no—
192C22×C3—416no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—68no—
196C2×D3—128no—
197C2×D3—1216no—
198C2×D3—248no—
199C2×D3—248no—
200C2×D3—2416no—
201C3×C4—28no—
202C3×C4—24no—
203Dic3—64no—
204Dic3—68no—
205C32#232811yescharacteristic, complemented, Sylow
206C23—91no—
207C23—94no—
208C23—184no—
209C23—188no—
210C23—188no—
211C23—184no—
212C23C22×#15714yes—
213D4—24no—
214D4—44no—
215D4—188no—
216D4—184no—
217D4—364no—
218D4—368no—
219C2×C4—91no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—94no—
223C2×C4—92no—
224C2×C4—184no—
225C2×C4—184no—
226C2×C4—182no—
227C2×C4—184no—
228C2×C4—184no—
229C2×C4—188no—
230C2×C4—3616no—
231C2×C4C22×#15712yes—
232C2×C4C22×#15711yescharacteristic
233C2×C3—22no—
234C2×C3—24no—
235C2×C3—88no—
236D3—64no—
237D3—64no—
238D3—248no—
239C22—24no—
240C22—28no—
241C22—91no—
242C22—91no—
243C22—94no—
244C22—184no—
245C22—188no—
246C22—364no—
247C22—364no—
248C22—368no—
249C22C23×#15711yescharacteristic
250C4—22no—
251C4—92no—
252C4—184no—
253C4—182no—
254C4—364no—
255C4—362no—
256C4D4×#15712yes—
257C3—22no—
258C2—44no—
259C2—92no—
260C2—92no—
261C2—364no—
262C2C2×D4×#15711yescharacteristic
263C2#1059664212yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#127C4
prime radicalC3⋊D3×#127C2
cosocleC22×C3⋊D3C24
hypercenter#127#157
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×D4×#157C2semidirect
3. #10593827C2semidirect
4. #10593826C2semidirect
5. #10593736C2semidirect
6. #10593733C2semidirect
16. C32×#127C4semidirect
17. #64149C4semidirect
18. #64149C4semidirect
19. #64083C4semidirect
30. C2×C32×D4C2×C4semidirect
31. C2×C32×D4C2×C4semidirect
32. C2×#638C2×C4semidirect
33. C2×#638C2×C4semidirect
37. C2×C4⋊(C3⋊D3)C2×C4semidirect
38. C2×C4⋊(C3⋊D3)C2×C4semidirect
45. C4×#157D4semidirect
46. C32×C42C2×C4semidirect
47. C4×C3⋊Dic3C2×C4semidirect
48. C4×C3⋊Dic3C2×C4semidirect
129. #127#157semidirect
173. C2×D4C2×#157semidirect
174. C2×D4C2×#157semidirect
189. C42C2×#157semidirect
205. C32#2328semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
C3⋊D3×#1272
#105938272
#105938262
#105937362
#105937332
#23289