Finite Group Databasebeta

← #11803883

Subgroups — #11803883

Order 1152.

1166 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64231C211yesmaximal, characteristic
2C4×#3802C212yesmaximal, complemented
3#10593733C211yesmaximal, characteristic, complemented
4#10593453C218yesmaximal, complemented
5#10593407C212yesmaximal, complemented
6#10593344C211yesmaximal, characteristic, complemented
7C22×GO+(4,𝔽2)C2214yes—
8C2×#3802C2212yes—
9C2×C4×D32C2214yes—
10C2×C4×#157C2211yescharacteristic
11C2×C4×#157C2211yescharacteristic
12C2×D32⋊C4C2218yes—
13#64231C418yescomplemented
14C42×C3⋊D3C2211yescharacteristic
15C3×C4×D12—22no—
16#63921C2214yes—
17#63902—22no—
18C4×#625—22no—
19#63900C2212yes—
20#63898—22no—
21#63781C2214yes—
22#63737C2214yes—
23C4×D3×D4—62no—
24C22×D32C2314yes—
25C22×#157C2312yes—
26C22×#157C2312yes—
27C2×GO+(4,𝔽2)—48no—
28C2×GO+(4,𝔽2)C2×C4116yescomplemented
29C2×C4×C3⋊D3C2312yes—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×D12—22no—
32C2×C3×C4×D3—24no—
33C2×#625—22no—
34C2×#624C2314yes—
35C2×D3×Dic3—24no—
36#3802—24no—
37#3802C2×C418yescomplemented
38C4×D32—48no—
39C4×#157—22no—
40C4×#157C2×C414yescomplemented
41D32⋊C4—48no—
42C32×C42D411yescharacteristic, complemented
43C4×C3⋊Dic3D411yescharacteristic, complemented
44C4×C3⋊Dic3D412yescomplemented
45C3×(C2×D3)⋊C4—24no—
46C3×C4⋊Dic3—22no—
47#3724—22no—
48(C2×D3)⋊Dic3—24no—
49#2328—91nomaximal, Sylow
50C2×D3×D4—62no—
51C22×C4×D3—64no—
52C3×C4×D4—62no—
53D4×Dic3—62no—
54C4×#67—64no—
55#893—62no—
56D3×C4⋊C4—62no—
57#67⋊C4—64no—
58D3×C22⋊C4—64no—
59C4×D12—22no—
60C42×D3—62no—
61C22×C3⋊D3C2411yescharacteristic
62C22×C3×D3—24no—
63C2×D32—24no—
64C2×D32—28no—
65C2×D32—28no—
66C2×D32C22×C418yes—
67C2×#157—24no—
68C2×#157—22no—
69C2×#157—24no—
70C2×#157C22×C414yes—
71GO+(4,𝔽2)—416no—
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—24no—
77C4×C3⋊D3C22×C412yes—
78C4×C3⋊D3#4112yes—
79C2×C3×Dic3—24no—
80C3×D12—28no—
81C3×C4×D3—48no—
82#625—28no—
83#624—28no—
84D3×Dic3—48no—
85C2×#127—91no—
86C2×C4×D4—92no—
87#390—92no—
88#386—98no—
89#382—91no—
90#376—91no—
91C23×D3—64no—
92C2×C3×D4—62no—
93C22×C3×C4—64no—
94C2×#67—64no—
95C22×Dic3—64no—
96D3×D4—68no—
97D3×D4—68no—
98C2×D12—22no—
99C2×C4×D3—24no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—64no—
103C2×C4×D3—62no—
104C2×C4×D3—64no—
105C2×C4×D3—1216no—
106C3×C4⋊C4—62no—
107C3×C22⋊C4—64no—
108C3×C42—22no—
109#217—64no—
110(C2×D3)⋊C4—24no—
111(C2×D3)⋊C4—64no—
112C4⋊Dic3—22no—
113Dic3⋊C4—64no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C22×C32C22×D411yescharacteristic
118C2×C3⋊D3C23×C411yescharacteristic
119C2×C3⋊D3C2×#4111yescharacteristic
120C2×C3⋊D3H(5,𝔽2)14yes—
121C2×C3×D3—28no—
122C2×C3×D3—44no—
123C2×C3×D3—44no—
124D32—216no—
125D32—48no—
126#157—24no—
127#157—42no—
128C32×C4—22no—
129C32×C4C4×D412yes—
130C3⋊Dic3—22no—
131C3⋊Dic3C4×D412yes—
132C3×Dic3—44no—
133C22×D4—92no—
134C22×D4—94no—
135C23×C4—94no—
136#127—98no—
137C4×D4—62no—
138C4×D4—182no—
139C4×D4—182no—
140C4×D4—182no—
141C2×C4⋊C4—92no—
142C2×C22⋊C4—94no—
143C2×C22⋊C4—98no—
144C2×C42—91no—
145C2×C42—91no—
146C2×C42—91no—
147#95—94no—
148#95—94no—
149C23×C3—64no—
150C22×D3—24no—
151C22×D3—68no—
152C22×D3—62no—
153C22×D3—68no—
154C22×D3—128no—
155C22×D3—128no—
156C3×D4—68no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—64no—
161C2×C3×C4—128no—
162#67—616no—
163C2×Dic3—24no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—128no—
168D12—28no—
169C4×D3—48no—
170C4×D3—64no—
171C4×D3—64no—
172C4×D3—68no—
173C4×D3—128no—
174C4×D3—124no—
175C4×D3—128no—
176C2×C32C2×C4×D411yescharacteristic
177C2×C32#53512yes—
178C3⋊D3#51812yes—
179C3⋊D3#54012yes—
180C3×D3—48no—
181C24—94no—
182C2×D4—62no—
183C2×D4—98no—
184C2×D4—916no—
185C2×D4—184no—
186C2×D4—182no—
187C2×D4—368no—
188C22×C4—64no—
189C22×C4—94no—
190C22×C4—91no—
191C22×C4—92no—
192C22×C4—92no—
193C22×C4—92no—
194C22×C4—184no—
195C22×C4—368no—
196C4⋊C4—62no—
197C4⋊C4—182no—
198C22⋊C4—64no—
199C22⋊C4—184no—
200C22⋊C4—368no—
201C42—94no—
202C42—92no—
203C42—91no—
204C42—182no—
205C42GO+(4,𝔽2)11yescharacteristic, complemented
206C22×C3—22no—
207C22×C3—68no—
208C22×C3—124no—
209C22×C3—124no—
210C2×D3—28no—
211C2×D3—44no—
212C2×D3—44no—
213C2×D3—64no—
214C2×D3—62no—
215C2×D3—62no—
216C2×D3—64no—
217C2×D3—1216no—
218C2×D3—1216no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—42no—
222C3×C4—124no—
223Dic3—44no—
224Dic3—64no—
225Dic3—64no—
226Dic3—122no—
227C32#232811yescharacteristic, complemented, Sylow
228C23—64no—
229C23—98no—
230C23—91no—
231C23—184no—
232C23—188no—
233C23—188no—
234D4—68no—
235D4—188no—
236D4—3616no—
237C2×C4—64no—
238C2×C4—91no—
239C2×C4—92no—
240C2×C4—92no—
241C2×C4—94no—
242C2×C4—92no—
243C2×C4—128no—
244C2×C4—184no—
245C2×C4—188no—
246C2×C4—184no—
247C2×C4—182no—
248C2×C4—184no—
249C2×C4—368no—
250C2×C4C2×GO+(4,𝔽2)12yes—
251C2×C4C2×GO+(4,𝔽2)11yescharacteristic
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—128no—
256D3—48no—
257D3—64no—
258D3—64no—
259C22—68no—
260C22—91no—
261C22—91no—
262C22—94no—
263C22—124no—
264C22—124no—
265C22—1816no—
266C22—368no—
267C22C22×GO+(4,𝔽2)11yescharacteristic
268C4—22no—
269C4—92no—
270C4—124no—
271C4—184no—
272C4—182no—
273C4—362no—
274C4C4×GO+(4,𝔽2)12yes—
275C3—22no—
276C2—92no—
277C2—92no—
278C2—128no—
279C2C2×C4×GO+(4,𝔽2)11yescharacteristic
280C2#1059651212yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#64231C2
cosocleC22×C3⋊D3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2328
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3802C2semidirect
3. #10593733C2semidirect
4. #10593453C2semidirect
5. #10593407C2semidirect
6. #10593344C2semidirect
13. #64231C4semidirect
28. C2×GO+(4,𝔽2)C2×C4semidirect
37. #3802C2×C4semidirect
40. C4×#157C2×C4semidirect
42. C32×C42D4semidirect
43. C4×C3⋊Dic3D4semidirect
44. C4×C3⋊Dic3D4semidirect
205. C42GO+(4,𝔽2)semidirect
227. C32#2328semidirect

Maximal subgroups

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

subgroupindex
C2×#642312
C4×#38022
#105937332
#105934532
#105934072
#105933442
#23289