Finite Group Databasebeta

← #13074358

Subgroups — #13074358

Order 1408.

632 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic
3C2×#66982C212yesmaximal, complemented
4#10622826C212yesmaximal, complemented
5#10622825C211yesmaximal, characteristic, complemented
6#10622607C214yesmaximal, complemented
7#10622604C212yesmaximal, complemented
8#10622596C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C22×D44C2211yescharacteristic
14C2×C11×C4⋊C4—24no—
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C4⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18#66983—24no—
19#66982—28no—
20C2×(C2×D11)⋊C4C2214yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2214yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C24×C11C2311yescharacteristic
29C23×D11C2312yes—
30C22×C4×C11—22no—
31C22×C4×C11—22no—
32C22×C4×C11—22no—
33C22×C4×C11—42no—
34C22×C4×C11—42no—
35C22×C4×C11D414yes—
36C22×C4×C11D414yescomplemented
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—24no—
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C22×Dic11C2312yes—
45C22×Dic11C2314yes—
46C2×D44—22no—
47C2×D44—42no—
48C11×C4⋊C4—24no—
49C11×C4⋊C4—24no—
50C22⋊Dic11—24no—
51(C2×D11)⋊C4—28no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—44no—
54C4⋊Dic11—22no—
55C4⋊Dic11—42no—
56Dic11⋊C4—28no—
57#2618—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11C2×D412yes—
61C23×C11C2×D412yes—
62C23×C11#4112yes—
63C23×C11C2411yescharacteristic
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11—24no—
68C22×D11—24no—
69C2×C4×C11—28no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—24no—
76C2×C4×C11—44no—
77C2×C4×C11—44no—
78C2×C4×C11C2×D414yes—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×D412yes—
81C22⋊D11—48no—
82C2×Dic11—22no—
83C2×Dic11—24no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—24no—
88D44—44no—
89C2×#123—112no—
90C2×#121—111no—
91C22×C4⋊C4D1111yescharacteristic, complemented
92#398—112no—
93#396—114no—
94#394—112no—
95#386—112no—
96#380—111no—
97C22×C11—22no—
98C22×C11—22no—
99C22×C11—24no—
100C22×C11—24no—
101C22×C11#12114yes—
102C22×C11C22×D411yescharacteristic
103C22×C11C22×D411yescharacteristic
104C22×C11C2×#4111yescharacteristic
105C22×C11H(5,𝔽2)12yes—
106C22×C112−1+412yes—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C2×D11—44no—
111C2×D11—44no—
112C4×C11—24no—
113C4×C11—22no—
114C4×C11—22no—
115C4×C11—42no—
116Dic11—42no—
117Dic11—44no—
118C22×D4—112no—
119C22×D4—111no—
120C23×C4C2×D1111yescharacteristic
121C23×C4C2×D1111yescharacteristic
122C23×C4C2×D1111yescharacteristic
123#123—228no—
124#121—224no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—111no—
127C2×C4⋊C4—114no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4C2×D1112yes—
130C2×C4⋊C4C2×D1112yes—
131C2×C22⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C22⋊C4—114no—
135#95—112no—
136#95—114no—
137C2×C11—24no—
138C2×C11C2×#12111yescharacteristic
139C2×C11#53411yescharacteristic
140C2×C11#53611yescharacteristic
141C2×C11#53712yes—
142C2×C11#53912yes—
143D11—82no—
144C24—112no—
145C24C22×D1111yescharacteristic
146C2×D4—224no—
147C2×D4—224no—
148C2×D4—224no—
149C2×D4—222no—
150C2×D4—442no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—114no—
157C22×C4—112no—
158C22×C4D4414yescomplemented
159C22×C4C22⋊D1114yes—
160C22×C4C22×D1112yes—
161C22×C4C22×D1112yes—
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1111yescharacteristic
164C4⋊C4—24no—
165C4⋊C4—24no—
166C4⋊C4—228no—
167C4⋊C4—222no—
168C4⋊C4—442no—
169C22⋊C4—224no—
170C22⋊C4—228no—
171C22⋊C4—224no—
172C22⋊C4—444no—
173C11#261811yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—222no—
177C23—222no—
178C23—224no—
179C23—224no—
180C23—222no—
181C23C2×D4412yes—
182C23#433912yes—
183C23C2×C22⋊D1112yes—
184C23C23×D1111yescharacteristic
185D4—444no—
186D4—448no—
187C2×C4—28no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—44no—
196C2×C4—224no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—224no—
200C2×C4—224no—
201C2×C4—222no—
202C2×C4C2×D4414yes—
203C2×C4C2×C22⋊D1112yes—
204C2×C4C2×C22⋊D1112yes—
205C22—24no—
206C22—24no—
207C22—22no—
208C22—22no—
209C22—444no—
210C22—444no—
211C22—442no—
212C22—442no—
213C22—442no—
214C22#6698314yes—
215C22C22×D4411yescharacteristic
216C22C2×#433911yescharacteristic
217C22#6703712yes—
218C22#6704012yes—
219C22C22×C22⋊D1111yescharacteristic
220C4—24no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—444no—
225C4—442no—
226C2—24no—
227C2—882no—
228C2#1062304112yes—
229C2#1062304612yes—
230C2C2×#6698311yescharacteristic
231C2#1062333511yescharacteristic
232C2#1062334711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C4⋊C4C2
prime radicalC2×#66983C2
hypercenterC22×C4⋊C4D11
hypocenterC11#2618
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C4C2semidirect
3. C2×#66982C2semidirect
4. #10622826C2semidirect
5. #10622825C2semidirect
6. #10622607C2semidirect
7. #10622604C2semidirect
8. #10622596C2semidirect
36. C22×C4×C11D4semidirect
91. C22×C4⋊C4D11semidirect
158. C22×C4D44semidirect
173. C11#2618semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×#669832
C2×#669822
#106228262
#106228252
#106226072
#106226042
#106225962
#261811