Finite Group Databasebeta

← #13076763

Subgroups — #13076763

Order 1408.

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

normal subgroups only

This group has 408 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
1C11×#398C211yesmaximal, characteristic, complemented
2#10622607C212yesmaximal, complemented
3#10622604C212yesmaximal
4#10622601C211yesmaximal, characteristic
5#10622594C212yesmaximal, complemented
6#10622592C211yesmaximal, characteristic, complemented
7#10622288C212yesmaximal, complemented
8#10622287C212yesmaximal, complemented
9#10622286C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C11×#95C2212yes—
25C11×#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—22no—
41C2×D44—41no—
42C2×D44—41no—
43C2×Dic22—42no—
44C2×Dic22—41no—
45C11×C4⋊C4—24no—
46C11×C4⋊C4—41no—
47C11×C4⋊C4—41no—
48(C2×D11)⋊C4—42no—
49(C2×D11)⋊C4—42no—
50(C2×D11)⋊C4—42no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
53(C2×D11)⋊C4—42no—
54C4⋊Dic11—42no—
55Dic11⋊C4—42no—
56C4×Dic11—41no—
57#2830—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11#4112yes—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88D44—44no—
89Dic22—44no—
90#398D1111yescharacteristic, complemented
91#397—112no—
92#397—112no—
93#396—112no—
94#395—111no—
95#394—112no—
96#393—112no—
97#390—111no—
98#387—112no—
99C22×C11C2×#4111yescharacteristic
100C22×C11H(5,𝔽2)11yescharacteristic
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)12yes—
103C22×C112−1+412yes—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C2×D11—42no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11—41no—
115C4×C11—41no—
116Dic11—42no—
117Dic11—42no—
118Dic11—42no—
119C22×Q8—111no—
120C22×D4—111no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4C2×D1112yes—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C22⋊C4—112no—
131C2×C22⋊C4—112no—
132C2×C42—111no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—111no—
138#95C2×D1112yes—
139#95C2×D1111yescharacteristic
140C2×C11#53811yescharacteristic
141C2×C11#54212yes—
142C2×C11#56011yescharacteristic
143C2×C11#56212yes—
144C2×C11#56311yescharacteristic
145D11—82no—
146C24—112no—
147C2×Q8—441no—
148C2×Q8—442no—
149C2×D4—222no—
150C2×D4—441no—
151C2×D4—441no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4—112no—
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1112yes—
158C22×C4C22×D1111yescharacteristic
159C22×C4C22×D1111yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—442no—
164C4⋊C4—442no—
165C22⋊C4—442no—
166C22⋊C4—442no—
167C22⋊C4—442no—
168C22⋊C4—442no—
169C22⋊C4—442no—
170C22⋊C4—442no—
171C42—441no—
172C11#283011yescharacteristic, complemented, Sylow
173C23—222no—
174C23—222no—
175C23—222no—
176C23—222no—
177C23—222no—
178C23—222no—
179C23—222no—
180C23C23×D1111yescharacteristic
181Q8—444no—
182D4—444no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4#434112yes—
205C22—442no—
206C22—442no—
207C22—442no—
208C22—442no—
209C22—442no—
210C22—442no—
211C22—442no—
212C22C2×#434111yescharacteristic
213C22#6703711yescharacteristic
214C22#6704012yes—
215C22#6704211yescharacteristic
216C22#6704212yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—442no—
223C4—442no—
224C4—442no—
225C2—882no—
226C2#1062314811yescharacteristic
227C2#1062317412yes—
228C2#1062319711yescharacteristic
229C2#1062323112yes—
230C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC22×D44C22
hypercenter#398D11
hypocenterC11#2830
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C11×#398C2semidirect
2. #10622607C2semidirect
5. #10622594C2semidirect
6. #10622592C2semidirect
7. #10622288C2semidirect
8. #10622287C2semidirect
9. #10622286C2semidirect
90. #398D11semidirect
172. C11#2830semidirect

Maximal subgroups

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

subgroupindex
C11×#3982
#106226072
#106226042
#106226012
#106225942
#106225922
#106222882
#106222872
#106222862
#283011