Finite Group Databasebeta

← #13076873

Subgroups — #13076873

Order 1408.

396 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 133 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×#381C211yesmaximal, characteristic
2#10622825C212yesmaximal
3#10622562C211yesmaximal, characteristic
4#10622561C212yesmaximal
5#10622560C211yesmaximal, characteristic
6#10622274C212yesmaximal, complemented
7#10622273C212yesmaximal, complemented
8#10622270C212yesmaximal, complemented
9#10622269C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic11C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C11×#95C2212yes—
24C11×#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C22×C4×C11—41no—
33C22×C4×C11—41no—
34C22×C4×C11Q814yescomplemented
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×Dic22—42no—
44C2×Dic22—41no—
45C11×C22⋊C4—41no—
46C11×C22⋊C4—41no—
47C22⋊Dic11—42no—
48C22⋊Dic11—42no—
49C4⋊Dic11—42no—
50C4⋊Dic11—42no—
51C4⋊Dic11—42no—
52C4⋊Dic11—41no—
53Dic11⋊C4—42no—
54Dic11⋊C4—42no—
55Dic11⋊C4—42no—
56#2841—111nomaximal, Sylow
57C23×C11—22no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—22no—
61C23×C11C2×Q812yes—
62C23×C11C2411yescharacteristic
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—44no—
73C2×C4×C11C2×Q814yes—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86Dic22—44no—
87#400—112no—
88#399—111no—
89#398—112no—
90#398—112no—
91#396—112no—
92#395—112no—
93#393—111no—
94#381D1111yescharacteristic
95#380—112no—
96C22×C11—22no—
97C22×C11—24no—
98C22×C11—41no—
99C22×C11—42no—
100C22×C11—41no—
101C22×C11C22×Q811yescharacteristic
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C11H(5,𝔽2)11yescharacteristic
104C22×C11H(5,𝔽2)12yes—
105C22×C112−1+412yes—
106C4×C11—24no—
107C4×C11—41no—
108C4×C11—42no—
109C4×C11—41no—
110Dic11—42no—
111Dic11—42no—
112Dic11—42no—
113Dic11—42no—
114C22×Q8—111no—
115C23×C4C2×D1111yescharacteristic
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—111no—
123C2×C22⋊C4—112no—
124C2×C22⋊C4—112no—
125C2×C22⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4C2×D1111yescharacteristic
127#95—112no—
128#95—112no—
129#95—111no—
130#95—112no—
131#95—112no—
132#95—111no—
133#95C2×D1112yes—
134#95C2×D1112yes—
135C2×C11—42no—
136C2×C11#54311yescharacteristic
137C2×C11#54412yes—
138C2×C11#56011yescharacteristic
139C2×C11#56212yes—
140C2×C11#56311yescharacteristic
141C24C22×D1111yescharacteristic
142C2×Q8—441no—
143C2×Q8—442no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—112no—
147C22×C4—112no—
148C22×C4—112no—
149C22×C4—112no—
150C22×C4Dic2214yescomplemented
151C22×C4C22×D1111yescharacteristic
152C22×C4C22×D1112yes—
153C22×C4C22×D1111yescharacteristic
154C22×C4C22×D1112yes—
155C4⋊C4—442no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C4⋊C4—442no—
159C4⋊C4—442no—
160C4⋊C4—441no—
161C4⋊C4—442no—
162C22⋊C4—41no—
163C22⋊C4—41no—
164C22⋊C4—442no—
165C22⋊C4—442no—
166C11#284111yescharacteristic, complemented, Sylow
167C23—21no—
168C23—21no—
169C23—22no—
170C23—22no—
171C23C2×Dic2212yes—
172C23C23×D1111yescharacteristic
173Q8—444no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4C2×Dic2214yes—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22C22×Dic2211yescharacteristic
203C22#6703711yescharacteristic
204C22#6703711yescharacteristic
205C22#6704212yes—
206C22#6704312yes—
207C4—24no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—442no—
212C4—442no—
213C4—442no—
214C4—442no—
215C2—42no—
216C2#1062301411yescharacteristic
217C2#1062305012yes—
218C2#1062318211yescharacteristic
219C2#1062319711yescharacteristic
220C2#1062319812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC24×C11C23
hypercenter#381D11
hypocenterC11#2841
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #10622274C2semidirect
7. #10622273C2semidirect
8. #10622270C2semidirect
9. #10622269C2semidirect
34. C22×C4×C11Q8semidirect
150. C22×C4Dic22semidirect
166. C11#2841semidirect

Maximal subgroups

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

subgroupindex
C11×#3812
#106228252
#106225622
#106225612
#106225602
#106222742
#106222732
#106222702
#106222692
#284111