Finite Group Databasebeta

← #13075993

Subgroups — #13075993

Order 1408.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2#10622826C212yesmaximal, complemented
3#10622573C211yesmaximal, characteristic
4#10622569C212yesmaximal, complemented
5#10622560C211yesmaximal, characteristic, complemented
6#10622286C212yesmaximal, complemented
7#10622278C212yesmaximal, complemented
8#10622277C212yesmaximal, complemented
9C11⋊#401C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×Dic22C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C11×#95C2212yes—
23C11×#95C2212yes—
24C11⋊#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2311yescharacteristic
32C23×D11C2312yes—
33C22×C4×C11—22no—
34C22×C4×C11—41no—
35C22×C4×C11—41no—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—24no—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—42no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C2×D44—24no—
47C2×D44—41no—
48C2×C4×D11—24no—
49C2×C4×D11—42no—
50C2×C4×D11—42no—
51C2×Dic22—42no—
52C2×Dic22—41no—
53C11×C22⋊C4—41no—
54C11×C22⋊C4—41no—
55C22⋊Dic11—42no—
56(C2×D11)⋊C4—42no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60#2760—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11#4112yes—
66C23×C11C2411yescharacteristic
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11#4114yes—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—44no—
85C22⋊D11—48no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95D44—44no—
96C4×D11—48no—
97Dic22—44no—
98#401—112no—
99#393—111no—
100#393—112no—
101#392—111no—
102#386—112no—
103#386—112no—
104#386—112no—
105#381—112no—
106#381D1111yescharacteristic, complemented
107C22×C11—22no—
108C22×C11—24no—
109C22×C11—42no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11C2×#4111yescharacteristic
113C22×C11C2×#4112yes—
114C22×C11H(5,𝔽2)11yescharacteristic
115C22×C11H(5,𝔽2)11yescharacteristic
116C22×C11H(5,𝔽2)12yes—
117C2×D11—24no—
118C2×D11—24no—
119C2×D11—24no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—42no—
123C2×D11—42no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11—41no—
128Dic11—42no—
129Dic11—42no—
130Dic11—42no—
131C22×Q8—111no—
132C22×D4—112no—
133C22×D4—111no—
134C23×C4—112no—
135C23×C4C2×D1111yescharacteristic
136C2×C22⋊C4—112no—
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4C2×D1111yescharacteristic
142C2×C22⋊C4C2×D1111yescharacteristic
143#95—111no—
144#95—112no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95—112no—
149#95—111no—
150#95C2×D1112yes—
151#95C2×D1112yes—
152C2×C11—42no—
153C2×C11#53811yescharacteristic
154C2×C11#53812yes—
155C2×C11#55112yes—
156C2×C11#55111yescharacteristic
157C2×C11#56011yescharacteristic
158D11—44no—
159C24—112no—
160C24C22×D1111yescharacteristic
161C2×Q8—441no—
162C2×Q8—442no—
163C2×D4—224no—
164C2×D4—224no—
165C2×D4—224no—
166C2×D4—441no—
167C2×D4—442no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—112no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—224no—
175C22×C4—442no—
176C22×C4—442no—
177C22×C4C22×D1111yescharacteristic
178C22×C4C22×D1112yes—
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—442no—
184C22⋊C4—442no—
185C22⋊C4—442no—
186C22⋊C4—442no—
187C22⋊C4—442no—
188C11#276011yescharacteristic, complemented, Sylow
189C23—21no—
190C23—21no—
191C23—22no—
192C23—22no—
193C23—114no—
194C23—222no—
195C23—222no—
196C23—222no—
197C23—222no—
198C23—222no—
199C23—222no—
200C23#433912yes—
201C23C23×D1111yescharacteristic
202Q8—444no—
203D4—444no—
204D4—448no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—448no—
226C22—22no—
227C22—24no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—224no—
232C22—224no—
233C22—224no—
234C22—442no—
235C22—442no—
236C22—442no—
237C22—442no—
238C22C2×#433911yescharacteristic
239C22#6703711yescharacteristic
240C22#6703711yescharacteristic
241C22#41×D1112yes—
242C22#6704212yes—
243C4—42no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—442no—
248C4—442no—
249C4—442no—
250C2—42no—
251C2—444no—
252C2#1062302511yescharacteristic
253C2#1062305812yes—
254C2#1062318812yes—
255C2#1062319011yescharacteristic
256C2#1062319711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radical#10622573C2
hypercenter#381D11
hypocenterC11#2760
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C11×#381C2semidirect
2. #10622826C2semidirect
4. #10622569C2semidirect
5. #10622560C2semidirect
6. #10622286C2semidirect
7. #10622278C2semidirect
8. #10622277C2semidirect
9. C11⋊#401C2semidirect
106. #381D11semidirect
188. C11#2760semidirect

Maximal subgroups

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

subgroupindex
C11×#3812
#106228262
#106225732
#106225692
#106225602
#106222862
#106222782
#106222772
C11⋊#4012
#276011