Finite Group Databasebeta

← #13069781

Subgroups — #13069781

Order 1408.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#10623014C211yesmaximal, characteristic, complemented
2#10622568C211yesmaximal, characteristic
3#10622568C212yesmaximal
4C11×#342C211yesmaximal, characteristic, complemented
5#10622165C212yesmaximal, complemented
6C24×D11C2211yescharacteristic
7C2×C11×C22⋊C4C2212yes—
8C2×C11×C22⋊C4C2211yescharacteristic
9C2×C22⋊Dic11C2211yescharacteristic
10C2×C22⋊Dic11C2212yes—
11C2×(C2×D11)⋊C4—22no—
12C2×(C2×D11)⋊C4—24no—
13#66977—22no—
14#66931—24no—
15C24×C11C2311yescharacteristic
16C23×D11—21no—
17C23×D11—22no—
18C23×D11—22no—
19C23×D11—21no—
20C23×D11—44no—
21C23×D11Q812yescomplemented
22C22×C4×C11—22no—
23C22×C4×C11D412yes—
24C22×Dic11—21no—
25C22×Dic11D414yes—
26C2×Dic22—22no—
27C11×C22⋊C4—22no—
28C11×C22⋊C4—22no—
29C11×C22⋊C4—22no—
30C22⋊Dic11—22no—
31C22⋊Dic11—22no—
32C22⋊Dic11—22no—
33(C2×D11)⋊C4—44no—
34(C2×D11)⋊C4—48no—
35C4⋊Dic11—22no—
36Dic11⋊C4—24no—
37#2029—111nomaximal, Sylow
38C23×C11—42no—
39C23×C11C2×D411yescharacteristic
40C23×C11C2×D412yes—
41C23×C11C2×Q811yescharacteristic
42C23×C11#4112yes—
43C23×C11#4111yescharacteristic
44C22×D11—24no—
45C22×D11—28no—
46C22×D11—24no—
47C22×D11—22no—
48C22×D11—44no—
49C22×D11—48no—
50C22×D11—44no—
51C22×D11—42no—
52C22×D11—44no—
53C22×D11—41no—
54C22×D11—41no—
55C22×D11—42no—
56C2×C4×C11—22no—
57C2×C4×C11—42no—
58C2×C4×C11—44no—
59C2×C4×C11—42no—
60C2×Dic11—24no—
61C2×Dic11—44no—
62C2×Dic11—42no—
63C2×Dic11—41no—
64Dic22—82no—
65#543—111no—
66#379—112no—
67#379—111no—
68#342—112no—
69#342D1111yescharacteristic, complemented
70C22×C11—22no—
71C22×C11—24no—
72C22×C11—41no—
73C22×C11—42no—
74C22×C11—41no—
75C22×C11#12011yescharacteristic
76C22×C11C22⋊Q812yes—
77C22×C11C22⋊Q811yescharacteristic
78C22×C11#12411yescharacteristic
79C22×C11#12412yes—
80C2×D11—28no—
81C2×D11—24no—
82C2×D11—44no—
83C2×D11—48no—
84C2×D11—44no—
85C2×D11—42no—
86C2×D11—42no—
87C2×D11—44no—
88C4×C11—42no—
89C4×C11—82no—
90Dic11—44no—
91Dic11—81no—
92C25—111no—
93C22⋊Q8—224no—
94C22⋊Q8—222no—
95C2×C22⋊C4—112no—
96C2×C22⋊C4—111no—
97C2×C22⋊C4—224no—
98C2×C22⋊C4—222no—
99C2×C22⋊C4C2×D1112yes—
100C2×C22⋊C4C2×D1111yescharacteristic
101C2×C11—21no—
102C2×C11—22no—
103C2×C11—22no—
104C2×C11—21no—
105C2×C11#39311yescharacteristic
106C2×C11B(4,𝔽2)12yes—
107D11—44no—
108C24—112no—
109C24—221no—
110C24—222no—
111C24—222no—
112C24—221no—
113C24—444no—
114C24C22×D1111yescharacteristic
115C2×Q8—222no—
116C22×C4—22no—
117C22×C4—114no—
118C22×C4—221no—
119C22×C4D4412yes—
120C4⋊C4—224no—
121C4⋊C4—222no—
122C22⋊C4—22no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—222no—
126C22⋊C4—222no—
127C22⋊C4—222no—
128C22⋊C4—444no—
129C22⋊C4—448no—
130C11#202911yescharacteristic, complemented, Sylow
131C23—42no—
132C23—224no—
133C23—228no—
134C23—224no—
135C23—222no—
136C23—442no—
137C23—444no—
138C23—444no—
139C23—448no—
140C23—444no—
141C23—441no—
142C23—441no—
143C23—442no—
144C23C2×D4411yescharacteristic
145C23#433912yes—
146C23D4×D1112yes—
147C23#434111yescharacteristic
148C23Q8×D1111yescharacteristic
149Q8—882no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—224no—
155C2×C4—444no—
156C2×C4—442no—
157C2×C4—441no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—228no—
164C22—224no—
165C22—448no—
166C22—444no—
167C22—444no—
168C22—442no—
169C22—442no—
170C22—444no—
171C22#6692811yescharacteristic
172C22#6693511yescharacteristic
173C22#6693812yes—
174C22#6694912yes—
175C22#6695011yescharacteristic
176C4—42no—
177C4—82no—
178C4—444no—
179C4—881no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—444no—
185C2#1062228611yescharacteristic
186C2#1062235412yes—
subgroupG/H
centerC22#66935
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#342C2
socleC22×C11#120
prime radicalC24×D11C22
hypercenter#342D11
hypocenterC11#2029
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #10623014C2semidirect
4. C11×#342C2semidirect
5. #10622165C2semidirect
21. C23×D11Q8semidirect
69. #342D11semidirect
130. C11#2029semidirect

Maximal subgroups

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

subgroupindex
#106230142
#106225682
C11×#3422
#106221652
#202911