Finite Group Databasebeta

← #13069780

Subgroups — #13069780

Order 1408.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C11×#379C211yesmaximal, characteristic
3#10622860C212yesmaximal
4#10622165C212yesmaximal, complemented
5#10622164C211yesmaximal, characteristic, complemented
6C25×C11C2211yescharacteristic
7C2×C11×C22⋊C4—22no—
8C2×C11×C22⋊C4C2211yescharacteristic
9C2×C11×C22⋊C4C2211yescharacteristic
10C2×C22⋊Dic11—24no—
11C2×C22⋊Dic11C2212yes—
12C2×C22⋊Dic11C2212yes—
13#66977—22no—
14#66931—24no—
15C24×C11—22no—
16C24×C11—21no—
17C24×C11—21no—
18C24×C11—22no—
19C24×C11—44no—
20C24×C11Q812yescomplemented
21C24×C11C2311yescharacteristic
22C22×C4×C11—21no—
23C22×C4×C11D412yes—
24C22×Dic11—22no—
25C22×Dic11D414yes—
26C2×Dic22—22no—
27C11×C22⋊C4—22no—
28C11×C22⋊C4—22no—
29C11×C22⋊C4—44no—
30C22⋊Dic11—22no—
31C22⋊Dic11—22no—
32C22⋊Dic11—22no—
33C22⋊Dic11—22no—
34C22⋊Dic11—48no—
35C4⋊Dic11—22no—
36Dic11⋊C4—24no—
37#2029—111nomaximal, Sylow
38C23×C11—28no—
39C23×C11—24no—
40C23×C11—24no—
41C23×C11—22no—
42C23×C11—44no—
43C23×C11—42no—
44C23×C11—42no—
45C23×C11—44no—
46C23×C11—44no—
47C23×C11—48no—
48C23×C11—41no—
49C23×C11—42no—
50C23×C11—41no—
51C23×C11C2×D412yes—
52C23×C11C2×D411yescharacteristic
53C23×C11C2×Q811yescharacteristic
54C23×C11#4111yescharacteristic
55C23×C11#4112yes—
56C2×C4×C11—22no—
57C2×C4×C11—42no—
58C2×C4×C11—42no—
59C2×C4×C11—41no—
60C2×Dic11—24no—
61C2×Dic11—44no—
62C2×Dic11—44no—
63C2×Dic11—42no—
64Dic22—82no—
65#543—111no—
66#379—112no—
67#379D1111yescharacteristic
68#342—111no—
69#342—112no—
70C22×C11—22no—
71C22×C11—24no—
72C22×C11—28no—
73C22×C11—24no—
74C22×C11—41no—
75C22×C11—41no—
76C22×C11—42no—
77C22×C11—48no—
78C22×C11—44no—
79C22×C11—44no—
80C22×C11—42no—
81C22×C11—42no—
82C22×C11—44no—
83C22×C11#12011yescharacteristic
84C22×C11C22⋊Q812yes—
85C22×C11C22⋊Q811yescharacteristic
86C22×C11#12412yes—
87C22×C11#12411yescharacteristic
88C4×C11—42no—
89C4×C11—81no—
90Dic11—44no—
91Dic11—82no—
92C25C2×D1111yescharacteristic
93C22⋊Q8—224no—
94C22⋊Q8—222no—
95C2×C22⋊C4—22no—
96C2×C22⋊C4—112no—
97C2×C22⋊C4—112no—
98C2×C22⋊C4—224no—
99C2×C22⋊C4C2×D1111yescharacteristic
100C2×C22⋊C4C2×D1111yescharacteristic
101C2×C11—22no—
102C2×C11—21no—
103C2×C11—22no—
104C2×C11—21no—
105C2×C11—44no—
106C2×C11#39311yescharacteristic
107C2×C11B(4,𝔽2)12yes—
108C24—22no—
109C24—21no—
110C24—21no—
111C24—22no—
112C24—44no—
113C24Dic2212yescomplemented
114C24C22×D1111yescharacteristic
115C2×Q8—222no—
116C22×C4—21no—
117C22×C4—114no—
118C22×C4—222no—
119C22×C4C22⋊D1112yes—
120C4⋊C4—224no—
121C4⋊C4—222no—
122C22⋊C4—22no—
123C22⋊C4—22no—
124C22⋊C4—44no—
125C22⋊C4—222no—
126C22⋊C4—222no—
127C22⋊C4—222no—
128C22⋊C4—222no—
129C22⋊C4—448no—
130C11#202911yescharacteristic, complemented, Sylow
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—42no—
136C23—44no—
137C23—42no—
138C23—44no—
139C23—44no—
140C23—48no—
141C23—42no—
142C23—41no—
143C23—41no—
144C23C2×Dic2211yescharacteristic
145C23#433911yescharacteristic
146C23D4×D1112yes—
147C23#434112yes—
148C23C2×C22⋊D1111yescharacteristic
149Q8—882no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—224no—
155C2×C4—444no—
156C2×C4—444no—
157C2×C4—442no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#6693112yes—
172C22#6693812yes—
173C22#6697711yescharacteristic
174C22#6698911yescharacteristic
175C22#6699011yescharacteristic
176C4—42no—
177C4—81no—
178C4—444no—
179C4—882no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#1062256011yescharacteristic
186C2#1062264512yes—
subgroupG/H
centerC22#66990
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#379C2
socleC22×C11#120
prime radicalC25×C11C22
hypercenter#379D11
hypocenterC11#2029
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #10623014C2semidirect
4. #10622165C2semidirect
5. #10622164C2semidirect
20. C24×C11Q8semidirect
113. C24Dic22semidirect
130. C11#2029semidirect

Maximal subgroups

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

subgroupindex
#106230142
C11×#3792
#106228602
#106221652
#106221642
#202911