Finite Group Databasebeta

← #13067331

Subgroups — #13067331

Order 1408.

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

normal subgroups only

This group has 228 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
1D11×C4⋊Q8C211yesmaximal, characteristic
2#10622448C211yesmaximal, characteristic
3#10622448C211yesmaximal, characteristic
4C11×#332C211yesmaximal, characteristic, complemented
5#10622185C211yesmaximal, characteristic, complemented
6#10622124C211yesmaximal, characteristic, complemented
7#10622120C211yesmaximal, characteristic, complemented
8C2×Q8×D11—21no—
9C11×C4⋊Q8C2211yescharacteristic
10#66997—21no—
11C4⋊C4×D11—21no—
12C4⋊C4×D11C412yes—
13#66941—21no—
14#66941C412yes—
15C42×D11C2211yescharacteristic
16#66922C2211yescharacteristic
17C11×C4⋊C8C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19(C2×D11)⋊C8—21no—
20(C2×D11)⋊C8—21no—
21#66879—21no—
22#66879—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4⋊(C11⋊C8)C2211yescharacteristic
25C2×Q8×C11—21no—
26Q8×D11—42no—
27Q8×D11—42no—
28C2×C4×D11—22no—
29C2×C4×D11C2×C411yescharacteristic
30C2×C4×D11D411yescharacteristic
31C2×C4×D11D411yescharacteristic
32C2×Dic22—22no—
33C2×Dic22—21no—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4C2×C412yes—
38C42×C11C2311yescharacteristic
39C4⋊Dic11—21no—
40C4⋊Dic11C2×C412yes—
41Dic11⋊C4—22no—
42Dic11⋊C4—22no—
43C4×Dic11C2×C411yescharacteristic
44C4×Dic11D411yescharacteristic
45C4×Dic11D411yescharacteristic
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48#1556—111nomaximal, Sylow
49C22×D11C22⋊C411yescharacteristic
50Q8×C11—41no—
51Q8×C11—41no—
52C2×C4×C11—22no—
53C2×C4×C11C22×C411yescharacteristic
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D411yescharacteristic
56C2×Dic11—22no—
57C2×Dic11C22⋊C411yescharacteristic
58C2×Dic11C22⋊C411yescharacteristic
59C2×Dic11C22⋊C411yescharacteristic
60C4×D11—22no—
61C4×D11—21no—
62C4×D11—21no—
63C4×D11—21no—
64C4×D11—21no—
65C4×D11—44no—
66Dic22—44no—
67Dic22—41no—
68Dic22—41no—
69C8×C11—41no—
70C8×C11—41no—
71C11⋊C8—41no—
72C11⋊C8—41no—
73C2×C4⋊Q8—111no—
74#432—111no—
75#432—111no—
76#332—111no—
77#332—111no—
78#332—111no—
79#332D1111yescharacteristic, complemented
80C22×C11C2×C22⋊C411yescharacteristic
81C2×D11—21no—
82C2×D11—21no—
83C2×D11#10112yes—
84C4×C11—21no—
85C4×C11—42no—
86C4×C11AGL(1,ℤ/8)11yescharacteristic
87C4×C11AGL(1,ℤ/8)11yescharacteristic
88C4×C11#13711yescharacteristic
89C4×C11#13711yescharacteristic
90Dic11—21no—
91Dic11—21no—
92Dic11—21no—
93Dic11—42no—
94C22×Q8—221no—
95C4⋊Q8—112no—
96C4⋊Q8—111no—
97C4⋊Q8—221no—
98C4⋊Q8—221no—
99C4⋊Q8C2×D1111yescharacteristic
100C2×C4⋊C4—112no—
101C2×C4⋊C4—221no—
102C2×C42—111no—
103C4⋊C8—111no—
104C4⋊C8—111no—
105C4⋊C8C2×D1111yescharacteristic
106C4⋊C8C2×D1111yescharacteristic
107C22⋊C8—221no—
108C22⋊C8—221no—
109#97—221no—
110#97—221no—
111C2×C11C2×#10111yescharacteristic
112C2×C11#41811yescharacteristic
113C2×C11#41911yescharacteristic
114D11—22no—
115C2×Q8—21no—
116C2×Q8—222no—
117C2×Q8—221no—
118C2×Q8—442no—
119C2×Q8—442no—
120C22×C4—111no—
121C22×C4—111no—
122C22×C4—111no—
123C22×C4—222no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—221no—
127C2×C8—221no—
128C4⋊C4—21no—
129C4⋊C4—112no—
130C4⋊C4—222no—
131C4⋊C4—222no—
132C4⋊C4—221no—
133C4⋊C4C4×D1112yes—
134C42—111no—
135C42—111no—
136C42—111no—
137C42C22×D1111yescharacteristic
138C11#155611yescharacteristic, complemented, Sylow
139C23—111no—
140Q8—41no—
141Q8—41no—
142Q8—444no—
143Q8—441no—
144Q8—441no—
145C2×C4—22no—
146C2×C4—111no—
147C2×C4—111no—
148C2×C4—111no—
149C2×C4—222no—
150C2×C4—221no—
151C2×C4—221no—
152C2×C4—221no—
153C2×C4—221no—
154C2×C4—222no—
155C2×C4—444no—
156C2×C4C2×C4×D1111yescharacteristic
157C2×C4D4×D1111yescharacteristic
158C2×C4D4×D1111yescharacteristic
159C8—41no—
160C8—41no—
161C8—441no—
162C8—441no—
163C22—112no—
164C22—221no—
165C22—221no—
166C22C22⋊C4×D1111yescharacteristic
167C4—21no—
168C4—42no—
169C4—221no—
170C4—221no—
171C4—221no—
172C4—442no—
173C4#6696411yescharacteristic
174C4#6696711yescharacteristic
175C4#6696811yescharacteristic
176C4#6697111yescharacteristic
177C2—222no—
178C2D11×#10111yescharacteristic
179C2#1062238311yescharacteristic
180C2#1062241511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D11
commutatorC2×C4×C11C22×C4
FrattiniC42C22×D11
FittingC11×#332C2
socleC22×C11C2×C22⋊C4
prime radicalC22×D11C22⋊C4
cosocleC42×C11C23
hypercenter#332D11
hypocenterC11#1556
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C11×#332C2semidirect
5. #10622185C2semidirect
6. #10622124C2semidirect
7. #10622120C2semidirect
79. #332D11semidirect
138. C11#1556semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106224482
C11×#3322
#106221852
#106221242
#106221202
#155611