Finite Group Databasebeta

← #13067713

Subgroups — #13067713

Order 1408.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#10623252C211yesmaximal, characteristic, complemented
2#10622701C211yesmaximal, characteristic
3#10622461C211yesmaximal, characteristic
4#10622461C211yesmaximal, characteristic
5C11×#332C211yesmaximal, characteristic, complemented
6#10622122C211yesmaximal, characteristic, complemented
7#10622122C211yesmaximal, characteristic, complemented
8C11×C4⋊Q8C2211yescharacteristic
9Q8×Dic11—21no—
10#66997—21no—
11C2×#4314—21no—
12C2×#4314—21no—
13#66943—21no—
14#66942—22no—
15#66940—21no—
16#66927C2211yescharacteristic
17C4×Dic22C2211yescharacteristic
18C4×Dic22C2211yescharacteristic
19C11×C4⋊C8C2211yescharacteristic
20C11×C4⋊C8C2211yescharacteristic
21#66885—21no—
22#66885—21no—
23#66873—22no—
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×D44—21no—
27C2×D44—21no—
28C2×D44—21no—
29C2×Dic22D411yescharacteristic
30C2×Dic22D411yescharacteristic
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4D412yes—
35C42×C11C2311yescharacteristic
36C4⋊Dic11—22no—
37C4⋊Dic11D411yescharacteristic
38C4⋊Dic11D411yescharacteristic
39Dic11⋊C4—22no—
40Dic11⋊C4—22no—
41Dic11⋊C4—21no—
42Dic11⋊C4—21no—
43C4×Dic11—22no—
44C4×Dic11—21no—
45C4×Dic11—21no—
46C2×C11⋊C8—21no—
47#4314—42no—
48#4314—42no—
49#1626—111nomaximal, Sylow
50C22×D11—41no—
51Q8×C11—41no—
52Q8×C11—41no—
53C2×C4×C11—22no—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D411yescharacteristic
56C2×C4×C11C2×D411yescharacteristic
57C2×Dic11—21no—
58C2×Dic11—21no—
59C2×Dic11—21no—
60C2×Dic11—21no—
61D44—42no—
62D44—41no—
63D44—41no—
64D44—41no—
65D44—41no—
66Dic22—21no—
67Dic22—21no—
68Dic22—21no—
69Dic22SD1612yescomplemented
70C8×C11—41no—
71C8×C11—41no—
72C11⋊C8—41no—
73#557—111no—
74#486—111no—
75#460—111no—
76#460—111no—
77#332D1111yescharacteristic, complemented
78Q8⋊C8—111no—
79Q8⋊C8—111no—
80C22×C11#12011yescharacteristic
81C2×D11—81no—
82C2×D11—81no—
83C2×D11—81no—
84C4×C11—21no—
85C4×C11—42no—
86C4×C11C2×SD1611yescharacteristic
87C4×C11#13511yescharacteristic
88C4×C11AGL(1,ℤ/8)11yescharacteristic
89C4×C11#13711yescharacteristic
90Dic11—22no—
91Dic11—41no—
92Dic11—41no—
93Dic11—41no—
94C2×SD16—221no—
95C2×SD16—221no—
96C4⋊Q8—221no—
97C4⋊Q8C2×D1111yescharacteristic
98#127—111no—
99#125—221no—
100#125—222no—
101C4×Q8—111no—
102C4×Q8—111no—
103C4×Q8—221no—
104C4×Q8—221no—
105C4⋊C8C2×D1111yescharacteristic
106C4⋊C8C2×D1111yescharacteristic
107#102—221no—
108#102—221no—
109#102—222no—
110C4×C8—111no—
111C2×C11#44811yescharacteristic
112C2×C11#44911yescharacteristic
113C2×C11#45411yescharacteristic
114D11—161no—
115C2×Q8—21no—
116C2×Q8—111no—
117C2×Q8—111no—
118C2×D4—221no—
119C2×D4—221no—
120C2×D4—221no—
121SD16—442no—
122SD16—442no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—221no—
126C4⋊C4—21no—
127C4⋊C4—111no—
128C4⋊C4—111no—
129C4⋊C4—222no—
130C4⋊C4—222no—
131C4⋊C4—222no—
132C4⋊C4—221no—
133C4⋊C4—221no—
134C4⋊C4D4412yes—
135C42—222no—
136C42—221no—
137C42—221no—
138C42C22×D1111yescharacteristic
139C11#162611yescharacteristic, complemented, Sylow
140C23—441no—
141Q8—41no—
142Q8—41no—
143Q8—112no—
144Q8—221no—
145Q8—221no—
146Q8—221no—
147D4—442no—
148D4—441no—
149D4—441no—
150D4—441no—
151D4—441no—
152C2×C4—22no—
153C2×C4—221no—
154C2×C4—221no—
155C2×C4—221no—
156C2×C4—221no—
157C2×C4C2×D4411yescharacteristic
158C2×C4D4×D1111yescharacteristic
159C2×C4D4×D1111yescharacteristic
160C8—41no—
161C8—41no—
162C8—441no—
163C22—881no—
164C22—881no—
165C22—881no—
166C22#6693511yescharacteristic
167C4—21no—
168C4—42no—
169C4—222no—
170C4—441no—
171C4—441no—
172C4—441no—
173C4#6696411yescharacteristic
174C4SD16×D1111yescharacteristic
175C4#6696911yescharacteristic
176C4#6697111yescharacteristic
177C2—1761no—
178C2#1062236611yescharacteristic
179C2#1062239411yescharacteristic
180C2#1062241911yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#332C2
socleC22×C11#120
prime radical#66927C22
hypercenter#332D11
hypocenterC11#1626
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #10623252C2semidirect
5. C11×#332C2semidirect
6. #10622122C2semidirect
7. #10622122C2semidirect
69. Dic22SD16semidirect
77. #332D11semidirect
139. C11#1626semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106227012
#106224612
C11×#3322
#106221222
#162611