Finite Group Databasebeta

← #13067916

Subgroups — #13067916

Order 1408.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#10623230C211yesmaximal, characteristic, complemented
2#10622680C211yesmaximal, characteristic, complemented
3#10622326C211yesmaximal, characteristic, complemented
4#10622325C211yesmaximal, characteristic
5C11×#330C211yesmaximal, characteristic, complemented
6#10622103C211yesmaximal, characteristic, complemented
7#10622102C211yesmaximal, characteristic, complemented
8C11×#125C2211yescharacteristic
9C2×D88—21no—
10C2×#4314—21no—
11#66951—21no—
12#66951—21no—
13#66950—21no—
14#66949—21no—
15#66947—21no—
16#66941—21no—
17#66928C2211yescharacteristic
18#66927C2211yescharacteristic
19#66923C2211yescharacteristic
20C11×#97C2211yescharacteristic
21C11×#97C2211yescharacteristic
22#66885—21no—
23#66885—21no—
24#66873—21no—
25#66873—21no—
26#66867C2211yescharacteristic
27C2×D44—21no—
28C2×D44—21no—
29C2×D44—21no—
30C2×D44D411yescharacteristic
31C2×C4×D11—21no—
32C2×Dic22—21no—
33C2×Dic22D411yescharacteristic
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4D411yescharacteristic
39C11×C4⋊C4D411yescharacteristic
40C42×C11C2311yescharacteristic
41(C2×D11)⋊C4—21no—
42(C2×D11)⋊C4—21no—
43(C2×D11)⋊C4—21no—
44(C2×D11)⋊C4—21no—
45(C2×D11)⋊C4—21no—
46C4⋊Dic11—21no—
47C4⋊Dic11D411yescharacteristic
48C4⋊Dic11D411yescharacteristic
49Dic11⋊C4—21no—
50Dic11⋊C4—21no—
51Dic11⋊C4—21no—
52C4×Dic11—21no—
53C2×C11⋊C8—21no—
54D88—42no—
55#4314—42no—
56#1657—111nomaximal, Sylow
57C22×D11—21no—
58C22×D11—41no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11C2×D411yescharacteristic
62C2×C4×C11C2×D411yescharacteristic
63C2×C4×C11C2×D411yescharacteristic
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—21no—
67D44—41no—
68D44—41no—
69D44—41no—
70D44—42no—
71D44—42no—
72C4×D11—81no—
73Dic22—41no—
74Dic22—81no—
75C8×C11—22no—
76C8×C11—41no—
77C11⋊C8—41no—
78#563—111no—
79#496—111no—
80#490—111no—
81#490—111no—
82#330—111no—
83#330D1111yescharacteristic, complemented
84#329—111no—
85C22×C11#12011yescharacteristic
86C2×D11—41no—
87C2×D11—41no—
88C2×D11—41no—
89C2×D11—81no—
90C2×D11—81no—
91C2×D11—81no—
92C4×C11—21no—
93C4×C11—21no—
94C4×C11—21no—
95C4×C11—41no—
96C4×C11—41no—
97Dic11—41no—
98Dic11—41no—
99Dic11—41no—
100C2×SD16—221no—
101C2×D8—221no—
102C4⋊Q8—221no—
103#127—111no—
104#126—221no—
105#126—221no—
106#125—111no—
107#125C2×D1111yescharacteristic
108#124—111no—
109#123—221no—
110C22⋊Q8—221no—
111C22⋊Q8—221no—
112#102—221no—
113#102—221no—
114#102—221no—
115#102—221no—
116#97—111no—
117#97C2×D1111yescharacteristic
118#97C2×D1111yescharacteristic
119C2×C11#45311yescharacteristic
120C2×C11#45411yescharacteristic
121C2×C11#45411yescharacteristic
122D11—81no—
123D11—161no—
124C2×Q8—111no—
125C2×Q8—221no—
126C2×D4—111no—
127C2×D4—221no—
128C2×D4—221no—
129C2×D4—221no—
130C22×C4—221no—
131SD16—442no—
132D8—442no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—221no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—111no—
139C4⋊C4—111no—
140C4⋊C4—221no—
141C4⋊C4—221no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C4⋊C4D4411yescharacteristic
145C4⋊C4D4411yescharacteristic
146C22⋊C4—221no—
147C22⋊C4—221no—
148C22⋊C4—221no—
149C22⋊C4—221no—
150C22⋊C4—221no—
151C42—221no—
152C42C22×D1111yescharacteristic
153C11#165711yescharacteristic, complemented, Sylow
154C23—221no—
155C23—441no—
156Q8—441no—
157Q8—881no—
158D4—441no—
159D4—441no—
160D4—441no—
161D4—442no—
162D4—442no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—221no—
166C2×C4—221no—
167C2×C4—221no—
168C2×C4—881no—
169C2×C4C2×D4411yescharacteristic
170C2×C4D4×D1111yescharacteristic
171C2×C4D4×D1111yescharacteristic
172C8—22no—
173C8—41no—
174C8—441no—
175C22—441no—
176C22—441no—
177C22—441no—
178C22—881no—
179C22—881no—
180C22—881no—
181C22#6693511yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—441no—
188C4—441no—
189C4—441no—
190C2—881no—
191C2—1761no—
192C2#1062236611yescharacteristic
193C2#1062243511yescharacteristic
194C2#1062244011yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#330C2
socleC22×C11#120
prime radical#10622325C2
hypercenter#330D11
hypocenterC11#1657
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #10623230C2semidirect
2. #10622680C2semidirect
3. #10622326C2semidirect
5. C11×#330C2semidirect
6. #10622103C2semidirect
7. #10622102C2semidirect
83. #330D11semidirect
153. C11#1657semidirect

Maximal subgroups

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

subgroupindex
#106232302
#106226802
#106223262
#106223252
C11×#3302
#106221032
#106221022
#165711