Finite Group Databasebeta

← #13067913

Subgroups — #13067913

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
2C11×#490C211yesmaximal, characteristic, complemented
3#10622687C211yesmaximal, characteristic
4#10622684C211yesmaximal, characteristic, complemented
5#10622181C211yesmaximal, characteristic, complemented
6#10622103C211yesmaximal, characteristic, complemented
7#10622102C211yesmaximal, characteristic, complemented
8C11×#127C2211yescharacteristic
9C11×#125C2211yescharacteristic
10C2×#4324—21no—
11C2×#4323—21no—
12#66951—21no—
13#66951—21no—
14#66950—21no—
15#66949—21no—
16#66947—21no—
17#66941—21no—
18#66928C2211yescharacteristic
19#66923C2211yescharacteristic
20C11×#102—21no—
21C11×#102—21no—
22C11×#97C2211yescharacteristic
23#66896—21no—
24#66896—21no—
25#66867C2211yescharacteristic
26#66867C2211yescharacteristic
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D44D411yescharacteristic
31C2×C4×D11—21no—
32C2×Dic22—21no—
33C2×Dic22D411yescharacteristic
34C2×C8×C11—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4D411yescharacteristic
38C11×C4⋊C4D411yescharacteristic
39C42×C11C2311yescharacteristic
40#4324—42no—
41#4323—42no—
42(C2×D11)⋊C4—21no—
43(C2×D11)⋊C4—21no—
44(C2×D11)⋊C4—21no—
45(C2×D11)⋊C4—21no—
46(C2×D11)⋊C4—21no—
47C4⋊Dic11—21no—
48C4⋊Dic11D411yescharacteristic
49C4⋊Dic11D411yescharacteristic
50Dic11⋊C4—21no—
51Dic11⋊C4—21no—
52Dic11⋊C4—21no—
53C4×Dic11—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56#1657—111nomaximal, Sylow
57C23×C11—41no—
58C22×D11—21no—
59D4×C11—41no—
60D4×C11—41no—
61D4×C11—42no—
62D4×C11—42no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×Dic11—21no—
69C2×Dic11—21no—
70C2×Dic11—21no—
71D44—41no—
72C4×D11—81no—
73Dic22—41no—
74Dic22—81no—
75C8×C11—41no—
76C11⋊C8—22no—
77C11⋊C8—41no—
78#563—111no—
79#496—111no—
80#490—111no—
81#490D1111yescharacteristic, complemented
82#330—111no—
83#330—111no—
84#329—111no—
85C22×C11—81no—
86C22×C11—81no—
87C22×C11—81no—
88C22×C11#12011yescharacteristic
89C2×D11—41no—
90C2×D11—41no—
91C2×D11—41no—
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#127C2×D1111yescharacteristic
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—21no—
113#102—21no—
114#102—221no—
115#102—221no—
116#97—111no—
117#97—111no—
118#97C2×D1111yescharacteristic
119C2×C11—161no—
120C2×C11#45311yescharacteristic
121C2×C11#45411yescharacteristic
122C2×C11#45411yescharacteristic
123D11—81no—
124C2×Q8—111no—
125C2×Q8—221no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—111no—
130C22×C4—221no—
131SD16—442no—
132D8—442no—
133C2×C8—21no—
134C2×C8—221no—
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⋊C4C22⋊D1111yescharacteristic
145C4⋊C4C22⋊D1111yescharacteristic
146C22⋊C4—221no—
147C22⋊C4—221no—
148C22⋊C4—221no—
149C22⋊C4—221no—
150C22⋊C4—221no—
151C42—221no—
152C42C22×D1111yescharacteristic
153C11#165711yescharacteristic, complemented, Sylow
154C23—41no—
155C23—221no—
156Q8—441no—
157Q8—881no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—221no—
166C2×C4—221no—
167C2×C4—221no—
168C2×C4—881no—
169C2×C4D4×D1111yescharacteristic
170C2×C4D4×D1111yescharacteristic
171C2×C4C2×C22⋊D1111yescharacteristic
172C8—41no—
173C8—222no—
174C8—441no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—441no—
179C22—441no—
180C22—441no—
181C22#6699011yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—441no—
188C4—441no—
189C4—441no—
190C2—161no—
191C2—881no—
192C2#1062267511yescharacteristic
193C2#1062281111yescharacteristic
194C2#1062281411yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#490C2
socleC22×C11#120
prime radical#10622687C2
hypercenter#490D11
hypocenterC11#1657
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #10623230C2semidirect
2. C11×#490C2semidirect
4. #10622684C2semidirect
5. #10622181C2semidirect
6. #10622103C2semidirect
7. #10622102C2semidirect
81. #490D11semidirect
153. C11#1657semidirect

Maximal subgroups

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

subgroupindex
#106232302
C11×#4902
#106226872
#106226842
#106221812
#106221032
#106221022
#165711