Finite Group Databasebeta

← #13067926

Subgroups — #13067926

Order 1408.

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

normal subgroups only

This group has 196 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
2C11×#501C211yesmaximal, characteristic, complemented
3#10622699C211yesmaximal, characteristic
4#10622693C211yesmaximal, characteristic, complemented
5#10622181C211yesmaximal, characteristic, complemented
6#10622103C211yesmaximal, characteristic, complemented
7#10622102C211yesmaximal, characteristic
8C11×C4⋊Q8C2211yescharacteristic
9C11×#125C2211yescharacteristic
10C2×#4326—21no—
11C2×#4325—21no—
12#66951—21no—
13#66951—21no—
14#66950—21no—
15#66949—21no—
16#66947—21no—
17#66941—21no—
18#66928C2211yescharacteristic
19#66923C2211yescharacteristic
20C11×#107—21no—
21C11×#106—21no—
22C11×#97C2211yescharacteristic
23#66872—21no—
24#66871—21no—
25#66867C2211yescharacteristic
26#66867C2211yescharacteristic
27C2×Q8×C11—21no—
28C2×D44D411yescharacteristic
29C2×C4×D11—21no—
30C2×Dic22—21no—
31C2×Dic22D411yescharacteristic
32C2×C8×C11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4D411yescharacteristic
38C11×C4⋊C4D411yescharacteristic
39C42×C11C2311yescharacteristic
40#4326—42no—
41#4325—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#1660—111nomaximal, Sylow
57C22×D11—21no—
58Q8×C11—41no—
59Q8×C11—41no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—41no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—21no—
69D44—41no—
70C4×D11—81no—
71Dic22—41no—
72Dic22—81no—
73C8×C11—22no—
74C11⋊C8—22no—
75C11⋊C8—22no—
76#563—111no—
77#501—111no—
78#501D1111yescharacteristic, complemented
79#497—111no—
80#330—111no—
81#330—111no—
82#329—111no—
83C22×C11#12011yescharacteristic
84C2×D11—41no—
85C2×D11—41no—
86C2×D11—41no—
87C4×C11—21no—
88C4×C11—21no—
89C4×C11—21no—
90C4×C11—41no—
91C4×C11—41no—
92C4×C11—81no—
93Dic11—41no—
94Dic11—41no—
95Dic11—41no—
96C2×Q16—221no—
97C2×SD16—221no—
98C4⋊Q8—221no—
99C4⋊Q8C2×D1111yescharacteristic
100#126—221no—
101#126—221no—
102#125—111no—
103#125C2×D1111yescharacteristic
104#124—111no—
105#123—221no—
106C22⋊Q8—221no—
107C22⋊Q8—221no—
108#107—21no—
109#107—221no—
110#106—21no—
111#106—221no—
112#97—111no—
113#97—111no—
114#97C2×D1111yescharacteristic
115C2×C11#45311yescharacteristic
116C2×C11#45611yescharacteristic
117C2×C11#45611yescharacteristic
118D11—81no—
119C2×Q8—21no—
120C2×Q8—111no—
121C2×Q8—221no—
122C2×D4—111no—
123C22×C4—221no—
124Q16—442no—
125SD16—442no—
126C2×C8—21no—
127C2×C8—221no—
128C2×C8—221no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—111no—
134C4⋊C4—111no—
135C4⋊C4—221no—
136C4⋊C4—221no—
137C4⋊C4—221no—
138C4⋊C4—221no—
139C4⋊C4C22⋊D1111yescharacteristic
140C4⋊C4C22⋊D1111yescharacteristic
141C22⋊C4—221no—
142C22⋊C4—221no—
143C22⋊C4—221no—
144C22⋊C4—221no—
145C22⋊C4—221no—
146C42—221no—
147C42C22×D1111yescharacteristic
148C11#166011yescharacteristic, complemented, Sylow
149C23—221no—
150Q8—41no—
151Q8—41no—
152Q8—441no—
153Q8—881no—
154D4—441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—221no—
159C2×C4—221no—
160C2×C4—221no—
161C2×C4—881no—
162C2×C4D4×D1111yescharacteristic
163C2×C4D4×D1111yescharacteristic
164C2×C4C2×C22⋊D1111yescharacteristic
165C8—22no—
166C8—222no—
167C8—222no—
168C22—441no—
169C22—441no—
170C22—441no—
171C22#6699011yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—441no—
179C4—441no—
180C4—441no—
181C2—881no—
182C2#1062270811yescharacteristic
183C2#1062281111yescharacteristic
184C2#1062281811yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#501C2
socleC22×C11#120
prime radicalC2×D44D4
hypercenter#501D11
hypocenterC11#1660
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. C11×#501C2semidirect
4. #10622693C2semidirect
5. #10622181C2semidirect
6. #10622103C2semidirect
78. #501D11semidirect
148. C11#1660semidirect

Maximal subgroups

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

subgroupindex
#106232302
C11×#5012
#106226992
#106226932
#106221812
#106221032
#106221022
#166011