Finite Group Databasebeta

← #13067950

Subgroups — #13067950

Order 1408.

184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C11×#563C211yesmaximal, characteristic
2#10622682C211yesmaximal, characteristic, complemented
3#10622678C211yesmaximal, characteristic, complemented
4#10622668C211yesmaximal, characteristic
5#10622181C211yesmaximal, characteristic, complemented
6#10622181C211yesmaximal, characteristic, complemented
7#10622178C211yesmaximal, characteristic
8C11×C4⋊Q8—21no—
9C11×#126—21no—
10C11×#126—21no—
11C11×#125C2211yescharacteristic
12C11×#125C2211yescharacteristic
13C11×#124C2211yescharacteristic
14C11×#123—21no—
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8—21no—
17#66922C2211yescharacteristic
18#66899—21no—
19#66896—21no—
20#66874—21no—
21#66874—21no—
22#66872—21no—
23#66871—21no—
24#66867C2211yescharacteristic
25#66867C2211yescharacteristic
26#66867C2211yescharacteristic
27C2×Q8×C11—21no—
28C2×Q8×C11D411yescharacteristic
29C2×D4×C11D411yescharacteristic
30C22×C4×C11—21no—
31C2×Dic22—21no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4D411yescharacteristic
39C11×C4⋊C4D411yescharacteristic
40C11×C4⋊C4D411yescharacteristic
41C11×C4⋊C4D411yescharacteristic
42C11×C22⋊C4—21no—
43C11×C22⋊C4—21no—
44C11×C22⋊C4—21no—
45C11×C22⋊C4—21no—
46C11×C22⋊C4—21no—
47C42×C11—21no—
48C42×C11C2311yescharacteristic
49C4⋊Dic11—21no—
50C4⋊Dic11—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—21no—
54#1664—111nomaximal, Sylow
55C23×C11—21no—
56Q8×C11—41no—
57Q8×C11—81no—
58D4×C11—41no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—81no—
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×Dic11—41no—
69Dic22—42no—
70C11⋊C8—22no—
71C11⋊C8—41no—
72C11⋊C8—41no—
73#563D1111yescharacteristic
74#501—111no—
75#491—111no—
76#489—111no—
77#330—111no—
78#330—111no—
79#329—111no—
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11#12011yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—21no—
87C4×C11—41no—
88C4×C11—41no—
89C4×C11—41no—
90C4×C11—41no—
91C4×C11—41no—
92Dic11—81no—
93C4⋊Q8—21no—
94C4⋊Q8—111no—
95#126—21no—
96#126—21no—
97#125C2×D1111yescharacteristic
98#125C2×D1111yescharacteristic
99#124C2×D1111yescharacteristic
100#123—21no—
101C22⋊Q8—21no—
102C22⋊Q8—21no—
103#107—221no—
104#106—221no—
105#103—221no—
106#103—221no—
107#103—221no—
108#102—221no—
109#97—111no—
110#97—111no—
111#97—111no—
112C2×C11—81no—
113C2×C11#45411yescharacteristic
114C2×C11#45511yescharacteristic
115C2×C11#45611yescharacteristic
116C2×Q8—21no—
117C2×Q8—221no—
118C2×Q8C22⋊D1111yescharacteristic
119C2×D4C22⋊D1111yescharacteristic
120C22×C4—21no—
121C2×C8—221no—
122C2×C8—221no—
123C2×C8—221no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—221no—
131C4⋊C4—221no—
132C4⋊C4C22⋊D1111yescharacteristic
133C4⋊C4C22⋊D1111yescharacteristic
134C4⋊C4C22⋊D1111yescharacteristic
135C4⋊C4C22⋊D1111yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C42—21no—
142C42C22×D1111yescharacteristic
143C11#166411yescharacteristic, complemented, Sylow
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—442no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—441no—
156C2×C4C2×C22⋊D1111yescharacteristic
157C2×C4C2×C22⋊D1111yescharacteristic
158C2×C4C2×C22⋊D1111yescharacteristic
159C8—222no—
160C8—441no—
161C8—441no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#6700611yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—881no—
175C2—81no—
176C2#1062285511yescharacteristic
177C2#1062285811yescharacteristic
178C2#1062285911yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#563C2
socleC22×C11#120
prime radicalC2×D4×C11D4
hypercenter#563D11
hypocenterC11#1664
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #10622682C2semidirect
3. #10622678C2semidirect
5. #10622181C2semidirect
6. #10622181C2semidirect
143. C11#1664semidirect

Maximal subgroups

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

subgroupindex
C11×#5632
#106226822
#106226782
#106226682
#106221812
#106221782
#166411