Finite Group Databasebeta

← #13067828

Subgroups — #13067828

Order 1408.

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

normal subgroups only

This group has 208 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#10623110C211yesmaximal, characteristic
2C11×#462C211yesmaximal, characteristic, complemented
3#10622706C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic
5Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#10622121C211yesmaximal, characteristic
7#10622119C211yesmaximal, characteristic, complemented
8C2×C11×Q16—21no—
9C11×C4⋊Q8C2211yescharacteristic
10C4×Q8×C11C2211yescharacteristic
11#66999—21no—
12#66949—22no—
13C4⋊C4×D11—21no—
14C4×D44—21no—
15C4×D44C2211yescharacteristic
16#66923—21no—
17#66922C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19C11×#103—21no—
20#66874—22no—
21#66873—21no—
22#66871—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×Q8×C11D411yescharacteristic
27C2×D44D411yescharacteristic
28C2×C4×D11—22no—
29C2×C4×D11—21no—
30C2×Dic22D412yes—
31C11×Q16—42no—
32C2×C8×C11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4D411yescharacteristic
37C42×C11—21no—
38C42×C11C2311yescharacteristic
39(C2×D11)⋊C4—22no—
40(C2×D11)⋊C4—21no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11D411yescharacteristic
44Dic11⋊C4—22no—
45Dic11⋊C4—22no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48#1644—111nomaximal, Sylow
49C22×D11—21no—
50Q8×C11—21no—
51Q8×C11—21no—
52Q8×C11—41no—
53Q8×C11—41no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—41no—
57C2×C4×C11C2×D411yescharacteristic
58C2×C4×C11C2×D411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×Dic11—21no—
61C2×Dic11—22no—
62D44—21no—
63D44Q1612yescomplemented
64C4×D11—41no—
65C4×D11—41no—
66C4×D11—82no—
67Dic22—42no—
68C8×C11—41no—
69C11⋊C8—41no—
70C11⋊C8—41no—
71#554—111no—
72#487—111no—
73#474—111no—
74#462D1111yescharacteristic, complemented
75#333—111no—
76Q8⋊C8—111no—
77D4⋊C8—111no—
78C22×C11#12011yescharacteristic
79C2×D11—22no—
80C2×D11—41no—
81C2×D11—41no—
82C4×C11—21no—
83C4×C11—41no—
84C4×C11—41no—
85C4×C11—81no—
86C4×C11C2×Q1611yescharacteristic
87C4×C11#13511yescharacteristic
88C4×C11AGL(1,ℤ/8)11yescharacteristic
89C4×C11#13711yescharacteristic
90Dic11—41no—
91Dic11—42no—
92C2×Q16—21no—
93C4⋊Q8—111no—
94C4⋊Q8C2×D1111yescharacteristic
95#125—221no—
96C22⋊Q8—222no—
97C22⋊Q8—221no—
98C4×Q8C2×D1111yescharacteristic
99C4×D4—111no—
100C4×D4—221no—
101C2×C4⋊C4—221no—
102#107—221no—
103C4⋊C8—111no—
104C4⋊C8C2×D1111yescharacteristic
105#103—21no—
106#103—222no—
107#102—221no—
108C4×C8—111no—
109C2×C11#44911yescharacteristic
110C2×C11#45111yescharacteristic
111C2×C11#45511yescharacteristic
112D11—42no—
113C2×Q8—21no—
114C2×Q8—112no—
115C2×Q8C22⋊D1111yescharacteristic
116C2×D4—111no—
117C22×C4—222no—
118C22×C4—221no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—221no—
122C2×C8—221no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—111no—
127C4⋊C4—222no—
128C4⋊C4—222no—
129C4⋊C4—221no—
130C4⋊C4—221no—
131C4⋊C4C22⋊D1111yescharacteristic
132C22⋊C4—222no—
133C22⋊C4—221no—
134C42—21no—
135C42C22×D1111yescharacteristic
136C11#164411yescharacteristic, complemented, Sylow
137C23—221no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—442no—
143D4—112no—
144D4—221no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—221no—
149C2×C4—222no—
150C2×C4—441no—
151C2×C4—441no—
152C2×C4—882no—
153C2×C4D4×D1111yescharacteristic
154C2×C4D4×D1111yescharacteristic
155C2×C4C2×C22⋊D1111yescharacteristic
156C8—41no—
157C8—441no—
158C8—441no—
159C22—222no—
160C22—441no—
161C22—441no—
162C22#6699011yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—442no—
168C4—441no—
169C4Q16×D1111yescharacteristic
170C4#6697111yescharacteristic
171C4#6698511yescharacteristic
172C4#6700311yescharacteristic
173C2—442no—
174C2#1062265011yescharacteristic
175C2#1062279911yescharacteristic
176C2#1062281511yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#462C2
socleC22×C11#120
prime radicalC2×D44D4
hypercenter#462D11
hypocenterC11#1644
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C11×#462C2semidirect
3. #10622706C2semidirect
5. Q8⋊(C11⋊C8)C2semidirect
7. #10622119C2semidirect
63. D44Q16semidirect
74. #462D11semidirect
136. C11#1644semidirect

Maximal subgroups

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

subgroupindex
#106231102
C11×#4622
#106227062
#106227002
Q8⋊(C11⋊C8)2
#106221212
#106221192
#164411