Finite Group Databasebeta

← #13070534

Subgroups — #13070534

Order 1408.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×Q16×D11C211yesmaximal, characteristic, complemented
2C2×#66892C211yesmaximal, characteristic, complemented
3C2×#66864C211yesmaximal, characteristic, complemented
4#10622496C211yesmaximal, characteristic
5C11×#358C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
7#10622130C211yesmaximal, characteristic, complemented
8C2×Q8×D11—21no—
9C2×C11×Q16C2211yescharacteristic
10C2×#4326—21no—
11Q16×D11—22no—
12Q16×D11—22no—
13C2×Dic44C2211yescharacteristic
14C2×D88C2211yescharacteristic
15C2×C8×D11C2211yescharacteristic
16#66948—21no—
17C2×C11×C16C2211yescharacteristic
18C11×#107C2211yescharacteristic
19#66892—22no—
20C2×C11⋊C16C2211yescharacteristic
21#66873—21no—
22#66864—22no—
23C2×Q8×C11—21no—
24Q8×D11—24no—
25Q8×D11—42no—
26C2×D44—21no—
27C2×D44—41no—
28C2×C4×D11—41no—
29C2×C4×D11D411yescharacteristic
30C2×Dic22—21no—
31C2×Dic22—41no—
32C11×Q16—21no—
33C11×Q16D412yescomplemented
34C2×C8×C11C2311yescharacteristic
35C11×C4⋊C4—21no—
36#4326—24no—
37(C2×D11)⋊C4—41no—
38C2×C11⋊C8D411yescharacteristic
39Dic44—21no—
40Dic44D412yescomplemented
41D88—21no—
42D88—21no—
43C8×D11—21no—
44C8×D11—21no—
45C11×C16—21no—
46C11⋊C16—21no—
47#2185—111nomaximal, Sylow
48C22×D11—41no—
49C22×D11D811yescharacteristic
50Q8×C11—22no—
51Q8×C11—41no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11C2×D411yescharacteristic
55C2×Dic11—41no—
56C2×Dic11D811yescharacteristic
57D44—41no—
58D44—41no—
59D44—82no—
60C4×D11—21no—
61C4×D11—21no—
62C4×D11—44no—
63Dic22—22no—
64Dic22—44no—
65Dic22—41no—
66C8×C11C2×D411yescharacteristic
67C8×C11C2×D411yescharacteristic
68C11⋊C8—21no—
69C22×Q16—111no—
70C2×SD32—111no—
71C2×SD32—111no—
72#466—111no—
73#358—111no—
74#358D1111yescharacteristic, complemented
75C22⋊C16—111no—
76C22×C11C2×D811yescharacteristic
77C2×D11—21no—
78C2×D11—21no—
79C2×D11—81no—
80C2×D11—81no—
81C2×D11—81no—
82C2×D11SD3212yescomplemented
83C4×C11—42no—
84C4×C11—81no—
85C4×C11#12011yescharacteristic
86C4×C11AGL(1,ℤ/8)11yescharacteristic
87Dic11—21no—
88Dic11—42no—
89C22×Q8—221no—
90C2×Q16—111no—
91C2×Q16—221no—
92C2×Q16—222no—
93C2×Q16—222no—
94C2×Q16C2×D1111yescharacteristic
95C2×D8—111no—
96C22×C8—111no—
97#121—221no—
98SD32—222no—
99SD32—222no—
100C2×C16—111no—
101C2×C16C2×D1111yescharacteristic
102#107C2×D1111yescharacteristic
103#102—221no—
104C2×C11#44711yescharacteristic
105C2×C11C2×SD3211yescharacteristic
106C2×C11#51011yescharacteristic
107D11—22no—
108D11—161no—
109C2×Q8—21no—
110C2×Q8—224no—
111C2×Q8—221no—
112C2×Q8—441no—
113C2×Q8—442no—
114C2×D4—221no—
115C2×D4—441no—
116C22×C4—111no—
117C22×C4—441no—
118Q16—21no—
119Q16—112no—
120Q16—224no—
121Q16—221no—
122Q16D4412yescomplemented
123D8—221no—
124D8—221no—
125C2×C8—111no—
126C2×C8—221no—
127C2×C8—221no—
128C2×C8C22×D1111yescharacteristic
129C4⋊C4—21no—
130C22⋊C4—441no—
131C16—21no—
132C16—221no—
133C11#218511yescharacteristic, complemented, Sylow
134C23—111no—
135C23—441no—
136Q8—22no—
137Q8—41no—
138Q8—222no—
139Q8—444no—
140Q8—441no—
141D4—441no—
142D4—441no—
143D4—882no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—111no—
147C2×C4—221no—
148C2×C4—221no—
149C2×C4—444no—
150C2×C4—441no—
151C2×C4D4×D1111yescharacteristic
152C8—221no—
153C8C2×D4411yescharacteristic
154C8D4×D1111yescharacteristic
155C22—112no—
156C22—221no—
157C22—221no—
158C22—881no—
159C22—881no—
160C22—881no—
161C22D8×D1111yescharacteristic
162C4—42no—
163C4—81no—
164C4—221no—
165C4—442no—
166C4#6693511yescharacteristic
167C4#6696711yescharacteristic
168C2—222no—
169C2—1761no—
170C2#1062238611yescharacteristic
171C2D11×SD3211yescharacteristic
172C2#1062253111yescharacteristic
subgroupG/H
centerC22D8×D11
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#358C2
socleC22×C11C2×D8
prime radical#10622496C2
hypercenter#358D11
hypocenterC11#2185
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D11C2semidirect
2. C2×#66892C2semidirect
3. C2×#66864C2semidirect
5. C11×#358C2semidirect
6. (C2×D11)⋊C16C2semidirect
7. #10622130C2semidirect
33. C11×Q16D4semidirect
40. Dic44D4semidirect
74. #358D11semidirect
82. C2×D11SD32semidirect
122. Q16D44semidirect
133. C11#2185semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D112
C2×#668922
C2×#668642
#106224962
C11×#3582
(C2×D11)⋊C162
#106221302
#218511