Finite Group Databasebeta

← #11807954

Subgroups — #11807954

Order 1152.

714 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593837C214yesmaximal
3#10593758C218yesmaximal
4#10593737C212yesmaximal
5C2×Q8×C3⋊D3C2212yes—
6C2×C4⋊#157C2214yes—
7C2×C4×#157C2214yes—
8C32×C4⋊Q8C411yescharacteristic, complemented
9#64153C412yescomplemented
10C4⋊C4×C3⋊D3C2214yes—
11#64097C414yescomplemented
12C42×C3⋊D3C2211yescharacteristic
13#64078C411yescharacteristic, complemented
14#63781C2214yes—
15#63781C2218yes—
16#63781C2218yes—
17D3×C4⋊Q8—62no—
18C22×#157C2318yes—
19C2×C32×Q8C2×C412yes—
20Q8×C3⋊D3—42no—
21Q8×C3⋊D3—42no—
22C2×C4×C3⋊D3C2314yes—
23C2×C4×C3⋊D3C2312yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#634C2×C412yes—
26C2×#634C2×C414yes—
27C4⋊#157—44no—
28C4×#157—44no—
29C32×C4⋊C4C2×C414yes—
30C32×C42C2×C411yescharacteristic
31C4⋊(C3⋊Dic3)C2×C414yes—
32#3750C2×C418yes—
33C4×C3⋊Dic3C2×C412yes—
34C4×C3⋊Dic3C2×C411yescharacteristic
35#2381—91nomaximal, Sylow
36C2×D3×Q8—64no—
37C3×C4⋊Q8—22no—
38#944—64no—
39D3×C4⋊C4—68no—
40#888—68no—
41C42×D3—62no—
42#869—62no—
43C22×C3⋊D3C2411yescharacteristic
44C2×#157—28no—
45C2×#157—216no—
46C32×Q8—42no—
47C2×C32×C4C22×C412yes—
48C2×C32×C4C22×C411yescharacteristic
49C2×C32×C4C22×C414yes—
50C2×C3⋊Dic3C22×C412yes—
51C2×C3⋊Dic3C22×C411yescharacteristic
52C2×C3⋊Dic3C22×C414yes—
53C4×C3⋊D3—22no—
54C4×C3⋊D3—24no—
55C4×C3⋊D3—24no—
56C4×C3⋊D3—24no—
57#634—44no—
58#634—42no—
59C2×C4⋊Q8—91no—
60#391—94no—
61#387—98no—
62#383—92no—
63C2×C3×Q8—24no—
64D3×Q8—128no—
65D3×Q8—128no—
66C2×C4×D3—64no—
67C2×C4×D3—62no—
68C2×C4×D3—68no—
69C2×Dic6—64no—
70C2×Dic6—68no—
71C3×C4⋊C4—28no—
72C3×C42—22no—
73C4⋊Dic3—68no—
74Dic3⋊C4—616no—
75C4×Dic3—64no—
76C4×Dic3—62no—
77C22×C32C23×C411yescharacteristic
78C2×C3⋊D3H(5,𝔽2)12yes—
79C2×C3⋊D32−1+414yes—
80#157—48no—
81C32×C4—21no—
82C32×C4—22no—
83C32×C4—24no—
84C3⋊Dic3—21no—
85C3⋊Dic3—22no—
86C3⋊Dic3—24no—
87C22×Q8—92no—
88C4⋊Q8—92no—
89C4⋊Q8—94no—
90C4⋊Q8—91no—
91C4⋊Q8#15711yescharacteristic, complemented
92C2×C4⋊C4—94no—
93C2×C4⋊C4—94no—
94C2×C42—91no—
95C2×C42—94no—
96#95—98no—
97#95—94no—
98#95—98no—
99C22×D3—62no—
100C3×Q8—48no—
101C2×C3×C4—24no—
102C2×C3×C4—22no—
103C2×C3×C4—28no—
104C2×Dic3—64no—
105C2×Dic3—62no—
106C2×Dic3—68no—
107C4×D3—616no—
108C4×D3—68no—
109C4×D3—128no—
110C4×D3—128no—
111Dic6—1216no—
112Dic6—128no—
113C2×C32#51811yescharacteristic
114C2×C32#51912yes—
115C3⋊D3#56314yes—
116C2×Q8—94no—
117C2×Q8—92no—
118C2×Q8—362no—
119C2×Q8—362no—
120C2×Q8C2×#15712yes—
121C22×C4—92no—
122C22×C4—91no—
123C22×C4—94no—
124C22×C4—98no—
125C4⋊C4—98no—
126C4⋊C4—94no—
127C4⋊C4—364no—
128C4⋊C4C2×#15714yes—
129C42—91no—
130C42—92no—
131C42—364no—
132C42C2×#15711yescharacteristic
133C22×C3—22no—
134C2×D3—64no—
135C2×D3—68no—
136C3×C4—24no—
137C3×C4—28no—
138C3×C4—48no—
139Dic3—64no—
140Dic3—68no—
141Dic3—128no—
142C32#238111yescharacteristic, complemented, Sylow
143C23—91no—
144Q8—42no—
145Q8—362no—
146Q8—364no—
147C2×C4—92no—
148C2×C4—91no—
149C2×C4—94no—
150C2×C4—184no—
151C2×C4—184no—
152C2×C4—182no—
153C2×C4—184no—
154C2×C4—188no—
155C2×C4—1816no—
156C2×C4C22×#15712yes—
157C2×C4C22×#15711yescharacteristic
158C2×C4C22×#15714yes—
159C2×C3—22no—
160C2×C3—24no—
161D3—68no—
162C22—92no—
163C22—94no—
164C22C23×#15711yescharacteristic
165C4—21no—
166C4—24no—
167C4—22no—
168C4—181no—
169C4—184no—
170C4—182no—
171C4—368no—
172C3—22no—
173C2—94no—
174C2#1059664211yescharacteristic
175C2#1059664612yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4⋊Q8C4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC4⋊Q8#157
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
8. C32×C4⋊Q8C4semidirect
9. #64153C4semidirect
11. #64097C4semidirect
13. #64078C4semidirect
91. C4⋊Q8#157semidirect
142. C32#2381semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105938372
#105937582
#105937372
#23819