Finite Group Databasebeta

← #11776580

Subgroups — #11776580

Order 1152.

830 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 60 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×#127C211yesmaximal, characteristic
2#10593731C212yesmaximal, complemented
3#10590214C214yesmaximal, complemented
4C2×D4×C3⋊D3—22no—
5C2×D4×C3⋊D3C412yes—
6C32×#127C411yescharacteristic
7#64149—22no—
8#64149C2212yes—
9#64083C411yescharacteristic
10C42×C3⋊D3C2211yescharacteristic
11#63779C2214yescomplemented
12#63778—22no—
13#63777—22no—
14D3×#127—62no—
15C23×C3⋊D3—22no—
16C2×C32×D4—22no—
17C2×C32×D4C2×C412yes—
18C2×#638—22no—
19C2×#638—24no—
20D4×C3⋊D3—48no—
21D4×C3⋊D3—44no—
22C2×C4⋊(C3⋊D3)—22no—
23C2×C4⋊(C3⋊D3)C2×C412yes—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3D412yes—
26C2×#622—24no—
27C32×C42C2×C411yescharacteristic
28C4×C3⋊Dic3D412yes—
29C4×C3⋊Dic3C2311yescharacteristic
30#1555—91nomaximal, Sylow
31C2×D3×D4—64no—
32C2×D3×D4—68no—
33C3×#127—22no—
34#940—64no—
35#940—68no—
36#874—62no—
37C42×D3—62no—
38C23×C32—22no—
39C22×C3⋊D3—22no—
40C22×C3⋊D3—48no—
41C22×C3⋊D3—44no—
42C22×C3⋊D3C22⋊C411yescharacteristic
43C32×D4—42no—
44C32×D4—44no—
45C2×C32×C4C22⋊C412yes—
46C2×C32×C4C22×C411yescharacteristic
47#638—44no—
48#638—48no—
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C2×D412yes—
51C4⋊(C3⋊D3)—42no—
52C4⋊(C3⋊D3)—44no—
53C4×C3⋊D3—22no—
54C4×C3⋊D3—24no—
55#622—44no—
56C2×#127—91no—
57#432—92no—
58#331—94no—
59C23×D3—68no—
60C2×C3×D4—28no—
61C2×C3×D4—24no—
62C2×#67—616no—
63C2×#67—68no—
64D3×D4—1216no—
65D3×D4—1232no—
66C2×D12—64no—
67C2×D12—68no—
68C2×C4×D3—62no—
69C2×C4×D3—64no—
70C3×C42—22no—
71C4×Dic3—64no—
72C4×Dic3—62no—
73C22×C32—42no—
74C22×C32—44no—
75C22×C32C2×C22⋊C411yescharacteristic
76C2×C3⋊D3—22no—
77C2×C3⋊D3—42no—
78C2×C3⋊D3—44no—
79C2×C3⋊D3—88no—
80C2×C3⋊D3#10012yes—
81C32×C4—21no—
82C32×C4—22no—
83C3⋊Dic3—21no—
84C3⋊Dic3AGL(1,ℤ/8)14yes—
85C22×D4—92no—
86C22×D4—182no—
87#127—92no—
88#127—91no—
89#127—182no—
90#127#15711yescharacteristic
91C2×C42—91no—
92C4⋊C8—94no—
93C22⋊C8—182no—
94#97—182no—
95C23×C3—28no—
96C22×D3—62no—
97C22×D3—68no—
98C22×D3—1216no—
99C22×D3—1232no—
100C3×D4—48no—
101C3×D4—416no—
102C2×C3×C4—22no—
103C2×C3×C4—24no—
104#67—1232no—
105#67—1216no—
106C2×Dic3—62no—
107C2×Dic3—64no—
108D12—128no—
109D12—1216no—
110C4×D3—616no—
111C4×D3—68no—
112C2×C32—82no—
113C2×C32C2×#10011yescharacteristic
114C2×C32#41812yes—
115C3⋊D3—22no—
116C3⋊D3—82no—
117C24—182no—
118C2×D4—22no—
119C2×D4—92no—
120C2×D4—184no—
121C2×D4—182no—
122C2×D4—182no—
123C2×D4—364no—
124C2×D4—368no—
125C2×D4C2×#15712yes—
126C22×C4—91no—
127C22×C4—92no—
128C2×C8—184no—
129C42—91no—
130C42—92no—
131C42C2×#15711yescharacteristic
132C22×C3—22no—
133C22×C3—416no—
134C22×C3—48no—
135C2×D3—64no—
136C2×D3—68no—
137C2×D3—1216no—
138C2×D3—128no—
139C2×D3—2432no—
140C3×C4—28no—
141C3×C4—24no—
142Dic3—68no—
143Dic3—64no—
144C32#155511yescharacteristic, complemented, Sylow
145C23—22no—
146C23—91no—
147C23—182no—
148C23—364no—
149C23—368no—
150D4—42no—
151D4—44no—
152D4—362no—
153D4—364no—
154D4—368no—
155D4—364no—
156C2×C4—92no—
157C2×C4—91no—
158C2×C4—184no—
159C2×C4—182no—
160C2×C4C22⋊#15712yes—
161C2×C4C22×#15711yescharacteristic
162C8—364no—
163C2×C3—24no—
164C2×C3—22no—
165C2×C3—88no—
166D3—68no—
167D3—248no—
168C22—44no—
169C22—42no—
170C22—92no—
171C22—182no—
172C22—364no—
173C22—362no—
174C22—728no—
175C22C2×C22⋊#15711yescharacteristic
176C4—22no—
177C4—21no—
178C4—94no—
179C4—181no—
180C3—22no—
181C2—82no—
182C2—182no—
183C2—722no—
184C2#1059381412yes—
185C2#1059382511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#127C2
cosocleC4×C3⋊Dic3C23
hypercenter#127#157
hypocenterC32#1555
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593731C2semidirect
3. #10590214C2semidirect
11. #63779C22semidirect
144. C32#1555semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
#105937312
#105902142
#15559