Finite Group Databasebeta

← #11781756

Subgroups — #11781756

Order 1152.

312 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593756C211yesmaximal, characteristic, complemented
2#10593418C211yesmaximal, characteristic
3#10590553C212yesmaximal, complemented
4#10590041C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C2×#3774—21no—
7C2×#3774—21no—
8#64096C2211yescharacteristic
9#63914C2212yes—
10C2×#3716—22no—
11#63777—21no—
12C4⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15C3×#809—22no—
16#63572C2212yes—
17#4762—62no—
18C2×#634D411yescharacteristic
19C2×C3×D12—22no—
20C2×#625—22no—
21C2×#625—22no—
22C2×#622—21no—
23C2×#622D411yescharacteristic
24C2×#622D411yescharacteristic
25#3774—42no—
26#3774—42no—
27C32×C4⋊C4D411yescharacteristic
28#3750—21no—
29C4×C3⋊Dic3—21no—
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3×C3⋊C8—22no—
32#3716—44no—
33#1688—91nomaximal, Sylow
34#940—62no—
35C2×#214—62no—
36C2×#204—62no—
37#887—62no—
38C3×#102—62no—
39Dic3⋊C8—62no—
40#809—22no—
41C22×C3×D3—42no—
42C2×C32×C4—21no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3C2×D411yescharacteristic
46C2×C3⋊Dic3#4111yescharacteristic
47#634—22no—
48C3×D12—42no—
49C3×D12—42no—
50#625—42no—
51#625—42no—
52#625—82no—
53#622—21no—
54#622—41no—
55#622SD1612yescomplemented
56C3×C3⋊C8—42no—
57#493—91no—
58#460—92no—
59#446—91no—
60#334—91no—
61#331—92no—
62C2×C3×D4—62no—
63C2×#67—122no—
64C2×#67—122no—
65C2×D12—22no—
66C2×Dic6—62no—
67C2×C3×C8—62no—
68C3×C4⋊C4—22no—
69#214—124no—
70Dic3⋊C4—122no—
71C4×Dic3—62no—
72C4×Dic3—122no—
73C2×C3⋊C8—22no—
74#204—124no—
75C22×C32#12111yescharacteristic
76C2×C3×D3—82no—
77C2×C3×D3—82no—
78C2×C3×D3—82no—
79C32×C4—41no—
80C32×C4AGL(1,ℤ/8)12yes—
81C3⋊Dic3—21no—
82C3⋊Dic3—41no—
83C3⋊Dic3C2×SD1611yescharacteristic
84C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
85C2×SD16—182no—
86C2×D8—181no—
87C2×D8—181no—
88#127—92no—
89C4×Q8—91no—
90C4⋊C8—92no—
91C4⋊C8—91no—
92C4⋊C8—181no—
93#102—62no—
94#97—181no—
95C4×C8—91no—
96C23×C3—122no—
97C22×D3—42no—
98C3×D4—122no—
99C3×D4—122no—
100C2×C3×C4—22no—
101C2×C3×C4—42no—
102#67—242no—
103#67—242no—
104#67—244no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—122no—
108D12—42no—
109D12—42no—
110Dic6—64no—
111Dic6—122no—
112C3×C8—122no—
113C3⋊C8—42no—
114C2×C32#46011yescharacteristic
115C2×C32#46911yescharacteristic
116C2×C32#47211yescharacteristic
117C3×D3—162no—
118C2×Q8—91no—
119C2×D4—62no—
120C2×D4—182no—
121C2×D4—182no—
122SD16—364no—
123D8—362no—
124D8—362no—
125C2×C8—62no—
126C2×C8—91no—
127C2×C8—91no—
128C2×C8—181no—
129C4⋊C4—181no—
130C4⋊C4GO+(4,𝔽2)11yescharacteristic
131C42—91no—
132C42—181no—
133C22×C3—22no—
134C22×C3—242no—
135C22×C3—242no—
136C22×C3—242no—
137C2×D3—82no—
138C2×D3—82no—
139C2×D3—82no—
140C3×C4—22no—
141C3×C4—22no—
142C3×C4—82no—
143Dic3—62no—
144Dic3—62no—
145Dic3—122no—
146Dic3—124no—
147C32#168811yescharacteristic, complemented, Sylow
148C23—122no—
149Q8—182no—
150D4—122no—
151D4—122no—
152D4—362no—
153D4—362no—
154D4—722no—
155C2×C4—21no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—181no—
159C2×C4C2×GO+(4,𝔽2)11yescharacteristic
160C8—92no—
161C8—122no—
162C8—181no—
163C8—361no—
164C2×C3—22no—
165C2×C3—22no—
166C2×C3—22no—
167C2×C3—482no—
168D3—162no—
169C22—242no—
170C22—242no—
171C22—242no—
172C22#6424211yescharacteristic
173C4—41no—
174C4—91no—
175C4—91no—
176C4—181no—
177C4—361no—
178C4#6422412yes—
179C3—22no—
180C2—482no—
181C2#1059342911yescharacteristic
182C2#1059346611yescharacteristic
183C2#1059347611yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radical#10593418C2
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1688
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10593756C2semidirect
3. #10590553C2semidirect
4. #10590041C2semidirect
5. #10590037C2semidirect
55. #622SD16semidirect
147. C32#1688semidirect

Maximal subgroups

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

subgroupindex
#105937562
#105934182
#105905532
#105900412
#105900372
#16889