Finite Group Databasebeta

← #11783044

Subgroups — #11783044

Order 1152.

474 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 158 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×#63767C212yesmaximal
2C2×C8×#157C212yesmaximal
3#10593733C211yesmaximal, characteristic
4C4×#3787C211yesmaximal, characteristic
5C3⋊D3×#97C211yesmaximal, characteristic
6C2×C4×#157C2212yes—
7C2×#3787C2211yescharacteristic
8C2×#3787C2211yescharacteristic
9C2×C8×C3⋊D3C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11#63781C414yes—
12C4×#622C414yescomplemented
13#63767C418yescomplemented
14C8×#157C418yescomplemented
15C32×#97C411yescharacteristic, complemented
16#63642C412yescomplemented
17#63630C411yescharacteristic, complemented
18D3×#97—62no—
19C22×#157C2×C414yes—
20C2×C4×C3⋊D3C2×C412yes—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×#622C2×C412yes—
23C2×#622C2×C412yes—
24C4×#157C2×C414yes—
25C4×#157C2×C414yes—
26#3787C2×C414yes—
27#3787C2×C414yes—
28C2×C32×C8C2×C412yes—
29C32×C42C2×C411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3C2×C412yes—
32C2×C3⋊(C3⋊C8)C2×C412yes—
33C8×C3⋊D3C2×C414yes—
34C8×C3⋊D3C2×C414yes—
35#1726—91nomaximal, Sylow
36C2×D3×C8—64no—
37C42×D3—62no—
38C3×#97—22no—
39#815—64no—
40#803—62no—
41C22×C3⋊D3C22×C411yescharacteristic
42C2×#157—28no—
43C2×#157C4218yes—
44C2×C32×C4C4212yes—
45C2×C32×C4C22×C411yescharacteristic
46C2×C3⋊Dic3C4212yes—
47C2×C3⋊Dic3C22×C411yescharacteristic
48C4×C3⋊D3—24no—
49C4×C3⋊D3C22×C412yes—
50C4×C3⋊D3C22×C412yes—
51#622C4214yes—
52#622C4214yes—
53C32×C8C4214yes—
54C3⋊(C3⋊C8)C4214yes—
55C2×#97—92no—
56C2×#97—91no—
57C2×C4×C8—91no—
58C2×C4×C8—92no—
59#376—91no—
60C2×C4×D3—62no—
61C2×C4×D3—64no—
62C2×C3×C8—24no—
63C3×C42—22no—
64C4×Dic3—62no—
65C4×Dic3—64no—
66C2×C3⋊C8—64no—
67D3×C8—68no—
68D3×C8—68no—
69C22×C32C2×C4211yescharacteristic
70C2×C3⋊D3C2×C4212yes—
71C2×C3⋊D3#13114yes—
72#157—28no—
73C32×C4—22no—
74C32×C4C2×C4212yes—
75C3⋊Dic3—22no—
76C3⋊Dic3C2×C4211yescharacteristic
77C3⋊Dic3C2×C4211yescharacteristic
78C22×C8—91no—
79C22×C8—91no—
80C22×C8—92no—
81C2×C42—92no—
82C2×C42—91no—
83#97—98no—
84#97—92no—
85#97—91no—
86#97#15711yescharacteristic, complemented
87C4×C8—98no—
88C4×C8—94no—
89#95—94no—
90C22×D3—62no—
91C2×C3×C4—22no—
92C2×C3×C4—24no—
93C2×Dic3—62no—
94C2×Dic3—64no—
95C4×D3—64no—
96C4×D3—64no—
97C4×D3—128no—
98C3×C8—28no—
99C3⋊C8—68no—
100C2×C32C4311yescharacteristic
101C2×C32#40512yes—
102C3⋊D3#40514yes—
103C22×C4—91no—
104C22×C4—94no—
105C22×C4—92no—
106C2×C8—94no—
107C2×C8—92no—
108C2×C8—92no—
109C2×C8—94no—
110C2×C8—92no—
111C2×C8—94no—
112C2×C8—94no—
113C2×C8C2×#15712yes—
114C42—94no—
115C42—94no—
116C42—91no—
117C42—92no—
118C42C2×#15711yescharacteristic
119C22×C3—22no—
120C2×D3—64no—
121C2×D3—68no—
122C3×C4—24no—
123C3×C4—44no—
124Dic3—62no—
125Dic3—62no—
126Dic3—124no—
127C32#172611yescharacteristic, complemented, Sylow
128C23—91no—
129C2×C4—91no—
130C2×C4—92no—
131C2×C4—92no—
132C2×C4—98no—
133C2×C4—92no—
134C2×C4—184no—
135C2×C4—188no—
136C2×C4C4×#15712yes—
137C2×C4C22×#15711yescharacteristic
138C8—94no—
139C8—94no—
140C8—94no—
141C8C4×#15714yes—
142C2×C3—22no—
143C2×C3—24no—
144D3—68no—
145C22—92no—
146C22—94no—
147C22C2×C4×#15711yescharacteristic
148C4—22no—
149C4—91no—
150C4—91no—
151C4—188no—
152C4—182no—
153C4C2×C4×#15712yes—
154C3—22no—
155C2—94no—
156C2C42×#15711yescharacteristic
157C2#1059377512yes—
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C43
FittingC32×#97C4
socleC22×C32C2×C42
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenter#97#157
hypocenterC32#1726
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
12. C4×#622C4semidirect
13. #63767C4semidirect
14. C8×#157C4semidirect
15. C32×#97C4semidirect
16. #63642C4semidirect
17. #63630C4semidirect
86. #97#157semidirect
127. C32#1726semidirect

Maximal subgroups

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

subgroupindex
C2×#637672
C2×C8×#1572
#105937332
C4×#37872
C3⋊D3×#972
#17269