Finite Group Databasebeta

← #11783513

Subgroups — #11783513

Order 1152.

402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593733C211yesmaximal, characteristic
2#10593723C211yesmaximal, characteristic
3C4×C8×C3⋊D3C211yesmaximal, characteristic
4#10590181C214yesmaximal
5C2×C4×#157C2212yes—
6C2×#3787C2212yes—
7C2×C8×C3⋊D3C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9#63781C414yes—
10#63777C414yescomplemented
11C32×C4×C8C411yescharacteristic, complemented
12C8×C3⋊Dic3C412yescomplemented
13C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
14C4×D3×C8—62no—
15C22×#157C2×C414yes—
16C2×C4×C3⋊D3C2×C412yes—
17C2×C4×C3⋊D3C2311yescharacteristic
18C2×#622C2×C414yes—
19C4×#157—24no—
20#3787—24no—
21C2×C32×C8C2×C412yes—
22C32×C42C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C412yes—
25C2×C3⋊(C3⋊C8)C2×C412yes—
26C8×C3⋊D3—24no—
27#1746—91nomaximal, Sylow
28C2×D3×C8—64no—
29C42×D3—62no—
30C3×C4×C8—22no—
31C8×Dic3—64no—
32C4×C3⋊C8—62no—
33C22×C3⋊D3C22×C411yescharacteristic
34C2×#157—24no—
35C2×#157—28no—
36C2×C32×C4C4212yes—
37C2×C32×C4C22×C411yescharacteristic
38C2×C3⋊Dic3C4212yes—
39C2×C3⋊Dic3C22×C411yescharacteristic
40C4×C3⋊D3—24no—
41C4×C3⋊D3#4114yes—
42#622—24no—
43C32×C8—22no—
44C3⋊(C3⋊C8)—22no—
45C2×#97—91no—
46C2×C4×C8—91no—
47#376—91no—
48#336—94no—
49C2×C4×D3—62no—
50C2×C4×D3—64no—
51C2×C3×C8—24no—
52C3×C42—22no—
53C4×Dic3—62no—
54C4×Dic3—64no—
55C2×C3⋊C8—64no—
56D3×C8—616no—
57C22×C32C2×C4211yescharacteristic
58C2×C3⋊D3#11712yes—
59C2×C3⋊D3#13114yes—
60#157—44no—
61C32×C4—22no—
62C32×C4#11712yes—
63C3⋊Dic3—22no—
64C3⋊Dic3#11712yes—
65C22×C8—92no—
66C22×C8—92no—
67C2×C42—91no—
68C2×C42—92no—
69#97—94no—
70C4×C8—92no—
71C4×C8—91no—
72C4×C8#15711yescharacteristic, complemented
73#95—94no—
74C22×D3—62no—
75C2×C3×C4—22no—
76C2×C3×C4—24no—
77C2×Dic3—64no—
78C2×Dic3—62no—
79C4×D3—68no—
80C4×D3—616no—
81C3×C8—28no—
82C3⋊C8—68no—
83C2×C32#37611yescharacteristic
84C2×C32#40512yes—
85C3⋊D3#43314yes—
86C22×C4—91no—
87C22×C4—92no—
88C22×C4—94no—
89C2×C8—94no—
90C2×C8—92no—
91C2×C8—184no—
92C2×C8—184no—
93C2×C8C2×#15712yes—
94C42—91no—
95C42—92no—
96C42—184no—
97C42C2×#15711yescharacteristic
98C22×C3—22no—
99C2×D3—64no—
100C2×D3—68no—
101C3×C4—28no—
102C3×C4—24no—
103Dic3—64no—
104Dic3—68no—
105C32#174611yescharacteristic, complemented, Sylow
106C23—91no—
107C2×C4—91no—
108C2×C4—94no—
109C2×C4—92no—
110C2×C4—184no—
111C2×C4—184no—
112C2×C4—188no—
113C2×C4C4×#15712yes—
114C2×C4C22×#15711yescharacteristic
115C8—22no—
116C8—184no—
117C8—182no—
118C2×C3—22no—
119C2×C3—24no—
120D3—68no—
121C22—92no—
122C22—94no—
123C22C2×C4×#15711yescharacteristic
124C4—22no—
125C4—92no—
126C4—182no—
127C4—364no—
128C4#6428612yes—
129C3—22no—
130C2—94no—
131C2#1059373311yescharacteristic
132C2#1059376512yes—
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC32×C4×C8C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×C8#157
hypocenterC32#1746
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
10. #63777C4semidirect
11. C32×C4×C8C4semidirect
12. C8×C3⋊Dic3C4semidirect
13. C4×C3⋊(C3⋊C8)C4semidirect
72. C4×C8#157semidirect
105. C32#1746semidirect

Maximal subgroups

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

subgroupindex
#105937332
#105937232
C4×C8×C3⋊D32
#105901812
#17469