Finite Group Databasebeta

← #11785987

Subgroups — #11785987

Order 1152.

354 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 71 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#10590331C212yesmaximal
3#10590044C214yesmaximal
4C2×C4×#157C2212yes—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3710C2214yes—
7#63781C414yes—
8C3×C4⋊(C3⋊C8)—22no—
9#63572—22no—
10D3×C4⋊C8—62no—
11C22×#157C2×C414yes—
12C2×C4×C3⋊D3C2×C412yes—
13C2×C4×C3⋊D3C2311yescharacteristic
14C4×#157—24no—
15C32×C42D411yescharacteristic
16C4×C3⋊Dic3D411yescharacteristic
17C4×C3⋊Dic3Q812yes—
18C2×C3×C3⋊C8—24no—
19#3710—28no—
20#1832—91nomaximal, Sylow
21C2×D3×C8—64no—
22C42×D3—62no—
23C3×C4⋊C8—62no—
24Dic3⋊C8—64no—
25C4⋊(C3⋊C8)—22no—
26C22×C3⋊D3C22×C411yescharacteristic
27C2×#157—24no—
28C2×#157—28no—
29C2×C32×C4C4⋊C412yes—
30C2×C32×C4C2×D411yescharacteristic
31C2×C3⋊Dic3C4⋊C412yes—
32C2×C3⋊Dic3C2×Q811yescharacteristic
33C4×C3⋊D3—24no—
34C4×C3⋊D3#4114yes—
35C3×C3⋊C8—44no—
36C2×C4⋊C8—92no—
37#376—91no—
38#336—94no—
39C2×C4×D3—62no—
40C2×C4×D3—62no—
41C2×C4×D3—62no—
42C2×C3×C8—64no—
43C3×C42—22no—
44C4×Dic3—62no—
45C4×Dic3—62no—
46C4×Dic3—62no—
47C2×C3⋊C8—24no—
48D3×C8—128no—
49C22×C32C2×C4⋊C411yescharacteristic
50C2×C3⋊D3#11712yes—
51C2×C3⋊D3#13114yes—
52#157—44no—
53C32×C4—22no—
54C32×C4#12412yes—
55C3⋊Dic3—22no—
56C3⋊Dic3#12512yes—
57C22×C8—94no—
58C2×C42—91no—
59C2×C42—92no—
60C4⋊C8—62no—
61C4⋊C8—182no—
62#95—94no—
63C22×D3—62no—
64C2×C3×C4—22no—
65C2×C3×C4—22no—
66C2×C3×C4—22no—
67C2×Dic3—62no—
68C2×Dic3—62no—
69C2×Dic3—62no—
70C4×D3—64no—
71C4×D3—64no—
72C4×D3—68no—
73C4×D3—124no—
74C3×C8—124no—
75C3⋊C8—44no—
76C2×C32#38211yescharacteristic
77C2×C32#42412yes—
78C3⋊D3#43314yes—
79C22×C4—91no—
80C22×C4—92no—
81C22×C4—94no—
82C2×C8—64no—
83C2×C8—188no—
84C42—91no—
85C42—92no—
86C42—184no—
87C42GO+(4,𝔽2)11yescharacteristic
88C22×C3—22no—
89C2×D3—64no—
90C2×D3—64no—
91C2×D3—64no—
92C3×C4—24no—
93C3×C4—22no—
94C3×C4—22no—
95C3×C4—42no—
96Dic3—64no—
97Dic3—64no—
98Dic3—122no—
99C32#183211yescharacteristic, complemented, Sylow
100C23—91no—
101C2×C4—91no—
102C2×C4—94no—
103C2×C4—92no—
104C2×C4—184no—
105C2×C4—184no—
106C2×C4—188no—
107C2×C4#377312yes—
108C2×C4C2×GO+(4,𝔽2)11yescharacteristic
109C8—124no—
110C2×C3—22no—
111C2×C3—22no—
112C2×C3—22no—
113D3—68no—
114C22—94no—
115C22—92no—
116C22C2×#377311yescharacteristic
117C4—22no—
118C4—92no—
119C4—182no—
120C4—364no—
121C4#6422112yes—
122C3—22no—
123C2—94no—
124C2#1059332712yes—
125C2#1059334411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutator, prime radicalC22×C3⋊D3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1832
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
99. C32#1832semidirect

Maximal subgroups

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

subgroupindex
#105937332
#105903312
#105900442
#18329