Finite Group Databasebeta

← #11771270

Subgroups — #11771270

Order 1152.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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#10593806C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3#10592418C211yesmaximal, characteristic
4C2×C4×C3⋊Dic3C2211yescharacteristic
5C22⋊#622C412yes—
6C22⋊#622C412yes—
7#63779—21no—
8#63777—21no—
9#63777—21no—
10C4⋊#622—21no—
11C32×C22⋊C8C411yescharacteristic
12#63657C411yescharacteristic
13#63642—21no—
14#63641—21no—
15#4719—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21C2×C32×C8—21no—
22C4×C3⋊Dic3D411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C2×C3⋊(C3⋊C8)—21no—
27#1308—91nomaximal, Sylow
28C2×C4×Dic3—62no—
29C3×C22⋊C8—22no—
30#830—62no—
31#815—64no—
32Dic3⋊C8—64no—
33C23×C32C4211yescharacteristic
34C2×C32×C4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C3⋊Dic3—41no—
38C2×C3⋊Dic3—41no—
39C2×C3⋊Dic3C22⋊C411yescharacteristic
40C2×C3⋊Dic3C22⋊C411yescharacteristic
41C2×C3⋊Dic3C4⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43#622—42no—
44#622—42no—
45C32×C8—41no—
46C3⋊(C3⋊C8)—41no—
47#432—91no—
48#432—91no—
49#432—91no—
50C22×C3×C4—22no—
51C22×Dic3—62no—
52C22×Dic3—62no—
53C2×C3×C8—24no—
54C4×Dic3—62no—
55C4×Dic3—62no—
56C4×Dic3—62no—
57C4×Dic3—62no—
58C2×C3⋊C8—64no—
59C22×C32—21no—
60C22×C32—21no—
61C22×C32—21no—
62C22×C32#9511yescharacteristic
63C32×C4—21no—
64C32×C4—21no—
65C3⋊Dic3—21no—
66C3⋊Dic3—21no—
67C3⋊Dic3—21no—
68C3⋊Dic3—21no—
69C2×C42—91no—
70C4⋊C8—181no—
71C4⋊C8—181no—
72C4⋊C8—181no—
73C22⋊C8—92no—
74C22⋊C8—92no—
75C22⋊C8—91no—
76C22⋊C8#15711yescharacteristic
77#97—181no—
78#97—181no—
79#97—181no—
80C23×C3—22no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—44no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87C2×Dic3—62no—
88C2×Dic3—124no—
89C2×Dic3—124no—
90C3×C8—44no—
91C3⋊C8—124no—
92C2×C32—41no—
93C2×C32#34411yescharacteristic
94C2×C32#34411yescharacteristic
95C2×C32#34411yescharacteristic
96C22×C4—91no—
97C22×C4—91no—
98C22×C4C2×#15711yescharacteristic
99C2×C8—21no—
100C2×C8—182no—
101C2×C8—182no—
102C2×C8—181no—
103C42—91no—
104C42—91no—
105C42—91no—
106C42—91no—
107C22×C3—24no—
108C22×C3—22no—
109C22×C3—42no—
110C22×C3—42no—
111C3×C4—24no—
112C3×C4—42no—
113Dic3—64no—
114Dic3—122no—
115Dic3—122no—
116Dic3—122no—
117C32#130811yescharacteristic, complemented, Sylow
118C23C4×#15711yescharacteristic
119C2×C4—41no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—91no—
124C2×C4—361no—
125C2×C4—361no—
126C2×C4C4⋊#15711yescharacteristic
127C2×C4C22⋊#15711yescharacteristic
128C8—41no—
129C8—361no—
130C8—362no—
131C8—362no—
132C2×C3—22no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—44no—
136C22—21no—
137C22—21no—
138C22—21no—
139C22#6378111yescharacteristic
140C4—21no—
141C4—21no—
142C4—181no—
143C4—181no—
144C4—181no—
145C4—181no—
146C3—22no—
147C2—41no—
148C2#1059015611yescharacteristic
149C2#1059018311yescharacteristic
150C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutator, prime radicalC23×C32C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22⋊C8#157
hypocenterC32#1308
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
117. C32#1308semidirect

Maximal subgroups

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

subgroupindex
#105938062
#105938042
#105924182
#13089