Finite Group Databasebeta

← #11772575

Subgroups — #11772575

Order 1152.

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

normal subgroups only

This group has 324 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#10593792C212yesmaximal
2#10592828C211yesmaximal, characteristic
3C2×#3828C2211yescharacteristic
4#64286—22no—
5C2×C32×M16C411yescharacteristic, complemented
6C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
7#63786C414yescomplemented
8#63774—22no—
9#63647—22no—
10#5129—62no—
11C22×C32×C4C2×C411yescharacteristic
12C2×#638C2×C412yes—
13#3828—41no—
14#3828—41no—
15C2×C4⋊(C3⋊D3)D411yescharacteristic
16C2×C4×C3⋊D3D412yes—
17C2×#634Q811yescharacteristic
18C22⋊#157—24no—
19C4⋊#157—42no—
20C4×#157—42no—
21C32×M16—41no—
22C2×C32×C8—21no—
23C2×C3⋊(C3⋊C8)—21no—
24C2×C3⋊(C3⋊C8)—41no—
25#1391—91nomaximal, Sylow
26C2×#235—62no—
27C2×C3×M16—22no—
28C22×C3⋊C8—62no—
29(C2×D3)⋊C8—68no—
30C23×C32C4211yescharacteristic
31C22×C3⋊D3C22⋊C412yes—
32C2×#157—44no—
33C2×C32×C4—21no—
34C2×C32×C4—21no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37#638—42no—
38C2×C3⋊Dic3C4⋊C412yes—
39C4⋊(C3⋊D3)—41no—
40C4×C3⋊D3—22no—
41C4×C3⋊D3—22no—
42#634—41no—
43C32×C8—41no—
44C3⋊(C3⋊C8)—41no—
45#410—92no—
46#408—91no—
47C22×C3×C4—22no—
48C2×#67—64no—
49#235—124no—
50#235—124no—
51C2×D12—62no—
52C2×C4×D3—64no—
53C2×Dic6—62no—
54C3×M16—44no—
55C2×C3×C8—24no—
56C2×C3⋊C8—64no—
57C2×C3⋊C8—124no—
58C22×C32—21no—
59C22×C32—41no—
60C22×C32#9511yescharacteristic
61C2×C3⋊D3—22no—
62C2×C3⋊D3—42no—
63#157—84no—
64C32×C4—21no—
65C32×C4#9911yescharacteristic
66C32×C4#9911yescharacteristic
67C3⋊Dic3—22no—
68C2×#41—91no—
69C2×M16#15711yescharacteristic, complemented
70C22×C8—91no—
71#117—182no—
72#99—94no—
73#99—182no—
74C22⋊C8—182no—
75C23×C3—22no—
76C22×D3—64no—
77C2×C3×C4—24no—
78C2×C3×C4—24no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81#67—128no—
82C2×Dic3—64no—
83D12—124no—
84C4×D3—124no—
85C4×D3—124no—
86Dic6—124no—
87C3×C8—44no—
88C3⋊C8—124no—
89C2×C32—21no—
90C2×C32—41no—
91C2×C32#34211yescharacteristic
92C3⋊D3—42no—
93#41—361no—
94#41—361no—
95C2×Q8—91no—
96C2×D4—92no—
97C2×D4—91no—
98C22×C4—92no—
99C22×C4C2×#15711yescharacteristic
100M16—41no—
101C2×C8—21no—
102C2×C8—181no—
103C2×C8—361no—
104C4⋊C4—362no—
105C22⋊C4—184no—
106C42—362no—
107C22×C3—24no—
108C22×C3—22no—
109C22×C3—44no—
110C2×D3—124no—
111C2×D3—128no—
112C3×C4—24no—
113C3×C4—22no—
114C3×C4—22no—
115Dic3—124no—
116C32#139111yescharacteristic, complemented, Sylow
117C23—92no—
118C23C4×#15711yescharacteristic
119Q8—361no—
120D4—361no—
121D4—362no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—92no—
125C2×C4—182no—
126C2×C4—182no—
127C2×C4—364no—
128C2×C4C4⋊#15711yescharacteristic
129C2×C4C22⋊#15711yescharacteristic
130C8—41no—
131C8—361no—
132C2×C3—24no—
133C2×C3—22no—
134C2×C3—44no—
135D3—244no—
136C22—21no—
137C22—41no—
138C22—182no—
139C22—362no—
140C22#6378111yescharacteristic
141C4—21no—
142C4—182no—
143C4—724no—
144C4#6377411yescharacteristic
145C4#6378611yescharacteristic
146C3—22no—
147C2—21no—
148C2—41no—
149C2—362no—
150C2#1059020611yescharacteristic
subgroupG/H
centerC4#63774
commutatorC23×C32C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC2×C32#342
prime radical, cosocleC2×#3828C22
hypercenterC2×M16#157
hypocenterC32#1391
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
5. C2×C32×M16C4semidirect
6. C22×C3⋊(C3⋊C8)C4semidirect
7. #63786C4semidirect
69. C2×M16#157semidirect
116. C32#1391semidirect

Maximal subgroups

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

subgroupindex
#105937922
#105928282
#13919