Finite Group Databasebeta

← #11797998

Subgroups — #11797998

Order 1152.

236 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592529C211yesmaximal, characteristic
2#10590177C212yesmaximal
3#10590174C212yesmaximal
4C4⋊#3708C211yesmaximal, characteristic
5C4×#3708C211yesmaximal, characteristic
6C4×#634C411yescharacteristic
7C2×#3708C2211yescharacteristic
8C2×#3708C2212yes—
9C2×#3708C2211yescharacteristic
10C32×C4⋊C8C411yescharacteristic
11#63641C412yes—
12C8×C3⋊Dic3C2212yes—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#4830—62no—
15C2×#634C811yescharacteristic
16C2×C32×C8C2×C412yes—
17C32×C42C2×C411yescharacteristic
18C4⋊(C3⋊Dic3)C811yescharacteristic
19#3750C812yes—
20C4×C3⋊Dic3C2×C412yes—
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23#3708—21no—
24#3708—22no—
25#3708Q812yescomplemented
26Q8×C16—91nomaximal, Sylow
27C4×Dic6—62no—
28C3×C4⋊C8—22no—
29Dic3⋊C8—64no—
30C8×Dic3—64no—
31C4×C3⋊C8—62no—
32C2×C32×C4C2×C811yescharacteristic
33C2×C32×C4C2×C811yescharacteristic
34C2×C32×C4C22×C411yescharacteristic
35C2×C3⋊Dic3C2×C812yes—
36C2×C3⋊Dic3C2×C812yes—
37#634C1614yescomplemented
38C32×C8—22no—
39C3⋊(C3⋊C8)—21no—
40C3⋊(C3⋊C8)C2×Q811yescharacteristic
41C3⋊(C3⋊C8)#4111yescharacteristic
42C8×Q8—91no—
43C4⋊C16—91no—
44C4⋊C16—92no—
45C4×C16—91no—
46C4×C16—92no—
47C2×Dic6—62no—
48C2×C3×C8—24no—
49C3×C42—22no—
50C4⋊Dic3—62no—
51Dic3⋊C4—64no—
52C4×Dic3—64no—
53C2×C3⋊C8—62no—
54C2×C3⋊C8—62no—
55C22×C32C22×C811yescharacteristic
56C32×C4—21no—
57C32×C4C2×C1612yes—
58C32×C4C4×Q811yescharacteristic
59C32×C4#13111yescharacteristic
60C3⋊Dic3—22no—
61C3⋊Dic3C2×C1614yes—
62C4×Q8—91no—
63C2×C16—91no—
64C2×C16—91no—
65C2×C16—92no—
66C4⋊C8—92no—
67C4⋊C8#15711yescharacteristic
68C4×C8—92no—
69C4×C8—91no—
70C2×C3×C4—22no—
71C2×C3×C4—22no—
72C2×C3×C4—22no—
73C2×Dic3—64no—
74C2×Dic3—64no—
75Dic6—68no—
76C3×C8—44no—
77C3⋊C8—62no—
78C3⋊C8—62no—
79C3⋊C8—122no—
80C2×C32C8×Q811yescharacteristic
81C2×C32C22×C1611yescharacteristic
82C2×C32#50411yescharacteristic
83C2×Q8—91no—
84C2×C8—91no—
85C2×C8—91no—
86C2×C8C2×#15712yes—
87C4⋊C4—92no—
88C4⋊C4—91no—
89C42—92no—
90C42C2×#15711yescharacteristic
91C16—92no—
92C16—181no—
93C16—182no—
94C22×C3—22no—
95C3×C4—24no—
96C3×C4—22no—
97C3×C4—22no—
98C3×C4—42no—
99Dic3—68no—
100Dic3—124no—
101C32Q8×C1611yescharacteristic, complemented, Sylow
102Q8—94no—
103C2×C4—92no—
104C2×C4—92no—
105C2×C4#378711yescharacteristic
106C2×C4#378711yescharacteristic
107C2×C4C22×#15711yescharacteristic
108C8—22no—
109C8—91no—
110C8—91no—
111C8—181no—
112C2×C3—22no—
113C2×C3—22no—
114C2×C3—22no—
115C22C2×#378711yescharacteristic
116C4—21no—
117C4—94no—
118C4—182no—
119C4#6376412yes—
120C4#6428711yescharacteristic
121C4Q8×#15711yescharacteristic
122C3—22no—
123C2#1059375011yescharacteristic
124C2C2×#6376411yescharacteristic
125C2#1059377211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C22×C16
FittingC32×C4⋊C8C4
socle, prime radicalC22×C32C22×C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4⋊C8#157
hypocenterC32Q8×C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
25. #3708Q8semidirect
37. #634C16semidirect
101. C32Q8×C16semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105901772
#105901742
C4⋊#37082
C4×#37082
Q8×C169