Finite Group Databasebeta

← #11776242

Subgroups — #11776242

Order 1152.

424 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596159C211yesmaximal, characteristic
2#10593725C212yesmaximal
3#10590162C214yesmaximal, complemented
4C32×#125C411yescharacteristic
5#64105—22no—
6#64101C412yes—
7#64097C2212yes—
8#64096—22no—
9C42×C3⋊D3C2211yescharacteristic
10#64079C411yescharacteristic
11#63779C2214yes—
12#63778—22no—
13C4×#622—22no—
14#5688—62no—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C4×C3⋊D3D412yes—
17C2×#634—22no—
18C2×#622—24no—
19C32×C4⋊C4—22no—
20C32×C4⋊C4C2×C412yes—
21C32×C42C2×C411yescharacteristic
22#3752—22no—
23C4⋊(C3⋊Dic3)C2×C412yes—
24#3750—22no—
25#3750—22no—
26C4×C3⋊Dic3—22no—
27C4×C3⋊Dic3D412yes—
28C4×C3⋊Dic3C2311yescharacteristic
29#1544—91nomaximal, Sylow
30C3×#125—22no—
31#896—68no—
32#892—64no—
33#888—64no—
34#887—68no—
35C42×D3—62no—
36#870—62no—
37C22×C3⋊D3C22⋊C411yescharacteristic
38C2×C32×C4—22no—
39C2×C32×C4C22⋊C412yes—
40C2×C32×C4C22×C411yescharacteristic
41C2×C3⋊Dic3—22no—
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C2×D412yes—
44C4×C3⋊D3—22no—
45C4×C3⋊D3—24no—
46#634—44no—
47#622—44no—
48#533—91no—
49#431—92no—
50#332—94no—
51C2×C4×D3—62no—
52C2×C4×D3—64no—
53C2×Dic6—68no—
54C3×C4⋊C4—28no—
55C3×C4⋊C4—24no—
56C3×C42—22no—
57(C2×D3)⋊C4—68no—
58C4⋊Dic3—64no—
59Dic3⋊C4—68no—
60Dic3⋊C4—68no—
61C4×Dic3—64no—
62C4×Dic3—62no—
63C4×Dic3—68no—
64C22×C32C2×C22⋊C411yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—22no—
67C32×C4—21no—
68C32×C4—22no—
69C32×C4—42no—
70C3⋊Dic3—42no—
71C3⋊Dic3#10112yes—
72C3⋊Dic3#13514yes—
73C4⋊Q8—92no—
74#125—91no—
75#125#15711yescharacteristic
76C22⋊Q8—182no—
77C4×Q8—182no—
78#117—92no—
79C2×C42—91no—
80C4⋊C8—94no—
81C22⋊C8—182no—
82C4×C8—182no—
83C22×D3—62no—
84C2×C3×C4—28no—
85C2×C3×C4—22no—
86C2×C3×C4—24no—
87C2×Dic3—62no—
88C2×Dic3—64no—
89C2×Dic3—68no—
90C4×D3—68no—
91C4×D3—128no—
92Dic6—1216no—
93C2×C32C2×#10111yescharacteristic
94C2×C32#41612yes—
95C3⋊D3—41no—
96C2×Q8—182no—
97C22×C4—91no—
98C22×C4—92no—
99C2×C8—184no—
100C4⋊C4—22no—
101C4⋊C4—92no—
102C4⋊C4—182no—
103C4⋊C4—182no—
104C4⋊C4C2×#15712yes—
105C22⋊C4—182no—
106C42—91no—
107C42—92no—
108C42—182no—
109C42C2×#15711yescharacteristic
110C22×C3—22no—
111C2×D3—64no—
112C2×D3—124no—
113C3×C4—24no—
114C3×C4—44no—
115C3×C4—48no—
116Dic3—68no—
117Dic3—64no—
118Dic3—128no—
119C32#154411yescharacteristic, complemented, Sylow
120C23—91no—
121Q8—364no—
122C2×C4—22no—
123C2×C4—91no—
124C2×C4—92no—
125C2×C4—182no—
126C2×C4—184no—
127C2×C4—182no—
128C2×C4C22⋊#15712yes—
129C2×C4C22×#15711yescharacteristic
130C8—364no—
131C2×C3—22no—
132C2×C3—24no—
133D3—124no—
134C22—181no—
135C22—182no—
136C22C2×C22⋊#15711yescharacteristic
137C4—21no—
138C4—22no—
139C4—42no—
140C4—92no—
141C4—94no—
142C4—362no—
143C3—22no—
144C2—361no—
145C2#1059383611yescharacteristic
146C2#1059384112yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#125C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenter#125#157
hypocenterC32#1544
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10590162C2semidirect
119. C32#1544semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105937252
#105901622
#15449