Finite Group Databasebeta

← #11772953

Subgroups — #11772953

Order 1152.

134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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#10590629C211yesmaximal, characteristic
2C2×#63540C211yesmaximal, characteristic, complemented
3#10589144C211yesmaximal, characteristic, complemented
4C3×#904—21no—
5C2×C3⋊(C3⋊C16)C2211yescharacteristic
6C3×#819—21no—
7#63550C411yescharacteristic
8#63547—21no—
9#63545C411yescharacteristic
10#63540—21no—
11#5194—61no—
12#4493—61no—
13C3×#235—41no—
14C2×C32×C8D411yescharacteristic
15C3×#208—41no—
16C3×Dic12—21no—
17C3×D24—21no—
18C3×#204—41no—
19C3⋊(C3⋊C16)C2×C411yescharacteristic
20C3⋊(C3⋊C16)D411yescharacteristic
21#1417—91nomaximal, Sylow
22C3×#135—61no—
23#904—21no—
24C3×#108—61no—
25#829—61no—
26#828—61no—
27#827—61no—
28#826—61no—
29#819—21no—
30C2×C3⋊C16—61no—
31C2×C3⋊C16—61no—
32C2×C32×C4D811yescharacteristic
33C3×#67—81no—
34C3×D12—41no—
35C3×C4×D3—81no—
36C3×Dic6—41no—
37C32×C8C22⋊C411yescharacteristic
38C32×C8SD1611yescharacteristic
39C3×C3⋊C8—81no—
40#508—91no—
41C2×C32—91no—
42#368—91no—
43C3×#41—121no—
44#235—41no—
45C3×Q16—61no—
46C3×SD16—121no—
47C3×D8—61no—
48C3×M16—121no—
49C2×C3×C8—21no—
50C2×C3×C8—21no—
51#208—41no—
52Dic12—21no—
53D24—21no—
54#204—41no—
55C3⋊C16—61no—
56C3⋊C16—61no—
57C3⋊C16—61no—
58C3⋊C16—61no—
59C22×C32SD3211yescharacteristic
60C2×C3×D3—81no—
61C32×C4#10211yescharacteristic
62C32×C4D1611yescharacteristic
63C3×Dic3—81no—
64#135—61no—
65Q32—91no—
66SD32—181no—
67D16—91no—
68C2×C16—91no—
69#108—61no—
70C32—181no—
71C3×Q8—121no—
72C3×D4—121no—
73C3×D4—241no—
74C2×C3×C4—21no—
75C2×C3×C4—21no—
76C2×C3×C4—241no—
77#67—81no—
78D12—41no—
79C4×D3—81no—
80Dic6—41no—
81C3×C8—21no—
82C3×C8—21no—
83C3×C8—21no—
84C3×C8—21no—
85C3×C8—241no—
86C3⋊C8—81no—
87C2×C32—21no—
88C2×C32#35711yescharacteristic
89C3×D3—161no—
90#41—121no—
91Q16—61no—
92SD16—121no—
93D8—61no—
94M16—121no—
95C2×C8GO+(4,𝔽2)11yescharacteristic
96C16—91no—
97C16—91no—
98C22×C3—21no—
99C22×C3—21no—
100C22×C3—241no—
101C2×D3—81no—
102C3×C4—21no—
103C3×C4—21no—
104C3×C4—21no—
105C3×C4—21no—
106C3×C4—241no—
107Dic3—81no—
108C32#141711yescharacteristic, complemented, Sylow
109Q8—121no—
110D4—121no—
111D4—241no—
112C2×C4—241no—
113C2×C4#377411yescharacteristic
114C8—241no—
115C8D32⋊C411yescharacteristic
116C8#377511yescharacteristic
117C2×C3—21no—
118C2×C3—21no—
119C2×C3—41no—
120C2×C3—41no—
121C2×C3—481no—
122D3—161no—
123C22—241no—
124C22#6373511yescharacteristic
125C4—241no—
126C4#6373411yescharacteristic
127C4#6373911yescharacteristic
128C3—21no—
129C3—21no—
130C2—21no—
131C2—481no—
132C2#1059006111yescharacteristic
subgroupG/H
centerC4#63734
commutatorC3⋊(C3⋊C16)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#357
prime radical#10590629C2
cosocleC2×C3⋊(C3⋊C16)C22
hypocenterC32#1417
LCSG ▷ C3⋊(C3⋊C16) ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63540C2semidirect
3. #10589144C2semidirect
108. C32#1417semidirect

Maximal subgroups

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

subgroupindex
#105906292
C2×#635402
#105891442
#14179