Finite Group Databasebeta

← #11772105

Subgroups — #11772105

Order 1152.

148 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 33 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#10590874C211yesmaximal, characteristic
2#10590170C211yesmaximal, characteristic
3#10589133C211yesmaximal, characteristic
4#63872—21no—
5C4⋊#622—21no—
6C8×C3⋊Dic3C2211yescharacteristic
7C3×#817—21no—
8C2×C3×C3⋊C16—21no—
9#63576C411yescharacteristic
10#63576C411yescharacteristic
11#4858—61no—
12Dic3⋊C16—61no—
13C2×#622—41no—
14C2×C32×C8D411yescharacteristic
15C4×C3⋊Dic3D411yescharacteristic
16C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
17C3×C4⋊Dic3—21no—
18C3×C4⋊Dic3—21no—
19Dic3⋊Dic3—41no—
20Dic3⋊Dic3—41no—
21C3×C3⋊C16—41no—
22#1363—91nomaximal, Sylow
23#890—61no—
24#890—61no—
25C2×C3×C16—61no—
26C3×#106—61no—
27#817—21no—
28C8×Dic3—61no—
29C8×Dic3—61no—
30C2×C3⋊C16—21no—
31#807—61no—
32#807—61no—
33C2×C32×C4C22⋊C411yescharacteristic
34C2×C3⋊Dic3D811yescharacteristic
35C2×C3⋊Dic3SD1611yescharacteristic
36C2×C3×Dic3—41no—
37C2×C3×Dic3—41no—
38#622—81no—
39C32×C8SD1611yescharacteristic
40C32×C8Q1611yescharacteristic
41C3⋊(C3⋊C8)—21no—
42#499—91no—
43C4⋊C16—91no—
44#334—91no—
45C2×C3×C8—21no—
46C2×C3×C8—21no—
47C3×C4⋊C4—61no—
48C3×C4⋊C4—61no—
49C4⋊Dic3—21no—
50C4⋊Dic3—21no—
51C4⋊Dic3—121no—
52C4⋊Dic3—121no—
53Dic3⋊C4—121no—
54Dic3⋊C4—121no—
55C4×Dic3—61no—
56C4×Dic3—61no—
57C2×C3⋊C8—61no—
58C2×C3⋊C8—61no—
59C3×C16—121no—
60C3⋊C16—41no—
61C22×C32#10211yescharacteristic
62C32×C4#10111yescharacteristic
63C32×C4#10311yescharacteristic
64C3⋊Dic3—21no—
65C3⋊Dic3—21no—
66C3×Dic3—81no—
67C3×Dic3—81no—
68#125—181no—
69C2×C16—61no—
70#107—91no—
71#107—91no—
72#106—61no—
73C4⋊C8—181no—
74C4×C8—91no—
75C2×C3×C4—21no—
76C2×C3×C4—21no—
77C2×C3×C4—121no—
78C2×C3×C4—121no—
79C2×Dic3—41no—
80C2×Dic3—41no—
81C2×Dic3—61no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C2×Dic3—61no—
85C3×C8—21no—
86C3×C8—21no—
87C3×C8—21no—
88C3×C8—21no—
89C3⋊C8—62no—
90C3⋊C8—121no—
91C2×C32#33211yescharacteristic
92C2×C32#35911yescharacteristic
93C2×C32#36011yescharacteristic
94C2×C8—91no—
95C2×C8—361no—
96C2×C8GO+(4,𝔽2)11yescharacteristic
97C4⋊C4—61no—
98C4⋊C4—61no—
99C4⋊C4—361no—
100C4⋊C4—361no—
101C42—91no—
102C16—121no—
103C22×C3—21no—
104C22×C3—21no—
105C3×C4—21no—
106C3×C4—21no—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—241no—
110C3×C4—241no—
111Dic3—62no—
112Dic3—81no—
113Dic3—81no—
114Dic3—121no—
115Dic3—121no—
116Dic3—121no—
117C32#136311yescharacteristic, complemented, Sylow
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—121no—
121C2×C4—121no—
122C2×C4D32⋊C411yescharacteristic
123C8—181no—
124C8—721no—
125C8#377511yescharacteristic
126C8#377611yescharacteristic
127C2×C3—21no—
128C2×C3—21no—
129C2×C3—21no—
130C2×C3—21no—
131C2×C3—21no—
132C2×C3—21no—
133C22#6372911yescharacteristic
134C4—181no—
135C4—181no—
136C4—241no—
137C4—241no—
138C4#6372811yescharacteristic
139C4#6374011yescharacteristic
140C3—21no—
141C3—21no—
142C2#1059001811yescharacteristic
143C2#1059001911yescharacteristic
144C2#1059003911yescharacteristic
subgroupG/H
centerC22#63729
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypocenterC32#1363
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
117. C32#1363semidirect

Maximal subgroups

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

subgroupindex
#105908742
#105901702
#105891332
#13639