Finite Group Databasebeta

← #11771512

Subgroups — #11771512

Order 1152.

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

normal subgroups only

This group has 188 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#10590666C211yesmaximal, characteristic
2#10590180C211yesmaximal, characteristic
3#10589110C211yesmaximal, characteristic
4C2×#3743C2211yescharacteristic
5C4×#624C411yescharacteristic
6C2×#3712C411yescharacteristic
7#63773—21no—
8C3×Dic3⋊C8—21no—
9C3×#812—21no—
10Dic3⋊(C3⋊C8)—21no—
11#4837—61no—
12#4514—61no—
13C2×C4×C3⋊D3C2×C411yescharacteristic
14C2×#624—21no—
15C2×C32×C8D411yescharacteristic
16C2×C3⋊(C3⋊C8)D411yescharacteristic
17#3743—41no—
18C3×C4×Dic3—21no—
19C2×C3×C3⋊C8—21no—
20Dic32C811yescharacteristic
21Dic32C811yescharacteristic
22#3712—41no—
23#3708—41no—
24C3×C3⋊C16—41no—
25#1327—91nomaximal, Sylow
26C2×ΓL(1,𝔽25)—61no—
27C2×ΓL(1,𝔽25)—61no—
28C2×ΓL(1,𝔽25)—61no—
29C42×D3—61no—
30C3×M32—61no—
31C3×C4⋊C8—61no—
32Dic3⋊C8—21no—
33Dic3⋊C8—61no—
34#812—21no—
35C4⋊(C3⋊C8)—61no—
36C22×C3⋊D3M1611yescharacteristic
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C3⋊Dic3C2×C811yescharacteristic
39C4×C3⋊D3—21no—
40C4×C3⋊D3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43#624—42no—
44C32×C8—21no—
45C3⋊(C3⋊C8)—21no—
46C3×C3⋊C8—41no—
47#423—91no—
48#349—91no—
49#349—91no—
50C2×C4×D3—61no—
51C2×C4×D3—61no—
52C2×C4×D3—61no—
53C2×C4×D3—61no—
54C2×C3×C8—21no—
55C2×C3×C8—21no—
56C2×C3×C8—61no—
57C3×C42—61no—
58C4×Dic3—21no—
59C4×Dic3—61no—
60C4×Dic3—61no—
61C2×C3⋊C8—21no—
62C2×C3⋊C8—61no—
63C2×C3⋊C8—61no—
64ΓL(1,𝔽25)—122no—
65ΓL(1,𝔽25)—121no—
66ΓL(1,𝔽25)—121no—
67ΓL(1,𝔽25)—122no—
68C3×C16—121no—
69C3⋊C16—41no—
70C22×C32C22⋊C811yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—41no—
73C32×C4#9911yescharacteristic
74C32×C4#10111yescharacteristic
75C3⋊Dic3—21no—
76C3×Dic3—22no—
77C3×Dic3—41no—
78C2×M16—91no—
79C2×M16—91no—
80C2×C42—91no—
81M32—61no—
82M32—181no—
83C4⋊C8—61no—
84C4⋊C8—181no—
85C22×D3—61no—
86C22×D3—61no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—61no—
90C2×C3×C4—61no—
91C2×Dic3—21no—
92C2×Dic3—21no—
93C2×Dic3—61no—
94C2×Dic3—61no—
95C4×D3—62no—
96C4×D3—62no—
97C4×D3—121no—
98C4×D3—121no—
99C4×D3—122no—
100C4×D3—122no—
101C3×C8—21no—
102C3×C8—21no—
103C3×C8—41no—
104C3×C8—121no—
105C3⋊C8—41no—
106C3⋊C8—121no—
107C3⋊C8—121no—
108C2×C32—21no—
109C2×C32#32411yescharacteristic
110C3⋊D3—41no—
111C22×C4—91no—
112C22×C4—181no—
113M16—361no—
114M16—361no—
115C2×C8—61no—
116C2×C8—91no—
117C2×C8GO+(4,𝔽2)11yescharacteristic
118C42—61no—
119C42—91no—
120C42—91no—
121C16—121no—
122C16—361no—
123C22×C3—21no—
124C22×C3—21no—
125C2×D3—62no—
126C2×D3—121no—
127C2×D3—121no—
128C2×D3—121no—
129C2×D3—241no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—21no—
133C3×C4—21no—
134C3×C4—62no—
135C3×C4—121no—
136Dic3—22no—
137Dic3—41no—
138Dic3—62no—
139Dic3—121no—
140C32#132711yescharacteristic, complemented, Sylow
141C23—91no—
142C2×C4—61no—
143C2×C4—61no—
144C2×C4—91no—
145C2×C4—181no—
146C2×C4—181no—
147C2×C4—362no—
148C2×C4D32⋊C411yescharacteristic
149C8—21no—
150C8—121no—
151C8—181no—
152C2×C3—21no—
153C2×C3—21no—
154C2×C3—21no—
155C2×C3—21no—
156C2×C3—41no—
157D3—122no—
158D3—241no—
159C22—181no—
160C22—361no—
161C22D32⋊C811yescharacteristic
162C4—62no—
163C4—121no—
164C4—181no—
165C4#6372811yescharacteristic
166C4#6373811yescharacteristic
167C3—21no—
168C3—21no—
169C2—21no—
170C2—361no—
171C2#1059002811yescharacteristic
subgroupG/H
centerC4#63738
commutatorC2×C3⋊Dic3C2×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#324
prime radicalC22×C3⋊D3M16
cosocleC2×#3743C22
hypocenterC32#1327
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
140. C32#1327semidirect

Maximal subgroups

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

subgroupindex
#105906662
#105901802
#105891102
#13279