Finite Group Databasebeta

← #11772501

Subgroups — #11772501

Order 1152.

234 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C2×#63769C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63818—21no—
7#63769—21no—
8#63769C412yes—
9C3×#819—21no—
10C3×#812—21no—
11#63578C412yescomplemented
12#63544C412yescomplemented
13#63542—21no—
14D3×M32—61no—
15D3×#108—61no—
16C22×#157—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18C4⋊#157—22no—
19C4⋊#157—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3D411yescharacteristic
25C8×C3⋊D3Q811yescharacteristic
26C3×#208—22no—
27#3712—41no—
28#3710—41no—
29C3×C3⋊C16—22no—
30#1387—91nomaximal, Sylow
31D3×M16—62no—
32C2×D3×C8—61no—
33C2×D3×C8—61no—
34C3×M32—61no—
35C3×#108—61no—
36#822—62no—
37#819—21no—
38#812—21no—
39#798—62no—
40D3×C16—62no—
41C22×C3⋊D3SD1611yescharacteristic
42C2×#157—42no—
43C2×#157—82no—
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C3⋊Dic3Q1611yescharacteristic
46C4×C3⋊D3C22⋊C411yescharacteristic
47C4×C3⋊D3C4⋊C411yescharacteristic
48C4×C3⋊D3D811yescharacteristic
49C4×C3⋊D3SD1611yescharacteristic
50C32×C8C22⋊C411yescharacteristic
51C32×C8C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4211yescharacteristic
53C3⋊(C3⋊C8)C4⋊C411yescharacteristic
54C3×C3⋊C8—42no—
55C2×M32—91no—
56C2×#108—91no—
57C2×#107—91no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C3×M16—62no—
61C2×C3×C8—21no—
62C2×C3×C8—21no—
63#208—22no—
64C2×C3⋊C8—61no—
65C2×C3⋊C8—61no—
66ΓL(1,𝔽25)—122no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75D3×C8—122no—
76C3×C16—62no—
77C3⋊C16—22no—
78C22×C32#10311yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3#10211yescharacteristic
82C2×C3⋊D3#10611yescharacteristic
83#157—82no—
84C32×C4#9511yescharacteristic
85C32×C4#10211yescharacteristic
86C3⋊Dic3#10311yescharacteristic
87C3⋊Dic3#10711yescharacteristic
88C2×M16—181no—
89C22×C8—91no—
90C2×C4⋊C4—181no—
91M32—61no—
92M32—92no—
93C2×C16—181no—
94#108—61no—
95#108—92no—
96#107—92no—
97#107—181no—
98C22×D3—61no—
99C22×D3—61no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C3×C8—21no—
113C3×C8—21no—
114C3×C8—21no—
115C3×C8—21no—
116C3×C8—122no—
117C3⋊C8—42no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C2×C32—21no—
123C2×C32#34011yescharacteristic
124C3⋊D3—21no—
125C3⋊D3#36111yescharacteristic
126C3⋊D3#36211yescharacteristic
127C22×C4—91no—
128C22×C4—361no—
129M16—62no—
130M16—361no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—91no—
134C2×C8—91no—
135C2×C8—91no—
136C2×C8—361no—
137C2×C8GO+(4,𝔽2)11yescharacteristic
138C4⋊C4—182no—
139C4⋊C4—361no—
140C16—62no—
141C22×C3—21no—
142C22×C3—21no—
143C2×D3—61no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—61no—
147C2×D3—121no—
148C2×D3—121no—
149C2×D3—121no—
150C2×D3—121no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155Dic3—61no—
156Dic3—61no—
157Dic3—61no—
158Dic3—61no—
159C32#138711yescharacteristic, complemented, Sylow
160C23—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—362no—
167C2×C4—722no—
168C2×C4D32⋊C411yescharacteristic
169C8—91no—
170C8—91no—
171C8—122no—
172C8D32⋊C411yescharacteristic
173C8#377311yescharacteristic
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—41no—
177C2×C3—41no—
178D3—61no—
179D3—61no—
180D3—61no—
181D3—61no—
182D3—121no—
183D3—121no—
184C22—91no—
185C22—91no—
186C22—181no—
187C22—181no—
188C22#6373011yescharacteristic
189C4—91no—
190C4—91no—
191C4—722no—
192C4#6372911yescharacteristic
193C4#6373711yescharacteristic
194C3—21no—
195C3—21no—
196C2—21no—
197C2—91no—
198C2—91no—
199C2—181no—
200C2#1059004911yescharacteristic
subgroupG/H
centerC2#10590049
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1387
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63578C4semidirect
12. #63544C4semidirect
159. C32#1387semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
#105909132
#105906252
#13879