Finite Group Databasebeta

← #11772480

Subgroups — #11772480

Order 1152.

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

normal subgroups only

This group has 250 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
1#10593768C211yesmaximal, characteristic
2#10590685C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4#64286—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63900—21no—
7#63769C412yescomplemented
8#63768—21no—
9C3×#817—21no—
10C3×#812—21no—
11#63574C412yescomplemented
12#63544C412yescomplemented
13#63542—21no—
14D3×M32—61no—
15D3×#106—61no—
16C2×C4×C3⋊D3D411yescharacteristic
17C2×#624—41no—
18C22⋊#157—41no—
19C4⋊#157—22no—
20C4×#157—41no—
21C2×C32×C8D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3C2×C411yescharacteristic
25C8×C3⋊D3D411yescharacteristic
26C8×C3⋊D3Q811yescharacteristic
27C3×C4⋊Dic3—22no—
28#3724—41no—
29C3×C3⋊C16—22no—
30#1386—91nomaximal, Sylow
31C2×D3×C8—61no—
32C2×D3×C8—61no—
33D3×C4⋊C4—62no—
34C3×M32—61no—
35C3×#106—61no—
36#817—21no—
37#812—21no—
38#808—62no—
39#798—62no—
40D3×C16—62no—
41C22×C3⋊D3D811yescharacteristic
42C2×#157—42no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C3⋊Dic3SD1611yescharacteristic
45C4×C3⋊D3C22⋊C411yescharacteristic
46C4×C3⋊D3C4⋊C411yescharacteristic
47C4×C3⋊D3SD1611yescharacteristic
48C4×C3⋊D3Q1611yescharacteristic
49C2×C3×Dic3—42no—
50#624—82no—
51C32×C8C22⋊C411yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C4211yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C2×M32—91no—
56#427—91no—
57C2×#106—91no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—122no—
61C2×C3×C8—21no—
62C2×C3×C8—21no—
63C3×C4⋊C4—62no—
64C4⋊Dic3—22no—
65Dic3⋊C4—122no—
66C2×C3⋊C8—61no—
67C2×C3⋊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—61no—
76C3×C16—62no—
77C3⋊C16—22no—
78C22×C32#10211yescharacteristic
79C2×C3⋊D3—22no—
80C2×C3⋊D3#10211yescharacteristic
81C2×C3⋊D3#10711yescharacteristic
82#157—82no—
83C32×C4#9511yescharacteristic
84C32×C4#10311yescharacteristic
85C3⋊Dic3#10311yescharacteristic
86C3⋊Dic3#10611yescharacteristic
87C3×Dic3—82no—
88C22×C8—91no—
89#117—181no—
90C2×C4⋊C4—181no—
91M32—61no—
92M32—92no—
93C2×C16—181no—
94#107—92no—
95#106—61no—
96#106—92no—
97#106—181no—
98C22×D3—61no—
99C22×D3—61no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—122no—
103C2×Dic3—42no—
104C2×Dic3—61no—
105C2×Dic3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C4×D3—61no—
113C4×D3—61no—
114C4×D3—244no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8—21no—
118C3×C8—21no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C2×C32—21no—
124C2×C32#34011yescharacteristic
125C3⋊D3—21no—
126C3⋊D3#36012yes—
127C22×C4—91no—
128C22×C4—361no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—91no—
134C2×C8GO+(4,𝔽2)11yescharacteristic
135C4⋊C4—62no—
136C4⋊C4—182no—
137C4⋊C4—361no—
138C22⋊C4—361no—
139C42—361no—
140C16—62no—
141C22×C3—21no—
142C22×C3—21no—
143C2×D3—61no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—61no—
147C2×D3—64no—
148C2×D3—122no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—242no—
154Dic3—61no—
155Dic3—61no—
156Dic3—61no—
157Dic3—61no—
158Dic3—82no—
159C32#138611yescharacteristic, complemented, Sylow
160C23—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—122no—
167C2×C4—362no—
168C2×C4—722no—
169C2×C4D32⋊C411yescharacteristic
170C8—91no—
171C8—91no—
172C8D32⋊C411yescharacteristic
173C8#377311yescharacteristic
174C2×C3—22no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—41no—
178D3—62no—
179D3—62no—
180D3—62no—
181D3—121no—
182C22—91no—
183C22—91no—
184C22—182no—
185C22#6372911yescharacteristic
186C4—91no—
187C4—91no—
188C4—242no—
189C4—722no—
190C4#6373011yescharacteristic
191C4#6373711yescharacteristic
192C3—21no—
193C3—21no—
194C2—21no—
195C2—92no—
196C2—181no—
197C2#1059004911yescharacteristic
subgroupG/H
centerC2#10590049
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#340
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1386
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
7. #63769C4semidirect
11. #63574C4semidirect
12. #63544C4semidirect
159. C32#1386semidirect

Maximal subgroups

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

subgroupindex
#105937682
#105906852
#105906252
#13869