Finite Group Databasebeta

← #11771150

Subgroups — #11771150

Order 1152.

298 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593733C211yesmaximal, characteristic
2C4×#3712C211yesmaximal, characteristic
3#10590299C211yesmaximal, characteristic
4C2×C4×#157—21no—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712—21no—
7#63781—21no—
8#63781C412yes—
9C3×#803—21no—
10C3×C4×C3⋊C8—21no—
11#63572C412yescomplemented
12#63557—21no—
13#63555C412yescomplemented
14#4705—61no—
15C4×ΓL(1,𝔽25)—61no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C4×#157—24no—
21C32×C42D411yescharacteristic
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3Q811yescharacteristic
25C2×C3×C3⋊C8—22no—
26C2×C3×C3⋊C8—22no—
27#3712—24no—
28#1300—91nomaximal, Sylow
29C2×ΓL(1,𝔽25)—62no—
30C42×D3—61no—
31C42×D3—61no—
32C3×#97—61no—
33C3×C4×C8—61no—
34(C2×D3)⋊C8—62no—
35#815—62no—
36Dic3⋊C8—62no—
37#803—21no—
38C4×C3⋊C8—21no—
39C22×C3⋊D3C22⋊C411yescharacteristic
40C2×#157—24no—
41C2×#157—42no—
42C2×#157—42no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4211yescharacteristic
47C2×C3⋊Dic3C4⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C4×C3⋊D3—22no—
50C4×C3⋊D3—22no—
51C4×C3⋊D3—41no—
52C3×C3⋊C8—24no—
53C3×C3⋊C8—42no—
54#432—91no—
55C4×M16—91no—
56#376—91no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C3×C8—62no—
64C2×C3×C8—62no—
65C3×C42—21no—
66C3×C42—21no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C2×C3⋊C8—22no—
74C2×C3⋊C8—22no—
75ΓL(1,𝔽25)—68no—
76C22×C32#9511yescharacteristic
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3#10412yes—
80#157—44no—
81C32×C4—21no—
82C32×C4—21no—
83C32×C4#10412yes—
84C3⋊Dic3—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C2×M16—181no—
88C2×C42—91no—
89C2×C42—181no—
90C4⋊C8—92no—
91C22⋊C8—181no—
92#97—61no—
93#97—92no—
94C4×C8—61no—
95#95—92no—
96#95—181no—
97C22×D3—61no—
98C22×D3—61no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C4×D3—64no—
112C4×D3—122no—
113C4×D3—122no—
114C4×D3—122no—
115C4×D3—122no—
116C4×D3—122no—
117C3×C8—64no—
118C3×C8—122no—
119C3⋊C8—24no—
120C3⋊C8—42no—
121C2×C32#33911yescharacteristic
122C2×C32#33911yescharacteristic
123C2×C32#34411yescharacteristic
124C3⋊D3—22no—
125C22×C4—91no—
126C22×C4—91no—
127C22×C4—91no—
128C22×C4—182no—
129M16—184no—
130C2×C8—62no—
131C2×C8—62no—
132C42—91no—
133C42—91no—
134C42—91no—
135C42—184no—
136C42GO+(4,𝔽2)11yescharacteristic
137C22×C3—21no—
138C22×C3—21no—
139C2×D3—62no—
140C2×D3—62no—
141C2×D3—121no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—121no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4—22no—
148C3×C4—22no—
149C3×C4—41no—
150C3×C4—41no—
151Dic3—62no—
152Dic3—62no—
153Dic3—121no—
154Dic3—121no—
155Dic3—121no—
156Dic3—121no—
157C32#130011yescharacteristic, complemented, Sylow
158C23—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—182no—
163C2×C4—182no—
164C2×C4—184no—
165C2×C4—361no—
166C2×C4—362no—
167C2×C4—362no—
168C2×C4D32⋊C411yescharacteristic
169C2×C4D32⋊C411yescharacteristic
170C2×C4#377311yescharacteristic
171C8—64no—
172C8—122no—
173C2×C3—21no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179D3—122no—
180D3—122no—
181C22—92no—
182C22—181no—
183C22—181no—
184C22#6373711yescharacteristic
185C4—21no—
186C4—21no—
187C4—181no—
188C4—181no—
189C4—181no—
190C4—364no—
191C4#6373112yes—
192C3—21no—
193C3—21no—
194C2—182no—
195C2#1059004711yescharacteristic
196C2#1059004811yescharacteristic
197C2#1059005511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1300
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #63572C4semidirect
13. #63555C4semidirect
157. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105937332
C4×#37122
#105902992
#13009