Finite Group Databasebeta

← #11771203

Subgroups — #11771203

Order 1152.

302 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C4×C4⋊#157C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157—21no—
6C2×#3743—21no—
7C42×C3⋊D3C2211yescharacteristic
8#63781C412yes—
9#63779C412yescomplemented
10#63778—21no—
11C4×#622—21no—
12C32×C4⋊C8C411yescharacteristic, complemented
13#63641—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
15#4837—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C4⋊#157—24no—
22C4×#157—41no—
23C4×#157—41no—
24C2×C32×C8—21no—
25C32×C42C2×C411yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30#3743—41no—
31#3743—41no—
32#1303—91nomaximal, Sylow
33C2×ΓL(1,𝔽25)—64no—
34C42×D3—62no—
35C3×C4⋊C8—22no—
36Dic3⋊C8—64no—
37C4⋊(C3⋊C8)—62no—
38C22×C3⋊D3C22⋊C411yescharacteristic
39C2×#157—24no—
40C2×#157—42no—
41C2×#157—42no—
42C2×C32×C4C4211yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C3⋊Dic3C22⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47C2×C3⋊Dic3C4⋊C411yescharacteristic
48C4×C3⋊D3—22no—
49C4×C3⋊D3—41no—
50C4×C3⋊D3D811yescharacteristic
51C4×C3⋊D3SD1611yescharacteristic
52C4×C3⋊D3SD1611yescharacteristic
53C4×C3⋊D3Q1611yescharacteristic
54#622—42no—
55C32×C8—41no—
56C3⋊(C3⋊C8)—41no—
57#431—91no—
58#423—91no—
59C4×C4⋊C4—91no—
60C2×C4×D3—62no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C3×C8—24no—
64C3×C42—22no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C2×C3⋊C8—64no—
69ΓL(1,𝔽25)—124no—
70ΓL(1,𝔽25)—124no—
71C22×C32#9511yescharacteristic
72C2×C3⋊D3—21no—
73C2×C3⋊D3—21no—
74C2×C3⋊D3#10211yescharacteristic
75C2×C3⋊D3#10311yescharacteristic
76#157—44no—
77C32×C4—21no—
78C32×C4—21no—
79C32×C4#10211yescharacteristic
80C32×C4#10311yescharacteristic
81C3⋊Dic3—21no—
82C3⋊Dic3#10412yes—
83C3⋊Dic3#10611yescharacteristic
84C3⋊Dic3#10711yescharacteristic
85C2×M16—181no—
86C2×C4⋊C4—181no—
87C2×C42—91no—
88C2×C42—181no—
89C4⋊C8—92no—
90C4⋊C8—91no—
91C4⋊C8—181no—
92C4⋊C8#15711yescharacteristic, complemented
93C22⋊C8—181no—
94C4×C8—181no—
95#95—92no—
96C22×D3—62no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—62no—
103C4×D3—62no—
104C4×D3—62no—
105C4×D3—62no—
106C4×D3—62no—
107C4×D3—124no—
108C4×D3—124no—
109C3×C8—44no—
110C3⋊C8—124no—
111C2×C32#33911yescharacteristic
112C2×C32#34011yescharacteristic
113C2×C32#34411yescharacteristic
114C3⋊D3—21no—
115C3⋊D3—21no—
116C22×C4—91no—
117C22×C4—91no—
118C22×C4—91no—
119C22×C4—182no—
120M16—361no—
121M16—361no—
122C2×C8—21no—
123C2×C8—182no—
124C2×C8—181no—
125C4⋊C4—184no—
126C42—91no—
127C42—91no—
128C42—91no—
129C42—361no—
130C42—361no—
131C42C2×#15711yescharacteristic
132C22×C3—22no—
133C2×D3—62no—
134C2×D3—62no—
135C2×D3—122no—
136C2×D3—122no—
137C3×C4—24no—
138C3×C4—22no—
139C3×C4—22no—
140C3×C4—42no—
141Dic3—62no—
142Dic3—62no—
143Dic3—64no—
144Dic3—122no—
145C32#130311yescharacteristic, complemented, Sylow
146C23—91no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—182no—
155C2×C4—184no—
156C2×C4—361no—
157C2×C4—362no—
158C2×C4—362no—
159C2×C4C4×#15711yescharacteristic
160C2×C4C4⋊#15711yescharacteristic
161C2×C4C22⋊#15711yescharacteristic
162C8—41no—
163C8—362no—
164C8—361no—
165C2×C3—22no—
166C2×C3—22no—
167C2×C3—22no—
168D3—122no—
169D3—122no—
170C22—91no—
171C22—91no—
172C22—181no—
173C22—181no—
174C22#6378111yescharacteristic
175C4—21no—
176C4—21no—
177C4—91no—
178C4—91no—
179C4—92no—
180C4—181no—
181C4—364no—
182C4#6378211yescharacteristic
183C4#6378411yescharacteristic
184C3—22no—
185C2—181no—
186C2—181no—
187C2#1059016311yescharacteristic
188C2#1059018311yescharacteristic
189C2#1059018911yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1303
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
9. #63779C4semidirect
12. C32×C4⋊C8C4semidirect
14. C4⋊(C3⋊(C3⋊C8))C4semidirect
92. C4⋊C8#157semidirect
145. C32#1303semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105937252
#105925362
#13039