Finite Group Databasebeta

← #11771165

Subgroups — #11771165

Order 1152.

286 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593728C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×C8×C3⋊D3—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63778C412yes—
8C4⋊#622—21no—
9C4⋊#622—21no—
10C4⋊#622C412yes—
11C4×#622—21no—
12C32×C4⋊C8C411yescharacteristic
13#63641—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
15D3×C4⋊C8—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21#3788—41no—
22#3788—41no—
23C2×C32×C8—21no—
24C32×C42C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29C8×C3⋊D3—41no—
30C8×C3⋊D3—41no—
31#1301—91nomaximal, Sylow
32C2×D3×C8—64no—
33C42×D3—62no—
34C3×C4⋊C8—22no—
35Dic3⋊C8—64no—
36C4⋊(C3⋊C8)—62no—
37C22×C3⋊D3C4⋊C411yescharacteristic
38C2×C32×C4C4211yescharacteristic
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46C4×C3⋊D3—41no—
47C4×C3⋊D3D811yescharacteristic
48C4×C3⋊D3SD1611yescharacteristic
49C4×C3⋊D3SD1611yescharacteristic
50C4×C3⋊D3Q1611yescharacteristic
51#622—42no—
52#622—42no—
53C32×C8—41no—
54C3⋊(C3⋊C8)—41no—
55#431—91no—
56#423—91no—
57C2×C4⋊C8—91no—
58C2×C4×D3—62no—
59C2×C4×D3—62no—
60C2×C4×D3—62no—
61C2×C3×C8—24no—
62C3×C42—22no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C2×C3⋊C8—64no—
67D3×C8—124no—
68D3×C8—124no—
69C22×C32#9511yescharacteristic
70C2×C3⋊D3—21no—
71C2×C3⋊D3—21no—
72C2×C3⋊D3#10611yescharacteristic
73C2×C3⋊D3#10711yescharacteristic
74C32×C4—21no—
75C32×C4#10211yescharacteristic
76C32×C4#10311yescharacteristic
77C32×C4#10811yescharacteristic
78C32×C4#10811yescharacteristic
79C3⋊Dic3—21no—
80C3⋊Dic3—21no—
81C3⋊Dic3#10211yescharacteristic
82C3⋊Dic3#10311yescharacteristic
83C2×M16—181no—
84C22×C8—181no—
85C2×C42—91no—
86C4⋊C8—92no—
87C4⋊C8—91no—
88C4⋊C8—181no—
89C4⋊C8—181no—
90C4⋊C8—181no—
91C4⋊C8#15711yescharacteristic
92C22⋊C8—92no—
93C4×C8—181no—
94C22×D3—62no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—62no—
104C4×D3—62no—
105C4×D3—64no—
106C4×D3—64no—
107C4×D3—124no—
108C3×C8—44no—
109C3⋊C8—124no—
110C2×C32#34011yescharacteristic
111C2×C32#34111yescharacteristic
112C2×C32#34411yescharacteristic
113C3⋊D3—21no—
114C3⋊D3—21no—
115C22×C4—91no—
116C22×C4—91no—
117C22×C4—91no—
118M16—361no—
119M16—361no—
120C2×C8—21no—
121C2×C8—182no—
122C2×C8—182no—
123C2×C8—181no—
124C2×C8—361no—
125C2×C8—361no—
126C42—91no—
127C42—91no—
128C42—91no—
129C42C2×#15711yescharacteristic
130C22×C3—22no—
131C2×D3—62no—
132C2×D3—62no—
133C2×D3—64no—
134C2×D3—64no—
135C3×C4—22no—
136C3×C4—22no—
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—42no—
140Dic3—62no—
141Dic3—62no—
142Dic3—64no—
143Dic3—122no—
144C32#130111yescharacteristic, complemented, Sylow
145C23—91no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4—361no—
156C2×C4C4×#15711yescharacteristic
157C2×C4C4⋊#15711yescharacteristic
158C2×C4C22⋊#15711yescharacteristic
159C8—41no—
160C8—362no—
161C8—362no—
162C8—361no—
163C2×C3—22no—
164C2×C3—22no—
165C2×C3—22no—
166D3—64no—
167D3—64no—
168C22—91no—
169C22—91no—
170C22—181no—
171C22—181no—
172C22#6378111yescharacteristic
173C4—21no—
174C4—91no—
175C4—91no—
176C4—181no—
177C4—181no—
178C4#6377011yescharacteristic
179C4#6377111yescharacteristic
180C4#6378211yescharacteristic
181C4#6378411yescharacteristic
182C3—22no—
183C2—181no—
184C2—181no—
185C2#1059016311yescharacteristic
186C2#1059018511yescharacteristic
187C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1301
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
144. C32#1301semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105937272
C3⋊D3×C4⋊C82
#13019