Finite Group Databasebeta

← #11771204

Subgroups — #11771204

Order 1152.

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

normal subgroups only

This group has 294 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
1C4×C4⋊#157C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157—21no—
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8#63781C412yes—
9C4⋊#622—21no—
10C4⋊#622C412yescomplemented
11C32×C4⋊C8C411yescharacteristic, complemented
12#63647—21no—
13C8×C3⋊Dic3—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
15#4833—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C4⋊#157—22no—
22C4⋊#157—22no—
23C4×#157—41no—
24C4×#157—41no—
25#3788—41no—
26#3788—41no—
27C2×C32×C8—21no—
28C32×C42C2×C411yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3Q811yescharacteristic
32C2×C3⋊(C3⋊C8)—21no—
33#1303—91nomaximal, Sylow
34C42×D3—62no—
35C3×C4⋊C8—22no—
36(C2×D3)⋊C8—64no—
37C8×Dic3—64no—
38C4⋊(C3⋊C8)—62no—
39C22×C3⋊D3C22⋊C411yescharacteristic
40C2×#157—24no—
41C2×#157—42no—
42C2×#157—42no—
43C2×C32×C4C4211yescharacteristic
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C3⋊Dic3C22⋊C411yescharacteristic
47C2×C3⋊Dic3C4⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C4×C3⋊D3—21no—
50C4×C3⋊D3—21no—
51C4×C3⋊D3—41no—
52C4×C3⋊D3D811yescharacteristic
53C4×C3⋊D3SD1611yescharacteristic
54C4×C3⋊D3SD1611yescharacteristic
55C4×C3⋊D3Q1611yescharacteristic
56#622—42no—
57C32×C8—41no—
58C3⋊(C3⋊C8)—41no—
59#431—91no—
60#423—91no—
61C4×C4⋊C4—91no—
62C2×C4×D3—62no—
63C2×C4×D3—62no—
64C2×C4×D3—62no—
65C2×C3×C8—24no—
66C3×C42—22no—
67C4×Dic3—62no—
68C4×Dic3—62no—
69C4×Dic3—62no—
70C2×C3⋊C8—64no—
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#10411yescharacteristic
79C32×C4#10411yescharacteristic
80C32×C4#10611yescharacteristic
81C32×C4#10711yescharacteristic
82C3⋊Dic3—21no—
83C3⋊Dic3—21no—
84C3⋊Dic3#10211yescharacteristic
85C3⋊Dic3#10311yescharacteristic
86C2×M16—181no—
87C2×C4⋊C4—181no—
88C2×C42—91no—
89C2×C42—181no—
90C4⋊C8—92no—
91C4⋊C8—91no—
92C4⋊C8—181no—
93C4⋊C8#15711yescharacteristic, complemented
94C22⋊C8—181no—
95C4×C8—181no—
96#95—92no—
97C22×D3—62no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—22no—
101C2×Dic3—62no—
102C2×Dic3—62no—
103C2×Dic3—62no—
104C4×D3—62no—
105C4×D3—62no—
106C4×D3—62no—
107C4×D3—62no—
108C4×D3—122no—
109C4×D3—122no—
110C4×D3—124no—
111C3×C8—44no—
112C3⋊C8—124no—
113C2×C32#33911yescharacteristic
114C2×C32#34011yescharacteristic
115C2×C32#34411yescharacteristic
116C3⋊D3—21no—
117C3⋊D3—21no—
118C22×C4—91no—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—182no—
122M16—361no—
123M16—361no—
124C2×C8—21no—
125C2×C8—182no—
126C2×C8—181no—
127C4⋊C4—182no—
128C4⋊C4—182no—
129C42—91no—
130C42—91no—
131C42—91no—
132C42—361no—
133C42—361no—
134C42C2×#15711yescharacteristic
135C22×C3—22no—
136C2×D3—62no—
137C2×D3—62no—
138C2×D3—122no—
139C2×D3—122no—
140C3×C4—22no—
141C3×C4—22no—
142C3×C4—22no—
143C3×C4—22no—
144C3×C4—42no—
145Dic3—62no—
146Dic3—62no—
147Dic3—64no—
148Dic3—122no—
149C32#130311yescharacteristic, complemented, Sylow
150C23—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—181no—
159C2×C4—181no—
160C2×C4—184no—
161C2×C4—361no—
162C2×C4—362no—
163C2×C4—362no—
164C2×C4C4×#15711yescharacteristic
165C2×C4C4⋊#15711yescharacteristic
166C2×C4C22⋊#15711yescharacteristic
167C8—41no—
168C8—362no—
169C8—361no—
170C2×C3—22no—
171C2×C3—22no—
172C2×C3—22no—
173D3—122no—
174D3—122no—
175C22—91no—
176C22—91no—
177C22—181no—
178C22—181no—
179C22#6378111yescharacteristic
180C4—21no—
181C4—91no—
182C4—91no—
183C4—181no—
184C4—181no—
185C4—364no—
186C4#6376811yescharacteristic
187C4#6376911yescharacteristic
188C4#6378311yescharacteristic
189C4#6378511yescharacteristic
190C3—22no—
191C2—181no—
192C2—181no—
193C2#1059016411yescharacteristic
194C2#1059018211yescharacteristic
195C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
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 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
10. C4⋊#622C4semidirect
11. C32×C4⋊C8C4semidirect
14. C4⋊(C3⋊(C3⋊C8))C4semidirect
93. C4⋊C8#157semidirect
149. 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
#105937282
#105925322
#13039