Finite Group Databasebeta

← #11771144

Subgroups — #11771144

Order 1152.

282 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 46 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×#3788C211yesmaximal, characteristic
3#10592534C211yesmaximal, characteristic
4C2×C4×#157—21no—
5C2×#3788—21no—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63781C412yes—
9#63777C412yescomplemented
10C4×#622—21no—
11C32×C4⋊C8C411yescharacteristic, complemented
12#63647—21no—
13#63642—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
15#4835—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—
23#3788—24no—
24C2×C32×C8—21no—
25C32×C42C2×C411yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30#1300—91nomaximal, Sylow
31C42×D3—62no—
32C3×C4⋊C8—22no—
33(C2×D3)⋊C8—64no—
34#815—64no—
35C4⋊(C3⋊C8)—62no—
36C22×C3⋊D3C22⋊C411yescharacteristic
37C2×#157—24no—
38C2×#157—42no—
39C2×#157—42no—
40C2×C32×C4C4211yescharacteristic
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C3⋊Dic3C22⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C4×C3⋊D3—22no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—41no—
50#622—24no—
51C32×C8—41no—
52C3⋊(C3⋊C8)—41no—
53#432—91no—
54C4×M16—91no—
55#376—91no—
56C2×C4×D3—62no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C3×C8—24no—
60C3×C42—22no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C2×C3⋊C8—64no—
65C22×C32#9511yescharacteristic
66C2×C3⋊D3—21no—
67C2×C3⋊D3—21no—
68C2×C3⋊D3#10412yes—
69#157—44no—
70C32×C4—21no—
71C32×C4—21no—
72C32×C4#10411yescharacteristic
73C32×C4#10411yescharacteristic
74C3⋊Dic3—21no—
75C3⋊Dic3—21no—
76C3⋊Dic3—21no—
77C2×M16—181no—
78C2×C42—91no—
79C2×C42—181no—
80C4⋊C8—91no—
81C4⋊C8#15711yescharacteristic, complemented
82C22⋊C8—181no—
83#97—92no—
84#97—181no—
85C4×C8—181no—
86#95—92no—
87#95—181no—
88C22×D3—62no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C4×D3—122no—
96C4×D3—122no—
97C4×D3—124no—
98C4×D3—124no—
99C3×C8—44no—
100C3⋊C8—124no—
101C2×C32#33911yescharacteristic
102C2×C32#33911yescharacteristic
103C2×C32#34411yescharacteristic
104C3⋊D3—22no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—91no—
108C22×C4—182no—
109M16—184no—
110C2×C8—21no—
111C2×C8—182no—
112C2×C8—181no—
113C42—91no—
114C42—91no—
115C42—91no—
116C42—182no—
117C42—182no—
118C42C2×#15711yescharacteristic
119C22×C3—22no—
120C2×D3—64no—
121C2×D3—122no—
122C2×D3—122no—
123C3×C4—24no—
124C3×C4—22no—
125C3×C4—22no—
126C3×C4—42no—
127Dic3—122no—
128Dic3—122no—
129Dic3—122no—
130C32#130011yescharacteristic, complemented, Sylow
131C23—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—182no—
136C2×C4—181no—
137C2×C4—181no—
138C2×C4—184no—
139C2×C4—361no—
140C2×C4—362no—
141C2×C4—362no—
142C2×C4C4×#15711yescharacteristic
143C2×C4C4⋊#15711yescharacteristic
144C2×C4C22⋊#15711yescharacteristic
145C8—41no—
146C8—184no—
147C8—361no—
148C2×C3—22no—
149C2×C3—22no—
150C2×C3—22no—
151D3—124no—
152C22—92no—
153C22—181no—
154C22—181no—
155C22#6378111yescharacteristic
156C4—21no—
157C4—21no—
158C4—181no—
159C4—181no—
160C4—181no—
161C4—364no—
162C4#6378311yescharacteristic
163C4#6378511yescharacteristic
164C3—22no—
165C2—182no—
166C2#1059016411yescharacteristic
167C2#1059018311yescharacteristic
168C2#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#1300
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. #63777C4semidirect
11. C32×C4⋊C8C4semidirect
14. C4⋊(C3⋊(C3⋊C8))C4semidirect
81. C4⋊C8#157semidirect
130. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105937332
C4×#37882
#105925342
#13009