Finite Group Databasebeta

← #11770901

Subgroups — #11770901

Order 1152.

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

normal subgroups only

This group has 274 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
1C4×C4⋊#157C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic
3#10592534C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157C412yes—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63778—21no—
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—
23C4×#157—42no—
24C2×C32×C8—21no—
25C32×C42C2×C411yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30#1285—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—21no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—21no—
50C4×C3⋊D3—41no—
51#622—42no—
52C32×C8—41no—
53C3⋊(C3⋊C8)—41no—
54#432—91no—
55#432—91no—
56C4×C4⋊C4—91no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C4×D3—62no—
60C2×C3×C8—24no—
61C3×C42—22no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C2×C3⋊C8—64no—
66C22×C32#9511yescharacteristic
67C2×C3⋊D3—21no—
68C2×C3⋊D3—21no—
69C2×C3⋊D3#10011yescharacteristic
70C2×C3⋊D3#10111yescharacteristic
71#157—44no—
72C32×C4—21no—
73C32×C4—21no—
74C32×C4#10411yescharacteristic
75C32×C4#10411yescharacteristic
76C3⋊Dic3—21no—
77C3⋊Dic3—21no—
78C3⋊Dic3—21no—
79C2×C4⋊C4—181no—
80C2×C42—91no—
81C2×C42—92no—
82C4⋊C8—91no—
83C4⋊C8—181no—
84C4⋊C8#15711yescharacteristic, complemented
85C22⋊C8—181no—
86C22⋊C8—181no—
87#97—92no—
88#97—181no—
89#95—181no—
90C22×D3—62no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C4×D3—122no—
98C4×D3—122no—
99C4×D3—122no—
100C4×D3—122no—
101C4×D3—124no—
102C3×C8—44no—
103C3⋊C8—124no—
104C2×C32H(3,ℤ/4)11yescharacteristic
105C2×C32#33911yescharacteristic
106C2×C32#34311yescharacteristic
107C3⋊D3—21no—
108C3⋊D3—21no—
109C22×C4—91no—
110C22×C4—91no—
111C22×C4—91no—
112C22×C4—182no—
113C2×C8—21no—
114C2×C8—182no—
115C2×C8—181no—
116C4⋊C4—182no—
117C4⋊C4—182no—
118C42—91no—
119C42—91no—
120C42—91no—
121C42—362no—
122C42C2×#15711yescharacteristic
123C22×C3—22no—
124C2×D3—62no—
125C2×D3—62no—
126C2×D3—122no—
127C2×D3—122no—
128C3×C4—24no—
129C3×C4—22no—
130C3×C4—22no—
131C3×C4—42no—
132Dic3—122no—
133Dic3—122no—
134Dic3—122no—
135C32#128511yescharacteristic, complemented, Sylow
136C23—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—181no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4—181no—
144C2×C4—184no—
145C2×C4—361no—
146C2×C4—362no—
147C2×C4—362no—
148C2×C4C4×#15711yescharacteristic
149C2×C4C4⋊#15711yescharacteristic
150C2×C4C22⋊#15711yescharacteristic
151C8—41no—
152C8—362no—
153C8—361no—
154C2×C3—22no—
155C2×C3—22no—
156C2×C3—22no—
157D3—122no—
158D3—122no—
159C22—91no—
160C22—91no—
161C22—181no—
162C22—181no—
163C22#6378111yescharacteristic
164C4—21no—
165C4—21no—
166C4—181no—
167C4—181no—
168C4—181no—
169C4—364no—
170C4#6378311yescharacteristic
171C4#6378511yescharacteristic
172C3—22no—
173C2—181no—
174C2—181no—
175C2#1059016411yescharacteristic
176C2#1059018411yescharacteristic
177C2#1059018811yescharacteristic
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#1285
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ 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
84. C4⋊C8#157semidirect
135. C32#1285semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105937302
#105925342
#12859