Finite Group Databasebeta

← #11770899

Subgroups — #11770899

Order 1152.

274 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593731C211yesmaximal, characteristic
3#10592404C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157C412yes—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63779C412yescomplemented
9#63778—21no—
10#63777—21no—
11C32×#97C411yescharacteristic, complemented
12#63647—21no—
13#63641—21no—
14#63630C411yescharacteristic, complemented
15#4705—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—42no—
23C2×C32×C8—21no—
24C32×C42C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3Q811yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29#1285—91nomaximal, Sylow
30C42×D3—62no—
31C3×#97—22no—
32(C2×D3)⋊C8—64no—
33Dic3⋊C8—64no—
34#803—62no—
35C22×C3⋊D3C22⋊C411yescharacteristic
36C2×#157—24no—
37C2×#157—42no—
38C2×#157—42no—
39C2×C32×C4C4211yescharacteristic
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C4×C3⋊D3—21no—
46C4×C3⋊D3—21no—
47C4×C3⋊D3—22no—
48C4×C3⋊D3—41no—
49#622—42no—
50C32×C8—41no—
51C3⋊(C3⋊C8)—41no—
52#432—91no—
53#432—91no—
54C4×C4⋊C4—91no—
55C2×C4×D3—62no—
56C2×C4×D3—62no—
57C2×C4×D3—62no—
58C2×C3×C8—24no—
59C3×C42—22no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C2×C3⋊C8—64no—
64C22×C32#9511yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—21no—
67C2×C3⋊D3#10011yescharacteristic
68C2×C3⋊D3#10111yescharacteristic
69#157—44no—
70C32×C4—21no—
71C32×C4—21no—
72C32×C4—21no—
73C3⋊Dic3—21no—
74C3⋊Dic3—21no—
75C3⋊Dic3#10412yes—
76C2×C4⋊C4—181no—
77C2×C42—91no—
78C2×C42—92no—
79C4⋊C8—92no—
80C4⋊C8—181no—
81C22⋊C8—181no—
82C22⋊C8—181no—
83#97—91no—
84#97—181no—
85#97#15711yescharacteristic, complemented
86#95—181no—
87C22×D3—62no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C4×D3—124no—
95C4×D3—122no—
96C4×D3—122no—
97C4×D3—124no—
98C3×C8—44no—
99C3⋊C8—124no—
100C2×C32H(3,ℤ/4)11yescharacteristic
101C2×C32#33911yescharacteristic
102C2×C32#34311yescharacteristic
103C3⋊D3—21no—
104C3⋊D3—21no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—91no—
108C22×C4—182no—
109C2×C8—21no—
110C2×C8—182no—
111C2×C8—181no—
112C4⋊C4—184no—
113C42—91no—
114C42—91no—
115C42—91no—
116C42—362no—
117C42C2×#15711yescharacteristic
118C22×C3—22no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—122no—
122C2×D3—122no—
123C3×C4—24no—
124C3×C4—42no—
125C3×C4—42no—
126Dic3—64no—
127Dic3—122no—
128Dic3—122no—
129C32#128511yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—182no—
135C2×C4—181no—
136C2×C4—181no—
137C2×C4—184no—
138C2×C4—361no—
139C2×C4—362no—
140C2×C4—362no—
141C2×C4C4×#15711yescharacteristic
142C2×C4C4⋊#15711yescharacteristic
143C2×C4C22⋊#15711yescharacteristic
144C8—41no—
145C8—361no—
146C8—362no—
147C2×C3—22no—
148C2×C3—22no—
149C2×C3—22no—
150D3—122no—
151D3—122no—
152C22—91no—
153C22—91no—
154C22—181no—
155C22—181no—
156C22#6378111yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—92no—
161C4—181no—
162C4—181no—
163C4—364no—
164C3—22no—
165C2—181no—
166C2—181no—
167C2#1059015211yescharacteristic
168C2#1059018811yescharacteristic
169C2#1059018911yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×#97C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenter#97#157
hypocenterC32#1285
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
8. #63779C4semidirect
11. C32×#97C4semidirect
14. #63630C4semidirect
85. #97#157semidirect
129. 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
#105937312
#105924042
#12859