Finite Group Databasebeta

← #11770710

Subgroups — #11770710

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#10593733C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic
4C2×C4×#157C412yes—
5C42×C3⋊D3C2211yescharacteristic
6#63781—21no—
7#63781—21no—
8#63779—21no—
9#63778—21no—
10C4×#622C412yescomplemented
11C32×C4×C8C411yescharacteristic, complemented
12#63647—21no—
13#63641—21no—
14C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
15#4685—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C4×#157—22no—
22C4×#157C814yescomplemented
23C2×C32×C8—21no—
24C32×C42C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3Q811yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29#1274—91nomaximal, Sylow
30C42×D3—62no—
31C3×C4×C8—22no—
32(C2×D3)⋊C8—64no—
33Dic3⋊C8—64no—
34C4×C3⋊C8—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—41no—
46C4×C3⋊D3—41no—
47C4×C3⋊D3C2×C812yes—
48C4×C3⋊D3M1612yes—
49#622—42no—
50C32×C8—41no—
51C3⋊(C3⋊C8)—41no—
52#431—91no—
53#431—91no—
54#376—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⋊D3C22⋊C812yes—
68#157—44no—
69C32×C4—21no—
70C32×C4—21no—
71C32×C4C4×C811yescharacteristic
72C32×C4#9711yescharacteristic
73C3⋊Dic3—21no—
74C3⋊Dic3—21no—
75C3⋊Dic3C4⋊C812yes—
76C2×C42—91no—
77C2×C42—92no—
78C4⋊C8—181no—
79C4⋊C8—181no—
80C22⋊C8—181no—
81C22⋊C8—181no—
82C4×C8—92no—
83C4×C8—91no—
84C4×C8#15711yescharacteristic, complemented
85#95—181no—
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—64no—
95C4×D3—64no—
96C4×D3—124no—
97C4×D3—124no—
98C3×C8—44no—
99C3⋊C8—124no—
100C2×C32#33611yescharacteristic
101C2×C32H(3,ℤ/4)11yescharacteristic
102C2×C32H(3,ℤ/4)11yescharacteristic
103C3⋊D3—22no—
104C22×C4—91no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—182no—
108C2×C8—21no—
109C2×C8—182no—
110C2×C8—181no—
111C42—91no—
112C42—91no—
113C42—91no—
114C42—94no—
115C42—182no—
116C42C2×#15711yescharacteristic
117C22×C3—22no—
118C2×D3—64no—
119C2×D3—122no—
120C2×D3—122no—
121C3×C4—24no—
122C3×C4—24no—
123C3×C4—22no—
124C3×C4—22no—
125Dic3—64no—
126Dic3—122no—
127Dic3—122no—
128C32#127411yescharacteristic, complemented, Sylow
129C23—91no—
130C2×C4—91no—
131C2×C4—92no—
132C2×C4—92no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—184no—
136C2×C4—361no—
137C2×C4—361no—
138C2×C4—362no—
139C2×C4—362no—
140C2×C4C4×#15711yescharacteristic
141C2×C4C4⋊#15711yescharacteristic
142C2×C4C22⋊#15711yescharacteristic
143C8—41no—
144C8—361no—
145C8—362no—
146C2×C3—22no—
147C2×C3—22no—
148C2×C3—22no—
149D3—124no—
150C22—92no—
151C22—181no—
152C22—181no—
153C22#6378111yescharacteristic
154C4—21no—
155C4—21no—
156C4—92no—
157C4—181no—
158C4—181no—
159C4—364no—
160C4C8×#15711yescharacteristic
161C4#6376711yescharacteristic
162C3—22no—
163C2—182no—
164C2#1059015211yescharacteristic
165C2#1059018111yescharacteristic
166C2#1059018411yescharacteristic
subgroupG/H
centerC2×C4C4×#157
commutatorC32×C4C4×C8
FrattiniC42C2×#157
FittingC32×C4×C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4×C8#157
hypocenterC32#1274
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C2×C4 ◁ 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
22. C4×#157C8semidirect
84. C4×C8#157semidirect
128. C32#1274semidirect

Maximal subgroups

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

subgroupindex
#105937332
#105937252
#105923842
#12749