Finite Group Databasebeta

← #11771096

Subgroups — #11771096

Order 1152.

436 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 48 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×C22⋊#157C212yesmaximal
2#10592825C211yesmaximal, characteristic
3C22×C4×C3⋊D3C2211yescharacteristic
4C2×C22⋊#157—22no—
5C2×C4×#157—22no—
6C2×C32×M16C411yescharacteristic, complemented
7C2×#3748C411yescharacteristic, complemented
8#63781C414yescomplemented
9#63647—22no—
10#5126—62no—
11C23×C3⋊D3D411yescharacteristic
12C22×#157—24no—
13C22×C32×C4C2×C411yescharacteristic
14C22×C3⋊Dic3Q811yescharacteristic
15C2×C4×C3⋊D3—41no—
16C2×C4×C3⋊D3—41no—
17C2×C4×C3⋊D3C2×C412yes—
18C2×C4×C3⋊D3D412yes—
19C22⋊#157—28no—
20C4×#157—42no—
21C4×#157—42no—
22C32×M16—41no—
23C2×C32×C8—21no—
24#3748—41no—
25C2×C3⋊(C3⋊C8)—21no—
26#1297—91nomaximal, Sylow
27C22×C4×D3—62no—
28C2×C3×M16—22no—
29C2×#208—62no—
30(C2×D3)⋊C8—68no—
31C23×C32C4⋊C411yescharacteristic
32C22×C3⋊D3—24no—
33C22×C3⋊D3—41no—
34C22×C3⋊D3C22⋊C412yes—
35C2×#157—28no—
36C2×#157—44no—
37C2×#157—44no—
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4C4211yescharacteristic
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3C4⋊C412yes—
44C4×C3⋊D3—22no—
45C4×C3⋊D3—22no—
46C4×C3⋊D3—42no—
47C32×C8—41no—
48C3⋊(C3⋊C8)—41no—
49#407—91no—
50C4×C22⋊C4—92no—
51C23×D3—62no—
52C22×C3×C4—22no—
53C22×Dic3—62no—
54C2×C4×D3—64no—
55C2×C4×D3—64no—
56C2×C4×D3—124no—
57C2×C4×D3—124no—
58C3×M16—44no—
59C2×C3×C8—24no—
60#208—124no—
61C2×C3⋊C8—64no—
62C22×C32—21no—
63C22×C32—22no—
64C22×C32#9511yescharacteristic
65C2×C3⋊D3—22no—
66C2×C3⋊D3—22no—
67C2×C3⋊D3—44no—
68C2×C3⋊D3#10414yes—
69#157—48no—
70C32×C4—21no—
71C32×C4#9911yescharacteristic
72C32×C4#9911yescharacteristic
73C3⋊Dic3—22no—
74C23×C4—91no—
75C2×M16—91no—
76C2×M16#15711yescharacteristic, complemented
77C2×C22⋊C4—182no—
78C2×C42—182no—
79C22⋊C8—182no—
80#95—94no—
81C23×C3—22no—
82C22×D3—64no—
83C22×D3—128no—
84C22×D3—124no—
85C2×C3×C4—24no—
86C2×C3×C4—24no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×Dic3—64no—
90C2×Dic3—124no—
91C4×D3—124no—
92C4×D3—124no—
93C4×D3—128no—
94C3×C8—44no—
95C3⋊C8—124no—
96C2×C32—41no—
97C2×C32#33912yes—
98C2×C32#34211yescharacteristic
99C3⋊D3—24no—
100C24—91no—
101C22×C4—91no—
102C22×C4—92no—
103C22×C4—92no—
104C22×C4—184no—
105C22×C4—361no—
106C22×C4—361no—
107C22×C4C2×#15711yescharacteristic
108M16—41no—
109M16—361no—
110C2×C8—21no—
111C2×C8—181no—
112C22⋊C4—188no—
113C42—362no—
114C42—362no—
115C22×C3—24no—
116C22×C3—22no—
117C22×C3—44no—
118C2×D3—68no—
119C2×D3—124no—
120C2×D3—124no—
121C2×D3—1216no—
122C3×C4—24no—
123C3×C4—22no—
124C3×C4—22no—
125Dic3—124no—
126C32#129711yescharacteristic, complemented, Sylow
127C23—92no—
128C23—184no—
129C23—361no—
130C23C4⋊#15711yescharacteristic
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—92no—
134C2×C4—182no—
135C2×C4—182no—
136C2×C4—188no—
137C2×C4—362no—
138C2×C4—361no—
139C2×C4—364no—
140C2×C4—364no—
141C2×C4C4×#15711yescharacteristic
142C2×C4C22⋊#15711yescharacteristic
143C8—41no—
144C8—361no—
145C2×C3—24no—
146C2×C3—22no—
147C2×C3—44no—
148D3—128no—
149C22—22no—
150C22—21no—
151C22—94no—
152C22—182no—
153C22—182no—
154C22—364no—
155C22#6378111yescharacteristic
156C4—21no—
157C4—182no—
158C4—368no—
159C4#6377411yescharacteristic
160C4#6378611yescharacteristic
161C3—22no—
162C2—41no—
163C2—184no—
164C2#1059018912yes—
165C2#1059020611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC22×C4×C3⋊D3C22
hypercenterC2×M16#157
hypocenterC32#1297
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. C2×C32×M16C4semidirect
7. C2×#3748C4semidirect
8. #63781C4semidirect
76. C2×M16#157semidirect
126. C32#1297semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105928252
#12979