Finite Group Databasebeta

← C4×C22⋊#157 #10593810

Subgroups — C4×C22⋊#157 #10593810

Order 576.

494 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C22×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C22⋊#157C212yesmaximal
3C2×C4×#157C212yesmaximal, complemented
4#63781C212yesmaximal, complemented
5C23×C3⋊D3C2211yescharacteristic
6C22×#157C2214yes—
7C22×C32×C4C411yescharacteristic, complemented
8C22×C3⋊Dic3C411yescharacteristic, complemented
9C2×C4×C3⋊D3—24no—
10C2×C4×C3⋊D3C411yescharacteristic, complemented
11C2×C4×C3⋊D3C411yescharacteristic, complemented
12C2×C4×C3⋊D3C2211yescharacteristic
13C2×C4×C3⋊D3C2211yescharacteristic
14C22⋊#157C418yesdirect product factor
15C4×#157—24no—
16C22×C4×D3—62no—
17C23×C32C2×C411yescharacteristic
18C22×C3⋊D3—22no—
19C22×C3⋊D3—22no—
20C22×C3⋊D3C2×C411yescharacteristic
21C22×C3⋊D3C2×C414yes—
22C22×C3⋊D3C2311yescharacteristic
23C2×#157—24no—
24C2×#157—24no—
25C2×#157C2×C418yescomplemented
26C2×C32×C4—22no—
27C2×C32×C4C2×C411yescharacteristic
28C2×C32×C4C2×C411yescharacteristic
29C2×C3⋊Dic3—22no—
30C2×C3⋊Dic3C2×C411yescharacteristic
31C2×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊D3—22no—
33C4×C3⋊D3—22no—
34C4×C3⋊D3—22no—
35C4×C3⋊D3D414yes—
36C4×C22⋊C4—91nomaximal, Sylow
37C23×D3—62no—
38C22×C3×C4—22no—
39C22×Dic3—62no—
40C2×C4×D3—62no—
41C2×C4×D3—62no—
42C2×C4×D3—62no—
43C2×C4×D3—62no—
44C2×C4×D3—616no—
45C22×C32—21no—
46C22×C32—21no—
47C22×C32C4212yescomplemented
48C22×C32C22×C411yescharacteristic
49C2×C3⋊D3—21no—
50C2×C3⋊D3—21no—
51C2×C3⋊D3—28no—
52C2×C3⋊D3C4212yescomplemented
53C2×C3⋊D3C22×C412yes—
54C2×C3⋊D3C2×D412yes—
55C2×C3⋊D3#4112yes—
56#157—28no—
57C32×C4—21no—
58C32×C4C22⋊C412yescomplemented
59C3⋊Dic3—21no—
60C3⋊Dic3C22⋊C412yescomplemented
61C23×C4—91no—
62C2×C22⋊C4—92no—
63C2×C42—92no—
64#95—92no—
65C23×C3—22no—
66C22×D3—62no—
67C22×D3—68no—
68C22×D3—62no—
69C22×D3—68no—
70C22×D3—68no—
71C2×C3×C4—28no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×Dic3—62no—
75C2×Dic3—62no—
76C2×Dic3—68no—
77C4×D3—68no—
78C4×D3—68no—
79C4×D3—68no—
80C4×D3—68no—
81C2×C32—22no—
82C2×C32C2×C4211yescharacteristic
83C2×C32C2×C22⋊C411yescharacteristic
84C2×C32#11711yescharacteristic
85C3⋊D3—22no—
86C3⋊D3C4×D414yes—
87C24—91no—
88C22×C4—91no—
89C22×C4—94no—
90C22×C4—91no—
91C22×C4—91no—
92C22×C4—91no—
93C22×C4—91no—
94C22×C4—184no—
95C22×C4#15711yescharacteristic, complemented
96C22⋊C4—98no—
97C42—184no—
98C22×C3—24no—
99C22×C3—24no—
100C22×C3—22no—
101C22×C3—24no—
102C2×D3—64no—
103C2×D3—64no—
104C2×D3—64no—
105C2×D3—64no—
106C2×D3—64no—
107C2×D3—632no—
108C2×D3—64no—
109C3×C4—24no—
110C3×C4—24no—
111Dic3—64no—
112Dic3—64no—
113C32C4×C22⋊C411yescharacteristic, complemented, Sylow
114C23—91no—
115C23—91no—
116C23—94no—
117C23—182no—
118C23—182no—
119C23C2×#15711yescharacteristic
120C2×C4—22no—
121C2×C4—91no—
122C2×C4—94no—
123C2×C4—98no—
124C2×C4—91no—
125C2×C4—182no—
126C2×C4—182no—
127C2×C4—182no—
128C2×C4—184no—
129C2×C4—184no—
130C2×C4—182no—
131C2×C4C2×#15711yescharacteristic
132C2×C4C2×#15711yescharacteristic
133C2×C3—28no—
134C2×C3—22no—
135C2×C3—22no—
136C2×C3—22no—
137D3—68no—
138D3—68no—
139C22—21no—
140C22—21no—
141C22—92no—
142C22—92no—
143C22—92no—
144C22—92no—
145C22—188no—
146C22—181no—
147C22—181no—
148C22C4×#15712yescomplemented
149C22C22×#15711yescharacteristic
150C4—21no—
151C4—92no—
152C4—188no—
153C4—181no—
154C4C22⋊#15712yesdirect product factor
155C3—22no—
156C2—22no—
157C2—94no—
158C2—182no—
159C2C2×C4×#15711yescharacteristic
160C2#6428611yescharacteristic
161C2C2×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C4C2×#157
commutatorC2×C32C2×C42
FrattiniC22C22×#157
FittingC22×C32×C4C4
socleC22×C32C22×C4
prime radicalC23×C3⋊D3C22
cosocleC22×C3⋊D3C23
hypercenterC22×C4#157
hypocenterC32C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#157C2semidirect
4. #63781C2semidirect
7. C22×C32×C4C4semidirect
8. C22×C3⋊Dic3C4semidirect
10. C2×C4×C3⋊D3C4semidirect
11. C2×C4×C3⋊D3C4semidirect
14. C22⋊#157C4direct (N × H)
25. C2×#157C2×C4semidirect
47. C22×C32C42semidirect
52. C2×C3⋊D3C42semidirect
58. C32×C4C22⋊C4semidirect
60. C3⋊Dic3C22⋊C4semidirect
95. C22×C4#157semidirect
113. C32C4×C22⋊C4semidirect
148. C22C4×#157semidirect
154. C4C22⋊#157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D32
C2×C22⋊#1572
C2×C4×#1572
#637812
C4×C22⋊C49