Finite Group Databasebeta

← C4⋊C4×#157 #10593757

Subgroups — C4⋊C4×#157 #10593757

Order 576.

286 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C4⋊#157C211yesmaximal, characteristic
2C2×C4×#157C212yesmaximal
3C2×C4×#157C211yesmaximal, characteristic
4C4⋊C4×C3⋊D3C211yesmaximal, characteristic
5#63781C212yesmaximal
6C22×#157C2212yes—
7C22×#157C2211yescharacteristic
8C22×#157C2211yescharacteristic
9C2×C4×C3⋊D3C2212yes—
10C2×C4×C3⋊D3C2211yescharacteristic
11C4⋊#157C414yescomplemented
12C4×#157—24no—
13C4×#157C414yescomplemented
14C32×C4⋊C4C411yescharacteristic, complemented
15C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16#3750C412yescomplemented
17D3×C4⋊C4—62no—
18C22×C3⋊D3C2311yescharacteristic
19C2×#157—22no—
20C2×#157—21no—
21C2×#157—21no—
22C2×#157—22no—
23C2×#157C2×C412yes—
24C2×#157C2×C414yes—
25C2×#157C2×C412yes—
26C2×#157D412yes—
27C2×#157Q812yes—
28C2×C32×C4C2×C412yes—
29C2×C32×C4C2×C411yescharacteristic
30C2×C3⋊Dic3C2×C412yes—
31C2×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊D3—22no—
33C4×C3⋊D3—22no—
34C4×C3⋊D3C2×C412yes—
35C4×C3⋊D3C2×C412yes—
36C4×C4⋊C4—91nomaximal, Sylow
37C2×C4×D3—62no—
38C2×C4×D3—64no—
39C3×C4⋊C4—22no—
40C4⋊Dic3—62no—
41Dic3⋊C4—64no—
42C22×C32C22×C411yescharacteristic
43C2×C3⋊D3C22×C411yescharacteristic
44C2×C3⋊D3C22×C411yescharacteristic
45C2×C3⋊D3C2×D411yescharacteristic
46C2×C3⋊D3C2×Q811yescharacteristic
47C2×C3⋊D3#4111yescharacteristic
48C2×C3⋊D3#4111yescharacteristic
49#157—22no—
50#157—24no—
51#157C4⋊C414yesdirect product factor
52C32×C4—22no—
53C32×C4C4212yescomplemented
54C3⋊Dic3—22no—
55C3⋊Dic3C4212yescomplemented
56C2×C4⋊C4—91no—
57C2×C4⋊C4—91no—
58C2×C42—91no—
59C2×C42—92no—
60#95—92no—
61C22×D3—62no—
62C2×C3×C4—22no—
63C2×C3×C4—24no—
64C2×Dic3—62no—
65C2×Dic3—64no—
66C4×D3—64no—
67C4×D3—64no—
68C4×D3—124no—
69C4×D3—124no—
70C2×C32C2×C4211yescharacteristic
71C2×C32C4×D411yescharacteristic
72C2×C32C4×Q811yescharacteristic
73C3⋊D3C2×C4⋊C411yescharacteristic
74C3⋊D3#11711yescharacteristic
75C3⋊D3C4×D411yescharacteristic
76C3⋊D3C4×Q811yescharacteristic
77C22×C4—91no—
78C22×C4—91no—
79C22×C4—91no—
80C22×C4—92no—
81C22×C4—92no—
82C4⋊C4—94no—
83C4⋊C4—92no—
84C4⋊C4—91no—
85C4⋊C4#15711yescharacteristic, direct product factor
86C42—94no—
87C42—184no—
88C22×C3—22no—
89C2×D3—62no—
90C2×D3—62no—
91C2×D3—62no—
92C2×D3—62no—
93C2×D3—62no—
94C2×D3—62no—
95C3×C4—24no—
96C3×C4—44no—
97Dic3—64no—
98Dic3—124no—
99C32C4×C4⋊C411yescharacteristic, complemented, Sylow
100C23—91no—
101C2×C4—92no—
102C2×C4—92no—
103C2×C4—92no—
104C2×C4—91no—
105C2×C4—92no—
106C2×C4—92no—
107C2×C4—92no—
108C2×C4—94no—
109C2×C4—92no—
110C2×C4—182no—
111C2×C4—182no—
112C2×C4—182no—
113C2×C4—181no—
114C2×C4—181no—
115C2×C4—182no—
116C2×C4C2×#15712yes—
117C2×C4C2×#15711yescharacteristic
118C2×C3—22no—
119C2×C3—22no—
120C2×C3—22no—
121D3—62no—
122D3—62no—
123D3—62no—
124D3—62no—
125C22—91no—
126C22—91no—
127C22—91no—
128C22—91no—
129C22—91no—
130C22—91no—
131C22C22×#15711yescharacteristic
132C4—22no—
133C4—94no—
134C4—92no—
135C4—184no—
136C4—182no—
137C4—182no—
138C4C4×#15712yescomplemented
139C3—22no—
140C2—91no—
141C2—91no—
142C2—91no—
143C2—91no—
144C2C2×C4×#15711yescharacteristic
145C2D4×#15711yescharacteristic
146C2Q8×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C22×#157
commutatorC2×C32C2×C42
FittingC32×C4⋊C4C4
socleC22×C32C22×C4
prime radical, cosocleC22×C3⋊D3C23
hypercenterC4⋊C4#157
hypocenterC32C4×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
11. C4⋊#157C4semidirect
13. C4×#157C4semidirect
14. C32×C4⋊C4C4semidirect
15. C4⋊(C3⋊Dic3)C4semidirect
16. #3750C4semidirect
51. #157C4⋊C4direct (N × H)
53. C32×C4C42semidirect
55. C3⋊Dic3C42semidirect
85. C4⋊C4#157direct (N × H)
99. C32C4×C4⋊C4semidirect
138. C4C4×#157semidirect

Maximal subgroups

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

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