Finite Group Databasebeta

← D157⋊#356 #34116425

Subgroups — D157⋊#356 #34116425

Order 20096.

240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D157⋊#101C212yesmaximal
2#23758184C212yesmaximal, complemented
3#23758183C212yesmaximal, complemented
4C4⋊Q8×D157C211yesmaximal, characteristic
5D157⋊M16—22no—
6#19097832—22no—
7#19097832C2214yes—
8C2×Q8×D157C411yescharacteristic
9C2×Q8×D157C2211yescharacteristic
10#19097771C2211yescharacteristic
11#19097770—22no—
12#19097769C411yescharacteristic
13#19097769C2211yescharacteristic
14C4⋊C4×D157—22no—
15C42×D157C411yescharacteristic
16C4⋊Q8×C157C411yescharacteristic
17#14578964—42no—
18#14578963—24no—
19D157⋊C8—42no—
20C2×Dic314—21no—
21C2×Dic314C2×C411yescharacteristic
22C2×Dic314D412yes—
23C2×Dic314C2311yescharacteristic
24Q8×D157—41no—
25Q8×D157—41no—
26Q8×D157—41no—
27Q8×D157—41no—
28C2×C4×D157—21no—
29C2×C4×D157—21no—
30C2×C4×D157C2×C411yescharacteristic
31C2×C4×D157D412yes—
32C4⋊Dic157—22no—
33#14578933—22no—
34#14578933—22no—
35C4×Dic157—21no—
36C4×Dic157C2×C411yescharacteristic
37C2×Q8×C157C2×C411yescharacteristic
38C2×Q8×C157C2×C411yescharacteristic
39C4⋊C4×C157—22no—
40C42×C157C2×C411yescharacteristic
41#11929441—44no—
42C22×D157C22⋊C411yescharacteristic
43Dic314—42no—
44Dic314—41no—
45Dic314—42no—
46Dic314—41no—
47C2×Dic157—21no—
48C2×Dic157—21no—
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C2×D412yes—
51C4×D157—24no—
52C4×D157—21no—
53C4×D157—21no—
54C4×D157—22no—
55C4×D157—22no—
56C4×D157—41no—
57C4×D157—41no—
58Q8×C157—41no—
59Q8×C157—41no—
60C2×C4×C157—21no—
61C2×C4×C157—21no—
62C2×C4×C157C22⋊C412yes—
63C2×C4×C157C22×C411yescharacteristic
64C22×C157C2×C22⋊C411yescharacteristic
65C2×D157—22no—
66C2×D157#9911yescharacteristic
67C2×D157#9911yescharacteristic
68C4×C157—22no—
69C4×C157—22no—
70C4×C157—21no—
71C4×C157—41no—
72Dic157—22no—
73Dic157—21no—
74Dic157—22no—
75Dic157—41no—
76C2×C157—21no—
77C2×C157C2×#9911yescharacteristic
78D157—21no—
79D157#35612yescomplemented
80C157C2×#35611yescharacteristic, complemented, Sylow
81C2×#356—1571nomaximal, Sylow
82C2×C4⋊Q8—1571no—
83C2×#101—1572no—
84#356—1572no—
85#356—1572no—
86C22×Q8—1571no—
87C22×Q8—1571no—
88C2×M16—3142no—
89C4⋊Q8—3142no—
90C4⋊Q8—1571no—
91C4⋊Q8—1571no—
92C4⋊Q8—1571no—
93C4⋊Q8#1059784511yescharacteristic
94C2×C4⋊C4—3142no—
95C2×C42—1571no—
96#101—3142no—
97#101—1574no—
98C2×Q8—3141no—
99C2×Q8—6281no—
100C2×Q8—6281no—
101C2×Q8—6281no—
102C2×Q8—6281no—
103C2×Q8—1571no—
104C2×Q8—1572no—
105C2×Q8—1571no—
106C2×Q8C2×#1059784511yescharacteristic
107C2×Q8C2×#1059784511yescharacteristic
108C22×C4—3141no—
109C22×C4—3141no—
110C22×C4—1572no—
111C22×C4—1571no—
112M16—3144no—
113M16—6282no—
114C2×C8—6282no—
115C4⋊C4—22no—
116C4⋊C4—3142no—
117C4⋊C4—3142no—
118C4⋊C4—3142no—
119C42—3141no—
120C42—1571no—
121C42C2×#1059784511yescharacteristic
122C23—1571no—
123Q8—41no—
124Q8—41no—
125Q8—6282no—
126Q8—6281no—
127Q8—6281no—
128Q8—6282no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—3144no—
132C2×C4—3142no—
133C2×C4—3142no—
134C2×C4—3141no—
135C2×C4—3141no—
136C2×C4—3141no—
137C2×C4—3141no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4—1571no—
141C2×C4—1572no—
142C2×C4C22⋊#1059784512yes—
143C2×C4C22×#1059784511yescharacteristic
144C8—6284no—
145C22—3142no—
146C22—1571no—
147C22—1571no—
148C22C2×C22⋊#1059784511yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—3142no—
154C4—3142no—
155C4—3141no—
156C4—6281no—
157C2—21no—
158C2—3141no—
159C2—1572no—
160C2D157⋊#9911yescharacteristic
subgroupG/H
centerC2D157⋊#99
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC4⋊Q8×C157C4
socleC2×C157C2×#99
prime radicalC22×D157C22⋊C4
cosocleC2×Dic314C23
hypercenterC4⋊Q8#10597845
hypocenterC157C2×#356
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23758184C2semidirect
3. #23758183C2semidirect
79. D157#356semidirect
80. C157C2×#356semidirect

Maximal subgroups

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

subgroupindex
D157⋊#1012
#237581842
#237581832
C4⋊Q8×D1572
C2×#356157