Finite Group Databasebeta

← D157⋊#354 #34116405

Subgroups — D157⋊#354 #34116405

Order 20096.

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

normal subgroups only

This group has 284 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⋊#99C212yesmaximal
2#23758180C212yesmaximal, complemented
3#23758179C212yesmaximal, complemented
4#124×D157C211yesmaximal, characteristic
5C2×C22⋊#10597845—22no—
6#19097830C2214yes—
7#19097829—22no—
8C2×Q8×D157C411yescharacteristic, complemented
9C2×D4×D157C2211yescharacteristic
10#19097760C2211yescharacteristic
11#19097759C2211yescharacteristic
12#19097758C411yescharacteristic, complemented
13#19097757—22no—
14C22⋊C4×D157—22no—
15C42×D157C411yescharacteristic, complemented
16#124×C157C411yescharacteristic, complemented
17C22×#10597845—42no—
18C22⋊#10597845—24no—
19C22⋊#10597845—42no—
20C23×D157D412yes—
21C2×Dic314—21no—
22C2×Dic314C2×C411yescharacteristic, complemented
23Q8×D157—41no—
24Q8×D157—41no—
25C2×D628C2311yescharacteristic
26C2×C22⋊D157D412yes—
27D4×D157—41no—
28D4×D157—41no—
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×C4×D157C2×C411yescharacteristic
32C22⋊Dic157—22no—
33#14578931—22no—
34#14578931—22no—
35C4×Dic157—21no—
36C4×Dic157C2×C411yescharacteristic, complemented
37C2×Q8×C157C2×C411yescharacteristic, complemented
38C2×D4×C157C2×C411yescharacteristic
39C22⋊C4×C157—22no—
40C42×C157C2×C411yescharacteristic, complemented
41C2×#10597845—44no—
42C2×#10597845—84no—
43C22×D157—22no—
44C22×D157—22no—
45C22×D157—44no—
46C22×D157C22⋊C411yescharacteristic
47C22×D157C2×D412yes—
48Dic314—42no—
49Dic314—41no—
50D628—41no—
51C22⋊D157—42no—
52C2×Dic157—21no—
53C2×Dic157—21no—
54C2×Dic157C22⋊C411yescharacteristic
55C4×D157—21no—
56C4×D157—21no—
57C4×D157—42no—
58C4×D157—41no—
59C4×D157—41no—
60C23×C157C22⋊C412yes—
61Q8×C157—41no—
62D4×C157—41no—
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157C22×C411yescharacteristic
66C22×C157—22no—
67C22×C157—42no—
68C22×C157C2×C22⋊C411yescharacteristic
69C2×D157—22no—
70C2×D157—22no—
71C2×D157—44no—
72C2×D157—42no—
73C2×D157—82no—
74C2×D157#9911yescharacteristic
75C2×D157#9911yescharacteristic
76#10597845—84no—
77C4×C157—21no—
78C4×C157—41no—
79C4×C157—41no—
80Dic157—21no—
81Dic157—41no—
82Dic157—41no—
83C2×C157—21no—
84C2×C157—42no—
85C2×C157C2×#9911yescharacteristic
86D157—21no—
87D157—42no—
88D157#35412yescomplemented
89C157C2×#35411yescharacteristic, complemented, Sylow
90C2×#354—1571nomaximal, Sylow
91C2×#124—1571no—
92C2×#99—1572no—
93#354—1572no—
94#354—1572no—
95C22×Q8—1571no—
96C22×D4—1571no—
97#124—3142no—
98#124—1571no—
99#124—1571no—
100#124—1571no—
101#124#1059784511yescharacteristic, complemented
102C2×C22⋊C4—3142no—
103C2×C22⋊C4—3142no—
104C2×C42—1571no—
105#99—3142no—
106#99—1574no—
107C24—1572no—
108C2×Q8—3141no—
109C2×Q8—6281no—
110C2×Q8—6281no—
111C2×Q8—1571no—
112C2×Q8C2×#1059784511yescharacteristic, complemented
113C2×D4—6281no—
114C2×D4—6281no—
115C2×D4—1572no—
116C2×D4—1571no—
117C2×D4C2×#1059784511yescharacteristic
118C22×C4—3141no—
119C22×C4—3141no—
120C22×C4—6282no—
121C22×C4—1571no—
122C22⋊C4—22no—
123C22⋊C4—3142no—
124C22⋊C4—3142no—
125C22⋊C4—3142no—
126C22⋊C4—3144no—
127C22⋊C4—6282no—
128C42—3141no—
129C42—1571no—
130C42C2×#1059784511yescharacteristic, complemented
131C23—3142no—
132C23—3142no—
133C23—6284no—
134C23—1571no—
135C23—1572no—
136C23C22⋊#1059784512yes—
137Q8—41no—
138Q8—6281no—
139Q8—6282no—
140D4—41no—
141D4—6281no—
142D4—6282no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3141no—
146C2×C4—3141no—
147C2×C4—3141no—
148C2×C4—3141no—
149C2×C4—6282no—
150C2×C4—6281no—
151C2×C4—6281no—
152C2×C4—6284no—
153C2×C4—1571no—
154C2×C4—12564no—
155C2×C4C22×#1059784511yescharacteristic
156C22—22no—
157C22—42no—
158C22—3142no—
159C22—3142no—
160C22—6282no—
161C22—6284no—
162C22—1571no—
163C22—1571no—
164C22—12562no—
165C22C2×C22⋊#1059784511yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—3141no—
170C4—6281no—
171C4—6281no—
172C4—12564no—
173C2—21no—
174C2—42no—
175C2—3141no—
176C2—6282no—
177C2—1572no—
178C2D157⋊#9911yescharacteristic
subgroupG/H
centerC2D157⋊#99
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#124×C157C4
socleC2×C157C2×#99
prime radicalC2×D4×D157C22
cosocleC2×D628C23
hypercenter#124#10597845
hypocenterC157C2×#354
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #23758180C2semidirect
3. #23758179C2semidirect
8. C2×Q8×D157C4semidirect
12. #19097758C4semidirect
15. C42×D157C4semidirect
16. #124×C157C4semidirect
22. C2×Dic314C2×C4semidirect
36. C4×Dic157C2×C4semidirect
37. C2×Q8×C157C2×C4semidirect
40. C42×C157C2×C4semidirect
88. D157#354semidirect
89. C157C2×#354semidirect
101. #124#10597845semidirect
112. C2×Q8C2×#10597845semidirect
130. C42C2×#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊#992
#237581802
#237581792
#124×D1572
C2×#354157