Finite Group Databasebeta

← #34098843

Subgroups — #34098843

Order 20096.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#23757828C211yesmaximal, characteristic
2#23757329C211yesmaximal, characteristic
3#23757325C211yesmaximal, characteristic
4#23757021C211yesmaximal, characteristic, complemented
5#23757021C211yesmaximal, characteristic, complemented
6#23757019C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8#19097771C2211yescharacteristic
9#19097762—21no—
10#19097751C412yes—
11#19097747—21no—
12Q8×Dic157—21no—
13#19097736C412yes—
14#19097729—21no—
15C42×D157C2211yescharacteristic
16C4⋊#11929434C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18#19097683—21no—
19#19097683—21no—
20#19097681—21no—
21C8×Dic157—21no—
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314C2×C412yes—
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157D411yescharacteristic
29C2×#11929434—21no—
30C2×#11929434—21no—
31C4⋊Dic157—22no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34#14578933—22no—
35#14578931—22no—
36C4×Dic157—22no—
37C4×Dic157C2×C411yescharacteristic
38C4×Dic157D411yescharacteristic
39C4×Dic157D411yescharacteristic
40C2×Q8×C157—21no—
41C2×C8×C157—21no—
42C2×C8×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157C2×C412yes—
45C42×C157C2311yescharacteristic
46C22×D157C22⋊C411yescharacteristic
47Dic314—42no—
48C2×Dic157—22no—
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C22⋊C411yescharacteristic
51C2×Dic157C22⋊C411yescharacteristic
52C4×D157—21no—
53C4×D157—21no—
54C4×D157—21no—
55C4×D157—21no—
56C4×D157—41no—
57#11929434—41no—
58#11929434—41no—
59Q8×C157—41no—
60Q8×C157—41no—
61C2×C4×C157—22no—
62C2×C4×C157C22×C411yescharacteristic
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C8×C157—41no—
66C8×C157—41no—
67C22×C157C2×C22⋊C411yescharacteristic
68C2×D157—21no—
69C2×D157—21no—
70C2×D157—21no—
71C4×C157—21no—
72C4×C157—42no—
73C4×C157#13511yescharacteristic
74C4×C157#13511yescharacteristic
75C4×C157#13711yescharacteristic
76C4×C157#13711yescharacteristic
77Dic157—21no—
78Dic157—21no—
79Dic157—21no—
80Dic157—42no—
81C2×C157#41311yescharacteristic
82C2×C157#41611yescharacteristic
83C2×C157#41911yescharacteristic
84D157—41no—
85C157#155411yescharacteristic, complemented, Sylow
86#1554—1571nomaximal, Sylow
87#533—1571no—
88#432—1571no—
89#431—1571no—
90#333—1571no—
91#333—1571no—
92#332—1571no—
93#332D15711yescharacteristic, complemented
94C4⋊Q8—1571no—
95C4⋊Q8C2×D15711yescharacteristic
96#125—3141no—
97C22⋊Q8—3141no—
98C22⋊Q8—1572no—
99C4×Q8—3141no—
100C4×Q8—1572no—
101#117—3141no—
102C2×C42—1571no—
103C4⋊C8—1571no—
104C4⋊C8—1571no—
105C4⋊C8C2×D15711yescharacteristic
106C4⋊C8C2×D15711yescharacteristic
107C22⋊C8—3141no—
108C22⋊C8—3141no—
109#97—3141no—
110C4×C8—3141no—
111C2×Q8—21no—
112C2×Q8—1572no—
113C22×C4—1571no—
114C22×C4—1571no—
115C22×C4—1571no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—3141no—
119C2×C8—3141no—
120C4⋊C4—21no—
121C4⋊C4—3142no—
122C4⋊C4—3142no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4C4×D15712yes—
126C22⋊C4—3142no—
127C42—3142no—
128C42—1571no—
129C42—1571no—
130C42—1571no—
131C42C22×D15711yescharacteristic
132C23—1571no—
133Q8—41no—
134Q8—41no—
135Q8—6282no—
136C2×C4—22no—
137C2×C4—3141no—
138C2×C4—3141no—
139C2×C4—3141no—
140C2×C4—3141no—
141C2×C4—3142no—
142C2×C4—6281no—
143C2×C4—1571no—
144C2×C4—1571no—
145C2×C4—1571no—
146C2×C4C2×C4×D15711yescharacteristic
147C2×C4D4×D15711yescharacteristic
148C2×C4D4×D15711yescharacteristic
149C8—41no—
150C8—41no—
151C8—6281no—
152C8—6281no—
153C22—3141no—
154C22—3141no—
155C22—3141no—
156C22C22⋊C4×D15711yescharacteristic
157C4—21no—
158C4—42no—
159C4—3141no—
160C4—3141no—
161C4—3141no—
162C4—6282no—
163C4#1909779011yescharacteristic
164C4#1909779211yescharacteristic
165C4#1909780011yescharacteristic
166C4#1909780311yescharacteristic
167C2—6281no—
168C2#2375725611yescharacteristic
169C2#2375726611yescharacteristic
170C2#2375728011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenter#332D157
hypocenterC157#1554
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #23757021C2semidirect
5. #23757021C2semidirect
6. #23757019C2semidirect
7. #332×C157C2semidirect
85. C157#1554semidirect
93. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237578282
#237573292
#237573252
#237570212
#237570192
#332×C1572
#1554157