Finite Group Databasebeta

← #34099466

Subgroups — #34099466

Order 20096.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C157⋊#564C211yesmaximal, characteristic
2#23757683C211yesmaximal, characteristic
3#23757682C211yesmaximal, characteristic
4#23757642C211yesmaximal, characteristic
5#23757014C211yesmaximal, characteristic
6#23757014C211yesmaximal, characteristic
7#330×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097763C2211yescharacteristic
10#19097763C2211yescharacteristic
11#19097762—21no—
12#19097762—21no—
13#19097761—21no—
14#19097761—21no—
15#19097761—21no—
16#19097761—21no—
17#19097705—21no—
18#19097704—21no—
19#19097703—21no—
20#19097702—21no—
21#19097696—21no—
22#19097696—21no—
23#19097682C2211yescharacteristic
24#125×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×#11929434—21no—
29C4⋊Dic157—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157D411yescharacteristic
34C4⋊Dic157D411yescharacteristic
35C4⋊Dic157D411yescharacteristic
36C4⋊Dic157D411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578933—21no—
44#14578933—21no—
45C4×Dic157—21no—
46C4×Dic157—21no—
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157D411yescharacteristic
52C4⋊C4×C157D411yescharacteristic
53C42×C157C2311yescharacteristic
54Dic314—42no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—41no—
60#11929434—22no—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C8×C157—22no—
67C8×C157—41no—
68C22×C157#12011yescharacteristic
69C4×C157—21no—
70C4×C157—21no—
71C4×C157—21no—
72C4×C157—41no—
73C4×C157—41no—
74Dic157—41no—
75Dic157—41no—
76Dic157—41no—
77Dic157—41no—
78Dic157—81no—
79C2×C157#45411yescharacteristic
80C2×C157#45611yescharacteristic
81C2×C157#45611yescharacteristic
82C157#166311yescharacteristic, complemented, Sylow
83#1663—1571nomaximal, Sylow
84#564—1571no—
85#501—1571no—
86#501—1571no—
87#491—1571no—
88#330—1571no—
89#330—1571no—
90#330D15711yescharacteristic
91C4⋊Q8—1571no—
92#125—3141no—
93#125—3141no—
94#125—3141no—
95#125—3141no—
96#125—3141no—
97#125—3141no—
98#125—1571no—
99#125—1571no—
100#125C2×D15711yescharacteristic
101#107—3141no—
102#107—3141no—
103#106—3141no—
104#106—3141no—
105#103—3141no—
106#103—3141no—
107#97—1571no—
108#97C2×D15711yescharacteristic
109#97C2×D15711yescharacteristic
110C2×Q8—3141no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—3141no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—3141no—
117C4⋊C4—3141no—
118C4⋊C4—3141no—
119C4⋊C4—3141no—
120C4⋊C4—3141no—
121C4⋊C4—3141no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—1571no—
129C4⋊C4—1571no—
130C4⋊C4—1571no—
131C4⋊C4—1571no—
132C4⋊C4D62811yescharacteristic
133C4⋊C4D62811yescharacteristic
134C42—3141no—
135C42—3141no—
136C42C22×D15711yescharacteristic
137Q8—6282no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—3141no—
141C2×C4—3141no—
142C2×C4—3141no—
143C2×C4—3141no—
144C2×C4—6281no—
145C2×C4D4×D15711yescharacteristic
146C2×C4D4×D15711yescharacteristic
147C2×C4C2×D62811yescharacteristic
148C8—22no—
149C8—41no—
150C8—3142no—
151C22#1909774111yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—6281no—
158C4—6281no—
159C4—6281no—
160C4—6281no—
161C4—12561no—
162C2#2375744711yescharacteristic
163C2#2375745711yescharacteristic
164C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socle, prime radicalC22×C157#120
hypercenter#330D157
hypocenterC157#1663
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
82. C157#1663semidirect

Maximal subgroups

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

subgroupindex
C157⋊#5642
#237576832
#237576822
#237576422
#237570142
#330×C1572
#1663157