Finite Group Databasebeta

← #34099463

Subgroups — #34099463

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#23757679C211yesmaximal, characteristic
3#23757641C211yesmaximal, characteristic
4#23757015C211yesmaximal, characteristic
5#23757014C211yesmaximal, characteristic
6#23757014C211yesmaximal, characteristic
7#501×C157C211yesmaximal, characteristic
8#19097763C2211yescharacteristic
9#19097763C2211yescharacteristic
10#19097762—21no—
11#19097762—21no—
12#19097761—21no—
13#19097761—21no—
14#19097761—21no—
15#19097761—21no—
16#19097704—21no—
17#19097702—21no—
18#19097695—21no—
19#19097695—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23#125×C157C2211yescharacteristic
24#107×C157—21no—
25#106×C157—21no—
26#97×C157C2211yescharacteristic
27C2×#11929434—21no—
28C2×#11929434—21no—
29C4⋊Dic157—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157D411yescharacteristic
32C4⋊Dic157D411yescharacteristic
33C4⋊Dic157D411yescharacteristic
34C4⋊Dic157D411yescharacteristic
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43C4×Dic157—21no—
44C4×Dic157—21no—
45C2×Q8×C157—21no—
46C2×C8×C157—21no—
47C4⋊C4×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157D411yescharacteristic
52C4⋊C4×C157D411yescharacteristic
53C42×C157C2311yescharacteristic
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58#11929434—22no—
59#11929434—41no—
60Q8×C157—42no—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—41no—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C8×C157—22no—
68C22×C157#12011yescharacteristic
69C4×C157—21no—
70C4×C157—21no—
71C4×C157—21no—
72C4×C157—41no—
73C4×C157—41no—
74C4×C157—81no—
75Dic157—41no—
76Dic157—41no—
77Dic157—41no—
78Dic157—41no—
79C2×C157#45411yescharacteristic
80C2×C157#45611yescharacteristic
81C2×C157#45611yescharacteristic
82C157#166311yescharacteristic, complemented, Sylow
83#1663—1571nomaximal, Sylow
84#564—1571no—
85#501—1571no—
86#501D15711yescharacteristic
87#491—1571no—
88#330—1571no—
89#330—1571no—
90#330—1571no—
91C4⋊Q8C2×D15711yescharacteristic
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—21no—
102#107—3141no—
103#106—21no—
104#106—3141no—
105#103—3141no—
106#103—3141no—
107#97—1571no—
108#97—1571no—
109#97C2×D15711yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—3141no—
113C2×C8—3141no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
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⋊C4C22⋊D15711yescharacteristic
133C4⋊C4C22⋊D15711yescharacteristic
134C42—3141no—
135C42—3141no—
136C42C22×D15711yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—3141no—
142C2×C4—3141no—
143C2×C4—3141no—
144C2×C4—3141no—
145C2×C4D4×D15711yescharacteristic
146C2×C4D4×D15711yescharacteristic
147C2×C4C2×C22⋊D15711yescharacteristic
148C8—22no—
149C8—3142no—
150C8—6281no—
151C22#1909773911yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—6281no—
159C4—6281no—
160C4—6281no—
161C4—6281no—
162C2#2375744411yescharacteristic
163C2#2375745411yescharacteristic
164C2#2375745511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#501×C157C2
socle, prime radicalC22×C157#120
hypercenter#501D157
hypocenterC157#1663
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #501

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
#237576792
#237576412
#237570152
#237570142
#501×C1572
#1663157