Finite Group Databasebeta

← #34099414

Subgroups — #34099414

Order 20096.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757998C211yesmaximal, characteristic
2#23757669C211yesmaximal, characteristic
3#23757559C211yesmaximal, characteristic
4#23757484C211yesmaximal, characteristic
5#23757003C211yesmaximal, characteristic
6#23757003C211yesmaximal, characteristic
7#332×C157C211yesmaximal, characteristic
8C2×Dic628—21no—
9#19097771C2211yescharacteristic
10#19097769—21no—
11#19097762—21no—
12#19097761—22no—
13Q8×Dic157—21no—
14C4×Dic314C2211yescharacteristic
15C4×Dic314C2211yescharacteristic
16#19097736—21no—
17#19097703—21no—
18#19097702—22no—
19#19097696—21no—
20#19097696—21no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×Dic314D411yescharacteristic
27C2×Dic314D411yescharacteristic
28Dic628—42no—
29C2×#11929434—21no—
30C4⋊Dic157—22no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157D411yescharacteristic
34C4⋊Dic157D411yescharacteristic
35#14578933—22no—
36#14578933—22no—
37#14578933—21no—
38#14578933—21no—
39C4×Dic157—22no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C2×Q8×C157—21no—
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157D412yes—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—21no—
50Dic314—21no—
51Dic314—41no—
52Dic314—41no—
53Dic314SD1612yes—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—41no—
59#11929434—22no—
60Q8×C157—41no—
61Q8×C157—41no—
62C2×C4×C157—22no—
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C8×C157—41no—
67C8×C157—41no—
68C22×C157#12011yescharacteristic
69C4×C157—21no—
70C4×C157—42no—
71C4×C157C2×SD1611yescharacteristic
72C4×C157#13511yescharacteristic
73C4×C157#13711yescharacteristic
74C4×C157#13711yescharacteristic
75Dic157—22no—
76Dic157—41no—
77Dic157—41no—
78Dic157—41no—
79Dic157—81no—
80C2×C157#44811yescharacteristic
81C2×C157#45211yescharacteristic
82C2×C157#45611yescharacteristic
83C157#165311yescharacteristic, complemented, Sylow
84#1653—1571nomaximal, Sylow
85#557—1571no—
86#498—1571no—
87#475—1571no—
88#462—1571no—
89#332D15711yescharacteristic
90Q8⋊C8—1571no—
91Q8⋊C8—1571no—
92C2×Q16—3141no—
93C4⋊Q8—3141no—
94C4⋊Q8—1571no—
95C4⋊Q8C2×D15711yescharacteristic
96#125—3141no—
97#125—3142no—
98C4×Q8—3141no—
99C4×Q8—3141no—
100C4×Q8—1571no—
101C4×Q8—1571no—
102#106—3141no—
103#106—3142no—
104C4⋊C8C2×D15711yescharacteristic
105C4⋊C8C2×D15711yescharacteristic
106#103—3141no—
107#103—3141no—
108C4×C8—1571no—
109C2×Q8—21no—
110C2×Q8—3141no—
111C2×Q8—1571no—
112C2×Q8—1571no—
113Q16—6282no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—3141no—
117C4⋊C4—21no—
118C4⋊C4—3142no—
119C4⋊C4—3142no—
120C4⋊C4—3142no—
121C4⋊C4—3141no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—1571no—
126C4⋊C4—1571no—
127C4⋊C4D62812yes—
128C42—3142no—
129C42—3141no—
130C42—3141no—
131C42C22×D15711yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—3141no—
135Q8—3141no—
136Q8—3141no—
137Q8—6281no—
138Q8—6281no—
139Q8—1572no—
140C2×C4—22no—
141C2×C4—3141no—
142C2×C4—3141no—
143C2×C4—3141no—
144C2×C4—3141no—
145C2×C4—6281no—
146C2×C4D4×D15711yescharacteristic
147C2×C4D4×D15711yescharacteristic
148C2×C4C2×D62811yescharacteristic
149C8—41no—
150C8—41no—
151C8—3142no—
152C22#1909774111yescharacteristic
153C4—21no—
154C4—42no—
155C4—3142no—
156C4—6281no—
157C4—6281no—
158C4—6281no—
159C4—12561no—
160C4SD16×D15711yescharacteristic
161C4#1909779011yescharacteristic
162C4#1909780011yescharacteristic
163C4#1909780311yescharacteristic
164C2#2375741311yescharacteristic
165C2#2375743611yescharacteristic
166C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#332×C157C2
socle, prime radicalC22×C157#120
hypercenter#332D157
hypocenterC157#1653
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
83. C157#1653semidirect

Maximal subgroups

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

subgroupindex
#237579982
#237576692
#237575592
#237574842
#237570032
#332×C1572
#1653157