Finite Group Databasebeta

← #34099295

Subgroups — #34099295

Order 20096.

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

normal subgroups only

This group has 188 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#23757625C211yesmaximal, characteristic
3#23757569C211yesmaximal, characteristic
4#23757569C211yesmaximal, characteristic
5#23757003C211yesmaximal, characteristic
6#23757003C211yesmaximal, characteristic
7#332×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097769—21no—
10#19097762—21no—
11#19097761—22no—
12Q8×Dic157—21no—
13C4×Dic314C2211yescharacteristic
14C4×Dic314C2211yescharacteristic
15#19097736—21no—
16#19097705—21no—
17#19097705—21no—
18#19097696—21no—
19#19097696—21no—
20#19097694—22no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×Dic314D411yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×#11929434—21no—
29C4⋊Dic157—22no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157D411yescharacteristic
33C4⋊Dic157D411yescharacteristic
34#14578933—22no—
35#14578933—22no—
36#14578933—21no—
37#14578933—21no—
38C4×Dic157—22no—
39C4×Dic157—21no—
40C4×Dic157—21no—
41C2×Q8×C157—21no—
42C2×C8×C157—21no—
43C2×C8×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157D412yes—
46C42×C157C2311yescharacteristic
47Dic314—21no—
48Dic314—21no—
49Dic314—21no—
50Dic314—42no—
51Dic314Q1612yes—
52C2×Dic157—21no—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157—41no—
57#11929434—41no—
58Q8×C157—41no—
59Q8×C157—41no—
60C2×C4×C157—22no—
61C2×C4×C157C2×D411yescharacteristic
62C2×C4×C157C2×D411yescharacteristic
63C2×C4×C157C2×D411yescharacteristic
64C8×C157—41no—
65C8×C157—41no—
66C22×C157#12011yescharacteristic
67C4×C157—21no—
68C4×C157—42no—
69C4×C157C2×Q1611yescharacteristic
70C4×C157#13511yescharacteristic
71C4×C157#13711yescharacteristic
72C4×C157#13711yescharacteristic
73Dic157—22no—
74Dic157—41no—
75Dic157—41no—
76Dic157—41no—
77Dic157—81no—
78C2×C157#45111yescharacteristic
79C2×C157#45211yescharacteristic
80C2×C157#45411yescharacteristic
81C157#163611yescharacteristic, complemented, Sylow
82#1636—1571nomaximal, Sylow
83#557—1571no—
84#487—1571no—
85#477—1571no—
86#477—1571no—
87#332D15711yescharacteristic
88Q8⋊C8—1571no—
89Q8⋊C8—1571no—
90C4⋊Q8—3141no—
91C4⋊Q8—1571no—
92C4⋊Q8C2×D15711yescharacteristic
93#125—3141no—
94#125—3142no—
95C4×Q8—3141no—
96C4×Q8—3141no—
97C4×Q8—1571no—
98C4×Q8—1571no—
99#107—3141no—
100#107—3141no—
101C4⋊C8C2×D15711yescharacteristic
102C4⋊C8C2×D15711yescharacteristic
103#103—3141no—
104#103—3141no—
105#103—3142no—
106C4×C8—1571no—
107C2×Q8—21no—
108C2×Q8—3141no—
109C2×Q8—1571no—
110C2×Q8—1571no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—3141no—
114C4⋊C4—21no—
115C4⋊C4—3142no—
116C4⋊C4—3142no—
117C4⋊C4—3142no—
118C4⋊C4—3141no—
119C4⋊C4—3141no—
120C4⋊C4—3141no—
121C4⋊C4—3141no—
122C4⋊C4—1571no—
123C4⋊C4—1571no—
124C4⋊C4D62812yes—
125C42—3142no—
126C42—3141no—
127C42—3141no—
128C42C22×D15711yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—3141no—
132Q8—3141no—
133Q8—3141no—
134Q8—6282no—
135Q8—1572no—
136C2×C4—22no—
137C2×C4—3141no—
138C2×C4—3141no—
139C2×C4—3141no—
140C2×C4—3141no—
141C2×C4—6281no—
142C2×C4D4×D15711yescharacteristic
143C2×C4D4×D15711yescharacteristic
144C2×C4C2×D62811yescharacteristic
145C8—41no—
146C8—41no—
147C8—6281no—
148C22#1909774111yescharacteristic
149C4—21no—
150C4—42no—
151C4—3142no—
152C4—6281no—
153C4—6281no—
154C4—6281no—
155C4—12561no—
156C4Q16×D15711yescharacteristic
157C4#1909779011yescharacteristic
158C4#1909780011yescharacteristic
159C4#1909780011yescharacteristic
160C2#2375743011yescharacteristic
161C2#2375743611yescharacteristic
162C2#2375744811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#332×C157C2
socle, prime radicalC22×C157#120
hypercenter#332D157
hypocenterC157#1636
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
81. C157#1636semidirect

Maximal subgroups

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

subgroupindex
#237579982
#237576252
#237575692
#237570032
#332×C1572
#1636157