Finite Group Databasebeta

← #34099296

Subgroups — #34099296

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#23758001C211yesmaximal, characteristic
2#23757624C211yesmaximal, characteristic
3#23757569C211yesmaximal, characteristic
4#23757568C211yesmaximal, characteristic
5#23757018C211yesmaximal, characteristic
6#23757005C211yesmaximal, characteristic
7Q8⋊C8×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097771C2211yescharacteristic
10#19097769—21no—
11#19097763—21no—
12#19097761—22no—
13C4×Dic314—21no—
14C4×Dic314C2211yescharacteristic
15#19097736—21no—
16#19097705—21no—
17#19097704—21no—
18C4⋊#11929434C2211yescharacteristic
19#19097696—22no—
20#19097696—21no—
21#19097695—21no—
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314D411yescharacteristic
28C2×#11929434—21no—
29C4⋊Dic157—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157D412yes—
33C4⋊Dic157D411yescharacteristic
34#14578933—22no—
35#14578933—22no—
36#14578933—22no—
37#14578933—21no—
38C4×Dic157—22no—
39C4×Dic157—21no—
40C2×Q8×C157D411yescharacteristic
41C2×C8×C157—21no—
42C2×C8×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157D411yescharacteristic
45C42×C157—21no—
46C42×C157C2311yescharacteristic
47Dic314—21no—
48Dic314—41no—
49Dic314—41no—
50Dic314—42no—
51Dic314Q1612yes—
52C2×Dic157—21no—
53C2×Dic157—22no—
54C2×Dic157—21no—
55C2×Dic157—41no—
56#11929434—41no—
57Q8×C157—21no—
58Q8×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157—21no—
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—41no—
69C4×C157—41no—
70C4×C157C2×Q1611yescharacteristic
71C4×C157#13511yescharacteristic
72C4×C157#13711yescharacteristic
73C4×C157#13711yescharacteristic
74Dic157—22no—
75Dic157—42no—
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#332—1571no—
88Q8⋊C8—1571no—
89Q8⋊C8D15711yescharacteristic
90C4⋊Q8—3141no—
91C4⋊Q8—1571no—
92C4⋊Q8—1571no—
93#125—3141no—
94#125—3142no—
95C4×Q8—3141no—
96C4×Q8—3141no—
97C4×Q8—1571no—
98C4×Q8C2×D15711yescharacteristic
99#107—3141no—
100#107—3141no—
101C4⋊C8—1571no—
102C4⋊C8C2×D15711yescharacteristic
103#103—3141no—
104#103—3141no—
105#103—3142no—
106C4×C8C2×D15711yescharacteristic
107C2×Q8—3141no—
108C2×Q8—3141no—
109C2×Q8—1571no—
110C2×Q8D62811yescharacteristic
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—1572no—
123C4⋊C4—1571no—
124C4⋊C4D62811yescharacteristic
125C42—21no—
126C42—3142no—
127C42—3141no—
128C42C22×D15711yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—3141no—
132Q8—6282no—
133Q8—6281no—
134Q8—6281no—
135Q8—1572no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—3141no—
139C2×C4—3141no—
140C2×C4—3142no—
141C2×C4—6281no—
142C2×C4D4×D15711yescharacteristic
143C2×C4D4×D15711yescharacteristic
144C2×C4C2×D62811yescharacteristic
145C8—41no—
146C8—41no—
147C8—6281no—
148C22#1909774111yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—3142no—
153C4—6282no—
154C4—6281no—
155C4—12561no—
156C4Q16×D15711yescharacteristic
157C4#1909779311yescharacteristic
158C4#1909780011yescharacteristic
159C4#1909780411yescharacteristic
160C2#2375743011yescharacteristic
161C2#2375743711yescharacteristic
162C2#2375744711yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingQ8⋊C8×C157C2
socle, prime radicalC22×C157#120
hypercenterQ8⋊C8D157
hypocenterC157#1636
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

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
#237580012
#237576242
#237575692
#237575682
#237570182
#237570052
Q8⋊C8×C1572
#1636157