Finite Group Databasebeta

← #34099467

Subgroups — #34099467

Order 20096.

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

normal subgroups only

This group has 184 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
1#23758027C211yesmaximal, characteristic
2#23757679C211yesmaximal, characteristic, complemented
3#23757635C211yesmaximal, characteristic
4#23757015C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic
7#491×C157C211yesmaximal, characteristic, complemented
8#19097770—21no—
9#19097766—21no—
10#19097766—21no—
11#19097763C2211yescharacteristic
12#19097759C2211yescharacteristic
13#19097756—21no—
14#19097751—21no—
15#19097749—21no—
16#19097704—21no—
17#19097702—21no—
18#19097694—21no—
19#19097691—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23#125×C157C2211yescharacteristic
24#103×C157—21no—
25#103×C157—21no—
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C2×D628D411yescharacteristic
30C2×C4×D157—21no—
31C2×#11929434—21no—
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35C4⋊Dic157D411yescharacteristic
36#14578933—21no—
37#14578933—21no—
38#14578933—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42#14578931—21no—
43#14578931—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
54C22×D157—21no—
55Dic314—41no—
56Dic314—81no—
57D628—41no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C4×D157—81no—
62#11929434—22no—
63#11929434—41no—
64Q8×C157—42no—
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—41no—
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C8×C157—41no—
72C22×C157#12011yescharacteristic
73C2×D157—41no—
74C2×D157—41no—
75C2×D157—41no—
76C4×C157—21no—
77C4×C157—21no—
78C4×C157—21no—
79C4×C157—41no—
80C4×C157—41no—
81C4×C157—81no—
82Dic157—41no—
83Dic157—41no—
84Dic157—41no—
85C2×C157#45411yescharacteristic
86C2×C157#45511yescharacteristic
87C2×C157#45611yescharacteristic
88D157—81no—
89C157#166411yescharacteristic, complemented, Sylow
90#1664—1571nomaximal, Sylow
91#563—1571no—
92#501—1571no—
93#491D15711yescharacteristic, complemented
94#489—1571no—
95#330—1571no—
96#330—1571no—
97#329—1571no—
98C4⋊Q8—3141no—
99C4⋊Q8C2×D15711yescharacteristic
100#126—3141no—
101#126—3141no—
102#125—1571no—
103#125C2×D15711yescharacteristic
104#124—1571no—
105#123—3141no—
106C22⋊Q8—3141no—
107C22⋊Q8—3141no—
108#107—3141no—
109#106—3141no—
110#103—21no—
111#103—21no—
112#103—3141no—
113#102—3141no—
114#97—1571no—
115#97—1571no—
116#97C2×D15711yescharacteristic
117C2×Q8—21no—
118C2×Q8—3141no—
119C2×Q8—1571no—
120C2×D4—1571no—
121C22×C4—3141no—
122C2×C8—21no—
123C2×C8—3141no—
124C2×C8—3141no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4—3141no—
132C4⋊C4—3141no—
133C4⋊C4—1571no—
134C4⋊C4—1571no—
135C4⋊C4C22⋊D15711yescharacteristic
136C4⋊C4C22⋊D15711yescharacteristic
137C22⋊C4—3141no—
138C22⋊C4—3141no—
139C22⋊C4—3141no—
140C22⋊C4—3141no—
141C22⋊C4—3141no—
142C42—3141no—
143C42C22×D15711yescharacteristic
144C23—3141no—
145Q8—42no—
146Q8—6281no—
147Q8—12561no—
148D4—6281no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—3141no—
153C2×C4—3141no—
154C2×C4—3141no—
155C2×C4—12561no—
156C2×C4D4×D15711yescharacteristic
157C2×C4D4×D15711yescharacteristic
158C2×C4C2×C22⋊D15711yescharacteristic
159C8—41no—
160C8—3142no—
161C8—6281no—
162C22—6281no—
163C22—6281no—
164C22—6281no—
165C22#1909773911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—6281no—
173C4—6281no—
174C4—6281no—
175C2—12561no—
176C2#2375744511yescharacteristic
177C2#2375744911yescharacteristic
178C2#2375745411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#491×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#491D157
hypocenterC157#1664
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #23757679C2semidirect
4. #23757015C2semidirect
5. #23757014C2semidirect
7. #491×C157C2semidirect
89. C157#1664semidirect
93. #491D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576792
#237576352
#237570152
#237570142
#237570122
#491×C1572
#1664157