Finite Group Databasebeta

← #34099472

Subgroups — #34099472

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#23757683C211yesmaximal, characteristic, complemented
3#23757642C211yesmaximal, characteristic, complemented
4#23757633C211yesmaximal, characteristic
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic
7#330×C157C211yesmaximal, characteristic, complemented
8#19097771C2211yescharacteristic
9#19097770—21no—
10#19097766—21no—
11#19097766—21no—
12#19097763C2211yescharacteristic
13#19097759C2211yescharacteristic
14#19097756—21no—
15#19097751—21no—
16#19097749—21no—
17#19097704—21no—
18#19097702—21no—
19#19097696—21no—
20#19097696—21no—
21#19097696—21no—
22#19097693—21no—
23#19097682C2211yescharacteristic
24#125×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314D411yescharacteristic
30C2×D628D411yescharacteristic
31C2×C4×D157—21no—
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578931—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157—21no—
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157D411yescharacteristic
52C4⋊C4×C157D411yescharacteristic
53C42×C157C2311yescharacteristic
54C22×D157—21no—
55Dic314—41no—
56Dic314—42no—
57Dic314—81no—
58D628—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—41no—
63C4×D157—81no—
64#11929434—22no—
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C8×C157—41no—
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—
81Dic157—41no—
82Dic157—41no—
83Dic157—41no—
84Dic157—81no—
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#491—1571no—
94#489—1571no—
95#330—1571no—
96#330D15711yescharacteristic, complemented
97#329—1571no—
98C4⋊Q8—3141no—
99C4⋊Q8—1571no—
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—3141no—
111#103—3141no—
112#103—3141no—
113#102—3141no—
114#97—1571no—
115#97C2×D15711yescharacteristic
116#97C2×D15711yescharacteristic
117C2×Q8—3141no—
118C2×Q8—3141no—
119C2×Q8—1571no—
120C2×D4—1571no—
121C22×C4—3141no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—3141no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3141no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4—3141no—
132C4⋊C4—3141no—
133C4⋊C4—1571no—
134C4⋊C4—1571no—
135C4⋊C4D62811yescharacteristic
136C4⋊C4D62811yescharacteristic
137C22⋊C4—3141no—
138C22⋊C4—3141no—
139C22⋊C4—3141no—
140C22⋊C4—3141no—
141C22⋊C4—3141no—
142C42—3141no—
143C42C22×D15711yescharacteristic
144C23—3141no—
145Q8—6281no—
146Q8—6282no—
147Q8—12561no—
148D4—6281no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—3141no—
152C2×C4—3141no—
153C2×C4—3141no—
154C2×C4—6281no—
155C2×C4—12561no—
156C2×C4D4×D15711yescharacteristic
157C2×C4D4×D15711yescharacteristic
158C2×C4C2×D62811yescharacteristic
159C8—41no—
160C8—41no—
161C8—3142no—
162C22—6281no—
163C22—6281no—
164C22—6281no—
165C22#1909774111yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—6281no—
172C4—6281no—
173C4—6281no—
174C4—12561no—
175C2—12561no—
176C2#2375744711yescharacteristic
177C2#2375745211yescharacteristic
178C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#330D157
hypocenterC157#1664
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23757683C2semidirect
3. #23757642C2semidirect
5. #23757014C2semidirect
7. #330×C157C2semidirect
89. C157#1664semidirect
96. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576832
#237576422
#237576332
#237570142
#237570122
#330×C1572
#1664157