Finite Group Databasebeta

← #34099449

Subgroups — #34099449

Order 20096.

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

normal subgroups only

This group has 196 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#23757682C211yesmaximal, characteristic, complemented
4#23757667C211yesmaximal, characteristic
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic
7#330×C157C211yesmaximal, characteristic, complemented
8C2×Dic628—21no—
9C2×#14578943—21no—
10#19097771C2211yescharacteristic
11#19097770—21no—
12#19097766—21no—
13#19097766—21no—
14#19097763C2211yescharacteristic
15#19097759C2211yescharacteristic
16#19097756—21no—
17#19097751—21no—
18#19097749—21no—
19#19097705—21no—
20#19097704—21no—
21#19097703—21no—
22#19097702—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—
32Dic628—42no—
33#14578943—42no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39C4⋊Dic157D411yescharacteristic
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47#14578931—21no—
48C4×Dic157—21no—
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D411yescharacteristic
54C4⋊C4×C157D411yescharacteristic
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57Dic314—41no—
58Dic314—41no—
59Dic314—41no—
60Dic314—81no—
61D628—41no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—41no—
66C4×D157—81no—
67#11929434—22no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—22no—
74C8×C157—22no—
75C22×C157#12011yescharacteristic
76C2×D157—41no—
77C2×D157—41no—
78C2×D157—41no—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82C4×C157—41no—
83C4×C157—41no—
84Dic157—41no—
85Dic157—41no—
86Dic157—41no—
87Dic157—81no—
88C2×C157#45311yescharacteristic
89C2×C157#45611yescharacteristic
90C2×C157#45611yescharacteristic
91D157—81no—
92C157#166011yescharacteristic, complemented, Sylow
93#1660—1571nomaximal, Sylow
94#563—1571no—
95#501—1571no—
96#501—1571no—
97#497—1571no—
98#330—1571no—
99#330D15711yescharacteristic, complemented
100#329—1571no—
101C2×Q16—3141no—
102C2×SD16—3141no—
103C4⋊Q8—3141no—
104C4⋊Q8—1571no—
105#126—3141no—
106#126—3141no—
107#125—1571no—
108#125C2×D15711yescharacteristic
109#124—1571no—
110#123—3141no—
111C22⋊Q8—3141no—
112C22⋊Q8—3141no—
113#107—3141no—
114#107—3141no—
115#106—3141no—
116#106—3141no—
117#97—1571no—
118#97C2×D15711yescharacteristic
119#97C2×D15711yescharacteristic
120C2×Q8—3141no—
121C2×Q8—3141no—
122C2×Q8—1571no—
123C2×D4—1571no—
124C22×C4—3141no—
125Q16—6282no—
126SD16—6282no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—3141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—3141no—
133C4⋊C4—3141no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—1571no—
139C4⋊C4—1571no—
140C4⋊C4D62811yescharacteristic
141C4⋊C4D62811yescharacteristic
142C22⋊C4—3141no—
143C22⋊C4—3141no—
144C22⋊C4—3141no—
145C22⋊C4—3141no—
146C22⋊C4—3141no—
147C42—3141no—
148C42C22×D15711yescharacteristic
149C23—3141no—
150Q8—6281no—
151Q8—6281no—
152Q8—6281no—
153Q8—12561no—
154D4—6281no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—3141no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—12561no—
162C2×C4D4×D15711yescharacteristic
163C2×C4D4×D15711yescharacteristic
164C2×C4C2×D62811yescharacteristic
165C8—22no—
166C8—22no—
167C8—3142no—
168C22—6281no—
169C22—6281no—
170C22—6281no—
171C22#1909774111yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—6281no—
178C4—6281no—
179C4—6281no—
180C4—12561no—
181C2—12561no—
182C2#2375744211yescharacteristic
183C2#2375745711yescharacteristic
184C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#330D157
hypocenterC157#1660
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. #23757682C2semidirect
5. #23757014C2semidirect
7. #330×C157C2semidirect
92. C157#1660semidirect
99. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576832
#237576822
#237576672
#237570142
#237570122
#330×C1572
#1660157