Finite Group Databasebeta

← #34099446

Subgroups — #34099446

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#23757679C211yesmaximal, characteristic, complemented
3#23757665C211yesmaximal, characteristic
4#23757015C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic
7#501×C157C211yesmaximal, characteristic, complemented
8C2×#14578944—21no—
9C2×#14578941—21no—
10#19097770—21no—
11#19097766—21no—
12#19097766—21no—
13#19097763C2211yescharacteristic
14#19097759C2211yescharacteristic
15#19097756—21no—
16#19097751—21no—
17#19097749—21no—
18#19097704—21no—
19#19097702—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23#125×C157C2211yescharacteristic
24#107×C157—21no—
25#106×C157—21no—
26#97×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C2×D628D411yescharacteristic
30C2×C4×D157—21no—
31#14578944—42no—
32#14578941—42no—
33C2×#11929434—21no—
34C2×#11929434—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×Q8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D411yescharacteristic
54C4⋊C4×C157D411yescharacteristic
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57Dic314—41no—
58Dic314—81no—
59D628—41no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C4×D157—81no—
64#11929434—22no—
65#11929434—22no—
66Q8×C157—41no—
67Q8×C157—41no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157—41no—
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
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—
84C4×C157—81no—
85Dic157—41no—
86Dic157—41no—
87Dic157—41no—
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#501D15711yescharacteristic, complemented
97#497—1571no—
98#330—1571no—
99#330—1571no—
100#329—1571no—
101C2×Q16—3141no—
102C2×SD16—3141no—
103C4⋊Q8—3141no—
104C4⋊Q8C2×D15711yescharacteristic
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—21no—
114#107—3141no—
115#106—21no—
116#106—3141no—
117#97—1571no—
118#97—1571no—
119#97C2×D15711yescharacteristic
120C2×Q8—21no—
121C2×Q8—3141no—
122C2×Q8—1571no—
123C2×D4—1571no—
124C22×C4—3141no—
125Q16—6282no—
126SD16—6282no—
127C2×C8—21no—
128C2×C8—3141no—
129C2×C8—3141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—1571no—
139C4⋊C4—1571no—
140C4⋊C4C22⋊D15711yescharacteristic
141C4⋊C4C22⋊D15711yescharacteristic
142C22⋊C4—3141no—
143C22⋊C4—3141no—
144C22⋊C4—3141no—
145C22⋊C4—3141no—
146C22⋊C4—3141no—
147C42—3141no—
148C42C22×D15711yescharacteristic
149C23—3141no—
150Q8—41no—
151Q8—41no—
152Q8—6281no—
153Q8—12561no—
154D4—6281no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—3141no—
161C2×C4—12561no—
162C2×C4D4×D15711yescharacteristic
163C2×C4D4×D15711yescharacteristic
164C2×C4C2×C22⋊D15711yescharacteristic
165C8—22no—
166C8—3142no—
167C8—3142no—
168C22—6281no—
169C22—6281no—
170C22—6281no—
171C22#1909773911yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—6281no—
179C4—6281no—
180C4—6281no—
181C2—12561no—
182C2#2375743911yescharacteristic
183C2#2375745411yescharacteristic
184C2#2375745511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#501×C157C2
socleC22×C157#120
prime radicalC2×D628D4
hypercenter#501D157
hypocenterC157#1660
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #23757679C2semidirect
4. #23757015C2semidirect
5. #23757014C2semidirect
7. #501×C157C2semidirect
92. C157#1660semidirect
96. #501D157semidirect

Maximal subgroups

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

subgroupindex
#237580272
#237576792
#237576652
#237570152
#237570142
#237570122
#501×C1572
#1660157