Finite Group Databasebeta

← #34098545

Subgroups — #34098545

Order 20096.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757807C211yesmaximal, characteristic
2#23757326C211yesmaximal, characteristic, complemented
3#23757005C212yesmaximal, complemented
4#23757002C212yesmaximal, complemented
5#431×C157C211yesmaximal, characteristic, complemented
6#19097765—21no—
7#19097763C411yescharacteristic
8#19097759C411yescharacteristic
9#19097754—21no—
10#19097750C411yescharacteristic
11#19097745C411yescharacteristic
12C4×Dic314C2211yescharacteristic
13C4×D628C2211yescharacteristic
14C4×C22⋊D157—21no—
15#19097728—21no—
16C4⋊#11929434C2212yes—
17C22⋊#11929434—21no—
18C4×#11929434—21no—
19C2×C42×C157C2211yescharacteristic
20C4⋊C8×C157—21no—
21C22⋊C8×C157—21no—
22C4×C8×C157C2212yes—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157—21no—
26C2×C4×D157—21no—
27C2×#11929434—22no—
28C4⋊Dic157C2×C411yescharacteristic
29C4⋊Dic157C2×C411yescharacteristic
30#14578933—21no—
31#14578933—21no—
32#14578933—21no—
33#14578933—21no—
34C22⋊Dic157—21no—
35#14578931—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39C4×Dic157—21no—
40C22×C4×C157C2×C411yescharacteristic
41C22×C4×C157D411yescharacteristic
42C22×C4×C157D411yescharacteristic
43C2×C8×C157—22no—
44C42×C157C2×C411yescharacteristic
45C42×C157D411yescharacteristic
46C42×C157D411yescharacteristic
47C42×C157C2311yescharacteristic
48C22×D157—21no—
49Dic314—22no—
50D628—22no—
51C22⋊D157—42no—
52C2×Dic157—21no—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C4×D157—42no—
56#11929434—42no—
57C23×C157C22⋊C411yescharacteristic
58C2×C4×C157—22no—
59C2×C4×C157—22no—
60C2×C4×C157—41no—
61C2×C4×C157C22⋊C411yescharacteristic
62C2×C4×C157C22⋊C411yescharacteristic
63C2×C4×C157C22⋊C411yescharacteristic
64C2×C4×C157C22×C411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C8×C157—42no—
68C22×C157—21no—
69C22×C157—21no—
70C22×C157—21no—
71C22×C157C2×C22⋊C411yescharacteristic
72C2×D157—41no—
73C2×D157—41no—
74C2×D157—41no—
75C4×C157—21no—
76C4×C157—21no—
77C4×C157—21no—
78C4×C157—21no—
79C4×C157#13112yes—
80C4×C157#13512yes—
81Dic157—41no—
82Dic157—41no—
83Dic157—41no—
84C2×C157—41no—
85C2×C157#40811yescharacteristic
86C2×C157#41611yescharacteristic
87C2×C157#42111yescharacteristic
88D157—81no—
89C157#148211yescharacteristic, complemented, Sylow
90#1482—1571nomaximal, Sylow
91#529—1571no—
92#431—1571no—
93#431D15711yescharacteristic, complemented
94Q8⋊C8—1572no—
95D4⋊C8—1572no—
96#126—3141no—
97#125—1571no—
98#124—1571no—
99#123—3141no—
100C22⋊Q8—1571no—
101#121—1571no—
102C4×Q8—1571no—
103C4×D4—3141no—
104C4×D4—1571no—
105#117—3141no—
106C2×C42C2×D15711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—1572no—
109C22⋊C8—21no—
110C22⋊C8—3141no—
111C4×C8—3141no—
112C4×C8C2×D15712yes—
113C2×Q8—1571no—
114C2×D4—3141no—
115C2×D4—1571no—
116C22×C4—3141no—
117C22×C4C4×D15711yescharacteristic
118C22×C4C22⋊D15711yescharacteristic
119C22×C4D62811yescharacteristic
120C2×C8—22no—
121C2×C8—3142no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—1571no—
127C4⋊C4—1571no—
128C22⋊C4—3141no—
129C22⋊C4—3141no—
130C22⋊C4—3141no—
131C22⋊C4—3141no—
132C22⋊C4—3141no—
133C42—3141no—
134C42C4×D15711yescharacteristic
135C42C22⋊D15711yescharacteristic
136C42D62811yescharacteristic
137C42C22×D15711yescharacteristic
138C23—3141no—
139C23#1457893111yescharacteristic
140Q8—3142no—
141D4—3142no—
142D4—6282no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—3141no—
147C2×C4—3141no—
148C2×C4—3141no—
149C2×C4—6282no—
150C2×C4#1457893111yescharacteristic
151C2×C4#1457893111yescharacteristic
152C2×C4#1457893111yescharacteristic
153C2×C4C2×C4×D15711yescharacteristic
154C2×C4C2×C22⋊D15711yescharacteristic
155C2×C4C2×D62811yescharacteristic
156C8—42no—
157C8—6282no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—6281no—
162C22—6281no—
163C22—6281no—
164C22C2×#1457893111yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—6281no—
170C4—6281no—
171C4—6281no—
172C4#1909777912yes—
173C4#1909779312yes—
174C2—41no—
175C2—12561no—
176C2#2375724111yescharacteristic
177C2#2375727011yescharacteristic
178C2#2375729111yescharacteristic
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#431×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097745C4
cosocleC42×C157C23
hypercenter#431D157
hypocenterC157#1482
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #23757326C2semidirect
3. #23757005C2semidirect
4. #23757002C2semidirect
5. #431×C157C2semidirect
89. C157#1482semidirect
93. #431D157semidirect

Maximal subgroups

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

subgroupindex
#237578072
#237573262
#237570052
#237570022
#431×C1572
#1482157