Finite Group Databasebeta

← #34115115

Subgroups — #34115115

Order 20096.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#23758151C211yesmaximal, characteristic, complemented
2#23758117C211yesmaximal, characteristic, complemented
3#23757183C211yesmaximal, characteristic
4C2×C22⋊#10597845—21no—
5C22⋊#11929441—21no—
6C22×D628—21no—
7C22×D628C411yescharacteristic, complemented
8C2×#14578931—21no—
9C2×#14578931C2211yescharacteristic
10#95×C157C411yescharacteristic, complemented
11C22×#10597845—41no—
12C2×#11929441—41no—
13C22⋊#10597845—22no—
14C22⋊#10597845—41no—
15C23×D157—21no—
16C23×D157D411yescharacteristic
17C2×D628—41no—
18C2×D628—42no—
19C2×D628—42no—
20C2×D628—41no—
21C2×D628—41no—
22C2×D628—42no—
23C22×Dic157D411yescharacteristic
24#14578931—41no—
25#14578931—42no—
26C22×C4×C157—21no—
27C22×C4×C157C2×C411yescharacteristic
28C2×#10597845—42no—
29C2×#10597845—81no—
30C2×#10597845—81no—
31#11929441—81no—
32C22×D157—21no—
33C22×D157—21no—
34C22×D157—22no—
35C22×D157—41no—
36C22×D157—41no—
37C22×D157—41no—
38C22×D157—41no—
39C22×D157—41no—
40C22×D157—41no—
41C22×D157—41no—
42C22×D157—41no—
43C22×D157D811yescharacteristic
44C22×D157SD1611yescharacteristic
45D628—42no—
46D628—44no—
47D628—44no—
48D628—42no—
49C2×Dic157—21no—
50C2×Dic157—41no—
51C23×C157C22⋊C411yescharacteristic
52C2×C4×C157—22no—
53C2×C4×C157—21no—
54C2×C4×C157—41no—
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C22×C157—21no—
58C22×C157—21no—
59C22×C157#9911yescharacteristic
60C22×C157#10211yescharacteristic
61C22×C157#10411yescharacteristic
62C2×D157—21no—
63C2×D157—21no—
64C2×D157—41no—
65C2×D157—41no—
66C2×D157—41no—
67C2×D157—41no—
68C2×D157—42no—
69C2×D157—42no—
70C2×D157—42no—
71C2×D157—81no—
72C2×D157—81no—
73C2×D157—81no—
74C2×D157—81no—
75C2×D157—81no—
76#10597845—82no—
77C4×C157—42no—
78C4×C157—41no—
79Dic157—41no—
80C2×C157—21no—
81C2×C157—21no—
82C2×C157#32711yescharacteristic
83C2×C157AΣL(1,𝔽16)11yescharacteristic
84C2×C157#35311yescharacteristic
85D157—41no—
86D157—41no—
87D157—82no—
88C157#134311yescharacteristic, complemented, Sylow
89#1343—1571nomaximal, Sylow
90#392—1571no—
91#342—1571no—
92#323—1571no—
93C22×D4—3141no—
94C22×D4—1571no—
95C2×C22⋊C4—3141no—
96C2×C22⋊C4—3141no—
97C2×C22⋊C4—1571no—
98C22⋊C8—3141no—
99#95#1059784511yescharacteristic, complemented
100C24—3141no—
101C24—1571no—
102C2×D4—6281no—
103C2×D4—6282no—
104C2×D4—6282no—
105C2×D4—6281no—
106C2×D4—6281no—
107C2×D4—6282no—
108C22×C4—21no—
109C22×C4—6281no—
110C22×C4—1571no—
111C22×C4C2×#1059784511yescharacteristic
112C2×C8—6281no—
113C22⋊C4—3142no—
114C22⋊C4—6281no—
115C22⋊C4—6282no—
116C22⋊C4—6281no—
117C23—3142no—
118C23—3141no—
119C23—3141no—
120C23—6281no—
121C23—6281no—
122C23—6281no—
123C23—6281no—
124C23—6281no—
125C23—6281no—
126C23—6281no—
127C23—6281no—
128C23—1571no—
129C23—1571no—
130C23C22⋊#1059784511yescharacteristic
131D4—6282no—
132D4—6284no—
133D4—6284no—
134D4—6282no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3141no—
141C2×C4—6281no—
142C2×C4—6282no—
143C2×C4—12561no—
144C2×C4—12561no—
145C8—12561no—
146C22—21no—
147C22—21no—
148C22—3141no—
149C22—3141no—
150C22—6281no—
151C22—6281no—
152C22—6282no—
153C22—6282no—
154C22—6281no—
155C22—6281no—
156C22—6282no—
157C22—12561no—
158C22—12561no—
159C22—12561no—
160C22—12561no—
161C22—12561no—
162C22#1909783011yescharacteristic
163C22#1909783311yescharacteristic
164C22#1909783611yescharacteristic
165C4—42no—
166C4—41no—
167C4—6281no—
168C4—12562no—
169C2—21no—
170C2—21no—
171C2—6281no—
172C2—6281no—
173C2—12562no—
174C2#2375812511yescharacteristic
175C2#2375817411yescharacteristic
176C2#2375817811yescharacteristic
subgroupG/H
centerC22#19097830
commutatorC22×C4×C157C2×C4
FrattiniC22×C4C2×#10597845
Fitting#95×C157C4
socleC22×C157#99
prime radical#23757183C2
cosocleC2×#14578931C22
hypercenter#95#10597845
hypocenterC157#1343
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #23758151C2semidirect
2. #23758117C2semidirect
7. C22×D628C4semidirect
10. #95×C157C4semidirect
88. C157#1343semidirect
99. #95#10597845semidirect

Maximal subgroups

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

subgroupindex
#237581512
#237581172
#237571832
#1343157