Finite Group Databasebeta

← #34115219

Subgroups — #34115219

Order 20096.

234 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D157⋊#100C211yesmaximal, characteristic
2#23758221C211yesmaximal, characteristic
3#99×D157C211yesmaximal, characteristic
4C23×#10597845C411yescharacteristic, complemented
5D157⋊M16—21no—
6C2×C22⋊#10597845—21no—
7C2×C22⋊#10597845C411yescharacteristic, complemented
8#19097831—21no—
9#19097831C412yescomplemented
10(C2×#10597845)⋊C4—21no—
11C2×D4×D157C2211yescharacteristic
12C22⋊C4×D157—21no—
13#19097686C411yescharacteristic, complemented
14#19097685—21no—
15#99×C157C411yescharacteristic, complemented
16C22×#10597845—21no—
17C22×#10597845—21no—
18C22×#10597845—41no—
19C22×#10597845—42no—
20#14578964—41no—
21#14578963—22no—
22D157⋊C8—41no—
23C22⋊#10597845—41no—
24C22⋊#10597845—42no—
25C23×D157C2×C411yescharacteristic
26C23×D157D411yescharacteristic
27C2×D628Q811yescharacteristic
28C2×C22⋊D157C2×C411yescharacteristic
29C2×C22⋊D157D411yescharacteristic
30D4×D157—41no—
31D4×D157—41no—
32C2×C4×D157—41no—
33C2×C4×D157D411yescharacteristic
34C22⋊Dic157—21no—
35#14578931—41no—
36C2×D4×C157C2×C411yescharacteristic
37C22⋊C4×C157—21no—
38C2×#10597845—22no—
39C2×#10597845—41no—
40C2×#10597845—42no—
41C2×#10597845—41no—
42C2×#10597845—42no—
43C2×#10597845—41no—
44C2×#10597845—41no—
45C2×#10597845—41no—
46#11929441—42no—
47C22×D157—21no—
48C22×D157—21no—
49C22×D157—21no—
50C22×D157—21no—
51C22×D157—41no—
52C22×D157—41no—
53C22×D157—41no—
54C22×D157—41no—
55C22×D157C22⋊C411yescharacteristic
56C22×D157C4⋊C411yescharacteristic
57C22×D157C4⋊C411yescharacteristic
58D628—41no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C2×Dic157—41no—
62C2×Dic157C22⋊C411yescharacteristic
63C4×D157—21no—
64C4×D157—21no—
65C4×D157—81no—
66C4×D157—81no—
67C23×C157C4211yescharacteristic
68C23×C157C22⋊C411yescharacteristic
69D4×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157C4⋊C411yescharacteristic
72C22×C157—21no—
73C22×C157—21no—
74C22×C157—41no—
75C22×C157—41no—
76C22×C157#9511yescharacteristic
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—21no—
80C2×D157—21no—
81C2×D157—42no—
82C2×D157—41no—
83C2×D157—41no—
84C2×D157—41no—
85C2×D157—41no—
86C2×D157—41no—
87C2×D157—41no—
88C2×D157—81no—
89C2×D157#9911yescharacteristic
90C2×D157#9911yescharacteristic
91#10597845—42no—
92#10597845—81no—
93C4×C157—21no—
94C4×C157—81no—
95Dic157—21no—
96Dic157—81no—
97C2×C157—21no—
98C2×C157—41no—
99C2×C157—41no—
100C2×C157#34211yescharacteristic
101D157—21no—
102D157—41no—
103D157—41no—
104D157AΣL(1,𝔽16)11yescharacteristic
105D157#35211yescharacteristic
106C157#139011yescharacteristic, complemented, Sylow
107#1390—1571nomaximal, Sylow
108C2×#100—1571no—
109C2×#99—1571no—
110#386—1571no—
111C22×D4—1571no—
112C23×C4—1571no—
113C2×M16—3141no—
114C2×C22⋊C4—3141no—
115C2×C22⋊C4—3141no—
116C2×C22⋊C4—1571no—
117#100—3141no—
118#100—1572no—
119#99—3141no—
120#99—1571no—
121#99#1059784511yescharacteristic, complemented
122#95—3141no—
123C24—1571no—
124C24—1571no—
125C2×D4—6281no—
126C2×D4—6281no—
127C2×D4—1571no—
128C2×D4—1571no—
129C2×D4—1571no—
130C2×D4C2×#1059784511yescharacteristic
131C22×C4—3141no—
132C22×C4—3141no—
133C22×C4—6281no—
134C22×C4—6282no—
135C22×C4—6281no—
136C22×C4—1571no—
137M16—3142no—
138M16—6281no—
139C2×C8—6281no—
140C22⋊C4—21no—
141C22⋊C4—3141no—
142C22⋊C4—6281no—
143C22⋊C4—6282no—
144C22⋊C4—6281no—
145C23—3141no—
146C23—3141no—
147C23—3141no—
148C23—3141no—
149C23—6281no—
150C23—6281no—
151C23—6281no—
152C23—6281no—
153C23—1571no—
154C23—1571no—
155C23—1571no—
156C23C4×#1059784511yescharacteristic
157C23C22⋊#1059784511yescharacteristic
158D4—41no—
159D4—6281no—
160D4—6281no—
161D4—6281no—
162C2×C4—41no—
163C2×C4—3141no—
164C2×C4—3141no—
165C2×C4—3142no—
166C2×C4—6281no—
167C2×C4—6282no—
168C2×C4—6281no—
169C2×C4—6282no—
170C2×C4—6281no—
171C2×C4—6281no—
172C2×C4—6281no—
173C2×C4—6281no—
174C2×C4—1571no—
175C2×C4—12561no—
176C2×C4—12561no—
177C2×C4C4⋊#1059784511yescharacteristic
178C8—6282no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—3141no—
184C22—3141no—
185C22—3141no—
186C22—3141no—
187C22—6281no—
188C22—6281no—
189C22—6282no—
190C22—6281no—
191C22—6281no—
192C22—6281no—
193C22—6281no—
194C22—1571no—
195C22—1571no—
196C22—12561no—
197C22(C2×#10597845)⋊C411yescharacteristic
198C4—21no—
199C4—81no—
200C4—3141no—
201C4—6282no—
202C4—12561no—
203C4—12561no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—3141no—
208C2—6281no—
209C2—6281no—
210C2—1571no—
211C2—1571no—
212C2#2375815011yescharacteristic
subgroupG/H
centerC2#23758150
commutatorC23×C157C42
FrattiniC2×D4C2×#10597845
Fitting#99×C157C4
socleC2×C157#342
prime radical, cosocleC2×D4×D157C22
hypercenter#99#10597845
hypocenterC157#1390
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C23×#10597845C4semidirect
7. C2×C22⋊#10597845C4semidirect
9. #19097831C4semidirect
13. #19097686C4semidirect
15. #99×C157C4semidirect
106. C157#1390semidirect
121. #99#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊#1002
#237582212
#99×D1572
#1390157