Finite Group Databasebeta

← #34115222

Subgroups — #34115222

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⋊#99C211yesmaximal, characteristic
2#23758221C211yesmaximal, characteristic
3#100×D157C211yesmaximal, characteristic
4C23×#10597845C411yescharacteristic, complemented
5C2×C22⋊#10597845—21no—
6C2×C22⋊#10597845—21no—
7C2×C22⋊#10597845C411yescharacteristic, complemented
8#19097830—21no—
9#19097829C412yescomplemented
10(C2×#10597845)⋊C4—21no—
11C2×D4×D157C2211yescharacteristic
12M16×D157—21no—
13#19097688C411yescharacteristic, complemented
14#19097687—21no—
15#100×C157C411yescharacteristic, complemented
16C22×#10597845—21no—
17C22×#10597845—21no—
18C22×#10597845—41no—
19C22×#10597845—41no—
20C22×#10597845—42no—
21C22⋊#10597845—22no—
22C22⋊#10597845—41no—
23C22⋊#10597845—41no—
24C22⋊#10597845—42no—
25C23×D157C2×C411yescharacteristic
26C23×D157D411yescharacteristic
27C2×D628D411yescharacteristic
28C2×C22⋊D157C2×C411yescharacteristic
29C2×C22⋊D157Q811yescharacteristic
30D4×D157—41no—
31D4×D157—41no—
32C2×C4×D157D411yescharacteristic
33#14578938—21no—
34#14578937—41no—
35C8×D157—41no—
36C2×D4×C157C2×C411yescharacteristic
37M16×C157—21no—
38C2×#10597845—22no—
39C2×#10597845—41no—
40C2×#10597845—42no—
41C2×#10597845—41no—
42C2×#10597845—42no—
43C2×#10597845—42no—
44C2×#10597845—41no—
45C2×#10597845—41no—
46C2×#10597845—41no—
47C2×#10597845—81no—
48C2×#10597845—81no—
49C22×D157—21no—
50C22×D157—21no—
51C22×D157—21no—
52C22×D157—21no—
53C22×D157—41no—
54C22×D157—41no—
55C22×D157—41no—
56C22×D157—41no—
57C22×D157C22⋊C411yescharacteristic
58C22×D157C22⋊C411yescharacteristic
59C22×D157C4⋊C411yescharacteristic
60D628—41no—
61C22⋊D157—41no—
62C22⋊D157—41no—
63C2×Dic157C4⋊C411yescharacteristic
64C4×D157—21no—
65C4×D157—21no—
66#11929434—41no—
67C23×C157C4211yescharacteristic
68C23×C157C4⋊C411yescharacteristic
69D4×C157—41no—
70C2×C4×C157C22⋊C411yescharacteristic
71C8×C157—41no—
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—
93#10597845—82no—
94C4×C157—21no—
95Dic157—21no—
96C2×C157—21no—
97C2×C157—41no—
98C2×C157—41no—
99C2×C157#34211yescharacteristic
100D157—21no—
101D157—41no—
102D157—41no—
103D157AΣL(1,𝔽16)11yescharacteristic
104D157#35211yescharacteristic
105C157#139011yescharacteristic, complemented, Sylow
106#1390—1571nomaximal, Sylow
107C2×#100—1571no—
108C2×#99—1571no—
109#386—1571no—
110C22×D4—1571no—
111C23×C4—1571no—
112C2×M16—3141no—
113C2×C22⋊C4—3141no—
114C2×C22⋊C4—3141no—
115C2×C22⋊C4—1571no—
116#100—3141no—
117#100—1571no—
118#100#1059784511yescharacteristic, complemented
119#99—3141no—
120#99—1572no—
121#95—3141no—
122C24—1571no—
123C24—1571no—
124C2×D4—6281no—
125C2×D4—6281no—
126C2×D4—1571no—
127C2×D4—1571no—
128C2×D4—1571no—
129C2×D4C2×#1059784511yescharacteristic
130C22×C4—3141no—
131C22×C4—3141no—
132C22×C4—6282no—
133C22×C4—6281no—
134C22×C4—6281no—
135C22×C4—1571no—
136M16—21no—
137M16—3141no—
138M16—6281no—
139C2×C8—6281no—
140C22⋊C4—3142no—
141C22⋊C4—6282no—
142C22⋊C4—6281no—
143C22⋊C4—6281no—
144C23—3141no—
145C23—3141no—
146C23—3141no—
147C23—3141no—
148C23—6281no—
149C23—6281no—
150C23—6281no—
151C23—6281no—
152C23—1571no—
153C23—1571no—
154C23—1571no—
155C23C4×#1059784511yescharacteristic
156C23C4⋊#1059784511yescharacteristic
157D4—41no—
158D4—6281no—
159D4—6281no—
160D4—6281no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—3142no—
164C2×C4—6281no—
165C2×C4—6282no—
166C2×C4—6281no—
167C2×C4—6282no—
168C2×C4—6282no—
169C2×C4—6281no—
170C2×C4—6281no—
171C2×C4—6281no—
172C2×C4—1571no—
173C2×C4—12561no—
174C2×C4—12561no—
175C2×C4C22⋊#1059784511yescharacteristic
176C8—41no—
177C8—6281no—
178C22—21no—
179C22—21no—
180C22—41no—
181C22—41no—
182C22—3141no—
183C22—3141no—
184C22—3141no—
185C22—3141no—
186C22—6281no—
187C22—6281no—
188C22—6282no—
189C22—6281no—
190C22—6281no—
191C22—6281no—
192C22—6281no—
193C22—1571no—
194C22—1571no—
195C22—12561no—
196C22(C2×#10597845)⋊C411yescharacteristic
197C4—21no—
198C4—3141no—
199C4—6282no—
200C4—12561no—
201C4—12562no—
202C2—21no—
203C2—41no—
204C2—41no—
205C2—3141no—
206C2—6281no—
207C2—6281no—
208C2—1571no—
209C2—1571no—
210C2#2375815011yescharacteristic
subgroupG/H
centerC2#23758150
commutatorC23×C157C42
FrattiniC2×D4C2×#10597845
Fitting#100×C157C4
socleC2×C157#342
prime radical, cosocleC2×D4×D157C22
hypercenter#100#10597845
hypocenterC157#1390
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
4. C23×#10597845C4semidirect
7. C2×C22⋊#10597845C4semidirect
9. #19097829C4semidirect
13. #19097688C4semidirect
15. #100×C157C4semidirect
105. C157#1390semidirect
118. #100#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊#992
#237582212
#100×D1572
#1390157