Finite Group Databasebeta

← #34115881

Subgroups — #34115881

Order 20096.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#19097830C212yesmaximal
2C4×C22⋊#10597845C212yesmaximal, complemented
3#23758151C212yesmaximal, complemented
4C2×#19097733C211yesmaximal, characteristic
5C2×C22⋊#10597845C2214yes—
6C2×C4×#10597845—22no—
7#19097830C418yescomplemented
8(C2×#10597845)⋊C4—22no—
9C22×D628C2211yescharacteristic
10C22×C4×D157C411yescharacteristic, complemented
11C22×C4×D157C2211yescharacteristic
12#19097733—22no—
13#19097733—22no—
14C2×#14578931C411yescharacteristic, complemented
15C2×#14578931C2211yescharacteristic
16C2×C4×Dic157C411yescharacteristic, complemented
17C2×C4⋊C4×C157C411yescharacteristic, complemented
18C22×#10597845—24no—
19C22⋊#10597845—24no—
20C22⋊#10597845C2×C418yescomplemented
21C4×#10597845—44no—
22C23×D157C2×C411yescharacteristic
23C23×D157C2311yescharacteristic
24C2×D628—22no—
25C2×D628—22no—
26C2×D628C2×C414yes—
27C22×Dic157C2×C411yescharacteristic
28C22×Dic157C2×C411yescharacteristic
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×C4×D157—42no—
32C2×C4×D157—42no—
33C2×C4×D157D412yes—
34C2×C4×D157D412yes—
35#14578931—22no—
36#14578931—22no—
37C4×Dic157—21no—
38C4×Dic157—21no—
39C22×C4×C157C2×C411yescharacteristic
40C22×C4×C157C2×C411yescharacteristic
41C22×C4×C157C2×C411yescharacteristic
42C4⋊C4×C157—22no—
43C2×#10597845—28no—
44C2×#10597845—44no—
45C2×#10597845—44no—
46C22×D157—21no—
47C22×D157—21no—
48C22×D157—41no—
49C22×D157—41no—
50C22×D157—41no—
51C22×D157—41no—
52C22×D157C4212yescomplemented
53C22×D157C22×C412yes—
54C22×D157C2×D412yes—
55C22×D157#4112yes—
56D628—28no—
57C2×Dic157—22no—
58C2×Dic157—21no—
59C2×Dic157—41no—
60C2×Dic157C22⋊C411yescharacteristic
61C2×Dic157C22⋊C411yescharacteristic
62C4×D157—24no—
63C4×D157—42no—
64C4×D157—42no—
65C4×D157—42no—
66C23×C157C22×C411yescharacteristic
67C2×C4×C157—21no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157C4212yescomplemented
73C2×C4×C157C22⋊C412yes—
74C22×C157—21no—
75C22×C157—21no—
76C22×C157C2×C4211yescharacteristic
77C22×C157C2×C22⋊C411yescharacteristic
78C22×C157#11711yescharacteristic
79C2×D157—22no—
80C2×D157—22no—
81C2×D157—22no—
82C2×D157—42no—
83C2×D157—42no—
84C2×D157—42no—
85C2×D157—41no—
86C2×D157—41no—
87C2×D157—42no—
88C2×D157C4×D414yes—
89#10597845—48no—
90C4×C157—22no—
91C4×C157—22no—
92C4×C157—41no—
93Dic157—21no—
94Dic157—41no—
95Dic157#9912yescomplemented
96C2×C157—21no—
97C2×C157—21no—
98C2×C157C4×C22⋊C411yescharacteristic
99C2×C157C2×#9911yescharacteristic
100C2×C157#41011yescharacteristic
101D157—24no—
102D157—42no—
103C157C4×#9911yescharacteristic, complemented, Sylow
104C4×#99—1571nomaximal, Sylow
105C2×C4×D4—1571no—
106C2×#99—1572no—
107C4×C22⋊C4—1572no—
108#342—1572no—
109C22×D4—1571no—
110C23×C4—1571no—
111C23×C4—1571no—
112C4×D4—3142no—
113C4×D4—3142no—
114C2×C4⋊C4#1059784511yescharacteristic, complemented
115C2×C22⋊C4—1571no—
116C2×C22⋊C4—1571no—
117C2×C22⋊C4—1574no—
118C2×C42—3142no—
119C2×C42—1571no—
120#99—1578no—
121#95—3142no—
122C24—1571no—
123C24—1571no—
124C2×D4—3142no—
125C2×D4—3142no—
126C2×D4—1574no—
127C22×C4—3141no—
128C22×C4—3141no—
129C22×C4—3144no—
130C22×C4—6282no—
131C22×C4—6282no—
132C22×C4—1571no—
133C22×C4—1572no—
134C22×C4—1571no—
135C22×C4—1572no—
136C22×C4C2×#1059784511yescharacteristic
137C22×C4C2×#1059784511yescharacteristic
138C22×C4C2×#1059784511yescharacteristic
139C4⋊C4—22no—
140C22⋊C4—3142no—
141C22⋊C4—3144no—
142C22⋊C4—3142no—
143C22⋊C4—1578no—
144C42—3141no—
145C42—3141no—
146C42—6284no—
147C23—3141no—
148C23—3141no—
149C23—6281no—
150C23—6281no—
151C23—6281no—
152C23—6281no—
153C23—1572no—
154C23—1572no—
155C23—1572no—
156C23—1572no—
157C23C22×#1059784511yescharacteristic
158D4—3148no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—3144no—
165C2×C4—3142no—
166C2×C4—3148no—
167C2×C4—3141no—
168C2×C4—6282no—
169C2×C4—6282no—
170C2×C4—6282no—
171C2×C4—6284no—
172C2×C4—6284no—
173C2×C4—6281no—
174C2×C4—1571no—
175C2×C4—1571no—
176C2×C4C4×#1059784512yescomplemented
177C2×C4C22⋊#1059784512yes—
178C22—21no—
179C22—21no—
180C22—3142no—
181C22—3142no—
182C22—3142no—
183C22—6282no—
184C22—6282no—
185C22—6282no—
186C22—6282no—
187C22—6281no—
188C22—6281no—
189C22—1574no—
190C22C2×C4×#1059784511yescharacteristic
191C22C2×C22⋊#1059784511yescharacteristic
192C22#1909785011yescharacteristic
193C4—22no—
194C4—22no—
195C4—41no—
196C4—3141no—
197C4—6288no—
198C4—6281no—
199C4—1572no—
200C2—21no—
201C2—21no—
202C2—3144no—
203C2—6282no—
204C2C4×C22⋊#1059784511yescharacteristic
205C2D157⋊#9911yescharacteristic
206C2#2375825411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC22×C157C2×C42
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×D628C22
cosocleC23×D157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157C4×#99
LCSG ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#10597845C2semidirect
3. #23758151C2semidirect
7. #19097830C4semidirect
10. C22×C4×D157C4semidirect
14. C2×#14578931C4semidirect
16. C2×C4×Dic157C4semidirect
17. C2×C4⋊C4×C157C4semidirect
20. C22⋊#10597845C2×C4semidirect
52. C22×D157C42semidirect
72. C2×C4×C157C42semidirect
95. Dic157#99semidirect
103. C157C4×#99semidirect
114. C2×C4⋊C4#10597845semidirect
176. C2×C4C4×#10597845semidirect

Maximal subgroups

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

subgroupindex
C2×#190978302
C4×C22⋊#105978452
#237581512
C2×#190977332
C4×#99157