Finite Group Databasebeta

← C2×#23757502 #34109696

Subgroups — C2×#23757502 #34109696

Order 20096.

564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×#14578943C211yesmaximal, characteristic, complemented
2C2×#19097750C211yesmaximal, characteristic, complemented
3C2×#19097745C211yesmaximal, characteristic
4#23757502C218yesmaximal, direct product factor
5C2×#19097703C211yesmaximal, characteristic, complemented
6C2×#19097696C211yesmaximal, characteristic, complemented
7C2×#19097693C211yesmaximal, characteristic, complemented
8C23×C8×C157C211yesmaximal, characteristic, complemented
9C22×Dic314C2211yescharacteristic
10C22×D628C2211yescharacteristic
11C22×C22⋊D157—21no—
12C2×#14578943—24no—
13C2×#14578943C2214yescomplemented
14#19097750—22no—
15#19097750C2214yescomplemented
16#19097745—22no—
17#19097745C2214yes—
18C2×C4⋊Dic157C2211yescharacteristic
19C2×C4⋊Dic157C2211yescharacteristic
20C2×#14578933—21no—
21C2×C22⋊Dic157—21no—
22C2×#14578931—21no—
23#19097703C2214yescomplemented
24#19097696C2214yescomplemented
25#19097693C2214yescomplemented
26C23×C4×C157C2211yescharacteristic
27C22×C8×C157—24no—
28C22×C8×C157C2211yescharacteristic
29C22×C8×C157C2211yescharacteristic
30C22×C8×C157C2214yescomplemented
31C23×D157—21no—
32C2×Dic314—21no—
33C2×Dic314—22no—
34C2×Dic314—22no—
35C2×Dic314C2312yes—
36C2×D628—22no—
37C2×D628—21no—
38C2×D628—22no—
39C2×D628C2312yes—
40C2×C22⋊D157—24no—
41C2×C22⋊D157—44no—
42C22×Dic157—21no—
43C22×Dic157—21no—
44C22×Dic157—21no—
45#14578943—28no—
46C4⋊Dic157—21no—
47C4⋊Dic157—21no—
48C4⋊Dic157C2312yes—
49C4⋊Dic157C2312yes—
50#14578933—24no—
51C22⋊Dic157—24no—
52#14578931—24no—
53C24×C157D411yescharacteristic
54C22×C4×C157—22no—
55C22×C4×C157—22no—
56C22×C4×C157D411yescharacteristic
57C22×C4×C157D412yes—
58C22×C4×C157C2312yes—
59C22×C4×C157C2311yescharacteristic
60C2×C8×C157—22no—
61C2×C8×C157—28no—
62C2×C8×C157D414yescomplemented
63C2×C8×C157C2312yes—
64C2×C8×C157C2312yes—
65C22×D157—22no—
66C22×D157—42no—
67C22×D157—42no—
68C22×D157—42no—
69Dic314—22no—
70Dic314—22no—
71Dic314—42no—
72D628—22no—
73D628—22no—
74D628—42no—
75C22⋊D157—48no—
76C2×Dic157—22no—
77C2×Dic157—22no—
78C2×Dic157—22no—
79C2×Dic157—42no—
80C2×Dic157—42no—
81C2×Dic157—42no—
82C23×C157—22no—
83C23×C157—22no—
84C23×C157SD1614yescomplemented
85C23×C157C2×D412yes—
86C23×C157C2×D411yescharacteristic
87C2×C4×C157—22no—
88C2×C4×C157—24no—
89C2×C4×C157—22no—
90C2×C4×C157—22no—
91C2×C4×C157C2×D412yes—
92C2×C4×C157C2×D412yes—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157#4112yes—
95C2×C4×C157C2411yescharacteristic
96C8×C157—22no—
97C8×C157C2×D414yescomplemented
98C22×C157—22no—
99C22×C157—22no—
100C22×C157—28no—
101C22×C157#12112yes—
102C22×C157C2×SD1612yes—
103C22×C157C2×SD1614yescomplemented
104C22×C157#13512yes—
105C22×C157C22×D411yescharacteristic
106C2×D157—42no—
107C2×D157—42no—
108C2×D157—42no—
109C2×D157—84no—
110C4×C157—22no—
111C4×C157#12112yes—
112C4×C157C22×D411yescharacteristic
113C4×C157C2×#4111yescharacteristic
114Dic157—42no—
115Dic157—42no—
116Dic157—42no—
117C2×C157—24no—
118C2×C157#46514yescomplemented
119C2×C157C2×#12111yescharacteristic
120C2×C157C22×SD1611yescharacteristic
121C2×C157C2×#13511yescharacteristic
122D157—82no—
123C157C2×#46511yescharacteristic, complemented, Sylow
124C2×#465—1571nomaximal, Sylow
125C22×SD16—1571no—
126C23×C8D15711yescharacteristic, complemented
127C2×C22⋊Q8—1571no—
128C2×#121—1571no—
129#465—1578no—
130C2×#106—1571no—
131C2×#103—1571no—
132C2×#102—1571no—
133C22×Q8—1571no—
134C22×D4—3141no—
135C22×D4—1571no—
136C23×C4C2×D15711yescharacteristic
137C2×SD16—3144no—
138C2×SD16—1574no—
139C22×C8—24no—
140C22×C8C2×D15711yescharacteristic
141C22×C8C2×D15711yescharacteristic
142C22×C8C2×D15714yescomplemented
143C22⋊Q8—3142no—
144C22⋊Q8—1574no—
145#121—3142no—
146#121—1574no—
147C2×C4⋊C4—3141no—
148C2×C4⋊C4—1571no—
149C2×C4⋊C4—1571no—
150C2×C22⋊C4—3141no—
151C2×C22⋊C4—3141no—
152#106—1574no—
153#103—1574no—
154#102—1574no—
155C24—3141no—
156C24D62811yescharacteristic
157C2×Q8—3141no—
158C2×Q8—3142no—
159C2×Q8—3142no—
160C2×Q8—1572no—
161C2×D4—3144no—
162C2×D4—3142no—
163C2×D4—3141no—
164C2×D4—3142no—
165C2×D4—6284no—
166C2×D4—1572no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—3141no—
170C22×C4—3141no—
171C22×C4—3141no—
172C22×C4D62812yes—
173C22×C4D62811yescharacteristic
174C22×C4C22×D15712yes—
175C22×C4C22×D15711yescharacteristic
176SD16—3148no—
177C2×C8—22no—
178C2×C8—28no—
179C2×C8C22⋊D15714yescomplemented
180C2×C8C22×D15712yes—
181C2×C8C22×D15712yes—
182C4⋊C4—3144no—
183C4⋊C4—3141no—
184C4⋊C4—3141no—
185C4⋊C4—1572no—
186C4⋊C4—1572no—
187C22⋊C4—3144no—
188C22⋊C4—3144no—
189C23—22no—
190C23—22no—
191C23—3142no—
192C23—6282no—
193C23—6282no—
194C23—6282no—
195C23#1457894314yescomplemented
196C23C2×D62812yes—
197C23C2×D62811yescharacteristic
198Q8—3142no—
199Q8—3142no—
200Q8—6282no—
201D4—3142no—
202D4—3142no—
203D4—6288no—
204D4—6282no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—3142no—
210C2×C4—3142no—
211C2×C4—3142no—
212C2×C4—6282no—
213C2×C4—6282no—
214C2×C4—6282no—
215C2×C4C2×C22⋊D15712yes—
216C2×C4C2×D62812yes—
217C2×C4C2×D62811yescharacteristic
218C2×C4#1457895412yes—
219C2×C4C23×D15711yescharacteristic
220C8—22no—
221C8C2×C22⋊D15714yescomplemented
222C22—28no—
223C22—22no—
224C22—22no—
225C22—6282no—
226C22—6282no—
227C22—6282no—
228C22—12564no—
229C22#1909774512yes—
230C22C2×#1457894312yes—
231C22C2×#1457894314yescomplemented
232C22#1909779312yes—
233C22C22×D62811yescharacteristic
234C4—22no—
235C4—6282no—
236C4—6282no—
237C4—6282no—
238C4#1909774512yes—
239C4C22×C22⋊D15711yescharacteristic
240C4C2×#1457895411yescharacteristic
241C2—24no—
242C2—12562no—
243C2#2375750214yesdirect product factor
244C2C2×#1909774511yescharacteristic
245C2C22×#1457894311yescharacteristic
246C2C2×#1909779311yescharacteristic
subgroupG/H
centerC23C2×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC23×C8×C157C2
socleC23×C157C2×D4
prime radicalC2×#19097745C2
hypercenterC23×C8D157
hypocenterC157C2×#465
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C22×#14578943C2semidirect
2. C2×#19097750C2semidirect
4. #23757502C2direct (N × H)
5. C2×#19097703C2semidirect
6. C2×#19097696C2semidirect
7. C2×#19097693C2semidirect
8. C23×C8×C157C2semidirect
13. C2×#14578943C22semidirect
15. #19097750C22semidirect
23. #19097703C22semidirect
24. #19097696C22semidirect
25. #19097693C22semidirect
30. C22×C8×C157C22semidirect
62. C2×C8×C157D4semidirect
84. C23×C157SD16semidirect
97. C8×C157C2×D4semidirect
103. C22×C157C2×SD16semidirect
118. C2×C157#465semidirect
123. C157C2×#465semidirect
126. C23×C8D157semidirect
142. C22×C8C2×D157semidirect
179. C2×C8C22⋊D157semidirect
195. C23#14578943semidirect
221. C8C2×C22⋊D157semidirect
231. C22C2×#14578943semidirect
243. C2#23757502direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145789432
C2×#190977502
C2×#190977452
#237575022
C2×#190977032
C2×#190976962
C2×#190976932
C23×C8×C1572
C2×#465157