Finite Group Databasebeta

← C2×#23757441 #34109460

Subgroups — C2×#23757441 #34109460

Order 20096.

844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19097796C212yesmaximal, complemented
2C2×#19097767C211yesmaximal, characteristic, complemented
3#23757441C218yesmaximal, direct product factor
4C2×#19097698C212yesmaximal, complemented
5C2×#19097688C211yesmaximal, characteristic, complemented
6C2×H(5,𝔽2)×C157C211yesmaximal, characteristic, complemented
7C22×D628C2211yescharacteristic, complemented
8C22×C22⋊D157—22no—
9#19097796—24no—
10#19097796C2218yescomplemented
11C2×#14578941—22no—
12C2×#14578939—22no—
13C2×#14578938C2212yescomplemented
14#19097767—22no—
15#19097767C2214yescomplemented
16C2×C4×Dic157C2211yescharacteristic, complemented
17#19097698C2218yescomplemented
18#19097688C2214yescomplemented
19H(5,𝔽2)×C157—24no—
20H(5,𝔽2)×C157—22no—
21H(5,𝔽2)×C157C2214yescomplemented
22C2×#41×C157—22no—
23C2×#41×C157C2212yes—
24C22×D4×C157—22no—
25C22×D4×C157—22no—
26C22×D4×C157C2211yescharacteristic
27C23×D157—21no—
28C2×D628—22no—
29C2×D628—22no—
30C2×D628—21no—
31C2×D628C2312yescomplemented
32C2×C22⋊D157—28no—
33C2×C22⋊D157—48no—
34C22×Dic157—21no—
35#14578941—28no—
36#14578939—28no—
37#14578938—22no—
38#14578938C2314yescomplemented
39C2×#11929434—22no—
40C4×Dic157—21no—
41C4×Dic157C2312yescomplemented
42C24×C157—22no—
43C24×C157D412yes—
44#41×C157—28no—
45#41×C157—28no—
46#41×C157—22no—
47#41×C157—22no—
48#41×C157D414yescomplemented
49#41×C157C2314yes—
50C2×Q8×C157D412yescomplemented
51C2×D4×C157—24no—
52C2×D4×C157—28no—
53C2×D4×C157—28no—
54C2×D4×C157—22no—
55C2×D4×C157—28no—
56C2×D4×C157—28no—
57C2×D4×C157—22no—
58C2×D4×C157—22no—
59C2×D4×C157D412yes—
60C2×D4×C157D412yescomplemented
61C2×D4×C157C2312yes—
62C22×C4×C157—22no—
63C22×C4×C157—22no—
64C22×C4×C157C2311yescharacteristic
65C22×D157—22no—
66C22×D157—44no—
67C22×D157—41no—
68C22×D157—41no—
69D628—24no—
70D628—42no—
71C22⋊D157—416no—
72C2×Dic157—24no—
73C2×Dic157—22no—
74#11929434—24no—
75C23×C157—28no—
76C23×C157—22no—
77C23×C157—22no—
78C23×C157—22no—
79C23×C157—44no—
80C23×C157—84no—
81C23×C157C2×D411yescharacteristic
82C23×C157C2×D414yes—
83Q8×C157—22no—
84Q8×C157C2×D414yescomplemented
85D4×C157—216no—
86D4×C157—24no—
87D4×C157—24no—
88D4×C157—24no—
89D4×C157—22no—
90D4×C157—24no—
91D4×C157C2×D414yescomplemented
92C2×C4×C157—28no—
93C2×C4×C157—22no—
94C2×C4×C157—24no—
95C2×C4×C157—24no—
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157C2×D412yes—
98C2×C4×C157C2×D412yes—
99C2×C4×C157C2411yescharacteristic
100C22×C157—22no—
101C22×C157—24no—
102C22×C157—24no—
103C22×C157—44no—
104C22×C157—44no—
105C22×C157—44no—
106C22×C157—82no—
107C22×C157—88no—
108C22×C157#12011yescharacteristic
109C22×C157#12011yescharacteristic
110C22×C157C22×D411yescharacteristic
111C2×D157—44no—
112C2×D157—42no—
113C2×D157—82no—
114C2×D157—82no—
115C4×C157—24no—
116C4×C157#12012yes—
117C4×C157C22×D412yes—
118Dic157—24no—
119C2×C157—21no—
120C2×C157—21no—
121C2×C157—44no—
122C2×C157—44no—
123C2×C157#45312yescomplemented
124C2×C157C2×#12011yescharacteristic
125D157—82no—
126C157C2×#45311yescharacteristic, complemented, Sylow
127C2×#453—1571nomaximal, Sylow
128C2×H(5,𝔽2)D15711yescharacteristic, complemented
129C2×AGL(1,ℤ/8)—1572no—
130C2×#127—1571no—
131#453—1578no—
132C2×#104—1572no—
133C2×#100—1571no—
134H(5,𝔽2)—24no—
135H(5,𝔽2)—22no—
136H(5,𝔽2)C2×D15714yescomplemented
137C2×#41—22no—
138C2×#41C2×D15712yes—
139C22×D4—22no—
140C22×D4—22no—
141C22×D4—3142no—
142C22×D4—1571no—
143C22×D4C2×D15711yescharacteristic
144AGL(1,ℤ/8)—3144no—
145AGL(1,ℤ/8)—1578no—
146C2×SD16—3142no—
147C2×D8—3142no—
148C2×M16—1572no—
149#127—3142no—
150#127—1574no—
151C2×C42—1571no—
152#104—1578no—
153#100—1574no—
154C24—22no—
155C24—3141no—
156C24C22⋊D15712yes—
157#41—28no—
158#41—28no—
159#41—22no—
160#41—22no—
161#41C22⋊D15714yescomplemented
162#41C22×D15714yes—
163C2×Q8C22⋊D15712yescomplemented
164C2×D4—24no—
165C2×D4—28no—
166C2×D4—28no—
167C2×D4—22no—
168C2×D4—28no—
169C2×D4—28no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—3148no—
173C2×D4—3142no—
174C2×D4—3142no—
175C2×D4—3141no—
176C2×D4—6288no—
177C2×D4—1572no—
178C2×D4C22⋊D15712yes—
179C2×D4C22⋊D15712yescomplemented
180C2×D4C22×D15712yes—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—3141no—
184C22×C4C22×D15711yescharacteristic
185SD16—3148no—
186D8—3148no—
187M16—3142no—
188M16—1574no—
189C2×C8—3142no—
190C42—3141no—
191C42—1572no—
192C23—28no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—44no—
197C23—84no—
198C23—3142no—
199C23—6284no—
200C23—6281no—
201C23—6281no—
202C23C2×C22⋊D15711yescharacteristic
203C23C2×C22⋊D15714yes—
204Q8—22no—
205Q8C2×C22⋊D15714yescomplemented
206D4—216no—
207D4—24no—
208D4—24no—
209D4—24no—
210D4—22no—
211D4—24no—
212D4—3144no—
213D4—62816no—
214D4—6282no—
215D4C2×C22⋊D15714yescomplemented
216C2×C4—28no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—24no—
220C2×C4—3144no—
221C2×C4—3142no—
222C2×C4C2×C22⋊D15711yescharacteristic
223C2×C4C2×C22⋊D15712yes—
224C2×C4C2×C22⋊D15712yes—
225C2×C4C23×D15711yescharacteristic
226C8—3144no—
227C22—22no—
228C22—24no—
229C22—24no—
230C22—44no—
231C22—44no—
232C22—44no—
233C22—82no—
234C22—88no—
235C22—6284no—
236C22—6282no—
237C22—12562no—
238C22—12562no—
239C22#1909774011yescharacteristic
240C22#1909774011yescharacteristic
241C22C22×C22⋊D15711yescharacteristic
242C4—24no—
243C4—3144no—
244C4#1909774012yes—
245C4C22×C22⋊D15712yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—44no—
250C2—12562no—
251C2#2375744112yesdirect product factor
252C2C2×#1909774011yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×H(5,𝔽2)×C157C2
socleC22×C157#120
hypercenterC2×H(5,𝔽2)D157
hypocenterC157C2×#453
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#19097796C2semidirect
2. C2×#19097767C2semidirect
3. #23757441C2direct (N × H)
4. C2×#19097698C2semidirect
5. C2×#19097688C2semidirect
6. C2×H(5,𝔽2)×C157C2semidirect
7. C22×D628C22semidirect
10. #19097796C22semidirect
13. C2×#14578938C22semidirect
15. #19097767C22semidirect
16. C2×C4×Dic157C22semidirect
17. #19097698C22semidirect
18. #19097688C22semidirect
21. H(5,𝔽2)×C157C22semidirect
31. C2×D628C23semidirect
38. #14578938C23semidirect
41. C4×Dic157C23semidirect
48. #41×C157D4semidirect
50. C2×Q8×C157D4semidirect
60. C2×D4×C157D4semidirect
84. Q8×C157C2×D4semidirect
91. D4×C157C2×D4semidirect
123. C2×C157#453semidirect
126. C157C2×#453semidirect
128. C2×H(5,𝔽2)D157semidirect
136. H(5,𝔽2)C2×D157semidirect
161. #41C22⋊D157semidirect
163. C2×Q8C22⋊D157semidirect
179. C2×D4C22⋊D157semidirect
205. Q8C2×C22⋊D157semidirect
215. D4C2×C22⋊D157semidirect
251. C2#23757441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190977962
C2×#190977672
#237574412
C2×#190976982
C2×#190976882
C2×H(5,𝔽2)×C1572
C2×#453157