Finite Group Databasebeta

← C2×#23757440 #34109459

Subgroups — C2×#23757440 #34109459

Order 20096.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097816C211yesmaximal, characteristic, complemented
2C2×#19097797C212yesmaximal, complemented
3#23757440C218yesmaximal, direct product factor
4C2×#19097699C212yesmaximal, complemented
5C2×#19097688C211yesmaximal, characteristic, complemented
6C2×#127×C157C211yesmaximal, characteristic, complemented
7#19097816—22no—
8#19097816—24no—
9#19097816C2214yescomplemented
10C2×#14578954C2212yes—
11C2×#14578953—22no—
12C22×C22⋊D157—22no—
13C2×D4×D157—22no—
14#19097797—24no—
15#19097797C2218yescomplemented
16C2×#14578942—22no—
17C2×#14578939—22no—
18C2×#14578938C2212yescomplemented
19#19097699C2218yescomplemented
20#19097688C2214yescomplemented
21C22×D4×C157—22no—
22C22×D4×C157C2211yescharacteristic
23C22×D4×C157C2211yescharacteristic, complemented
24#127×C157—22no—
25#127×C157C2214yescomplemented
26C2×C42×C157C2211yescharacteristic, complemented
27C23×D157—22no—
28#14578954—22no—
29#14578954—22no—
30#14578954D414yescomplemented
31#14578954C2314yes—
32#14578953—28no—
33#14578953—28no—
34C2×Dic314D412yescomplemented
35C2×D628D412yescomplemented
36C2×C22⋊D157—24no—
37C2×C22⋊D157—28no—
38C2×C22⋊D157—22no—
39C2×C22⋊D157—28no—
40D4×D157—28no—
41D4×D157—28no—
42C22×Dic157—22no—
43C2×C4×D157—22no—
44#14578942—28no—
45#14578939—28no—
46#14578938—22no—
47#14578938C2314yescomplemented
48C2×#11929434—22no—
49C24×C157—21no—
50C24×C157D412yes—
51C2×D4×C157—28no—
52C2×D4×C157—22no—
53C2×D4×C157—22no—
54C2×D4×C157—22no—
55C2×D4×C157—22no—
56C2×D4×C157—21no—
57C2×D4×C157—48no—
58C2×D4×C157D412yes—
59C2×D4×C157C2312yes—
60C2×D4×C157C2312yescomplemented
61C22×C4×C157—21no—
62C22×C4×C157C2311yescharacteristic
63C42×C157—21no—
64C42×C157C2312yescomplemented
65C22×D157—22no—
66C22×D157—28no—
67C22×D157—84no—
68Dic314—22no—
69Dic314C2×D414yescomplemented
70D628—22no—
71D628C2×D414yescomplemented
72C22⋊D157—216no—
73C22⋊D157—24no—
74C22⋊D157—24no—
75C2×Dic157—28no—
76C2×Dic157—22no—
77C4×D157—24no—
78C4×D157—24no—
79#11929434—24no—
80C23×C157—22no—
81C23×C157—22no—
82C23×C157—22no—
83C23×C157—44no—
84C23×C157—44no—
85C23×C157—41no—
86C23×C157—41no—
87C23×C157C2×D411yescharacteristic
88C23×C157C2×D414yes—
89D4×C157—24no—
90D4×C157—24no—
91D4×C157—24no—
92D4×C157—416no—
93D4×C157—42no—
94C2×C4×C157—24no—
95C2×C4×C157—22no—
96C2×C4×C157C2×D412yes—
97C2×C4×C157C2×D412yes—
98C2×C4×C157C2×D411yescharacteristic
99C2×C4×C157C2411yescharacteristic
100C22×C157—22no—
101C22×C157—24no—
102C22×C157—44no—
103C22×C157—44no—
104C22×C157—44no—
105C22×C157—42no—
106C22×C157—82no—
107C22×C157—82no—
108C22×C157—82no—
109C22×C157#12011yescharacteristic
110C22×C157#12011yescharacteristic
111C22×C157C22×D411yescharacteristic
112C2×D157—24no—
113C2×D157—44no—
114C2×D157—88no—
115C4×C157—24no—
116C4×C157#12012yes—
117C4×C157C22×D412yes—
118Dic157—24no—
119C2×C157—21no—
120C2×C157—21no—
121C2×C157—44no—
122C2×C157—82no—
123C2×C157#45312yescomplemented
124C2×C157C2×#12011yescharacteristic
125D157—44no—
126C157C2×#45311yescharacteristic, complemented, Sylow
127C2×#453—1571nomaximal, Sylow
128C2×H(5,𝔽2)—1571no—
129C2×AGL(1,ℤ/8)—1572no—
130C2×#127D15711yescharacteristic, complemented
131#453—1578no—
132C2×#104—1572no—
133C2×#100—1571no—
134H(5,𝔽2)—3144no—
135H(5,𝔽2)—3142no—
136H(5,𝔽2)—1574no—
137C2×#41—3142no—
138C2×#41—1572no—
139C22×D4—22no—
140C22×D4—3142no—
141C22×D4—3142no—
142C22×D4C2×D15711yescharacteristic
143C22×D4C2×D15711yescharacteristic, complemented
144AGL(1,ℤ/8)—3144no—
145AGL(1,ℤ/8)—1578no—
146C2×SD16—3142no—
147C2×D8—3142no—
148C2×M16—1572no—
149#127—22no—
150#127C2×D15714yescomplemented
151C2×C42C2×D15711yescharacteristic, complemented
152#104—1578no—
153#100—1574no—
154C24—21no—
155C24—3142no—
156C24C22⋊D15712yes—
157#41—3148no—
158#41—3148no—
159#41—3142no—
160#41—3142no—
161#41—1574no—
162#41—1574no—
163C2×Q8—1572no—
164C2×D4—28no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—48no—
171C2×D4—3148no—
172C2×D4—3148no—
173C2×D4—3144no—
174C2×D4—3148no—
175C2×D4—3142no—
176C2×D4—3148no—
177C2×D4—1572no—
178C2×D4C22⋊D15712yes—
179C2×D4C22×D15712yes—
180C2×D4C22×D15712yescomplemented
181C22×C4—21no—
182C22×C4—3142no—
183C22×C4—3142no—
184C22×C4C22×D15711yescharacteristic
185SD16—3148no—
186D8—3148no—
187M16—3142no—
188M16—1574no—
189C2×C8—3142no—
190C42—21no—
191C42C22×D15712yescomplemented
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—3148no—
200C23—3142no—
201C23—12564no—
202C23C2×C22⋊D15711yescharacteristic
203C23C2×C22⋊D15714yes—
204Q8—3142no—
205Q8—1574no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—31416no—
212D4—3144no—
213D4—3144no—
214D4—3142no—
215D4—1574no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—3148no—
219C2×C4—3142no—
220C2×C4—3144no—
221C2×C4—3144no—
222C2×C4D4×D15712yes—
223C2×C4D4×D15712yes—
224C2×C4C2×C22⋊D15711yescharacteristic
225C2×C4C23×D15711yescharacteristic
226C8—3144no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—3144no—
237C22—6284no—
238C22—12568no—
239C22#1909773911yescharacteristic
240C22#1909773911yescharacteristic
241C22C22×C22⋊D15711yescharacteristic
242C4—24no—
243C4—3144no—
244C4#1909773912yes—
245C4C2×D4×D15712yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—6284no—
251C2#2375744012yesdirect product factor
252C2C2×#1909773911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#127×C157C2
socleC22×C157#120
hypercenterC2×#127D157
hypocenterC157C2×#453
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#19097816C2semidirect
2. C2×#19097797C2semidirect
3. #23757440C2direct (N × H)
4. C2×#19097699C2semidirect
5. C2×#19097688C2semidirect
6. C2×#127×C157C2semidirect
9. #19097816C22semidirect
15. #19097797C22semidirect
18. C2×#14578938C22semidirect
19. #19097699C22semidirect
20. #19097688C22semidirect
23. C22×D4×C157C22semidirect
25. #127×C157C22semidirect
26. C2×C42×C157C22semidirect
30. #14578954D4semidirect
34. C2×Dic314D4semidirect
35. C2×D628D4semidirect
47. #14578938C23semidirect
60. C2×D4×C157C23semidirect
64. C42×C157C23semidirect
69. Dic314C2×D4semidirect
71. D628C2×D4semidirect
123. C2×C157#453semidirect
126. C157C2×#453semidirect
130. C2×#127D157semidirect
143. C22×D4C2×D157semidirect
150. #127C2×D157semidirect
151. C2×C42C2×D157semidirect
180. C2×D4C22×D157semidirect
191. C42C22×D157semidirect
251. C2#23757440direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978162
C2×#190977972
#237574402
C2×#190976992
C2×#190976882
C2×#127×C1572
C2×#453157