Finite Group Databasebeta

← C2×#23757419 #34109338

Subgroups — C2×#23757419 #34109338

Order 20096.

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

normal subgroups only

This group has 812 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
1C22×#14578953C211yesmaximal, characteristic, complemented
2C22×#14578943C211yesmaximal, characteristic, complemented
3C22×#14578939C211yesmaximal, characteristic, complemented
4C2×#19097746C211yesmaximal, characteristic, complemented
5#23757419C218yesmaximal, direct product factor
6C2×#19097694C211yesmaximal, characteristic, complemented
7C2×#19097683C211yesmaximal, characteristic, complemented
8C2×#102×C157C211yesmaximal, characteristic, complemented
9C2×#14578953—24no—
10C2×#14578953—24no—
11C2×#14578953—22no—
12C2×#14578953C2214yescomplemented
13C22×Dic314C2211yescharacteristic
14C22×D628—21no—
15C22×D628C2211yescharacteristic
16C22×C22⋊D157—21no—
17C23×Dic157—21no—
18C22×C4×D157C2211yescharacteristic
19C2×#14578943—24no—
20C2×#14578943C2214yescomplemented
21C2×#14578939—24no—
22C2×#14578939C2214yescomplemented
23C22×#11929434C2211yescharacteristic
24#19097746—22no—
25#19097746C2214yescomplemented
26C2×#14578931—21no—
27#19097694C2214yescomplemented
28#19097683C2214yescomplemented
29C22×D4×C157C2211yescharacteristic
30C22×C8×C157C2211yescharacteristic
31C2×C4⋊C4×C157C2211yescharacteristic
32#102×C157C2214yescomplemented
33C23×D157—21no—
34C23×D157D411yescharacteristic
35#14578953—216no—
36#14578953—28no—
37#14578953—28no—
38C2×Dic314—21no—
39C2×Dic314—22no—
40C2×Dic314D414yescomplemented
41C2×Dic314C2312yes—
42C2×D628—24no—
43C2×D628—22no—
44C2×D628—22no—
45C2×D628—21no—
46C2×D628—44no—
47C2×D628C2312yes—
48C2×C22⋊D157—28no—
49C2×C22⋊D157—24no—
50C22×Dic157—28no—
51C22×Dic157—24no—
52C22×Dic157—21no—
53C22×Dic157D411yescharacteristic
54C2×C4×D157—22no—
55C2×C4×D157—22no—
56C2×C4×D157D412yes—
57C2×C4×D157C2312yes—
58#14578943—28no—
59#14578939—28no—
60C2×#11929434—22no—
61C2×#11929434C2312yes—
62#14578931—24no—
63C24×C157—21no—
64C2×D4×C157—21no—
65C2×D4×C157—22no—
66C2×D4×C157D414yescomplemented
67C2×D4×C157C2312yes—
68C22×C4×C157—21no—
69C22×C4×C157C2311yescharacteristic
70C2×C8×C157—22no—
71C2×C8×C157C2312yes—
72C4⋊C4×C157—21no—
73C4⋊C4×C157C2312yes—
74C22×D157—22no—
75C22×D157—22no—
76C22×D157—22no—
77C22×D157—22no—
78C22×D157—42no—
79C22×D157—42no—
80C22×D157—42no—
81C22×D157C2×D412yes—
82Dic314—24no—
83Dic314—22no—
84Dic314C2×D414yescomplemented
85D628—22no—
86D628—22no—
87D628—48no—
88D628—42no—
89C22⋊D157—216no—
90C2×Dic157—216no—
91C2×Dic157—22no—
92C2×Dic157—24no—
93C2×Dic157—22no—
94C2×Dic157C2×D412yes—
95C4×D157—24no—
96C4×D157—22no—
97C4×D157—22no—
98#11929434—22no—
99C23×C157—24no—
100C23×C157—22no—
101C23×C157—42no—
102C23×C157—42no—
103C23×C157C2×D411yescharacteristic
104D4×C157—24no—
105D4×C157—22no—
106D4×C157C2×D414yescomplemented
107C2×C4×C157—22no—
108C2×C4×C157—42no—
109C2×C4×C157C2×D411yescharacteristic
110C2×C4×C157C2×D412yes—
111C2×C4×C157C2×D412yes—
112C2×C4×C157C2411yescharacteristic
113C8×C157—22no—
114C22×C157—24no—
115C22×C157—42no—
116C22×C157—42no—
117C22×C157—48no—
118C22×C157#12012yes—
119C22×C157#13512yes—
120C22×C157AGL(1,ℤ/8)12yes—
121C22×C157C22×D411yescharacteristic
122C2×D157—22no—
123C2×D157—22no—
124C2×D157—22no—
125C2×D157—44no—
126C2×D157—42no—
127C2×D157—42no—
128C2×D157—42no—
129C2×D157—84no—
130C4×C157—42no—
131C4×C157#12012yes—
132C4×C157C22×D411yescharacteristic
133C4×C157C22×D411yescharacteristic
134Dic157—22no—
135Dic157—24no—
136C2×C157—44no—
137C2×C157#44914yescomplemented
138C2×C157C2×#12011yescharacteristic
139C2×C157C2×#13511yescharacteristic
140C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
141D157—42no—
142D157—82no—
143C157C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—1571nomaximal, Sylow
145C22×#41—1571no—
146C22×SD16—1571no—
147C22×D8—1571no—
148C2×#121—1571no—
149#449—1578no—
150C2×#103—1571no—
151C2×#102D15711yescharacteristic, complemented
152C2×C22⋊C8—1571no—
153C2×#41—3144no—
154C2×#41—3144no—
155C2×#41—3142no—
156C2×#41—1574no—
157C22×Q8—1571no—
158C22×D4—3141no—
159C22×D4—3141no—
160C22×D4—1571no—
161C22×D4C2×D15711yescharacteristic
162C23×C4—3141no—
163C23×C4—1571no—
164C2×SD16—3144no—
165C2×SD16—1574no—
166C2×D8—3144no—
167C2×D8—1574no—
168C22×C8—1571no—
169C22×C8C2×D15711yescharacteristic
170#121—3142no—
171#121—1574no—
172C2×C4⋊C4C2×D15711yescharacteristic
173C2×C22⋊C4—3141no—
174#103—1574no—
175#102C2×D15714yescomplemented
176C22⋊C8—1574no—
177C24—21no—
178C24—3141no—
179C24—1571no—
180#41—31416no—
181#41—3148no—
182#41—3148no—
183C2×Q8—3141no—
184C2×Q8—3142no—
185C2×Q8—1574no—
186C2×Q8—1572no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—3144no—
190C2×D4—3148no—
191C2×D4—3144no—
192C2×D4—3142no—
193C2×D4—3141no—
194C2×D4—3142no—
195C2×D4—6284no—
196C2×D4—1572no—
197C2×D4D62814yescomplemented
198C2×D4C22×D15712yes—
199C22×C4—21no—
200C22×C4—3148no—
201C22×C4—3141no—
202C22×C4—3144no—
203C22×C4—3142no—
204C22×C4—3142no—
205C22×C4—1571no—
206C22×C4—1572no—
207C22×C4—1572no—
208C22×C4C22×D15711yescharacteristic
209SD16—3148no—
210D8—3148no—
211C2×C8—22no—
212C2×C8—3142no—
213C2×C8—1572no—
214C2×C8C22×D15712yes—
215C4⋊C4—21no—
216C4⋊C4C22×D15712yes—
217C22⋊C4—3144no—
218C23—24no—
219C23—22no—
220C23—42no—
221C23—42no—
222C23—3142no—
223C23—3142no—
224C23—3142no—
225C23—3142no—
226C23—6282no—
227C23—6282no—
228C23—6282no—
229C23—1572no—
230C23D4×D15711yescharacteristic
231Q8—3144no—
232Q8—3142no—
233Q8—1574no—
234D4—24no—
235D4—22no—
236D4—31416no—
237D4—3142no—
238D4—3142no—
239D4—6288no—
240D4—6282no—
241D4C2×D62814yescomplemented
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—31416no—
245C2×C4—3142no—
246C2×C4—3144no—
247C2×C4—3142no—
248C2×C4—3144no—
249C2×C4—3142no—
250C2×C4—3142no—
251C2×C4—1572no—
252C2×C4D4×D15711yescharacteristic
253C2×C4D4×D15712yes—
254C2×C4C2×D62812yes—
255C2×C4C23×D15711yescharacteristic
256C8—22no—
257C8—3142no—
258C22—24no—
259C22—48no—
260C22—42no—
261C22—42no—
262C22—3142no—
263C22—3142no—
264C22—3142no—
265C22—6284no—
266C22—6282no—
267C22—6282no—
268C22—6282no—
269C22—12564no—
270C22#1909774112yes—
271C22#1909779212yes—
272C22#1909779512yes—
273C22C2×D4×D15711yescharacteristic
274C4—42no—
275C4—3142no—
276C4—3144no—
277C4#1909774112yes—
278C4C2×D4×D15711yescharacteristic
279C4C22×D62811yescharacteristic
280C2—44no—
281C2—6282no—
282C2—12562no—
283C2#2375741914yesdirect product factor
284C2C2×#1909774111yescharacteristic
285C2C2×#1909779211yescharacteristic
286C2C2×#1909779511yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#102×C157C2
socleC23×C157C2×D4
hypercenterC2×#102D157
hypocenterC157C2×#449
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14578953C2semidirect
2. C22×#14578943C2semidirect
3. C22×#14578939C2semidirect
4. C2×#19097746C2semidirect
5. #23757419C2direct (N × H)
6. C2×#19097694C2semidirect
7. C2×#19097683C2semidirect
8. C2×#102×C157C2semidirect
12. C2×#14578953C22semidirect
20. C2×#14578943C22semidirect
22. C2×#14578939C22semidirect
25. #19097746C22semidirect
27. #19097694C22semidirect
28. #19097683C22semidirect
32. #102×C157C22semidirect
40. C2×Dic314D4semidirect
66. C2×D4×C157D4semidirect
84. Dic314C2×D4semidirect
106. D4×C157C2×D4semidirect
137. C2×C157#449semidirect
143. C157C2×#449semidirect
151. C2×#102D157semidirect
175. #102C2×D157semidirect
197. C2×D4D628semidirect
241. D4C2×D628semidirect
283. C2#23757419direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145789532
C22×#145789432
C22×#145789392
C2×#190977462
#237574192
C2×#190976942
C2×#190976832
C2×#102×C1572
C2×#449157