Finite Group Databasebeta

← C2×#23757408 #34109313

Subgroups — C2×#23757408 #34109313

Order 20096.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D157C211yesmaximal, characteristic, complemented
2C22×D1256C211yesmaximal, characteristic, complemented
3C22×#14578939C211yesmaximal, characteristic, complemented
4C2×#19097746C211yesmaximal, characteristic, complemented
5#23757408C218yesmaximal, direct product factor
6C2×#19097691C211yesmaximal, characteristic, complemented
7C2×#19097683C211yesmaximal, characteristic, complemented
8C2×#102×C157C211yesmaximal, characteristic, complemented
9C24×D157—21no—
10C22×D628—21no—
11C22×D628C2211yescharacteristic
12C22×D628C2211yescharacteristic, complemented
13C22×C22⋊D157—21no—
14C2×D4×D157—24no—
15C2×D4×D157—24no—
16C2×D4×D157—22no—
17C2×D4×D157C2214yescomplemented
18C22×C4×D157C2211yescharacteristic
19C2×D1256—24no—
20C2×D1256C2214yescomplemented
21C2×#14578939—24no—
22C2×#14578939C2214yescomplemented
23C22×#11929434C2211yescharacteristic, complemented
24#19097746—22no—
25#19097746C2214yescomplemented
26C2×#14578931—21no—
27#19097691C2214yescomplemented
28#19097683C2214yescomplemented
29C22×D4×C157C2211yescharacteristic
30C22×C8×C157C2211yescharacteristic, complemented
31C2×C4⋊C4×C157C2211yescharacteristic, complemented
32#102×C157C2214yescomplemented
33C23×D157—28no—
34C23×D157—24no—
35C23×D157—21no—
36C23×D157—21no—
37C23×D157—44no—
38C23×D157—44no—
39C23×D157D411yescharacteristic
40C2×D628—24no—
41C2×D628—21no—
42C2×D628—22no—
43C2×D628—22no—
44C2×D628—22no—
45C2×D628—21no—
46C2×D628—44no—
47C2×D628D414yescomplemented
48C2×D628C2312yes—
49C2×D628C2312yescomplemented
50C2×C22⋊D157—28no—
51C2×C22⋊D157—24no—
52D4×D157—216no—
53D4×D157—28no—
54D4×D157—28no—
55C22×Dic157D411yescharacteristic
56C2×C4×D157—22no—
57C2×C4×D157—22no—
58C2×C4×D157D412yes—
59C2×C4×D157C2312yes—
60D1256—28no—
61#14578939—28no—
62C2×#11929434—22no—
63C2×#11929434C2312yescomplemented
64#14578931—24no—
65C24×C157—21no—
66C2×D4×C157—21no—
67C2×D4×C157—22no—
68C2×D4×C157D414yescomplemented
69C2×D4×C157C2312yes—
70C22×C4×C157—21no—
71C22×C4×C157C2311yescharacteristic
72C2×C8×C157—22no—
73C2×C8×C157C2312yescomplemented
74C4⋊C4×C157—21no—
75C4⋊C4×C157C2312yescomplemented
76C22×D157—22no—
77C22×D157—22no—
78C22×D157—216no—
79C22×D157—24no—
80C22×D157—22no—
81C22×D157—22no—
82C22×D157—48no—
83C22×D157—432no—
84C22×D157—42no—
85C22×D157—42no—
86C22×D157—48no—
87C22×D157—42no—
88C22×D157—42no—
89C22×D157—42no—
90C22×D157D814yescomplemented
91C22×D157C2×D412yes—
92D628—24no—
93D628—22no—
94D628—22no—
95D628—22no—
96D628—48no—
97D628—42no—
98D628C2×D414yescomplemented
99C22⋊D157—216no—
100C2×Dic157—22no—
101C2×Dic157C2×D412yes—
102C4×D157—24no—
103C4×D157—22no—
104C4×D157—22no—
105#11929434—22no—
106C23×C157—24no—
107C23×C157—22no—
108C23×C157—42no—
109C23×C157—42no—
110C23×C157C2×D411yescharacteristic
111D4×C157—24no—
112D4×C157—22no—
113D4×C157C2×D414yescomplemented
114C2×C4×C157—22no—
115C2×C4×C157—42no—
116C2×C4×C157C2×D411yescharacteristic
117C2×C4×C157C2×D412yes—
118C2×C4×C157C2×D412yes—
119C2×C4×C157C2411yescharacteristic
120C8×C157—22no—
121C22×C157—24no—
122C22×C157—42no—
123C22×C157—42no—
124C22×C157—48no—
125C22×C157#12012yes—
126C22×C157C2×D812yes—
127C22×C157AGL(1,ℤ/8)12yes—
128C22×C157C22×D411yescharacteristic
129C2×D157—22no—
130C2×D157—22no—
131C2×D157—28no—
132C2×D157—24no—
133C2×D157—432no—
134C2×D157—42no—
135C2×D157—42no—
136C2×D157—48no—
137C2×D157—42no—
138C2×D157—42no—
139C2×D157—42no—
140C2×D157—84no—
141C2×D157C2×D814yescomplemented
142C4×C157—42no—
143C4×C157#12012yes—
144C4×C157C22×D411yescharacteristic
145C4×C157C22×D411yescharacteristic
146Dic157—22no—
147C2×C157—44no—
148C2×C157#44714yescomplemented
149C2×C157C2×#12011yescharacteristic
150C2×C157C22×D811yescharacteristic
151C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
152D157—24no—
153D157—44no—
154D157—82no—
155C157C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—1571nomaximal, Sylow
157C23×D4—1571no—
158C22×D8—1571no—
159C22×D8—1571no—
160C2×#121—1571no—
161#447—1578no—
162C2×#102—1571no—
163C2×#102D15711yescharacteristic, complemented
164C2×C22⋊C8—1571no—
165C25—3141no—
166C22×D4—3141no—
167C22×D4—3144no—
168C22×D4—3144no—
169C22×D4—3142no—
170C22×D4—3141no—
171C22×D4—1574no—
172C22×D4—1571no—
173C22×D4—1571no—
174C22×D4C2×D15711yescharacteristic
175C23×C4—1571no—
176C2×D8—3144no—
177C2×D8—3144no—
178C2×D8—1574no—
179C2×D8—1574no—
180C22×C8—1571no—
181C22×C8C2×D15711yescharacteristic, complemented
182#121—3142no—
183#121—1574no—
184C2×C4⋊C4C2×D15711yescharacteristic, complemented
185C2×C22⋊C4—3141no—
186#102—1574no—
187#102C2×D15714yescomplemented
188C22⋊C8—1574no—
189C24—21no—
190C24—3148no—
191C24—3144no—
192C24—3141no—
193C24—3141no—
194C24—6284no—
195C24—6284no—
196C24—1571no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—3144no—
200C2×D4—31416no—
201C2×D4—3148no—
202C2×D4—3148no—
203C2×D4—3148no—
204C2×D4—3144no—
205C2×D4—3141no—
206C2×D4—3142no—
207C2×D4—3141no—
208C2×D4—3142no—
209C2×D4—3142no—
210C2×D4—6284no—
211C2×D4—1574no—
212C2×D4—1572no—
213C2×D4—1572no—
214C2×D4D62814yescomplemented
215C2×D4C22×D15712yes—
216C22×C4—21no—
217C22×C4—3142no—
218C22×C4—3142no—
219C22×C4—1571no—
220C22×C4—1572no—
221C22×C4—1572no—
222C22×C4C22×D15711yescharacteristic
223D8—3148no—
224D8—3148no—
225C2×C8—22no—
226C2×C8—3142no—
227C2×C8—1572no—
228C2×C8C22×D15712yescomplemented
229C4⋊C4—21no—
230C4⋊C4C22×D15712yescomplemented
231C22⋊C4—3144no—
232C23—24no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23—31416no—
237C23—3142no—
238C23—3142no—
239C23—3144no—
240C23—3142no—
241C23—3142no—
242C23—62832no—
243C23—6288no—
244C23—6288no—
245C23—6282no—
246C23—6282no—
247C23—6282no—
248C23—6282no—
249C23—6282no—
250C23—1574no—
251C23—1572no—
252C23D4×D15711yescharacteristic
253D4—24no—
254D4—22no—
255D4—31416no—
256D4—3144no—
257D4—3142no—
258D4—3142no—
259D4—3142no—
260D4—6288no—
261D4—6282no—
262D4—1574no—
263D4C2×D62814yescomplemented
264C2×C4—22no—
265C2×C4—42no—
266C2×C4—3142no—
267C2×C4—3144no—
268C2×C4—3142no—
269C2×C4—3142no—
270C2×C4—1572no—
271C2×C4D4×D15711yescharacteristic
272C2×C4D4×D15712yes—
273C2×C4C2×D62812yes—
274C2×C4C23×D15711yescharacteristic
275C8—22no—
276C8—3142no—
277C22—24no—
278C22—48no—
279C22—42no—
280C22—42no—
281C22—3148no—
282C22—3142no—
283C22—3142no—
284C22—3144no—
285C22—62832no—
286C22—6288no—
287C22—6282no—
288C22—6282no—
289C22—6282no—
290C22—6282no—
291C22—6282no—
292C22—1574no—
293C22—12564no—
294C22#1909774112yes—
295C22D8×D15712yes—
296C22#1909779812yes—
297C22C2×D4×D15711yescharacteristic
298C4—42no—
299C4—3142no—
300C4#1909774112yes—
301C4C2×D4×D15711yescharacteristic
302C4C22×D62811yescharacteristic
303C2—44no—
304C2—3144no—
305C2—6284no—
306C2—12562no—
307C2#2375740814yesdirect product factor
308C2C2×#1909774111yescharacteristic
309C2C2×D8×D15711yescharacteristic
310C2C2×#1909779811yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#102×C157C2
socleC23×C157C2×D4
hypercenterC2×#102D157
hypocenterC157C2×#447
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×D4×D157C2semidirect
2. C22×D1256C2semidirect
3. C22×#14578939C2semidirect
4. C2×#19097746C2semidirect
5. #23757408C2direct (N × H)
6. C2×#19097691C2semidirect
7. C2×#19097683C2semidirect
8. C2×#102×C157C2semidirect
12. C22×D628C22semidirect
17. C2×D4×D157C22semidirect
20. C2×D1256C22semidirect
22. C2×#14578939C22semidirect
23. C22×#11929434C22semidirect
25. #19097746C22semidirect
27. #19097691C22semidirect
28. #19097683C22semidirect
30. C22×C8×C157C22semidirect
31. C2×C4⋊C4×C157C22semidirect
32. #102×C157C22semidirect
47. C2×D628D4semidirect
49. C2×D628C23semidirect
63. C2×#11929434C23semidirect
68. C2×D4×C157D4semidirect
73. C2×C8×C157C23semidirect
75. C4⋊C4×C157C23semidirect
90. C22×D157D8semidirect
98. D628C2×D4semidirect
113. D4×C157C2×D4semidirect
141. C2×D157C2×D8semidirect
148. C2×C157#447semidirect
155. C157C2×#447semidirect
163. C2×#102D157semidirect
181. C22×C8C2×D157semidirect
184. C2×C4⋊C4C2×D157semidirect
187. #102C2×D157semidirect
214. C2×D4D628semidirect
228. C2×C8C22×D157semidirect
230. C4⋊C4C22×D157semidirect
263. D4C2×D628semidirect
307. C2#23757408direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1572
C22×D12562
C22×#145789392
C2×#190977462
#237574082
C2×#190976912
C2×#190976832
C2×#102×C1572
C2×#447157