Finite Group Databasebeta

← C2×#23757405 #34109310

Subgroups — C2×#23757405 #34109310

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×#14578939C211yesmaximal, characteristic, complemented
3C2×#19097742C211yesmaximal, characteristic, complemented
4#23757405C218yesmaximal, direct product factor
5C2×#19097693C211yesmaximal, characteristic, complemented
6C2×#19097692C211yesmaximal, characteristic, complemented
7C2×#19097683C211yesmaximal, characteristic, complemented
8C22×D8×C157C211yesmaximal, characteristic, complemented
9C24×D157—21no—
10C22×D628C2211yescharacteristic
11C22×C22⋊D157—21no—
12C22×C22⋊D157—21no—
13C2×D4×D157—24no—
14C2×D4×D157—24no—
15C2×D4×D157—22no—
16C2×D4×D157C2214yescomplemented
17C22×C4×D157C2211yescharacteristic
18C2×#14578939—24no—
19C2×#14578939C2214yescomplemented
20C22×#11929434C2211yescharacteristic, complemented
21#19097742—22no—
22#19097742C2214yescomplemented
23C2×C4⋊Dic157C2211yescharacteristic, complemented
24C2×C22⋊Dic157—21no—
25#19097693C2214yescomplemented
26#19097692C2214yescomplemented
27#19097683C2214yescomplemented
28C22×D4×C157C2211yescharacteristic
29C22×D4×C157C2211yescharacteristic, complemented
30C2×D8×C157—24no—
31C2×D8×C157C2214yescomplemented
32C22×C8×C157C2211yescharacteristic, complemented
33C23×D157—28no—
34C23×D157—24no—
35C23×D157—21no—
36C23×D157—44no—
37C23×D157—44no—
38C23×D157D411yescharacteristic
39C2×D628—21no—
40C2×D628—22no—
41C2×D628D414yescomplemented
42C2×D628C2312yes—
43C2×C22⋊D157—28no—
44C2×C22⋊D157—24no—
45C2×C22⋊D157—24no—
46C2×C22⋊D157—44no—
47D4×D157—216no—
48D4×D157—28no—
49D4×D157—28no—
50C22×Dic157—21no—
51C22×Dic157D411yescharacteristic
52C2×C4×D157—22no—
53C2×C4×D157—22no—
54C2×C4×D157D412yes—
55C2×C4×D157C2312yes—
56#14578939—28no—
57C2×#11929434—22no—
58C2×#11929434C2312yescomplemented
59C4⋊Dic157—21no—
60C4⋊Dic157C2312yescomplemented
61C22⋊Dic157—24no—
62C24×C157—21no—
63C24×C157—21no—
64C2×D4×C157—21no—
65C2×D4×C157—22no—
66C2×D4×C157—22no—
67C2×D4×C157—22no—
68C2×D4×C157—21no—
69C2×D4×C157D414yescomplemented
70C2×D4×C157C2312yes—
71C2×D4×C157C2312yescomplemented
72C22×C4×C157C2311yescharacteristic
73D8×C157—28no—
74C2×C8×C157—22no—
75C2×C8×C157C2312yescomplemented
76C22×D157—22no—
77C22×D157—22no—
78C22×D157—216no—
79C22×D157—24no—
80C22×D157—22no—
81C22×D157—48no—
82C22×D157—432no—
83C22×D157—42no—
84C22×D157—42no—
85C22×D157—48no—
86C22×D157D814yescomplemented
87C22×D157C2×D412yes—
88D628—24no—
89D628—22no—
90D628C2×D414yescomplemented
91C22⋊D157—216no—
92C22⋊D157—48no—
93C2×Dic157—22no—
94C2×Dic157—22no—
95C2×Dic157—42no—
96C2×Dic157C2×D412yes—
97C4×D157—24no—
98C4×D157—22no—
99C4×D157—22no—
100#11929434—22no—
101C23×C157—24no—
102C23×C157—22no—
103C23×C157—22no—
104C23×C157—42no—
105C23×C157—42no—
106C23×C157—42no—
107C23×C157—42no—
108C23×C157—42no—
109C23×C157C2×D411yescharacteristic
110D4×C157—24no—
111D4×C157—22no—
112D4×C157—22no—
113D4×C157—22no—
114D4×C157—42no—
115D4×C157C2×D414yescomplemented
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—42no—
126C22×C157—42no—
127C22×C157—42no—
128C22×C157—84no—
129C22×C157#12012yes—
130C22×C157C2×D812yes—
131C22×C157AGL(1,ℤ/8)12yes—
132C22×C157C22×D411yescharacteristic
133C2×D157—22no—
134C2×D157—22no—
135C2×D157—28no—
136C2×D157—24no—
137C2×D157—432no—
138C2×D157—42no—
139C2×D157—42no—
140C2×D157—48no—
141C2×D157C2×D814yescomplemented
142C4×C157#12012yes—
143C4×C157C22×D411yescharacteristic
144C4×C157C22×D411yescharacteristic
145Dic157—22no—
146Dic157—42no—
147C2×C157—44no—
148C2×C157—82no—
149C2×C157#44714yescomplemented
150C2×C157C2×#12011yescharacteristic
151C2×C157C22×D811yescharacteristic
152C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
153D157—24no—
154D157—44no—
155C157C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—1571nomaximal, Sylow
157C23×D4—1571no—
158C22×D8—1571no—
159C22×D8D15711yescharacteristic, complemented
160C2×#121—1571no—
161#447—1578no—
162C2×#102—1571no—
163C2×#102—1571no—
164C2×C22⋊C8—1571no—
165C25—3141no—
166C22×D4—3144no—
167C22×D4—3144no—
168C22×D4—3141no—
169C22×D4—3142no—
170C22×D4—3141no—
171C22×D4—1574no—
172C22×D4—1571no—
173C22×D4C2×D15711yescharacteristic
174C22×D4C2×D15711yescharacteristic, complemented
175C23×C4—1571no—
176C2×D8—24no—
177C2×D8—3144no—
178C2×D8—1574no—
179C2×D8C2×D15714yescomplemented
180C22×C8—1571no—
181C22×C8C2×D15711yescharacteristic, complemented
182#121—3142no—
183#121—1574no—
184C2×C4⋊C4—1571no—
185C2×C22⋊C4—3141no—
186#102—1574no—
187#102—1574no—
188C22⋊C8—1574no—
189C24—21no—
190C24—21no—
191C24—3148no—
192C24—3144no—
193C24—3141no—
194C24—6284no—
195C24—6284no—
196C24—1571no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—31416no—
203C2×D4—3148no—
204C2×D4—3148no—
205C2×D4—3148no—
206C2×D4—3144no—
207C2×D4—3144no—
208C2×D4—3141no—
209C2×D4—3142no—
210C2×D4—6284no—
211C2×D4—1574no—
212C2×D4—1572no—
213C2×D4C22⋊D15714yescomplemented
214C2×D4C22×D15712yes—
215C2×D4C22×D15712yescomplemented
216C22×C4—3142no—
217C22×C4—3142no—
218C22×C4—3141no—
219C22×C4—1571no—
220C22×C4—1572no—
221C22×C4—1572no—
222C22×C4C22×D15711yescharacteristic
223D8—28no—
224D8—3148no—
225C2×C8—22no—
226C2×C8—3142no—
227C2×C8—1572no—
228C2×C8C22×D15712yescomplemented
229C4⋊C4—3141no—
230C4⋊C4—1572no—
231C22⋊C4—3144no—
232C23—24no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—31416no—
241C23—3142no—
242C23—3142no—
243C23—3144no—
244C23—3142no—
245C23—62832no—
246C23—6288no—
247C23—6288no—
248C23—6282no—
249C23—6282no—
250C23—1574no—
251C23—1572no—
252C23D4×D15711yescharacteristic
253D4—24no—
254D4—22no—
255D4—22no—
256D4—22no—
257D4—42no—
258D4—31416no—
259D4—3144no—
260D4—3142no—
261D4—6288no—
262D4—1574no—
263D4C2×C22⋊D15714yescomplemented
264C2×C4—3142no—
265C2×C4—3144no—
266C2×C4—3142no—
267C2×C4—3142no—
268C2×C4—3142no—
269C2×C4—6282no—
270C2×C4—1572no—
271C2×C4D4×D15711yescharacteristic
272C2×C4D4×D15712yes—
273C2×C4C2×C22⋊D15712yes—
274C2×C4C23×D15711yescharacteristic
275C8—22no—
276C8—3142no—
277C22—24no—
278C22—48no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—3148no—
286C22—3142no—
287C22—3142no—
288C22—3144no—
289C22—62832no—
290C22—6288no—
291C22—6282no—
292C22—6282no—
293C22—1574no—
294C22#1909773912yes—
295C22D8×D15712yes—
296C22#1909779512yes—
297C22C2×D4×D15711yescharacteristic
298C4—3142no—
299C4—6282no—
300C4#1909773912yes—
301C4C2×D4×D15711yescharacteristic
302C4C22×C22⋊D15711yescharacteristic
303C2—44no—
304C2—82no—
305C2—3144no—
306C2—6284no—
307C2#2375740514yesdirect product factor
308C2C2×#1909773911yescharacteristic
309C2C2×D8×D15711yescharacteristic
310C2C2×#1909779511yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC22×D8×C157C2
socleC23×C157C2×D4
hypercenterC22×D8D157
hypocenterC157C2×#447
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D157C2semidirect
2. C22×#14578939C2semidirect
3. C2×#19097742C2semidirect
4. #23757405C2direct (N × H)
5. C2×#19097693C2semidirect
6. C2×#19097692C2semidirect
7. C2×#19097683C2semidirect
8. C22×D8×C157C2semidirect
16. C2×D4×D157C22semidirect
19. C2×#14578939C22semidirect
20. C22×#11929434C22semidirect
22. #19097742C22semidirect
23. C2×C4⋊Dic157C22semidirect
25. #19097693C22semidirect
26. #19097692C22semidirect
27. #19097683C22semidirect
29. C22×D4×C157C22semidirect
31. C2×D8×C157C22semidirect
32. C22×C8×C157C22semidirect
41. C2×D628D4semidirect
58. C2×#11929434C23semidirect
60. C4⋊Dic157C23semidirect
69. C2×D4×C157D4semidirect
71. C2×D4×C157C23semidirect
75. C2×C8×C157C23semidirect
86. C22×D157D8semidirect
90. D628C2×D4semidirect
115. D4×C157C2×D4semidirect
141. C2×D157C2×D8semidirect
149. C2×C157#447semidirect
155. C157C2×#447semidirect
159. C22×D8D157semidirect
174. C22×D4C2×D157semidirect
179. C2×D8C2×D157semidirect
181. C22×C8C2×D157semidirect
213. C2×D4C22⋊D157semidirect
215. C2×D4C22×D157semidirect
228. C2×C8C22×D157semidirect
263. D4C2×C22⋊D157semidirect
307. C2#23757405direct (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×#145789392
C2×#190977422
#237574052
C2×#190976932
C2×#190976922
C2×#190976832
C22×D8×C1572
C2×#447157