Finite Group Databasebeta

← D4×#13083563 #26031950

Subgroups — D4×#13083563 #26031950

Order 11392.

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

normal subgroups only

This group has 546 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
1C22×#13083563C212yesmaximal, complemented
2D4×Dic178C211yesmaximal, characteristic, complemented
3D4×D356C211yesmaximal, characteristic
4#19151971C211yesmaximal, characteristic, complemented
5#19151827C212yesmaximal, complemented
6#19151804C211yesmaximal, characteristic, complemented
7#19151799C211yesmaximal, characteristic, complemented
8#19151751C212yesmaximal, complemented
9#19151739C212yesmaximal, complemented
10C4×#13083563C211yesmaximal, characteristic, complemented
11C8×D4×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2212yescomplemented
13C22×D356C2212yes—
14C2×D4×D89—21no—
15C2×#13083563—28no—
16C2×#13083563C2212yes—
17C2×#13083563C2211yescharacteristic
18C2×#13083563C2212yescomplemented
19C2×#13083563C2212yescomplemented
20C2×#13083563C2212yescomplemented
21#15668012C2211yescharacteristic, complemented
22#15668011—21no—
23#15668009C2211yescharacteristic
24#15667991C2212yescomplemented
25#15667989—22no—
26#15667987—21no—
27#15667986C2212yes—
28#15667982—22no—
29C4×Dic178C2211yescharacteristic, complemented
30C4×D356C2211yescharacteristic
31D4×Dic89—21no—
32#15667944C2211yescharacteristic, complemented
33#15667937C2211yescharacteristic, complemented
34#15667937C2212yescomplemented
35#15667934C2211yescharacteristic
36#15667934C2212yescomplemented
37C22×C8×C89C2212yescomplemented
38C4×D4×C89C2211yescharacteristic
39C4⋊C8×C89C2211yescharacteristic, complemented
40C22⋊C8×C89C2212yescomplemented
41C4×C8×C89C2211yescharacteristic, complemented
42C23×D89—22no—
43C2×Dic178—24no—
44C2×Dic178—22no—
45C2×Dic178—42no—
46C2×Dic178C2312yes—
47C2×Dic178C2311yescharacteristic
48C2×D356—24no—
49C2×D356—22no—
50C2×D356—21no—
51C2×D356—21no—
52C2×D356—42no—
53C2×D356C2312yes—
54C2×D356C2311yescharacteristic
55C2×C22⋊D89—22no—
56D4×D89—44no—
57C22×Dic89—22no—
58C2×C4×D89—21no—
59#13083563—24no—
60#13083563—24no—
61#13083563—24no—
62#13083563—42no—
63#13083563D414yesdirect product factor
64C4⋊Dic89—21no—
65C4⋊Dic89—21no—
66C4⋊Dic89C2311yescharacteristic
67C4⋊Dic89C2311yescharacteristic
68#13083553—21no—
69#13083553—22no—
70C22⋊Dic89—22no—
71#13083551—21no—
72#13083551—22no—
73C4×Dic89—21no—
74C2×D4×C89D411yescharacteristic
75C22×C4×C89C2312yes—
76C2×C8×C89—24no—
77C2×C8×C89C2312yes—
78C2×C8×C89C2311yescharacteristic
79C2×C8×C89C2311yescharacteristic
80C4⋊C4×C89D411yescharacteristic
81C22⋊C4×C89D412yes—
82C42×C89C2311yescharacteristic
83C23×C89C2×D412yes—
84C22×D89—21no—
85C22×D89—22no—
86C22×D89—44no—
87C22×D89—44no—
88C22×D89—82no—
89D4×C89SD1614yescomplemented
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89C2×D411yescharacteristic
93C2×C4×C89C2×D412yes—
94C2×C4×C89C2×D411yescharacteristic
95C2×C4×C89C2411yescharacteristic
96C22⋊D89—44no—
97C2×Dic89—21no—
98C2×Dic89—21no—
99C2×Dic89—21no—
100C2×Dic89—22no—
101C2×Dic89—44no—
102D356—22no—
103D356—21no—
104D356—22no—
105D356—44no—
106D356—42no—
107D356—81no—
108D356C2×D412yes—
109C4×D89—42no—
110Dic178—21no—
111Dic178—22no—
112Dic178—22no—
113Dic178—44no—
114Dic178C2×D412yescomplemented
115C8×C89—22no—
116C8×C89—21no—
117C8×C89C2×D412yescomplemented
118C22×C89—22no—
119C22×C89—22no—
120C22×C89C2×SD1614yescomplemented
121C22×C89C22×D411yescharacteristic
122C2×D89—22no—
123C2×D89—41no—
124C2×D89—41no—
125C2×D89—42no—
126C2×D89—42no—
127C2×D89—42no—
128C2×D89—88no—
129C4×C89—22no—
130C4×C89—21no—
131C4×C89C2×SD1612yescomplemented
132C4×C89C22×D411yescharacteristic
133C4×C89H(5,𝔽2)11yescharacteristic
134Dic89—22no—
135Dic89—42no—
136Dic89—41no—
137Dic89—41no—
138C2×C89—24no—
139C2×C89D4211yescharacteristic
140C2×C89C22×SD1611yescharacteristic
141C2×C89#57711yescharacteristic
142D89—42no—
143D89—82no—
144D4×SD16—891nomaximal, Sylow
145C89D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—892no—
147D4×Q8—891no—
148D42—891no—
149#492—891no—
150#465—892no—
151#461—891no—
152#460—891no—
153#450—892no—
154#448—892no—
155C4×SD16—891no—
156C8×D4D8911yescharacteristic, complemented
157C22×Q8—892no—
158C22×D4—892no—
159C22×D4—1781no—
160C2×SD16—891no—
161C2×SD16—892no—
162C2×SD16—892no—
163C2×SD16—892no—
164C2×SD16—892no—
165C2×SD16—1788no—
166C22×C8C2×D8912yescomplemented
167C4⋊Q8—891no—
168C4⋊Q8—1781no—
169#127—891no—
170C22⋊Q8—892no—
171C22⋊Q8—1782no—
172#121—892no—
173#121—1781no—
174#120—1782no—
175C4×Q8—891no—
176C4×D4—891no—
177C4×D4—1781no—
178C4×D4C2×D8911yescharacteristic
179#106—891no—
180C4⋊C8C2×D8911yescharacteristic, complemented
181#103—891no—
182#103—892no—
183#102—891no—
184#102—892no—
185C22⋊C8C2×D8912yescomplemented
186C4×C8C2×D8911yescharacteristic, complemented
187C24—1782no—
188C2×Q8—891no—
189C2×Q8—892no—
190C2×Q8—3562no—
191C2×Q8—1784no—
192C2×Q8—1782no—
193C2×D4—891no—
194C2×D4—892no—
195C2×D4—3562no—
196C2×D4—3564no—
197C2×D4—1784no—
198C2×D4—1782no—
199C2×D4—1782no—
200C2×D4—1781no—
201C2×D4—1781no—
202C2×D4D35611yescharacteristic
203C22×C4—1782no—
204C22×C4—1781no—
205C22×C4C22×D8912yes—
206SD16—894no—
207SD16—3562no—
208SD16—1784no—
209SD16—1784no—
210SD16—1784no—
211C2×C8—24no—
212C2×C8C22×D8911yescharacteristic
213C2×C8C22×D8912yes—
214C2×C8C22×D8911yescharacteristic
215C4⋊C4—891no—
216C4⋊C4—891no—
217C4⋊C4—1781no—
218C4⋊C4—1781no—
219C4⋊C4—1782no—
220C4⋊C4—1781no—
221C4⋊C4D35611yescharacteristic
222C22⋊C4—1782no—
223C22⋊C4—1781no—
224C22⋊C4—1782no—
225C22⋊C4D35612yes—
226C42—1781no—
227C42C22×D8911yescharacteristic
228C23—3564no—
229C23—3564no—
230C23—1782no—
231C23—1781no—
232C23—7122no—
233C23C2×D35612yes—
234Q8—892no—
235Q8—3564no—
236Q8—1782no—
237Q8—1782no—
238Q8—1781no—
239D4—892no—
240D4—3564no—
241D4—3564no—
242D4—3562no—
243D4—1782no—
244D4—1782no—
245D4—1781no—
246D4—7121no—
247D4#1308356314yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—3564no—
251C2×C4—3562no—
252C2×C4—1781no—
253C2×C4—1781no—
254C2×C4—1782no—
255C2×C4—1781no—
256C2×C4C2×D35611yescharacteristic
257C2×C4C2×D35612yes—
258C2×C4C2×D35611yescharacteristic
259C2×C4C23×D8911yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D8912yescomplemented
263C22—22no—
264C22—22no—
265C22—3561no—
266C22—3561no—
267C22—3562no—
268C22—3562no—
269C22—3562no—
270C22—1782no—
271C22—7128no—
272C22C2×#1308356314yescomplemented
273C22C22×D35611yescharacteristic
274C4—21no—
275C4—22no—
276C4—3561no—
277C4—3562no—
278C4—3561no—
279C4—1782no—
280C4C2×#1308356312yescomplemented
281C4C2×D4×D8911yescharacteristic
282C4#1566805811yescharacteristic
283C2—24no—
284C2—3562no—
285C2—7122no—
286C2D4×D35611yescharacteristic
287C2C22×#1308356311yescharacteristic
288C2#1915241011yescharacteristic
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC8×D4×C89C2
socleC22×C89C22×D4
prime radicalD4×D356C2
hypercenterC8×D4D89
hypocenterC89D4×SD16
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13083563C2semidirect
2. D4×Dic178C2semidirect
4. #19151971C2semidirect
5. #19151827C2semidirect
6. #19151804C2semidirect
7. #19151799C2semidirect
8. #19151751C2semidirect
9. #19151739C2semidirect
10. C4×#13083563C2semidirect
11. C8×D4×C89C2semidirect
12. C22×Dic178C22semidirect
18. C2×#13083563C22semidirect
19. C2×#13083563C22semidirect
20. C2×#13083563C22semidirect
21. #15668012C22semidirect
24. #15667991C22semidirect
29. C4×Dic178C22semidirect
32. #15667944C22semidirect
33. #15667937C22semidirect
34. #15667937C22semidirect
36. #15667934C22semidirect
37. C22×C8×C89C22semidirect
39. C4⋊C8×C89C22semidirect
40. C22⋊C8×C89C22semidirect
41. C4×C8×C89C22semidirect
63. #13083563D4direct (N × H)
89. D4×C89SD16semidirect
114. Dic178C2×D4semidirect
117. C8×C89C2×D4semidirect
120. C22×C89C2×SD16semidirect
131. C4×C89C2×SD16semidirect
145. C89D4×SD16semidirect
156. C8×D4D89semidirect
166. C22×C8C2×D89semidirect
180. C4⋊C8C2×D89semidirect
185. C22⋊C8C2×D89semidirect
186. C4×C8C2×D89semidirect
247. D4#13083563direct (N × H)
262. C8D4×D89semidirect
272. C22C2×#13083563semidirect
280. C4C2×#13083563semidirect

Maximal subgroups

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

subgroupindex
C22×#130835632
D4×Dic1782
D4×D3562
#191519712
#191518272
#191518042
#191517992
#191517512
#191517392
C4×#130835632
C8×D4×C892
D4×SD1689