Finite Group Databasebeta

← #26031926

Subgroups — #26031926

Order 11392.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D712C211yesmaximal, characteristic, complemented
2C2×D8×D89C211yesmaximal, characteristic, complemented
3#19152232C212yesmaximal, complemented
4#19151973C211yesmaximal, characteristic, complemented
5#19151835C211yesmaximal, characteristic, complemented
6#19151792C212yesmaximal, complemented
7#19151733C212yesmaximal, complemented
8#19151731C212yesmaximal, complemented
9#19151680C211yesmaximal, characteristic, complemented
10C8×C22⋊D89C211yesmaximal, characteristic, complemented
11#466×C89C211yesmaximal, characteristic, complemented
12C22×D356C2212yescomplemented
13C2×D4×D89—22no—
14C2×D4×D89C2212yescomplemented
15C2×D712—24no—
16C2×D712C2211yescharacteristic
17C2×D712C2211yescharacteristic, complemented
18C2×D712C2212yescomplemented
19C2×#13083559C2212yescomplemented
20C2×#13083559C2212yescomplemented
21D8×D89—24no—
22C2×C8×D89C2211yescharacteristic, complemented
23#15668008C2212yescomplemented
24#15667987C2212yescomplemented
25#15667985—22no—
26#15667982—22no—
27#15667980—22no—
28#15667974C2212yescomplemented
29C4×C22⋊D89C2211yescharacteristic
30#15667941C2211yescharacteristic, complemented
31#15667932C2212yescomplemented
32#15667932C2212yescomplemented
33C22⋊#10623494C2211yescharacteristic, complemented
34#15667924C2211yescharacteristic, complemented
35C8×Dic89C2211yescharacteristic, complemented
36C2×D8×C89C2211yescharacteristic, complemented
37C22×C8×C89C2211yescharacteristic, complemented
38#121×C89C2212yescomplemented
39#107×C89C2211yescharacteristic, complemented
40#102×C89C2212yescomplemented
41C23×D89—22no—
42C23×D89—22no—
43C2×D356—24no—
44C2×D356—22no—
45C2×D356—22no—
46C2×D356—42no—
47C2×D356C2312yes—
48C2×D356C2312yes—
49C2×C22⋊D89—22no—
50C2×C22⋊D89—22no—
51C2×C22⋊D89—22no—
52C2×C22⋊D89D411yescharacteristic
53D4×D89—24no—
54D4×D89—42no—
55D4×D89—48no—
56C2×C4×D89—22no—
57C2×C4×D89C2311yescharacteristic
58D712—24no—
59D712—22no—
60D712D414yescomplemented
61#13083559—24no—
62#13083559—42no—
63C2×#10623494C2311yescharacteristic
64C2×#10623494C2311yescharacteristic
65C8×D89—22no—
66#13083553D411yescharacteristic
67C22⋊Dic89D411yescharacteristic
68#13083551—22no—
69#13083551—22no—
70#13083551D411yescharacteristic
71C4×Dic89C2311yescharacteristic
72C2×D4×C89—22no—
73C2×D4×C89C2312yes—
74C22×C4×C89C2311yescharacteristic
75D8×C89—22no—
76C2×C8×C89—22no—
77C2×C8×C89C2311yescharacteristic
78C2×C8×C89C2311yescharacteristic
79C4⋊C4×C89C2312yes—
80C22⋊C4×C89—22no—
81C23×C89—22no—
82C23×C89C2×D411yescharacteristic
83C22×D89—22no—
84C22×D89—22no—
85C22×D89—44no—
86C22×D89—44no—
87C22×D89—44no—
88C22×D89—44no—
89C22×D89—82no—
90C22×D89—82no—
91C22×D89C2×D411yescharacteristic
92D4×C89—22no—
93D4×C89—22no—
94D4×C89—44no—
95C2×C4×C89—21no—
96C2×C4×C89—21no—
97C2×C4×C89—22no—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2411yescharacteristic
100C22⋊D89—44no—
101C22⋊D89—44no—
102C22⋊D89—82no—
103C22⋊D89D814yescomplemented
104C2×Dic89C2×D411yescharacteristic
105C2×Dic89C2×D411yescharacteristic
106C2×Dic89C2×D411yescharacteristic
107D356—22no—
108D356—22no—
109D356—22no—
110D356—44no—
111D356—44no—
112D356C2×D414yescomplemented
113C4×D89—21no—
114C4×D89—21no—
115C4×D89—44no—
116C8×C89—21no—
117C8×C89C2×D412yescomplemented
118#10623494—21no—
119#10623494—21no—
120C22×C89—21no—
121C22×C89—21no—
122C22×C89—42no—
123C22×C89—42no—
124C22×C89—42no—
125C22×C89C2×D812yescomplemented
126C22×C89C22×D411yescharacteristic
127C2×D89—21no—
128C2×D89—21no—
129C2×D89—24no—
130C2×D89—42no—
131C2×D89—42no—
132C2×D89—42no—
133C2×D89—42no—
134C2×D89—42no—
135C2×D89—88no—
136C2×D89—88no—
137C2×D89C2×D812yescomplemented
138C4×C89—21no—
139C4×C89—42no—
140C4×C89C22×D411yescharacteristic
141C4×C89H(5,𝔽2)11yescharacteristic
142Dic89—21no—
143Dic89—21no—
144Dic89C2×D812yescomplemented
145C2×C89—22no—
146C2×C89—82no—
147C2×C89D4211yescharacteristic
148C2×C89C22×D811yescharacteristic
149C2×C89#57611yescharacteristic
150D89—22no—
151D89—44no—
152D89—82no—
153D4×D8—891nomaximal, Sylow
154C89D4×D811yescharacteristic, complemented, Sylow
155C22×D8—891no—
156C22×D8—891no—
157D42—892no—
158#493—891no—
159#466—891no—
160#466D8911yescharacteristic, complemented
161#459—892no—
162#447—892no—
163#447—892no—
164C4×D8—891no—
165C8×D4—891no—
166C22×D4—892no—
167C22×D4—892no—
168C22×D4—1782no—
169C2×D8—892no—
170C2×D8—892no—
171C2×D8—891no—
172C2×D8—892no—
173C2×D8—891no—
174C2×D8—1784no—
175C2×D8—1784no—
176C2×D8C2×D8911yescharacteristic, complemented
177C22×C8—891no—
178C22×C8C2×D8911yescharacteristic, complemented
179#127—892no—
180#121—892no—
181#121—1782no—
182#121C2×D8912yescomplemented
183#120—1782no—
184#120—1782no—
185C4×D4—891no—
186C4×D4—892no—
187#107C2×D8911yescharacteristic, complemented
188C4⋊C8—891no—
189#102—892no—
190#102—892no—
191#102C2×D8912yescomplemented
192C22⋊C8—891no—
193C22⋊C8—891no—
194C4×C8—891no—
195C24—1782no—
196C24—1782no—
197C2×D4—22no—
198C2×D4—891no—
199C2×D4—892no—
200C2×D4—892no—
201C2×D4—3562no—
202C2×D4—3568no—
203C2×D4—3562no—
204C2×D4—1784no—
205C2×D4—1782no—
206C2×D4—1782no—
207C2×D4—1782no—
208C2×D4—1782no—
209C2×D4—1784no—
210C2×D4—1782no—
211C2×D4C22×D8912yes—
212C22×C4—891no—
213C22×C4—1782no—
214C22×C4C22×D8911yescharacteristic
215D8—22no—
216D8—894no—
217D8—3562no—
218D8—1784no—
219D8—1784no—
220D8—1782no—
221C2×C8—22no—
222C2×C8—891no—
223C2×C8—891no—
224C2×C8—1782no—
225C2×C8C22×D8911yescharacteristic
226C2×C8C22×D8911yescharacteristic
227C4⋊C4—891no—
228C4⋊C4C22×D8912yes—
229C22⋊C4—22no—
230C22⋊C4—891no—
231C22⋊C4—891no—
232C22⋊C4—1782no—
233C22⋊C4—1782no—
234C42—891no—
235C23—22no—
236C23—891no—
237C23—3564no—
238C23—3564no—
239C23—3564no—
240C23—3564no—
241C23—1782no—
242C23—1782no—
243C23—7122no—
244C23—7122no—
245C23D4×D8911yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—894no—
250D4—894no—
251D4—3564no—
252D4—3564no—
253D4—3564no—
254D4—3564no—
255D4—1782no—
256D4—1782no—
257D4—1782no—
258D4—7122no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—891no—
263C2×C4—891no—
264C2×C4—891no—
265C2×C4—3564no—
266C2×C4—1781no—
267C2×C4—1781no—
268C2×C4D4×D8911yescharacteristic
269C2×C4C23×D8911yescharacteristic
270C8—21no—
271C8—1781no—
272C8—1781no—
273C8D4×D8912yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—892no—
280C22—3562no—
281C22—3562no—
282C22—3562no—
283C22—3562no—
284C22—3562no—
285C22—1784no—
286C22—1781no—
287C22—1781no—
288C22—7128no—
289C22—7128no—
290C22D8×D8912yescomplemented
291C22C2×D4×D8911yescharacteristic
292C4—21no—
293C4—42no—
294C4—892no—
295C4—1781no—
296C4—1781no—
297C4C2×D4×D8911yescharacteristic
298C4#1566805811yescharacteristic
299C2—22no—
300C2—82no—
301C2—3564no—
302C2—1782no—
303C2—7122no—
304C2#1915223211yescharacteristic
305C2C2×D8×D8911yescharacteristic
306C2#1915240011yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#466×C89C2
socleC22×C89C22×D4
hypercenter#466D89
hypocenterC89D4×D8
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D712C2semidirect
2. C2×D8×D89C2semidirect
3. #19152232C2semidirect
4. #19151973C2semidirect
5. #19151835C2semidirect
6. #19151792C2semidirect
7. #19151733C2semidirect
8. #19151731C2semidirect
9. #19151680C2semidirect
10. C8×C22⋊D89C2semidirect
11. #466×C89C2semidirect
12. C22×D356C22semidirect
14. C2×D4×D89C22semidirect
17. C2×D712C22semidirect
18. C2×D712C22semidirect
19. C2×#13083559C22semidirect
20. C2×#13083559C22semidirect
22. C2×C8×D89C22semidirect
23. #15668008C22semidirect
24. #15667987C22semidirect
28. #15667974C22semidirect
30. #15667941C22semidirect
31. #15667932C22semidirect
32. #15667932C22semidirect
33. C22⋊#10623494C22semidirect
34. #15667924C22semidirect
35. C8×Dic89C22semidirect
36. C2×D8×C89C22semidirect
37. C22×C8×C89C22semidirect
38. #121×C89C22semidirect
39. #107×C89C22semidirect
40. #102×C89C22semidirect
60. D712D4semidirect
103. C22⋊D89D8semidirect
112. D356C2×D4semidirect
117. C8×C89C2×D4semidirect
125. C22×C89C2×D8semidirect
137. C2×D89C2×D8semidirect
144. Dic89C2×D8semidirect
154. C89D4×D8semidirect
160. #466D89semidirect
176. C2×D8C2×D89semidirect
178. C22×C8C2×D89semidirect
182. #121C2×D89semidirect
187. #107C2×D89semidirect
191. #102C2×D89semidirect
273. C8D4×D89semidirect
290. C22D8×D89semidirect

Maximal subgroups

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

subgroupindex
C22×D7122
C2×D8×D892
#191522322
#191519732
#191518352
#191517922
#191517332
#191517312
#191516802
C8×C22⋊D892
#466×C892
D4×D889