Finite Group Databasebeta

← #26031947

Subgroups — #26031947

Order 11392.

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

normal subgroups only

This group has 546 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
1C2×SD16×D89C212yesmaximal, complemented
2#19152263C211yesmaximal, characteristic, complemented
3#19152233C211yesmaximal, characteristic
4#19151824C212yesmaximal, complemented
5#19151800C211yesmaximal, characteristic, complemented
6#19151795C211yesmaximal, characteristic, complemented
7#19151747C212yesmaximal, complemented
8#19151735C212yesmaximal, complemented
9C4×#13083563C211yesmaximal, characteristic, complemented
10C8×D356C211yesmaximal, characteristic, complemented
11#492×C89C211yesmaximal, characteristic, complemented
12C2×Q8×D89C2212yescomplemented
13C2×D4×D89—21no—
14C2×D4×D89C2212yes—
15C2×#13083563C2211yescharacteristic
16C2×#13083562C2212yescomplemented
17C2×#13083561C2212yes—
18SD16×D89—28no—
19C2×C8×D89C2212yescomplemented
20#15668011—21no—
21#15667990—22no—
22#15667988C2212yescomplemented
23#15667983—21no—
24#15667983C2212yes—
25#15667980—22no—
26C4×Dic178C2211yescharacteristic, complemented
27C4×D356C2211yescharacteristic
28C4×D356C2211yescharacteristic
29#15667974—21no—
30#15667944C2211yescharacteristic, complemented
31C4⋊#10623494C2211yescharacteristic, complemented
32#15667937C2211yescharacteristic, complemented
33#15667936C2212yescomplemented
34#15667934C2211yescharacteristic
35#15667933C2212yescomplemented
36#15667924C2212yescomplemented
37C2×SD16×C89C2212yescomplemented
38C2×SD16×C89C2212yescomplemented
39C4⋊Q8×C89C2211yescharacteristic, complemented
40#127×C89C2211yescharacteristic
41C4×C8×C89C2211yescharacteristic, complemented
42C23×D89—22no—
43C2×Dic178—22no—
44C2×Dic178C2311yescharacteristic
45Q8×D89—24no—
46Q8×D89—42no—
47C2×D356D411yescharacteristic
48C2×D356C2311yescharacteristic
49C2×C22⋊D89—22no—
50C2×C22⋊D89—22no—
51D4×D89—24no—
52D4×D89—42no—
53D4×D89—44no—
54C2×C4×D89—22no—
55C2×C4×D89—21no—
56C2×C4×D89C2312yes—
57#13083563D414yescomplemented
58#13083562—24no—
59#13083561—24no—
60C2×#10623494C2312yes—
61C8×D89—24no—
62C4⋊Dic89D411yescharacteristic
63C4⋊Dic89C2311yescharacteristic
64C4⋊Dic89C2311yescharacteristic
65#13083553—21no—
66#13083553—22no—
67C22⋊Dic89—22no—
68#13083551—22no—
69#13083551—21no—
70#13083551D412yes—
71C4×Dic89—21no—
72C2×Q8×C89C2312yes—
73C2×D4×C89—21no—
74C2×D4×C89—21no—
75C2×D4×C89C2312yes—
76SD16×C89—24no—
77SD16×C89—42no—
78C2×C8×C89C2311yescharacteristic
79C2×C8×C89C2311yescharacteristic
80C4⋊C4×C89—21no—
81C4⋊C4×C89—21no—
82C42×C89C2311yescharacteristic
83C23×C89—22no—
84C22×D89—21no—
85C22×D89—44no—
86C22×D89—44no—
87C22×D89—82no—
88C22×D89C2×D412yes—
89Q8×C89—22no—
90Q8×C89—22no—
91D4×C89—22no—
92D4×C89—22no—
93D4×C89—42no—
94D4×C89—81no—
95C2×C4×C89—22no—
96C2×C4×C89C2×D411yescharacteristic
97C2×C4×C89C2×D411yescharacteristic
98C2×C4×C89C2411yescharacteristic
99C22⋊D89—44no—
100C22⋊D89—44no—
101C2×Dic89—21no—
102C2×Dic89—21no—
103C2×Dic89—21no—
104C2×Dic89C2×D412yes—
105D356—21no—
106D356SD1614yescomplemented
107D356C2×D412yes—
108C4×D89—22no—
109C4×D89—22no—
110C4×D89—44no—
111C4×D89—42no—
112Dic178—21no—
113Dic178—44no—
114Dic178C2×D412yescomplemented
115C8×C89—21no—
116C8×C89C2×D412yescomplemented
117#10623494—22no—
118C22×C89—42no—
119C22×C89—42no—
120C22×C89—42no—
121C22×C89C22×D411yescharacteristic
122C2×D89—22no—
123C2×D89—22no—
124C2×D89—22no—
125C2×D89—41no—
126C2×D89—41no—
127C2×D89—88no—
128C2×D89C2×SD1614yescomplemented
129C4×C89—21no—
130C4×C89—42no—
131C4×C89C2×SD1612yescomplemented
132C4×C89C22×D411yescharacteristic
133C4×C89H(5,𝔽2)11yescharacteristic
134Dic89—22no—
135Dic89—22no—
136Dic89—41no—
137Dic89—41no—
138C2×C89—82no—
139C2×C89D4211yescharacteristic
140C2×C89C22×SD1611yescharacteristic
141C2×C89#57711yescharacteristic
142D89—24no—
143D89—42no—
144D4×SD16—891nomaximal, Sylow
145C89D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—892no—
147D4×Q8—891no—
148D42—891no—
149#492D8911yescharacteristic, complemented
150#465—892no—
151#461—891no—
152#460—891no—
153#450—892no—
154#448—892no—
155C4×SD16—891no—
156C8×D4—891no—
157C22×Q8—892no—
158C22×D4—892no—
159C22×D4—1781no—
160C2×SD16—892no—
161C2×SD16—892no—
162C2×SD16—891no—
163C2×SD16—1788no—
164C2×SD16C2×D8912yescomplemented
165C2×SD16C2×D8912yescomplemented
166C22×C8—892no—
167C4⋊Q8—1781no—
168C4⋊Q8C2×D8911yescharacteristic, complemented
169#127C2×D8911yescharacteristic
170C22⋊Q8—892no—
171C22⋊Q8—1782no—
172#121—892no—
173#121—1781no—
174#120—1782no—
175C4×Q8—891no—
176C4×D4—891no—
177C4×D4—891no—
178C4×D4—1781no—
179#106—891no—
180C4⋊C8—891no—
181#103—892no—
182#103—891no—
183#102—892no—
184#102—891no—
185C22⋊C8—892no—
186C4×C8C2×D8911yescharacteristic, complemented
187C24—1782no—
188C2×Q8—891no—
189C2×Q8—3562no—
190C2×Q8—1782no—
191C2×Q8—1784no—
192C2×Q8C22×D8912yes—
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—891no—
196C2×D4—891no—
197C2×D4—3564no—
198C2×D4—3562no—
199C2×D4—1782no—
200C2×D4—1784no—
201C2×D4—1782no—
202C2×D4C22×D8912yes—
203C22×C4—892no—
204C22×C4—1782no—
205C22×C4—1781no—
206SD16—24no—
207SD16—42no—
208SD16—894no—
209SD16—1784no—
210SD16—1784no—
211C2×C8—892no—
212C2×C8—1784no—
213C2×C8C22×D8911yescharacteristic
214C2×C8C22×D8911yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—891no—
218C4⋊C4—891no—
219C4⋊C4—891no—
220C4⋊C4—1782no—
221C4⋊C4—1781no—
222C22⋊C4—892no—
223C22⋊C4—1782no—
224C22⋊C4—1782no—
225C22⋊C4—1781no—
226C42—1781no—
227C42C22×D8911yescharacteristic
228C23—22no—
229C23—892no—
230C23—3564no—
231C23—3564no—
232C23—1781no—
233C23—7122no—
234Q8—22no—
235Q8—22no—
236Q8—892no—
237Q8—3564no—
238Q8—1781no—
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—894no—
244D4—892no—
245D4—3564no—
246D4—3564no—
247D4—1781no—
248C2×C4—22no—
249C2×C4—892no—
250C2×C4—3564no—
251C2×C4—3562no—
252C2×C4—1781no—
253C2×C4—1781no—
254C2×C4—1781no—
255C2×C4—1782no—
256C2×C4—1782no—
257C2×C4D4×D8911yescharacteristic
258C2×C4D4×D8911yescharacteristic
259C2×C4C23×D8911yescharacteristic
260C8—21no—
261C8—1782no—
262C8D4×D8912yescomplemented
263C22—42no—
264C22—42no—
265C22—42no—
266C22—894no—
267C22—3561no—
268C22—3561no—
269C22—1782no—
270C22—1782no—
271C22—1782no—
272C22—7128no—
273C22C2×D4×D8911yescharacteristic
274C4—21no—
275C4—42no—
276C4—3561no—
277C4—3561no—
278C4—1782no—
279C4—1782no—
280C4SD16×D8912yescomplemented
281C4C2×D4×D8911yescharacteristic
282C4#1566805711yescharacteristic
283C2—82no—
284C2—3562no—
285C2—1784no—
286C2#1915223311yescharacteristic
287C2C2×SD16×D8911yescharacteristic
288C2#1915240411yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#492×C89C2
socleC22×C89C22×D4
prime radical#19152233C2
hypercenter#492D89
hypocenterC89D4×SD16
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D89C2semidirect
2. #19152263C2semidirect
4. #19151824C2semidirect
5. #19151800C2semidirect
6. #19151795C2semidirect
7. #19151747C2semidirect
8. #19151735C2semidirect
9. C4×#13083563C2semidirect
10. C8×D356C2semidirect
11. #492×C89C2semidirect
12. C2×Q8×D89C22semidirect
16. C2×#13083562C22semidirect
19. C2×C8×D89C22semidirect
22. #15667988C22semidirect
26. C4×Dic178C22semidirect
30. #15667944C22semidirect
31. C4⋊#10623494C22semidirect
32. #15667937C22semidirect
33. #15667936C22semidirect
35. #15667933C22semidirect
36. #15667924C22semidirect
37. C2×SD16×C89C22semidirect
38. C2×SD16×C89C22semidirect
39. C4⋊Q8×C89C22semidirect
41. C4×C8×C89C22semidirect
57. #13083563D4semidirect
106. D356SD16semidirect
114. Dic178C2×D4semidirect
116. C8×C89C2×D4semidirect
128. C2×D89C2×SD16semidirect
131. C4×C89C2×SD16semidirect
145. C89D4×SD16semidirect
149. #492D89semidirect
164. C2×SD16C2×D89semidirect
165. C2×SD16C2×D89semidirect
168. C4⋊Q8C2×D89semidirect
186. C4×C8C2×D89semidirect
262. C8D4×D89semidirect
280. C4SD16×D89semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D892
#191522632
#191522332
#191518242
#191518002
#191517952
#191517472
#191517352
C4×#130835632
C8×D3562
#492×C892
D4×SD1689