Finite Group Databasebeta

← #26032477

Subgroups — #26032477

Order 11392.

448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×D356C211yesmaximal, characteristic
2#19151946C211yesmaximal, characteristic, complemented
3#19151922C212yesmaximal, complemented
4#19151875C211yesmaximal, characteristic, complemented
5#19151846C212yesmaximal, complemented
6#19151798C211yesmaximal, characteristic, complemented
7#19151748C212yesmaximal, complemented
8C4×#13083561C211yesmaximal, characteristic, complemented
9#19151676C211yesmaximal, characteristic, complemented
10#19151602C212yesmaximal, complemented
11#556×C89C211yesmaximal, characteristic, complemented
12C22×D356C2212yes—
13C2×D4×D89—21no—
14C2×#13083561C2211yescharacteristic
15C2×#13083561C2212yescomplemented
16C2×#13083558C2212yescomplemented
17#15668009C2211yescharacteristic
18#15667987—21no—
19#15667986C2212yes—
20#15667982—22no—
21C4×D356C2211yescharacteristic
22#15667945C2212yescomplemented
23#15667943C2211yescharacteristic, complemented
24C4⋊#10623494C2211yescharacteristic, complemented
25#15667936C2211yescharacteristic, complemented
26#15667932C2212yes—
27#15667932C2211yescharacteristic
28#15667932C2212yescomplemented
29#15667932C2212yescomplemented
30#15667932C2212yescomplemented
31C22⋊#10623494C2212yescomplemented
32C4×#10623494C2211yescharacteristic, complemented
33C4⋊Q8×C89C2211yescharacteristic, complemented
34#126×C89—22no—
35#124×C89—21no—
36C22⋊Q8×C89C2212yescomplemented
37C4×Q8×C89—21no—
38C4×Q8×C89C2211yescharacteristic, complemented
39C4×D4×C89C2211yescharacteristic
40#117×C89C2212yescomplemented
41C23×D89—22no—
42C2×D356—24no—
43C2×D356—22no—
44C2×D356—21no—
45C2×D356—21no—
46C2×D356—42no—
47C2×D356C2312yes—
48C2×D356C2311yescharacteristic
49C2×C22⋊D89—22no—
50D4×D89—44no—
51C2×C4×D89—21no—
52#13083561—22no—
53#13083561—42no—
54#13083558—42no—
55C2×#10623494C2311yescharacteristic
56C2×#10623494C2312yes—
57C2×#10623494C2311yescharacteristic
58C4⋊Dic89C2311yescharacteristic
59#13083551—21no—
60#13083551—22no—
61C2×Q8×C89—21no—
62C2×Q8×C89C2311yescharacteristic
63C2×D4×C89D411yescharacteristic
64C22×C4×C89C2312yes—
65C4⋊C4×C89—22no—
66C4⋊C4×C89—21no—
67C4⋊C4×C89—21no—
68C4⋊C4×C89D411yescharacteristic
69C4⋊C4×C89C2311yescharacteristic
70C4⋊C4×C89C2312yes—
71C22⋊C4×C89—22no—
72C22⋊C4×C89—22no—
73C22⋊C4×C89D412yes—
74C42×C89—22no—
75C42×C89—21no—
76C42×C89C2311yescharacteristic
77C23×C89C2×D412yes—
78C22×D89—21no—
79C22×D89—22no—
80C22×D89—44no—
81C22×D89—44no—
82C22×D89—82no—
83Q8×C89—21no—
84Q8×C89—21no—
85Q8×C89—42no—
86D4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—21no—
90C2×C4×C89—21no—
91C2×C4×C89—22no—
92C2×C4×C89C2×D412yes—
93C2×C4×C89C2×D411yescharacteristic
94C2×C4×C89C2×D411yescharacteristic
95C2×C4×C89C2411yescharacteristic
96C22⋊D89—44no—
97C2×Dic89—21no—
98D356—22no—
99D356—21no—
100D356—22no—
101D356—44no—
102D356—42no—
103D356—81no—
104D356#4112yes—
105C4×D89—42no—
106#10623494—21no—
107#10623494—21no—
108#10623494—22no—
109C22×C89—22no—
110C22×C89—22no—
111C22×C89—22no—
112C22×C89C22×D411yescharacteristic
113C2×D89—22no—
114C2×D89—41no—
115C2×D89—41no—
116C2×D89—42no—
117C2×D89—42no—
118C2×D89—42no—
119C2×D89—88no—
120C4×C89—22no—
121C4×C89—21no—
122C4×C89—41no—
123C4×C89—42no—
124C4×C89—41no—
125C4×C89AGL(1,ℤ/8)12yes—
126C4×C89C2×#4111yescharacteristic
127C4×C89H(5,𝔽2)11yescharacteristic
128Dic89—41no—
129C2×C89—42no—
130C2×C89#54611yescharacteristic
131C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C89#57711yescharacteristic
133D89—42no—
134D89—82no—
135#3324—891nomaximal, Sylow
136C89#332411yescharacteristic, complemented, Sylow
137#556D8911yescharacteristic, complemented
138D42—891no—
139#486—891no—
140#482—892no—
141#474—891no—
142#468—892no—
143#460—891no—
144#450—892no—
145C4×SD16—891no—
146#436—891no—
147#418—892no—
148C22×D4—892no—
149C22×D4—1781no—
150C2×SD16—892no—
151C2×SD16—891no—
152C2×M16—892no—
153C4⋊Q8C2×D8911yescharacteristic, complemented
154#127—891no—
155#126—22no—
156#124—21no—
157C22⋊Q8C2×D8912yescomplemented
158#121—892no—
159#121—1781no—
160#120—1782no—
161C4×Q8—21no—
162C4×Q8C2×D8911yescharacteristic, complemented
163C4×D4—891no—
164C4×D4C2×D8911yescharacteristic
165#117C2×D8912yescomplemented
166#107—892no—
167#106—891no—
168C4⋊C8—891no—
169#103—891no—
170#102—891no—
171#102—892no—
172#102—892no—
173#102—892no—
174#102—892no—
175C22⋊C8—892no—
176C4×C8—891no—
177C24—1782no—
178C2×Q8—21no—
179C2×Q8C22×D8911yescharacteristic
180C2×D4—891no—
181C2×D4—892no—
182C2×D4—3562no—
183C2×D4—3564no—
184C2×D4—1784no—
185C2×D4—1782no—
186C2×D4—1782no—
187C2×D4—1781no—
188C2×D4—1781no—
189C2×D4C22⋊D8911yescharacteristic
190C22×C4—1781no—
191C22×C4C22×D8912yes—
192SD16—3562no—
193SD16—1782no—
194M16—3562no—
195C2×C8—891no—
196C2×C8—891no—
197C2×C8—892no—
198C4⋊C4—22no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—891no—
202C4⋊C4C22⋊D8911yescharacteristic
203C4⋊C4C22×D8911yescharacteristic
204C4⋊C4C22×D8912yes—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—1781no—
208C22⋊C4—1782no—
209C22⋊C4C22⋊D8912yes—
210C42—22no—
211C42—21no—
212C42C22×D8911yescharacteristic
213C23—3564no—
214C23—3564no—
215C23—1782no—
216C23—1781no—
217C23—7122no—
218C23C2×C22⋊D8912yes—
219Q8—21no—
220Q8—21no—
221Q8—42no—
222D4—22no—
223D4—892no—
224D4—3564no—
225D4—3564no—
226D4—3562no—
227D4—1782no—
228D4—1782no—
229D4—1781no—
230D4—7121no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—3562no—
237C2×C4—1781no—
238C2×C4C2×C22⋊D8912yes—
239C2×C4C2×C22⋊D8911yescharacteristic
240C2×C4C2×C22⋊D8911yescharacteristic
241C2×C4C23×D8911yescharacteristic
242C8—1781no—
243C8—1781no—
244C8—1782no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—3561no—
249C22—3561no—
250C22—3562no—
251C22—3562no—
252C22—3562no—
253C22—1782no—
254C22—7128no—
255C22C22×C22⋊D8911yescharacteristic
256C4—21no—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—3561no—
262C4#1566803712yes—
263C4#41×D8911yescharacteristic
264C4#1566805811yescharacteristic
265C2—42no—
266C2—3562no—
267C2—7122no—
268C2#1915223611yescharacteristic
269C2C2×#1566803711yescharacteristic
270C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#556×C89C2
socleC22×C89C22×D4
prime radicalD4×D356C2
hypercenter#556D89
hypocenterC89#3324
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #19151946C2semidirect
3. #19151922C2semidirect
4. #19151875C2semidirect
5. #19151846C2semidirect
6. #19151798C2semidirect
7. #19151748C2semidirect
8. C4×#13083561C2semidirect
9. #19151676C2semidirect
10. #19151602C2semidirect
11. #556×C89C2semidirect
15. C2×#13083561C22semidirect
16. C2×#13083558C22semidirect
22. #15667945C22semidirect
23. #15667943C22semidirect
24. C4⋊#10623494C22semidirect
25. #15667936C22semidirect
28. #15667932C22semidirect
29. #15667932C22semidirect
30. #15667932C22semidirect
31. C22⋊#10623494C22semidirect
32. C4×#10623494C22semidirect
33. C4⋊Q8×C89C22semidirect
36. C22⋊Q8×C89C22semidirect
38. C4×Q8×C89C22semidirect
40. #117×C89C22semidirect
136. C89#3324semidirect
137. #556D89semidirect
153. C4⋊Q8C2×D89semidirect
157. C22⋊Q8C2×D89semidirect
162. C4×Q8C2×D89semidirect
165. #117C2×D89semidirect

Maximal subgroups

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

subgroupindex
D4×D3562
#191519462
#191519222
#191518752
#191518462
#191517982
#191517482
C4×#130835612
#191516762
#191516022
#556×C892
#332489