Finite Group Databasebeta

← #26030734

Subgroups — #26030734

Order 11392.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15668039C212yesmaximal, complemented
2C2×#15668035C211yesmaximal, characteristic, complemented
3C2×D8×D89C211yesmaximal, characteristic, complemented
4#19152166C212yesmaximal, complemented
5#19151988C212yesmaximal, complemented
6#19151984C212yesmaximal, complemented
7#19151983C211yesmaximal, characteristic, complemented
8#19151975C211yesmaximal, characteristic, complemented
9#19151973C211yesmaximal, characteristic, complemented
10#19151552C211yesmaximal, characteristic, complemented
11#495×C89C211yesmaximal, characteristic, complemented
12C2×#13083575C2212yes—
13C2×D4×D89C2212yes—
14#15668039—28no—
15#15668035—24no—
16C2×#13083561C2212yescomplemented
17C2×#13083561C2212yescomplemented
18C2×D712C2211yescharacteristic
19C2×D712C2212yescomplemented
20C2×D712C2211yescharacteristic, complemented
21C2×#13083559C2212yes—
22C2×#13083559C2212yescomplemented
23D8×D89—24no—
24C2×#13083557C2211yescharacteristic
25C2×C8×D89C2211yescharacteristic
26#15668009C2212yescomplemented
27#15668008C2212yescomplemented
28#15668001C2212yescomplemented
29#15667985—24no—
30#15667982—24no—
31#15667969C2211yescharacteristic
32#15667923C2211yescharacteristic, complemented
33#15667922C2211yescharacteristic, complemented
34C8×Dic89C2211yescharacteristic, complemented
35C2×Q16×C89C2211yescharacteristic, complemented
36C2×SD16×C89C2212yescomplemented
37C2×D8×C89C2211yescharacteristic
38#124×C89C2212yescomplemented
39C4×C8×C89C2211yescharacteristic, complemented
40C23×D89—22no—
41#13083575—24no—
42#13083575—24no—
43C2×D356—22no—
44C2×D356—24no—
45C2×D356C2312yes—
46C2×D356C2312yes—
47C2×C22⋊D89—22no—
48C2×C22⋊D89—24no—
49D4×D89—24no—
50D4×D89—24no—
51C2×C4×D89—22no—
52C2×C4×D89C2311yescharacteristic
53#13083561—24no—
54#13083561—24no—
55D712—22no—
56D712—22no—
57D712—24no—
58#13083559—24no—
59#13083559—24no—
60#13083557D414yescomplemented
61C2×#10623494C2311yescharacteristic
62C2×#10623494C2311yescharacteristic
63C8×D89D414yescomplemented
64#13083553D412yes—
65#13083551—24no—
66#13083551D412yes—
67C4×Dic89C2311yescharacteristic
68C2×Q8×C89C2312yes—
69C2×D4×C89C2312yes—
70Q16×C89—22no—
71SD16×C89—24no—
72D8×C89—22no—
73C2×C8×C89C2311yescharacteristic
74C2×C8×C89C2311yescharacteristic
75C22⋊C4×C89—24no—
76C42×C89C2311yescharacteristic
77C23×C89—22no—
78C22×D89—22no—
79C22×D89—22no—
80C22×D89—44no—
81C22×D89—84no—
82C22×D89C2×D411yescharacteristic
83Q8×C89—22no—
84Q8×C89—22no—
85D4×C89—22no—
86D4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89C2×D412yes—
89C2×C4×C89C2411yescharacteristic
90C22⋊D89—44no—
91C22⋊D89—84no—
92C2×Dic89C2×D412yes—
93C2×Dic89C2×D411yescharacteristic
94D356—22no—
95D356—22no—
96D356—22no—
97D356—22no—
98D356—44no—
99D356—84no—
100C4×D89—44no—
101C4×D89C2×D412yes—
102C4×D89C2×D412yes—
103C8×C89C2×D412yes—
104C8×C89C2×D412yes—
105#10623494C2×D412yes—
106#10623494C2×D412yes—
107C22×C89—42no—
108C22×C89—44no—
109C22×C89C22×D411yescharacteristic
110C2×D89—22no—
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—44no—
114C2×D89—44no—
115C2×D89—88no—
116C2×D89#12712yes—
117C4×C89—22no—
118C4×C89—42no—
119C4×C89C22×D411yescharacteristic
120C4×C89C22×D411yescharacteristic
121Dic89—22no—
122Dic89#12712yes—
123C2×C89—82no—
124C2×C89C2×#12711yescharacteristic
125C2×C89#57612yes—
126D89—22no—
127D89—82no—
128D89—82no—
129#3155—891nomaximal, Sylow
130C89#315511yescharacteristic, complemented, Sylow
131C2×AGL(1,ℤ/8)—892no—
132C2×#135—891no—
133C22×D8—891no—
134#535—892no—
135#496—892no—
136#496—892no—
137#495—891no—
138#495D8911yescharacteristic, complemented
139#493—891no—
140#493—891no—
141#405—891no—
142C2×#41—892no—
143C22×D4—892no—
144AGL(1,ℤ/8)—1788no—
145#135—1784no—
146C2×Q16C2×D8911yescharacteristic, complemented
147C2×SD16—892no—
148C2×SD16—892no—
149C2×SD16C2×D8912yescomplemented
150C2×D8—892no—
151C2×D8—892no—
152C2×D8—891no—
153C2×D8—891no—
154C2×D8—892no—
155C2×D8—1784no—
156C2×D8C2×D8911yescharacteristic
157C2×M16—891no—
158C22×C8—891no—
159#127—892no—
160#127—892no—
161#124—892no—
162#124C2×D8912yescomplemented
163#121—1784no—
164#120—1784no—
165#117—891no—
166#97—891no—
167#97—891no—
168C4×C8—891no—
169C4×C8C2×D8911yescharacteristic, complemented
170C24—1782no—
171#41—1784no—
172#41—1784no—
173C2×Q8C22×D8912yes—
174C2×D4—892no—
175C2×D4—892no—
176C2×D4—1782no—
177C2×D4—1784no—
178C2×D4—1784no—
179C2×D4—1782no—
180C2×D4—1784no—
181C2×D4—1784no—
182C2×D4C22×D8912yes—
183C22×C4—891no—
184C22×C4—1782no—
185Q16—22no—
186SD16—24no—
187SD16—1784no—
188SD16—1784no—
189D8—22no—
190D8—1784no—
191D8—1784no—
192D8—1782no—
193D8—1782no—
194D8—1784no—
195M16—894no—
196C2×C8—891no—
197C2×C8—891no—
198C2×C8—894no—
199C2×C8C22×D8911yescharacteristic
200C2×C8C22×D8911yescharacteristic
201C4⋊C4—892no—
202C22⋊C4—24no—
203C22⋊C4—892no—
204C22⋊C4—1784no—
205C42—891no—
206C42C22×D8911yescharacteristic
207C23—22no—
208C23—891no—
209C23—3564no—
210C23—1782no—
211C23—1782no—
212C23—7124no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—3564no—
218D4—3564no—
219D4—1782no—
220D4—1782no—
221D4—1782no—
222D4—1782no—
223D4—7124no—
224D4—7124no—
225C2×C4—22no—
226C2×C4—891no—
227C2×C4—892no—
228C2×C4—892no—
229C2×C4—892no—
230C2×C4—3564no—
231C2×C4D4×D8912yes—
232C2×C4C23×D8911yescharacteristic
233C8—892no—
234C8—892no—
235C8D4×D8912yes—
236C8D4×D8912yes—
237C22—42no—
238C22—44no—
239C22—892no—
240C22—3562no—
241C22—3562no—
242C22—3564no—
243C22—3564no—
244C22—1782no—
245C22—7128no—
246C22C2×D4×D8911yescharacteristic
247C4—22no—
248C4—42no—
249C4—892no—
250C4—1782no—
251C4C2×D4×D8911yescharacteristic
252C4C2×D4×D8911yescharacteristic
253C2—82no—
254C2—1782no—
255C2—7122no—
256C2—7122no—
257C2#127×D8911yescharacteristic
258C2#1915240012yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#495×C89C2
socleC22×C89C22×D4
hypercenter#495D89
hypocenterC89#3155
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#15668039C2semidirect
2. C2×#15668035C2semidirect
3. C2×D8×D89C2semidirect
4. #19152166C2semidirect
5. #19151988C2semidirect
6. #19151984C2semidirect
7. #19151983C2semidirect
8. #19151975C2semidirect
9. #19151973C2semidirect
10. #19151552C2semidirect
11. #495×C89C2semidirect
16. C2×#13083561C22semidirect
17. C2×#13083561C22semidirect
19. C2×D712C22semidirect
20. C2×D712C22semidirect
22. C2×#13083559C22semidirect
26. #15668009C22semidirect
27. #15668008C22semidirect
28. #15668001C22semidirect
32. #15667923C22semidirect
33. #15667922C22semidirect
34. C8×Dic89C22semidirect
35. C2×Q16×C89C22semidirect
36. C2×SD16×C89C22semidirect
38. #124×C89C22semidirect
39. C4×C8×C89C22semidirect
60. #13083557D4semidirect
63. C8×D89D4semidirect
130. C89#3155semidirect
138. #495D89semidirect
146. C2×Q16C2×D89semidirect
149. C2×SD16C2×D89semidirect
162. #124C2×D89semidirect
169. C4×C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680392
C2×#156680352
C2×D8×D892
#191521662
#191519882
#191519842
#191519832
#191519752
#191519732
#191515522
#495×C892
#315589