Finite Group Databasebeta

← #26030496

Subgroups — #26030496

Order 11392.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#19152203C211yesmaximal, characteristic, complemented
2#19152072C211yesmaximal, characteristic, complemented
3#19151923C212yesmaximal, complemented
4#19151899C212yesmaximal, complemented
5#19151794C212yesmaximal, complemented
6#19151734C212yesmaximal, complemented
7#19151711C212yesmaximal, complemented
8C4×D712C212yesmaximal, complemented
9#433×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C2×D712C2212yes—
12C2×D712C2212yes—
13#15668009C2211yescharacteristic, complemented
14#15668004C2211yescharacteristic, complemented
15#15667997—22no—
16#15667986C2212yes—
17#15667985—22no—
18C4×D356C2212yes—
19C4×D356C2212yes—
20C4×D356C2212yescomplemented
21#15667974—22no—
22#15667971C2211yescharacteristic
23C22⋊C4×D89—22no—
24#15667946C2212yescomplemented
25#15667944C2212yescomplemented
26#15667934C2212yes—
27#15667934C2212yes—
28#15667934C2212yescomplemented
29#15667934C2212yescomplemented
30#117×C89C2211yescharacteristic
31C4⋊C8×C89C2212yescomplemented
32C22⋊C8×C89C2212yes—
33#97×C89C2211yescharacteristic, complemented
34C4×C8×C89C2211yescharacteristic, complemented
35C23×D89—21no—
36C2×D356—21no—
37C2×D356—24no—
38C2×D356—22no—
39C2×D356C2312yes—
40C2×D356C2312yes—
41C2×C22⋊D89—22no—
42C2×C4×D89—22no—
43C2×C4×D89—22no—
44C2×C4×D89—22no—
45D712—24no—
46D712—24no—
47C4⋊Dic89C2312yes—
48C4⋊Dic89C2312yes—
49#13083553—22no—
50C22⋊Dic89—21no—
51#13083551—22no—
52#13083551—22no—
53#13083551—22no—
54#13083551—22no—
55C4×Dic89—21no—
56C22×C4×C89C2311yescharacteristic
57C2×C8×C89C2312yes—
58C2×C8×C89C2312yes—
59C4⋊C4×C89D412yes—
60C22⋊C4×C89D412yes—
61C42×C89C2311yescharacteristic
62C42×C89C2311yescharacteristic
63C23×C89C2×D411yescharacteristic
64C22×D89—22no—
65C22×D89—24no—
66C22×D89—22no—
67C22×D89—82no—
68C2×C4×C89—22no—
69C2×C4×C89C2×D412yes—
70C2×C4×C89C2×D412yes—
71C2×C4×C89C2×D411yescharacteristic
72C2×C4×C89C2411yescharacteristic
73C22⋊D89—82no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76D356—24no—
77D356—22no—
78D356—22no—
79D356—22no—
80D356—82no—
81D356#4114yes—
82C4×D89—82no—
83C4×D89—82no—
84C4×D89—82no—
85C8×C89—22no—
86C8×C89—22no—
87C22×C89—21no—
88C22×C89—22no—
89C22×C89C22×D411yescharacteristic
90C2×D89—24no—
91C2×D89—42no—
92C2×D89—42no—
93C2×D89—42no—
94C2×D89—42no—
95C2×D89—42no—
96C2×D89—84no—
97C4×C89—21no—
98C4×C89—22no—
99C4×C89—22no—
100C4×C89C2×#4112yes—
101Dic89—42no—
102Dic89—42no—
103C2×C89—41no—
104C2×C89#52511yescharacteristic
105C2×C89#57612yes—
106D89—44no—
107D89—82no—
108#3122—891nomaximal, Sylow
109C89#312211yescharacteristic, complemented, Sylow
110#540—891no—
111#518—891no—
112#482—892no—
113#478—892no—
114#459—892no—
115#447—892no—
116#442—892no—
117C4×D8—892no—
118#433D8911yescharacteristic, complemented
119C22×D4—891no—
120C2×D8—892no—
121C2×D8—892no—
122#127—891no—
123#125—891no—
124#123—1782no—
125#121—892no—
126#121—1782no—
127C4×D4—892no—
128C4×D4—892no—
129C4×D4—892no—
130C4×D4—1782no—
131#117—891no—
132#117C2×D8911yescharacteristic
133C2×C22⋊C4—1782no—
134#107—892no—
135#106—892no—
136C4⋊C8C2×D8912yescomplemented
137#102—892no—
138#102—892no—
139#102—892no—
140#102—892no—
141C22⋊C8C2×D8912yes—
142#97C2×D8911yescharacteristic, complemented
143C4×C8C2×D8911yescharacteristic, complemented
144C24—1781no—
145C2×D4—892no—
146C2×D4—892no—
147C2×D4—1784no—
148C2×D4—1782no—
149C2×D4—1781no—
150C2×D4—1782no—
151C22×C4—1782no—
152C22×C4—1782no—
153C22×C4—1782no—
154C22×C4C22×D8911yescharacteristic
155D8—1784no—
156D8—1784no—
157C2×C8C22×D8912yes—
158C2×C8C22×D8912yes—
159C4⋊C4—892no—
160C4⋊C4—892no—
161C4⋊C4—1782no—
162C4⋊C4D35612yes—
163C22⋊C4—1781no—
164C22⋊C4—1782no—
165C22⋊C4—1782no—
166C22⋊C4—1782no—
167C22⋊C4—1782no—
168C22⋊C4D35612yes—
169C42—1781no—
170C42C22×D8911yescharacteristic
171C42C22×D8911yescharacteristic
172C23—1784no—
173C23—1782no—
174C23—1782no—
175C23—7122no—
176C23C2×D35611yescharacteristic
177D4—894no—
178D4—1784no—
179D4—1782no—
180D4—1782no—
181D4—1782no—
182D4—7122no—
183D4—7122no—
184C2×C4—22no—
185C2×C4—1782no—
186C2×C4—1782no—
187C2×C4—7122no—
188C2×C4—7122no—
189C2×C4—7122no—
190C2×C4C2×D35611yescharacteristic
191C2×C4C2×D35612yes—
192C2×C4C2×D35612yes—
193C2×C4C23×D8911yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—3562no—
199C22—3562no—
200C22—3562no—
201C22—3562no—
202C22—3562no—
203C22—1784no—
204C22—7124no—
205C22C22×D35611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—3562no—
210C4—3562no—
211C4#41×D8912yes—
212C2—41no—
213C2—3564no—
214C2—7122no—
215C2#1915211011yescharacteristic
216C2#1915240312yes—
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#433×C89C2
socleC22×C89C22×D4
hypercenter#433D89
hypocenterC89#3122
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19152203C2semidirect
2. #19152072C2semidirect
3. #19151923C2semidirect
4. #19151899C2semidirect
5. #19151794C2semidirect
6. #19151734C2semidirect
7. #19151711C2semidirect
8. C4×D712C2semidirect
9. #433×C89C2semidirect
13. #15668009C22semidirect
14. #15668004C22semidirect
20. C4×D356C22semidirect
24. #15667946C22semidirect
25. #15667944C22semidirect
28. #15667934C22semidirect
29. #15667934C22semidirect
31. C4⋊C8×C89C22semidirect
33. #97×C89C22semidirect
34. C4×C8×C89C22semidirect
109. C89#3122semidirect
118. #433D89semidirect
136. C4⋊C8C2×D89semidirect
142. #97C2×D89semidirect
143. C4×C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522032
#191520722
#191519232
#191518992
#191517942
#191517342
#191517112
C4×D7122
#433×C892
#312289