Finite Group Databasebeta

← #26029100

Subgroups — #26029100

Order 11392.

528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13083559C211yesmaximal, characteristic
2#19152073C211yesmaximal, characteristic, complemented
3#19152072C211yesmaximal, characteristic, complemented
4#19151707C214yesmaximal, complemented
5#19151678C214yesmaximal, complemented
6#19151634C211yesmaximal, characteristic, complemented
7#19151604C211yesmaximal, characteristic, complemented
8#19151556C211yesmaximal, characteristic, complemented
9#418×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C2×#13083559C418yescomplemented
12C2×#13083559C2212yes—
13C2×#13083559C2212yes—
14C22×#10623494C2211yescharacteristic
15C4×D356—22no—
16D4×Dic89—22no—
17D4×Dic89C2214yescomplemented
18#15667974C2214yescomplemented
19#15667971C2211yescharacteristic
20#15667971C2211yescharacteristic
21C2×C22⋊Dic89—22no—
22C22⋊C4×D89—22no—
23#15667945C2212yescomplemented
24#15667943C2212yescomplemented
25#15667934C2214yescomplemented
26#15667922C2212yescomplemented
27C8×Dic89C2212yescomplemented
28C22×D4×C89C2211yescharacteristic
29C2×M16×C89C2211yescharacteristic
30#117×C89C2211yescharacteristic
31#102×C89C2214yescomplemented
32C23×D89—21no—
33C2×D356—21no—
34C2×D356—22no—
35C2×D356C2×C414yescomplemented
36C2×D356C2312yes—
37C22×Dic89—24no—
38C2×C4×D89—24no—
39#13083559C2×C418yescomplemented
40#13083559C2×C418yescomplemented
41C2×#10623494C2×C414yescomplemented
42C2×#10623494C2311yescharacteristic
43C2×#10623494C2311yescharacteristic
44C4⋊Dic89D412yes—
45C4⋊Dic89C2312yes—
46C22⋊Dic89—21no—
47C22⋊Dic89—24no—
48C22⋊Dic89D412yes—
49#13083551—24no—
50C4×Dic89—21no—
51C4×Dic89C2312yes—
52C24×C89—21no—
53C2×D4×C89—21no—
54C2×D4×C89—22no—
55C2×D4×C89C2×C414yescomplemented
56C2×D4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58M16×C89—22no—
59C2×C8×C89C2312yes—
60C4⋊C4×C89C2312yes—
61C22⋊C4×C89—21no—
62C42×C89—21no—
63C23×C89—22no—
64C23×C89—24no—
65C23×C89—82no—
66C23×C89C2×D411yescharacteristic
67C22×D89—22no—
68C22×D89—24no—
69C22×D89—82no—
70D4×C89—24no—
71D4×C89—22no—
72D4×C89C22×C414yes—
73C2×C4×C89—22no—
74C2×C4×C89C22×C412yes—
75C2×C4×C89C2×D411yescharacteristic
76C2×C4×C89#4112yes—
77C2×C4×C89C2411yescharacteristic
78C2×Dic89—22no—
79C2×Dic89—84no—
80C2×Dic89C2×D414yes—
81D356—24no—
82D356—22no—
83D356C22×C414yes—
84C4×D89—84no—
85C8×C89—22no—
86#10623494C22×C412yes—
87#10623494C22×C412yes—
88C22×C89—22no—
89C22×C89—24no—
90C22×C89—44no—
91C22×C89—84no—
92C22×C89C4×D412yes—
93C22×C89C22×D411yescharacteristic
94C2×D89—24no—
95C2×D89—44no—
96C2×D89—84no—
97C4×C89—42no—
98C4×C89C4×D412yes—
99C4×C89C23×C411yescharacteristic
100C4×C89C2×#4111yescharacteristic
101Dic89—24no—
102Dic89—42no—
103C2×C89—22no—
104C2×C89—44no—
105C2×C89C2×C4×D411yescharacteristic
106C2×C89#57612yes—
107D89—44no—
108#2948—891nomaximal, Sylow
109C89#294811yescharacteristic, complemented, Sylow
110C22×D8—891no—
111#518—891no—
112#518—891no—
113#442—894no—
114C4×D8—894no—
115#427—891no—
116#418—891no—
117#418D8911yescharacteristic, complemented
118#405—891no—
119C22×D4—891no—
120C22×D4C2×D8911yescharacteristic
121C2×D8—898no—
122C2×D8—892no—
123C2×D8—892no—
124C2×M16C2×D8911yescharacteristic
125C22×C8—891no—
126C4×D4—894no—
127C4×D4—894no—
128C4×D4—1782no—
129C4×D4—1782no—
130#117—891no—
131#117—891no—
132#117C2×D8911yescharacteristic
133C2×C22⋊C4—1782no—
134C2×C22⋊C4—1782no—
135#107—892no—
136#106—892no—
137#102—894no—
138#102C2×D8914yescomplemented
139#97—892no—
140C4×C8—892no—
141C24—21no—
142C24—1781no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4—894no—
146C2×D4—892no—
147C2×D4—1781no—
148C2×D4—1782no—
149C2×D4C4×D8914yescomplemented
150C2×D4C22×D8912yes—
151C22×C4—1784no—
152C22×C4—1784no—
153C22×C4C22×D8911yescharacteristic
154D8—898no—
155D8—898no—
156M16—22no—
157C2×C8—894no—
158C2×C8—891no—
159C2×C8—891no—
160C2×C8C22×D8912yes—
161C4⋊C4—892no—
162C4⋊C4—892no—
163C4⋊C4C22×D8912yes—
164C22⋊C4—21no—
165C22⋊C4—892no—
166C22⋊C4—1784no—
167C22⋊C4—1784no—
168C22⋊C4—1781no—
169C42—21no—
170C42—892no—
171C42—1781no—
172C23—22no—
173C23—24no—
174C23—82no—
175C23—1782no—
176C23—1784no—
177C23—7122no—
178C23D4×D8911yescharacteristic
179D4—24no—
180D4—22no—
181D4—894no—
182D4—1784no—
183D4—1782no—
184D4C2×C4×D8914yes—
185C2×C4—22no—
186C2×C4—894no—
187C2×C4—1782no—
188C2×C4—7124no—
189C2×C4—7124no—
190C2×C4C2×C4×D8912yes—
191C2×C4D4×D8911yescharacteristic
192C2×C4#1308357312yes—
193C2×C4C23×D8911yescharacteristic
194C8—22no—
195C8—892no—
196C8—892no—
197C22—22no—
198C22—24no—
199C22—44no—
200C22—84no—
201C22—3564no—
202C22—1784no—
203C22—7124no—
204C22#1566797212yes—
205C22C2×D4×D8911yescharacteristic
206C4—42no—
207C4—3562no—
208C4—1784no—
209C4#1566797212yes—
210C4C22×C4×D8911yescharacteristic
211C4C2×#1308357311yescharacteristic
212C2—22no—
213C2—44no—
214C2—3564no—
215C2C2×#1566797211yescharacteristic
216C2#1915240212yes—
subgroupG/H
centerC22C2×D4×D89
commutatorC4×C89C23×C4
FrattiniC2×C4C23×D89
Fitting#418×C89C2
socleC22×C89C22×D4
prime radicalC22×#13083559C2
cosocleC2×C4×C89C24
hypercenter#418D89
hypocenterC89#2948
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #19152073C2semidirect
3. #19152072C2semidirect
4. #19151707C2semidirect
5. #19151678C2semidirect
6. #19151634C2semidirect
7. #19151604C2semidirect
8. #19151556C2semidirect
9. #418×C89C2semidirect
11. C2×#13083559C4semidirect
17. D4×Dic89C22semidirect
18. #15667974C22semidirect
23. #15667945C22semidirect
24. #15667943C22semidirect
25. #15667934C22semidirect
26. #15667922C22semidirect
27. C8×Dic89C22semidirect
31. #102×C89C22semidirect
35. C2×D356C2×C4semidirect
39. #13083559C2×C4semidirect
40. #13083559C2×C4semidirect
41. C2×#10623494C2×C4semidirect
55. C2×D4×C89C2×C4semidirect
109. C89#2948semidirect
117. #418D89semidirect
138. #102C2×D89semidirect
149. C2×D4C4×D89semidirect

Maximal subgroups

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

subgroupindex
C22×#130835592
#191520732
#191520722
#191517072
#191516782
#191516342
#191516042
#191515562
#418×C892
#294889