Finite Group Databasebeta

← #26034946

Subgroups — #26034946

Order 11392.

958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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#19152348C213yesmaximal, complemented
2#19152317C216yesmaximal, complemented
3#19152279C216yesmaximal, complemented
4#19152212C216yesmaximal, complemented
5#19152183C216yesmaximal, complemented
6#19152127C213yesmaximal, complemented
7H(3,𝔽4)×C89C211yesmaximal, characteristic, complemented
8#15668010C2216yescomplemented
9#15668006C2212yescomplemented
10#15668005C2216yescomplemented
11#15668005C2216yescomplemented
12#15668005C2216yescomplemented
13#15668005C2216yescomplemented
14#15668004C2213yescomplemented
15#15667999C2216yes—
16#15667998C2216yescomplemented
17#15667994C2216yescomplemented
18#15667993C2216yes—
19#15667993C2216yes—
20#15667989C2216yescomplemented
21#15667989C2216yescomplemented
22#15667989C2216yescomplemented
23#15667988C2213yescomplemented
24#15667984C2216yes—
25#15667983C2213yes—
26#15667981C2212yescomplemented
27Q8×Dic89C2213yescomplemented
28C4×Dic178C2216yescomplemented
29D4×Dic89C2216yes—
30D4×Dic89C2213yes—
31#15667972C2216yescomplemented
32#15667968C2216yescomplemented
33#15667968C2216yescomplemented
34C2×C22⋊Dic89C2216yescomplemented
35C42×D89C2211yescharacteristic, complemented
36#124×C89C2216yes—
37#124×C89C2213yes—
38#120×C89C2216yes—
39C2×Dic178C2316yes—
40C2×C22⋊D89C2316yes—
41C22×Dic89C2316yes—
42C22×Dic89C2316yes—
43C2×C4×D89C2313yes—
44C4⋊Dic89C2316yes—
45C4⋊Dic89C2313yes—
46C4⋊Dic89C2313yes—
47#13083553C2316yes—
48#13083553C2316yes—
49#13083553C2316yes—
50#13083553C2316yes—
51#13083553C2316yes—
52C22⋊Dic89C2316yes—
53C22⋊Dic89C2316yes—
54C22⋊Dic89C2316yes—
55C22⋊Dic89C2316yes—
56C22⋊Dic89C2316yes—
57#13083551C2316yes—
58C4×Dic89C2316yes—
59C4×Dic89C2313yes—
60C4×Dic89C2316yes—
61C24×C89C2312yes—
62C2×Q8×C89C2313yes—
63C2×D4×C89C2313yes—
64C2×D4×C89C2316yes—
65C22⋊C4×C89C2316yes—
66C22⋊C4×C89C2316yes—
67C22⋊C4×C89C2316yes—
68C42×C89C2312yes—
69C42×C89C2311yescharacteristic
70C23×C89—46no—
71C23×C89C2416yes—
72C22×D89C2411yescharacteristic
73Q8×C89—43no—
74D4×C89—46no—
75D4×C89—43no—
76C2×C4×C89C2416yes—
77C2×C4×C89C2413yes—
78C22⋊D89—46no—
79C2×Dic89—46no—
80C2×Dic89—46no—
81C2×Dic89C2413yes—
82C2×Dic89C2416yes—
83C2×Dic89C2416yes—
84C4×D89—43no—
85Dic178—46no—
86C22×C89—26no—
87C22×C89—26no—
88C22×C89—26no—
89C22×C89—84no—
90C22×C89C2511yescharacteristic
91C2×D89—23no—
92C4×C89—26no—
93C4×C89—23no—
94Dic89—26no—
95Dic89—26no—
96Dic89—23no—
97C2×C89—46no—
98C2×C89#58513yes—
99D89—41no—
100#3568—891nomaximal, Sylow
101C89#356811yescharacteristic, complemented, Sylow
102#563—893no—
103H(3,𝔽4)D8911yescharacteristic, complemented
104#556—896no—
105#551—896no—
106#542—896no—
107#538—896no—
108#529—893no—
109C4⋊Q8—896no—
110#126—896no—
111#126—896no—
112#126—896no—
113#126—896no—
114#126—892no—
115#125—893no—
116#124—896no—
117#124—896no—
118#124C2×D8913yes—
119#124C2×D8916yes—
120#123—896no—
121#123—896no—
122#123—896no—
123C22⋊Q8—893no—
124C22⋊Q8—896no—
125C22⋊Q8—896no—
126C22⋊Q8—896no—
127#121—893no—
128#121—896no—
129#120—892no—
130#120C2×D8916yes—
131C4×Q8—893no—
132C4×Q8—896no—
133C4×D4—893no—
134C4×D4—896no—
135C4×D4—896no—
136#117—896no—
137#117—896no—
138C2×C22⋊C4—896no—
139C2×C42—891no—
140C24C22×D8912yes—
141C2×Q8—896no—
142C2×Q8C22×D8913yes—
143C2×D4—896no—
144C2×D4C22×D8913yes—
145C2×D4C22×D8916yes—
146C22×C4—896no—
147C22×C4—896no—
148C22×C4—893no—
149C4⋊C4—896no—
150C4⋊C4—896no—
151C4⋊C4—896no—
152C4⋊C4—896no—
153C4⋊C4—893no—
154C4⋊C4—896no—
155C4⋊C4—893no—
156C4⋊C4—896no—
157C22⋊C4—896no—
158C22⋊C4—896no—
159C22⋊C4—896no—
160C22⋊C4—896no—
161C22⋊C4—896no—
162C22⋊C4—896no—
163C22⋊C4C22×D8916yes—
164C22⋊C4C22×D8916yes—
165C22⋊C4C22×D8916yes—
166C42—893no—
167C42—896no—
168C42—896no—
169C42C22×D8911yescharacteristic
170C42C22×D8912yes—
171C23—46no—
172C23—891no—
173C23C23×D8916yes—
174Q8—43no—
175Q8—3566no—
176D4—43no—
177D4—46no—
178D4—3566no—
179C2×C4—893no—
180C2×C4—896no—
181C2×C4—896no—
182C2×C4—3563no—
183C2×C4—3566no—
184C2×C4—3566no—
185C2×C4C23×D8916yes—
186C2×C4C23×D8913yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—1783no—
192C22C24×D8911yescharacteristic
193C4—23no—
194C4—26no—
195C4—1783no—
196C4—1786no—
197C4—1786no—
198C2—46no—
199C2—3561no—
200C2#1915243313yes—
subgroupG/H
center, FrattiniC22C24×D89
commutator, socle, cosocleC22×C89C25
FittingH(3,𝔽4)×C89C2
hypercenterH(3,𝔽4)D89
hypocenterC89#3568
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #19152348C2semidirect
2. #19152317C2semidirect
3. #19152279C2semidirect
4. #19152212C2semidirect
5. #19152183C2semidirect
6. #19152127C2semidirect
7. H(3,𝔽4)×C89C2semidirect
8. #15668010C22semidirect
9. #15668006C22semidirect
10. #15668005C22semidirect
11. #15668005C22semidirect
12. #15668005C22semidirect
13. #15668005C22semidirect
14. #15668004C22semidirect
16. #15667998C22semidirect
17. #15667994C22semidirect
20. #15667989C22semidirect
21. #15667989C22semidirect
22. #15667989C22semidirect
23. #15667988C22semidirect
26. #15667981C22semidirect
27. Q8×Dic89C22semidirect
28. C4×Dic178C22semidirect
31. #15667972C22semidirect
32. #15667968C22semidirect
33. #15667968C22semidirect
34. C2×C22⋊Dic89C22semidirect
35. C42×D89C22semidirect
101. C89#3568semidirect
103. H(3,𝔽4)D89semidirect

Maximal subgroups

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

subgroupindex
#191523482
#191523172
#191522792
#191522122
#191521832
#191521272
H(3,𝔽4)×C892
#356889