Finite Group Databasebeta

← #26034656

Subgroups — #26034656

Order 11392.

1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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#19152340C213yesmaximal, complemented
2#19152310C216yesmaximal, complemented
3#19152230C216yesmaximal, complemented
4#19152166C216yesmaximal, complemented
5#19152163C216yesmaximal, complemented
6#19152147C213yesmaximal, complemented
7H(3,𝔽4)×C89C211yesmaximal, characteristic, complemented
8C2×#13083575C2213yescomplemented
9C2×#13083573C2213yescomplemented
10C22×C22⋊D89C2216yescomplemented
11C2×D4×D89C2216yescomplemented
12#15668010C2213yescomplemented
13#15668009C2212yescomplemented
14#15668008C2213yes—
15#15668008C2216yescomplemented
16#15668001C2216yescomplemented
17#15668000C2213yescomplemented
18#15667998C22112yescomplemented
19#15667985C22112yescomplemented
20#15667985C22112yescomplemented
21#15667984C22112yescomplemented
22#15667982C2216yescomplemented
23#15667982C22112yescomplemented
24#15667981C2212yescomplemented
25#15667980C2216yescomplemented
26#15667972C22112yescomplemented
27#15667969C2216yescomplemented
28#15667968C2216yescomplemented
29C42×D89C2211yescharacteristic, complemented
30#124×C89C2213yescomplemented
31#124×C89C2216yescomplemented
32#120×C89C2216yescomplemented
33C23×D89C2316yes—
34#13083575—46no—
35#13083573—46no—
36C2×Dic178C2313yes—
37C2×D356C2313yes—
38C2×D356C2316yes—
39C2×D356C2316yes—
40C2×C22⋊D89—412no—
41C2×C22⋊D89C23112yes—
42C2×C22⋊D89C23112yes—
43C2×C22⋊D89C2316yes—
44D4×D89—412no—
45C22×Dic89C2316yes—
46C2×C4×D89C2316yes—
47C2×C4×D89C2313yes—
48#13083553C23112yes—
49C22⋊Dic89C2316yes—
50#13083551C23112yes—
51#13083551C23112yes—
52C4×Dic89C2316yes—
53C4×Dic89C2313yes—
54C24×C89C2312yes—
55C2×Q8×C89C2313yes—
56C2×D4×C89C2313yes—
57C2×D4×C89C2316yes—
58C22⋊C4×C89C2316yes—
59C22⋊C4×C89C23112yes—
60C42×C89C2312yes—
61C42×C89C2311yescharacteristic
62C23×C89—46no—
63C23×C89C2416yes—
64C22×D89—412no—
65C22×D89—46no—
66C22×D89C2416yes—
67C22×D89C2411yescharacteristic
68Q8×C89—43no—
69D4×C89—46no—
70D4×C89—43no—
71C2×C4×C89C2413yes—
72C2×C4×C89C2416yes—
73C22⋊D89—224no—
74C22⋊D89—412no—
75C22⋊D89—46no—
76C2×Dic89—212no—
77C2×Dic89C2416yes—
78C2×Dic89C2413yes—
79D356—46no—
80D356—43no—
81D356—46no—
82C4×D89—212no—
83C4×D89—26no—
84Dic178—43no—
85C22×C89—26no—
86C22×C89—212no—
87C22×C89—84no—
88C22×C89C2511yescharacteristic
89C2×D89—23no—
90C2×D89—26no—
91C2×D89—212no—
92C2×D89—812no—
93C4×C89—23no—
94C4×C89—26no—
95Dic89—26no—
96Dic89H(5,𝔽2)16yes—
97C2×C89—46no—
98C2×C89C2×H(5,𝔽2)13yes—
99D89—41no—
100D89—46no—
101#3549—891nomaximal, Sylow
102C89#354911yescharacteristic, complemented, Sylow
103H(3,𝔽4)—893no—
104H(3,𝔽4)D8911yescharacteristic, complemented
105#555—896no—
106D42—896no—
107#535—896no—
108#535—896no—
109#532—893no—
110C2×#41—893no—
111C2×#41—893no—
112C22×D4—896no—
113C22×D4—896no—
114C4⋊Q8—893no—
115#127—893no—
116#127—896no—
117#127—892no—
118#124—896no—
119#124—8912no—
120#124—893no—
121#124C2×D8913yescomplemented
122#124C2×D8916yescomplemented
123#121—8912no—
124#121—8912no—
125#121—8912no—
126#120—892no—
127#120—896no—
128#120—896no—
129#120—8912no—
130#120C2×D8916yescomplemented
131C4×D4—8912no—
132#117—896no—
133#117—896no—
134C2×C42—891no—
135C24—896no—
136C24C22×D8912yes—
137#41—3566no—
138#41—3566no—
139C2×Q8—893no—
140C2×Q8C22×D8913yes—
141C2×D4—8912no—
142C2×D4—896no—
143C2×D4—8912no—
144C2×D4—893no—
145C2×D4—896no—
146C2×D4—896no—
147C2×D4—35612no—
148C2×D4—35612no—
149C2×D4C22×D8913yes—
150C2×D4C22×D8916yes—
151C22×C4—896no—
152C22×C4—893no—
153C22×C4—896no—
154C4⋊C4—8912no—
155C22⋊C4—896no—
156C22⋊C4—8912no—
157C22⋊C4—8912no—
158C22⋊C4C22×D8916yes—
159C22⋊C4C22×D89112yes—
160C42—893no—
161C42—896no—
162C42C22×D8911yescharacteristic
163C42C22×D8912yes—
164C23—46no—
165C23—896no—
166C23—891no—
167C23—3566no—
168C23—35612no—
169C23C23×D8916yes—
170Q8—43no—
171Q8—3563no—
172D4—46no—
173D4—43no—
174D4—3566no—
175D4—3566no—
176D4—3563no—
177D4—35612no—
178D4—3566no—
179D4—17824no—
180C2×C4—893no—
181C2×C4—896no—
182C2×C4—17812no—
183C2×C4—1786no—
184C2×C4—17812no—
185C2×C4C23×D8913yes—
186C2×C4C23×D8916yes—
187C22—26no—
188C22—212no—
189C22—84no—
190C22—1783no—
191C22—1786no—
192C22—17812no—
193C22—71212no—
194C22C24×D8911yescharacteristic
195C4—26no—
196C4—23no—
197C4—896no—
198C4—1786no—
199C2—46no—
200C2—3561no—
201C2—3566no—
202C2H(5,𝔽2)×D8913yes—
subgroupG/H
center, FrattiniC22C24×D89
commutator, socle, cosocleC22×C89C25
FittingH(3,𝔽4)×C89C2
hypercenterH(3,𝔽4)D89
hypocenterC89#3549
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #19152340C2semidirect
2. #19152310C2semidirect
3. #19152230C2semidirect
4. #19152166C2semidirect
5. #19152163C2semidirect
6. #19152147C2semidirect
7. H(3,𝔽4)×C89C2semidirect
8. C2×#13083575C22semidirect
9. C2×#13083573C22semidirect
10. C22×C22⋊D89C22semidirect
11. C2×D4×D89C22semidirect
12. #15668010C22semidirect
13. #15668009C22semidirect
15. #15668008C22semidirect
16. #15668001C22semidirect
17. #15668000C22semidirect
18. #15667998C22semidirect
19. #15667985C22semidirect
20. #15667985C22semidirect
21. #15667984C22semidirect
22. #15667982C22semidirect
23. #15667982C22semidirect
24. #15667981C22semidirect
25. #15667980C22semidirect
26. #15667972C22semidirect
27. #15667969C22semidirect
28. #15667968C22semidirect
29. C42×D89C22semidirect
30. #124×C89C22semidirect
31. #124×C89C22semidirect
32. #120×C89C22semidirect
102. C89#3549semidirect
104. H(3,𝔽4)D89semidirect
121. #124C2×D89semidirect
122. #124C2×D89semidirect
130. #120C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191523402
#191523102
#191522302
#191521662
#191521632
#191521472
H(3,𝔽4)×C892
#354989