Finite Group Databasebeta

← #26034030

Subgroups — #26034030

Order 11392.

1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 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×#15668058C212yesmaximal, complemented
2#19152270C214yesmaximal, complemented
3D4×D356C2112yesmaximal, complemented
4#19152167C216yesmaximal, complemented
5#19152148C213yesmaximal, complemented
6C2×#15668009C213yesmaximal, complemented
7C4×#41×C89C211yesmaximal, characteristic, complemented
8#15668058—216no—
9C2×#13083575C2214yescomplemented
10C2×#13083574C2216yescomplemented
11C22×D356C2216yescomplemented
12C22×D356C22112yescomplemented
13C2×D4×D89C22112yescomplemented
14#15668012C2211yescharacteristic, complemented
15#15668009C2213yescomplemented
16#15668009C2216yescomplemented
17#15668009C22112yescomplemented
18#15668000C2216yescomplemented
19#15667987C22124yescomplemented
20#15667986C22112yescomplemented
21#15667982C22124yescomplemented
22C4×D356C22112yescomplemented
23C2×#41×C89C2211yescharacteristic
24C4×Q8×C89C2212yescomplemented
25C4×D4×C89C2216yescomplemented
26#117×C89C2213yescomplemented
27C2×C42×C89C2213yescomplemented
28C23×D89C23112yes—
29#13083575—216no—
30#13083574—224no—
31C2×Dic178C2312yes—
32C2×D356—224no—
33C2×D356—424no—
34C2×D356C23112yes—
35C2×D356C23112yes—
36C2×D356C2316yes—
37C2×D356C23124yes—
38C2×C22⋊D89C23112yes—
39D4×D89—248no—
40C2×C4×D89C23112yes—
41C4⋊Dic89C2314yes—
42#13083551C23124yes—
43#41×C89D418yescomplemented
44C2×Q8×C89C2311yescharacteristic
45C2×D4×C89C2313yes—
46C22×C4×C89C2316yes—
47C22×C4×C89C2313yes—
48C4⋊C4×C89C2316yes—
49C22⋊C4×C89C2316yes—
50C42×C89C2316yes—
51C42×C89C2313yes—
52C42×C89C2311yescharacteristic
53C23×C89C2413yes—
54C22×D89—224no—
55C22×D89—424no—
56C22×D89C24112yes—
57Q8×C89C2×D414yescomplemented
58D4×C89C2×D4112yescomplemented
59C2×C4×C89—212no—
60C2×C4×C89C2×D4112yescomplemented
61C2×C4×C89C2416yes—
62C2×C4×C89C2411yescharacteristic
63C2×C4×C89C2413yes—
64C2×C4×C89C2412yes—
65C22⋊D89—224no—
66C2×Dic89C2414yes—
67D356—224no—
68D356—212no—
69D356—224no—
70D356—424no—
71C4×D89—224no—
72Dic178—24no—
73C22×C89—26no—
74C22×C89C22×D416yes—
75C22×C89C2511yescharacteristic
76C2×D89—212no—
77C2×D89—224no—
78C2×D89—824no—
79C4×C89—26no—
80C4×C89C22×D412yes—
81C4×C89C22×D416yes—
82C4×C89H(5,𝔽2)14yescomplemented
83Dic89—24no—
84C2×C89—26no—
85C2×C89C23×D411yescharacteristic
86C2×C89C2×H(5,𝔽2)12yes—
87D89—412no—
88#3498—891nomaximal, Sylow
89C89#349811yescharacteristic, complemented, Sylow
90C2×H(5,𝔽2)—892no—
91#550—894no—
92D42—8912no—
93#535—896no—
94#532—893no—
95C2×#127—893no—
96C4×#41D8911yescharacteristic, complemented
97H(5,𝔽2)—17816no—
98C2×#41—894no—
99C2×#41—896no—
100C2×#41C2×D8911yescharacteristic
101C22×D4—8912no—
102C22×D4—8912no—
103C22×D4—896no—
104C4⋊Q8—891no—
105#127—893no—
106#127—896no—
107#127—8912no—
108#124—896no—
109#121—8912no—
110#121—8924no—
111#120—8924no—
112C4×Q8C2×D8912yescomplemented
113C4×D4—8912no—
114C4×D4C2×D8916yescomplemented
115#117C2×D8913yescomplemented
116C2×C42C2×D8913yescomplemented
117C24—8912no—
118#41—17816no—
119#41—17824no—
120#41D35618yescomplemented
121C2×Q8—892no—
122C2×Q8C22×D8911yescharacteristic
123C2×D4—8912no—
124C2×D4—8924no—
125C2×D4—8912no—
126C2×D4—8912no—
127C2×D4—896no—
128C2×D4—35624no—
129C2×D4—17848no—
130C2×D4—17824no—
131C2×D4C22×D8913yes—
132C22×C4—8912no—
133C22×C4C22×D8916yes—
134C22×C4C22×D8913yes—
135C4⋊C4—894no—
136C4⋊C4C22×D8916yes—
137C22⋊C4—8924no—
138C22⋊C4C22×D8916yes—
139C42C22×D8911yescharacteristic
140C42C22×D8913yes—
141C42C22×D8916yes—
142C23—8912no—
143C23—35624no—
144C23—17824no—
145C23C23×D8913yes—
146Q8—1784no—
147Q8C2×D35614yescomplemented
148D4—35624no—
149D4—17824no—
150D4—17824no—
151D4—17812no—
152D4—17824no—
153D4C2×D356112yescomplemented
154C2×C4—212no—
155C2×C4—894no—
156C2×C4—17824no—
157C2×C4C2×D356112yescomplemented
158C2×C4C23×D8916yes—
159C2×C4C23×D8911yescharacteristic
160C2×C4C23×D8913yes—
161C2×C4C23×D8912yes—
162C22—26no—
163C22—17812no—
164C22—17824no—
165C22—71224no—
166C22C22×D35616yes—
167C22C24×D8911yescharacteristic
168C4—26no—
169C4—1784no—
170C4C22×D35616yes—
171C4C22×D35612yes—
172C4#1566805814yescomplemented
173C2—26no—
174C2—35612no—
175C2C23×D35611yescharacteristic
176C2C2×#1566805812yes—
subgroupG/H
center, FrattiniC22C24×D89
commutator, socle, cosocleC22×C89C25
FittingC4×#41×C89C2
hypercenterC4×#41D89
hypocenterC89#3498
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#15668058C2semidirect
2. #19152270C2semidirect
3. D4×D356C2semidirect
4. #19152167C2semidirect
5. #19152148C2semidirect
6. C2×#15668009C2semidirect
7. C4×#41×C89C2semidirect
9. C2×#13083575C22semidirect
10. C2×#13083574C22semidirect
11. C22×D356C22semidirect
12. C22×D356C22semidirect
13. C2×D4×D89C22semidirect
14. #15668012C22semidirect
15. #15668009C22semidirect
16. #15668009C22semidirect
17. #15668009C22semidirect
18. #15668000C22semidirect
19. #15667987C22semidirect
20. #15667986C22semidirect
21. #15667982C22semidirect
22. C4×D356C22semidirect
24. C4×Q8×C89C22semidirect
25. C4×D4×C89C22semidirect
26. #117×C89C22semidirect
27. C2×C42×C89C22semidirect
43. #41×C89D4semidirect
57. Q8×C89C2×D4semidirect
58. D4×C89C2×D4semidirect
60. C2×C4×C89C2×D4semidirect
82. C4×C89H(5,𝔽2)semidirect
89. C89#3498semidirect
96. C4×#41D89semidirect
112. C4×Q8C2×D89semidirect
114. C4×D4C2×D89semidirect
115. #117C2×D89semidirect
116. C2×C42C2×D89semidirect
120. #41D356semidirect
147. Q8C2×D356semidirect
153. D4C2×D356semidirect
157. C2×C4C2×D356semidirect
172. C4#15668058semidirect

Maximal subgroups

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

subgroupindex
C2×#156680582
#191522702
D4×D3562
#191521672
#191521482
C2×#156680092
C4×#41×C892
#349889