Finite Group Databasebeta

← C2×#19152341 #26034373

Subgroups — C2×#19152341 #26034373

Order 11392.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#19152341C2116yesmaximal, direct product factor
2C2×#15667999C213yesmaximal, complemented
3C2×#15667998C216yesmaximal, complemented
4C2×#15667981C212yesmaximal, complemented
5C2×#15667980C213yesmaximal, complemented
6C2×#120×C89C211yesmaximal, characteristic, complemented
7C24×D89C2211yescharacteristic, complemented
8C22×Dic178C2213yescomplemented
9C22×C22⋊D89C2216yes—
10#15667999C22124yescomplemented
11#15667998C22148yescomplemented
12#15667981C22116yescomplemented
13#15667980C22124yescomplemented
14C2×C22⋊Dic89C2213yescomplemented
15C2×C22⋊Dic89C2216yescomplemented
16C2×#13083551C2216yescomplemented
17C2×C4×Dic89C2213yescomplemented
18C25×C89C2211yescharacteristic, complemented
19C22×D4×C89C2213yes—
20#120×C89C2218yescomplemented
21C2×C22⋊C4×C89C2213yescomplemented
22C23×D89—46no—
23C23×D89C2312yes—
24C23×D89C2314yescomplemented
25C2×Dic178—46no—
26C2×Dic178C23112yescomplemented
27C2×C22⋊D89—412no—
28C2×C22⋊D89C23124yes—
29C22×Dic89C2316yes—
30C22⋊Dic89C23112yescomplemented
31C22⋊Dic89C23124yescomplemented
32#13083551C23124yescomplemented
33C4×Dic89C23112yescomplemented
34C24×C89—46no—
35C24×C89C2313yes—
36C24×C89C2311yescharacteristic
37C24×C89C2314yescomplemented
38C2×D4×C89—46no—
39C2×D4×C89C23112yes—
40C22×C4×C89C2313yes—
41C22⋊C4×C89C23112yescomplemented
42C23×C89—26no—
43C23×C89—26no—
44C23×C89—212no—
45C23×C89—412no—
46C23×C89—416no—
47C23×C89C2416yes—
48C23×C89C2412yes—
49C23×C89C2411yescharacteristic
50C22×D89—212no—
51C22×D89—412no—
52C22×D89—416no—
53C22×D89C2414yes—
54D4×C89—412no—
55C2×C4×C89—26no—
56C2×C4×C89C2416yes—
57C22⋊D89—424no—
58C2×Dic89—212no—
59C2×Dic89C24112yes—
60Dic178—412no—
61C22×C89—212no—
62C22×C89—26no—
63C22×C89—26no—
64C22×C89—416no—
65C22×C89—44no—
66C22×C89—412no—
67C22×C89H(5,𝔽2)16yes—
68C22×C89C2511yescharacteristic
69C2×D89—212no—
70C2×D89—416no—
71C2×D89—48no—
72C4×C89—26no—
73Dic89—212no—
74C2×C89—42no—
75C2×C89—46no—
76C2×C89H(3,𝔽4)14yescomplemented
77C2×C89C2×H(5,𝔽2)13yes—
78D89—44no—
79C2×H(3,𝔽4)—891nomaximal, Sylow
80C89C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
81H(3,𝔽4)—8916no—
82C2×#124—893no—
83C2×#124—896no—
84C2×#120—892no—
85C2×#120—893no—
86C2×#120D8911yescharacteristic, complemented
87C25—891no—
88C25C2×D8911yescharacteristic, complemented
89C22×Q8—893no—
90C22×D4—896no—
91C22×D4C2×D8913yes—
92#124—8924no—
93#124—8948no—
94#120—8916no—
95#120—8924no—
96#120C2×D8918yescomplemented
97C2×C22⋊C4—893no—
98C2×C22⋊C4—896no—
99C2×C22⋊C4—896no—
100C2×C22⋊C4C2×D8913yescomplemented
101C2×C42—893no—
102C24—46no—
103C24—894no—
104C24—892no—
105C24—3566no—
106C24C22×D8911yescharacteristic
107C24C22×D8913yes—
108C24C22×D8914yescomplemented
109C2×Q8—8912no—
110C2×Q8—3566no—
111C2×D4—46no—
112C2×D4—8924no—
113C2×D4—35612no—
114C2×D4C22×D89112yes—
115C22×C4—896no—
116C22×C4C22×D8913yes—
117C22⋊C4—8912no—
118C22⋊C4—8924no—
119C22⋊C4—8924no—
120C22⋊C4C22×D89112yescomplemented
121C42—8912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—894no—
128C23—35612no—
129C23—35616no—
130C23—17812no—
131C23C23×D8912yes—
132C23C23×D8916yes—
133C23C23×D8911yescharacteristic
134Q8—35612no—
135D4—412no—
136D4—35624no—
137C2×C4—26no—
138C2×C4—8912no—
139C2×C4—17812no—
140C2×C4C23×D8916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—35616no—
148C22—3568no—
149C22—17812no—
150C22#1566805716yes—
151C22C24×D8911yescharacteristic
152C4—26no—
153C4—17812no—
154C2—46no—
155C2—42no—
156C2—3564no—
157C2#1915234114yesdirect product factor
158C2C2×#1566805713yes—
subgroupG/H
centerC23C23×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC2×#120×C89C2
socleC23×C89C24
hypercenterC2×#120D89
hypocenterC89C2×H(3,𝔽4)
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #19152341C2direct (N × H)
2. C2×#15667999C2semidirect
3. C2×#15667998C2semidirect
4. C2×#15667981C2semidirect
5. C2×#15667980C2semidirect
6. C2×#120×C89C2semidirect
7. C24×D89C22semidirect
8. C22×Dic178C22semidirect
10. #15667999C22semidirect
11. #15667998C22semidirect
12. #15667981C22semidirect
13. #15667980C22semidirect
14. C2×C22⋊Dic89C22semidirect
15. C2×C22⋊Dic89C22semidirect
16. C2×#13083551C22semidirect
17. C2×C4×Dic89C22semidirect
18. C25×C89C22semidirect
20. #120×C89C22semidirect
21. C2×C22⋊C4×C89C22semidirect
24. C23×D89C23semidirect
26. C2×Dic178C23semidirect
30. C22⋊Dic89C23semidirect
31. C22⋊Dic89C23semidirect
32. #13083551C23semidirect
33. C4×Dic89C23semidirect
37. C24×C89C23semidirect
41. C22⋊C4×C89C23semidirect
76. C2×C89H(3,𝔽4)semidirect
80. C89C2×H(3,𝔽4)semidirect
86. C2×#120D89semidirect
88. C25C2×D89semidirect
96. #120C2×D89semidirect
100. C2×C22⋊C4C2×D89semidirect
108. C24C22×D89semidirect
120. C22⋊C4C22×D89semidirect
157. C2#19152341direct (N × H)

Maximal subgroups

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

subgroupindex
#191523412
C2×#156679992
C2×#156679982
C2×#156679812
C2×#156679802
C2×#120×C892
C2×H(3,𝔽4)89