Finite Group Databasebeta

← C2×#14271906 #16833613

Subgroups — C2×#14271906 #16833613

Order 3712.

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#14271906C2116yesmaximal, direct product factor
2C2×#11745298C213yesmaximal, complemented
3C2×#11745247C216yesmaximal, complemented
4C2×#11745315C212yesmaximal, complemented
5C2×#11745299C213yesmaximal, complemented
6C2×C29×#120C211yesmaximal, characteristic, complemented
7C25×C29C2211yescharacteristic, complemented
8C24×D29C2211yescharacteristic, complemented
9C22×D4×C29C2213yes—
10C22×C22⋊D29C2216yes—
11C22×Dic58C2213yescomplemented
12C29×#120C2218yescomplemented
13C2×C22⋊C4×C29C2213yescomplemented
14#11745315C22116yescomplemented
15C2×C22⋊Dic29C2213yescomplemented
16C2×C22⋊Dic29C2216yescomplemented
17#11745299C22124yescomplemented
18#11745298C22124yescomplemented
19C2×#90781C2216yescomplemented
20C2×C4×Dic29C2213yescomplemented
21#11745247C22148yescomplemented
22C24×C29—46no—
23C24×C29C2311yescharacteristic
24C24×C29C2313yes—
25C24×C29C2314yescomplemented
26C23×D29—46no—
27C23×D29C2312yes—
28C23×D29C2314yescomplemented
29C2×D4×C29—46no—
30C2×D4×C29C23112yes—
31C22×C4×C29C2313yes—
32C2×C22⋊D29—412no—
33C2×C22⋊D29C23124yes—
34C22×Dic29C2316yes—
35C2×Dic58—46no—
36C2×Dic58C23112yescomplemented
37C22⋊C4×C29C23112yescomplemented
38C22⋊Dic29C23112yescomplemented
39C22⋊Dic29C23124yescomplemented
40#90781C23124yescomplemented
41C4×Dic29C23112yescomplemented
42C23×C29—212no—
43C23×C29—26no—
44C23×C29—26no—
45C23×C29—412no—
46C23×C29—416no—
47C23×C29C2412yes—
48C23×C29C2416yes—
49C23×C29C2411yescharacteristic
50C22×D29—212no—
51C22×D29—412no—
52C22×D29—416no—
53C22×D29C2414yes—
54D4×C29—412no—
55C2×C4×C29—26no—
56C2×C4×C29C2416yes—
57C22⋊D29—424no—
58C2×Dic29—212no—
59C2×Dic29C24112yes—
60Dic58—412no—
61C2×H(3,𝔽4)—291nomaximal, Sylow
62C22×C29—212no—
63C22×C29—26no—
64C22×C29—26no—
65C22×C29—416no—
66C22×C29—44no—
67C22×C29—412no—
68C22×C29H(5,𝔽2)16yes—
69C22×C29C2511yescharacteristic
70C2×D29—212no—
71C2×D29—416no—
72C2×D29—48no—
73C4×C29—26no—
74Dic29—212no—
75H(3,𝔽4)—2916no—
76C2×#124—293no—
77C2×#124—296no—
78C2×#120—292no—
79C2×#120—293no—
80C2×#120D2911yescharacteristic, complemented
81C2×C29—42no—
82C2×C29—46no—
83C2×C29H(3,𝔽4)14yescomplemented
84C2×C29C2×H(5,𝔽2)13yes—
85D29—44no—
86C25—291no—
87C25C2×D2911yescharacteristic, complemented
88C22×Q8—293no—
89C22×D4—296no—
90C22×D4C2×D2913yes—
91#124—2924no—
92#124—2948no—
93#120—2916no—
94#120—2924no—
95#120C2×D2918yescomplemented
96C2×C22⋊C4—293no—
97C2×C22⋊C4—296no—
98C2×C22⋊C4—296no—
99C2×C22⋊C4C2×D2913yescomplemented
100C2×C42—293no—
101C29C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C24—46no—
103C24—292no—
104C24—294no—
105C24—1166no—
106C24C22×D2911yescharacteristic
107C24C22×D2913yes—
108C24C22×D2914yescomplemented
109C2×Q8—2912no—
110C2×Q8—1166no—
111C2×D4—46no—
112C2×D4—2924no—
113C2×D4—11612no—
114C2×D4C22×D29112yes—
115C22×C4—296no—
116C22×C4C22×D2913yes—
117C22⋊C4—2912no—
118C22⋊C4—2924no—
119C22⋊C4—2924no—
120C22⋊C4C22×D29112yescomplemented
121C42—2912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—294no—
128C23—5812no—
129C23—11612no—
130C23—11616no—
131C23C23×D2912yes—
132C23C23×D2916yes—
133C23C23×D2911yescharacteristic
134Q8—11612no—
135D4—412no—
136D4—11624no—
137C2×C4—26no—
138C2×C4—2912no—
139C2×C4—5812no—
140C2×C4C23×D2916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—5812no—
148C22—11616no—
149C22—1168no—
150C22#1174535916yes—
151C22C24×D2911yescharacteristic
152C4—26no—
153C4—5812no—
154C2—46no—
155C2—42no—
156C2—1164no—
157C2#1427190614yesdirect product factor
158C2C2×#1174535913yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#120C2
socleC23×C29C24
hypercenterC2×#120D29
hypocenterC29C2×H(3,𝔽4)
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #14271906C2direct (N × H)
2. C2×#11745298C2semidirect
3. C2×#11745247C2semidirect
4. C2×#11745315C2semidirect
5. C2×#11745299C2semidirect
6. C2×C29×#120C2semidirect
7. C25×C29C22semidirect
8. C24×D29C22semidirect
11. C22×Dic58C22semidirect
12. C29×#120C22semidirect
13. C2×C22⋊C4×C29C22semidirect
14. #11745315C22semidirect
15. C2×C22⋊Dic29C22semidirect
16. C2×C22⋊Dic29C22semidirect
17. #11745299C22semidirect
18. #11745298C22semidirect
19. C2×#90781C22semidirect
20. C2×C4×Dic29C22semidirect
21. #11745247C22semidirect
25. C24×C29C23semidirect
28. C23×D29C23semidirect
36. C2×Dic58C23semidirect
37. C22⋊C4×C29C23semidirect
38. C22⋊Dic29C23semidirect
39. C22⋊Dic29C23semidirect
40. #90781C23semidirect
41. C4×Dic29C23semidirect
80. C2×#120D29semidirect
83. C2×C29H(3,𝔽4)semidirect
87. C25C2×D29semidirect
95. #120C2×D29semidirect
99. C2×C22⋊C4C2×D29semidirect
101. C29C2×H(3,𝔽4)semidirect
108. C24C22×D29semidirect
120. C22⋊C4C22×D29semidirect
157. C2#14271906direct (N × H)

Maximal subgroups

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

subgroupindex
#142719062
C2×#117452982
C2×#117452472
C2×#117453152
C2×#117452992
C2×C29×#1202
C2×H(3,𝔽4)29