Finite Group Databasebeta

← C2×#14271900 #16833606

Subgroups — C2×#14271900 #16833606

Order 3712.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 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#14271900C2116yesmaximal, direct product factor
2C2×#11745238C212yesmaximal, complemented
3C2×#11745297C213yesmaximal, complemented
4C2×#11745301C216yesmaximal, complemented
5C2×#11745299C213yesmaximal, complemented
6C2×C29×#127C211yesmaximal, characteristic, complemented
7C24×D29C2211yescharacteristic
8C22×D4×C29C2213yes—
9C22×D4×C29C2213yescomplemented
10C22×C22⋊D29C2216yes—
11C23×Dic29C2213yescomplemented
12C29×#127C2218yescomplemented
13C2×C42×C29C2211yescharacteristic, complemented
14C2×C22⋊Dic29C2213yes—
15C2×C22⋊Dic29C2213yescomplemented
16#11745301C22148yescomplemented
17#11745299C22124yescomplemented
18#11745297C22124yescomplemented
19C2×#90781C2216yes—
20C2×#90779C2216yescomplemented
21#11745238C22116yescomplemented
22C24×C29C2311yescharacteristic
23C24×C29C2313yes—
24C23×D29—46no—
25C23×D29C2312yes—
26C23×D29C2314yes—
27C2×D4×C29—46no—
28C2×D4×C29—46no—
29C2×D4×C29C23112yes—
30C2×D4×C29C23112yescomplemented
31C22×C4×C29C2313yes—
32C2×C22⋊D29—412no—
33C2×C22⋊D29C23124yes—
34C22×Dic29—46no—
35C22×Dic29C2316yes—
36C22×Dic29C23112yescomplemented
37C42×C29C2314yescomplemented
38C22⋊Dic29C23112yes—
39C22⋊Dic29C23112yescomplemented
40#90781C23124yes—
41#90779C23124yescomplemented
42C23×C29—26no—
43C23×C29—212no—
44C23×C29—26no—
45C23×C29C2412yes—
46C23×C29C2416yes—
47C23×C29C2411yescharacteristic
48C22×D29—212no—
49C22×D29—412no—
50C22×D29—416no—
51C22×D29C2414yes—
52D4×C29—412no—
53D4×C29—412no—
54C2×C4×C29—26no—
55C2×C4×C29C2416yes—
56C22⋊D29—424no—
57C2×Dic29—212no—
58C2×Dic29—412no—
59C2×Dic29C24112yes—
60C2×#560—291nomaximal, Sylow
61C22×C29—26no—
62C22×C29—212no—
63C22×C29—26no—
64C22×C29—44no—
65C22×C29—412no—
66C22×C29H(5,𝔽2)16yes—
67C22×C29C2511yescharacteristic
68C2×D29—212no—
69C2×D29—416no—
70C2×D29—48no—
71C4×C29—26no—
72Dic29—212no—
73#560—2916no—
74C2×#127D2911yescharacteristic, complemented
75C2×#126—292no—
76C2×#123—293no—
77C2×#121—296no—
78C2×#120—293no—
79C2×C29—42no—
80C2×C29—46no—
81C2×C29#56014yescomplemented
82C2×C29C2×H(5,𝔽2)13yes—
83D29—44no—
84C25—291no—
85C22×D4—296no—
86C22×D4C2×D2913yes—
87C22×D4C2×D2913yescomplemented
88C23×C4—293no—
89#127C2×D2918yescomplemented
90#126—2916no—
91#123—2924no—
92#121—2948no—
93#120—2924no—
94C2×C4⋊C4—296no—
95C2×C22⋊C4—293no—
96C2×C22⋊C4—293no—
97C2×C22⋊C4—296no—
98C2×C42C2×D2911yescharacteristic, complemented
99C29C2×#56011yescharacteristic, complemented, Sylow
100C24—292no—
101C24—294no—
102C24—1166no—
103C24C22×D2911yescharacteristic
104C24C22×D2913yes—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4—2924no—
108C2×D4—11612no—
109C2×D4C22×D29112yes—
110C2×D4C22×D29112yescomplemented
111C22×C4—296no—
112C22×C4—2912no—
113C22×C4—1166no—
114C22×C4C22×D2913yes—
115C4⋊C4—2924no—
116C22⋊C4—2912no—
117C22⋊C4—2912no—
118C22⋊C4—2924no—
119C42C22×D2914yescomplemented
120C23—26no—
121C23—212no—
122C23—26no—
123C23—294no—
124C23—5812no—
125C23—11612no—
126C23—11616no—
127C23C23×D2912yes—
128C23C23×D2916yes—
129C23C23×D2911yescharacteristic
130D4—412no—
131D4—412no—
132D4—11624no—
133C2×C4—26no—
134C2×C4—2912no—
135C2×C4—5812no—
136C2×C4—11612no—
137C2×C4C23×D2916yes—
138C22—26no—
139C22—212no—
140C22—26no—
141C22—44no—
142C22—412no—
143C22—5812no—
144C22—11616no—
145C22—1168no—
146C22#1174535916yes—
147C22C24×D2911yescharacteristic
148C4—26no—
149C4—5812no—
150C2—42no—
151C2—46no—
152C2—1164no—
153C2#1427190014yesdirect product factor
154C2C2×#1174535913yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#127C2
socleC23×C29C24
hypercenterC2×#127D29
hypocenterC29C2×#560
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14271900C2direct (N × H)
2. C2×#11745238C2semidirect
3. C2×#11745297C2semidirect
4. C2×#11745301C2semidirect
5. C2×#11745299C2semidirect
6. C2×C29×#127C2semidirect
9. C22×D4×C29C22semidirect
11. C23×Dic29C22semidirect
12. C29×#127C22semidirect
13. C2×C42×C29C22semidirect
15. C2×C22⋊Dic29C22semidirect
16. #11745301C22semidirect
17. #11745299C22semidirect
18. #11745297C22semidirect
20. C2×#90779C22semidirect
21. #11745238C22semidirect
30. C2×D4×C29C23semidirect
36. C22×Dic29C23semidirect
37. C42×C29C23semidirect
39. C22⋊Dic29C23semidirect
41. #90779C23semidirect
74. C2×#127D29semidirect
81. C2×C29#560semidirect
87. C22×D4C2×D29semidirect
89. #127C2×D29semidirect
98. C2×C42C2×D29semidirect
99. C29C2×#560semidirect
110. C2×D4C22×D29semidirect
119. C42C22×D29semidirect
153. C2#14271900direct (N × H)

Maximal subgroups

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

subgroupindex
#142719002
C2×#117452382
C2×#117452972
C2×#117453012
C2×#117452992
C2×C29×#1272
C2×#56029