Finite Group Databasebeta

← C2×#11763546 #14542898

Subgroups — C2×#11763546 #14542898

Order 2176.

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#11763546C2116yesmaximal, direct product factor
2C2×#10587562C212yesmaximal, complemented
3C2×#10587621C213yesmaximal, complemented
4C2×#10587625C216yesmaximal, complemented
5C2×#10587623C213yesmaximal, complemented
6C2×C17×#127C211yesmaximal, characteristic, complemented
7C24×D17C2211yescharacteristic
8C22×D4×C17C2213yes—
9C22×D4×C17C2213yescomplemented
10C22×C22⋊D17C2216yes—
11C23×Dic17C2213yescomplemented
12C17×#127C2218yescomplemented
13C2×C42×C17C2211yescharacteristic, complemented
14C2×C22⋊Dic17C2213yes—
15C2×C22⋊Dic17C2213yescomplemented
16#10587625C22148yescomplemented
17#10587623C22124yescomplemented
18#10587621C22124yescomplemented
19C2×#63227C2216yes—
20C2×#63225C2216yescomplemented
21#10587562C22116yescomplemented
22C24×C17C2313yes—
23C24×C17C2311yescharacteristic
24C23×D17—46no—
25C23×D17C2312yes—
26C23×D17C2314yes—
27C2×D4×C17—46no—
28C2×D4×C17—46no—
29C2×D4×C17C23112yes—
30C2×D4×C17C23112yescomplemented
31C22×C4×C17C2313yes—
32C2×C22⋊D17—412no—
33C2×C22⋊D17C23124yes—
34C22×Dic17—46no—
35C22×Dic17C2316yes—
36C22×Dic17C23112yescomplemented
37C42×C17C2314yescomplemented
38C22⋊Dic17C23112yes—
39C22⋊Dic17C23112yescomplemented
40#63227C23124yes—
41#63225C23124yescomplemented
42C23×C17—26no—
43C23×C17—212no—
44C23×C17—26no—
45C23×C17C2412yes—
46C23×C17C2416yes—
47C23×C17C2411yescharacteristic
48C22×D17—212no—
49C22×D17—412no—
50C22×D17—416no—
51C22×D17C2414yes—
52D4×C17—412no—
53D4×C17—412no—
54C2×C4×C17—26no—
55C2×C4×C17C2416yes—
56C22⋊D17—424no—
57C2×Dic17—212no—
58C2×Dic17—412no—
59C2×Dic17C24112yes—
60C2×#560—171nomaximal, Sylow
61C22×C17—26no—
62C22×C17—212no—
63C22×C17—26no—
64C22×C17—44no—
65C22×C17—412no—
66C22×C17H(5,𝔽2)16yes—
67C22×C17C2511yescharacteristic
68C2×D17—212no—
69C2×D17—416no—
70C2×D17—48no—
71C4×C17—26no—
72Dic17—212no—
73#560—1716no—
74C2×#127D1711yescharacteristic, complemented
75C2×#126—172no—
76C2×#123—173no—
77C2×#121—176no—
78C2×#120—173no—
79C2×C17—42no—
80C2×C17—46no—
81C2×C17#56014yescomplemented
82C2×C17C2×H(5,𝔽2)13yes—
83D17—44no—
84C25—171no—
85C22×D4—176no—
86C22×D4C2×D1713yes—
87C22×D4C2×D1713yescomplemented
88C23×C4—173no—
89#127C2×D1718yescomplemented
90#126—1716no—
91#123—1724no—
92#121—1748no—
93#120—1724no—
94C2×C4⋊C4—176no—
95C2×C22⋊C4—173no—
96C2×C22⋊C4—173no—
97C2×C22⋊C4—176no—
98C2×C42C2×D1711yescharacteristic, complemented
99C17C2×#56011yescharacteristic, complemented, Sylow
100C24—172no—
101C24—174no—
102C24—686no—
103C24C22×D1711yescharacteristic
104C24C22×D1713yes—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4—1724no—
108C2×D4—6812no—
109C2×D4C22×D17112yes—
110C2×D4C22×D17112yescomplemented
111C22×C4—176no—
112C22×C4—1712no—
113C22×C4—686no—
114C22×C4C22×D1713yes—
115C4⋊C4—1724no—
116C22⋊C4—1712no—
117C22⋊C4—1712no—
118C22⋊C4—1724no—
119C42C22×D1714yescomplemented
120C23—26no—
121C23—212no—
122C23—26no—
123C23—174no—
124C23—3412no—
125C23—6812no—
126C23—6816no—
127C23C23×D1712yes—
128C23C23×D1716yes—
129C23C23×D1711yescharacteristic
130D4—412no—
131D4—412no—
132D4—6824no—
133C2×C4—26no—
134C2×C4—1712no—
135C2×C4—3412no—
136C2×C4—6812no—
137C2×C4C23×D1716yes—
138C22—26no—
139C22—212no—
140C22—26no—
141C22—44no—
142C22—412no—
143C22—3412no—
144C22—6816no—
145C22—688no—
146C22#1058769116yes—
147C22C24×D1711yescharacteristic
148C4—26no—
149C4—3412no—
150C2—42no—
151C2—46no—
152C2—684no—
153C2#1176354614yesdirect product factor
154C2C2×#1058769113yes—
subgroupG/H
centerC23C23×D17
commutator, cosocleC22×C17C25
FrattiniC22C24×D17
FittingC2×C17×#127C2
socleC23×C17C24
hypercenterC2×#127D17
hypocenterC17C2×#560
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #11763546C2direct (N × H)
2. C2×#10587562C2semidirect
3. C2×#10587621C2semidirect
4. C2×#10587625C2semidirect
5. C2×#10587623C2semidirect
6. C2×C17×#127C2semidirect
9. C22×D4×C17C22semidirect
11. C23×Dic17C22semidirect
12. C17×#127C22semidirect
13. C2×C42×C17C22semidirect
15. C2×C22⋊Dic17C22semidirect
16. #10587625C22semidirect
17. #10587623C22semidirect
18. #10587621C22semidirect
20. C2×#63225C22semidirect
21. #10587562C22semidirect
30. C2×D4×C17C23semidirect
36. C22×Dic17C23semidirect
37. C42×C17C23semidirect
39. C22⋊Dic17C23semidirect
41. #63225C23semidirect
74. C2×#127D17semidirect
81. C2×C17#560semidirect
87. C22×D4C2×D17semidirect
89. #127C2×D17semidirect
98. C2×C42C2×D17semidirect
99. C17C2×#560semidirect
110. C2×D4C22×D17semidirect
119. C42C22×D17semidirect
153. C2#11763546direct (N × H)

Maximal subgroups

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

subgroupindex
#117635462
C2×#105875622
C2×#105876212
C2×#105876252
C2×#105876232
C2×C17×#1272
C2×#56017