Finite Group Databasebeta

← C2×#13093154 #15687511

Subgroups — C2×#13093154 #15687511

Order 2944.

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#13093154C2116yesmaximal, direct product factor
2C2×#10625047C212yesmaximal, complemented
3C2×#10625106C213yesmaximal, complemented
4C2×#10625110C216yesmaximal, complemented
5C2×#10625108C213yesmaximal, complemented
6C2×C23×#127C211yesmaximal, characteristic, complemented
7C24×D23C2211yescharacteristic
8C22×D4×C23C2213yes—
9C22×D4×C23C2213yescomplemented
10C22×C22⋊D23C2216yes—
11C23×Dic23C2213yescomplemented
12C23×#127C2218yescomplemented
13C2×C42×C23C2211yescharacteristic, complemented
14C2×C22⋊Dic23C2213yes—
15C2×C22⋊Dic23C2213yescomplemented
16#10625110C22148yescomplemented
17#10625108C22124yescomplemented
18#10625106C22124yescomplemented
19C2×(C2×D23)⋊C4C2216yes—
20C2×Dic23⋊C4C2216yescomplemented
21#10625047C22116yescomplemented
22C24×C23C2311yescharacteristic
23C24×C23C2313yes—
24C23×D23—46no—
25C23×D23C2312yes—
26C23×D23C2314yes—
27C2×D4×C23—46no—
28C2×D4×C23—46no—
29C2×D4×C23C23112yes—
30C2×D4×C23C23112yescomplemented
31C22×C4×C23C2313yes—
32C2×C22⋊D23—412no—
33C2×C22⋊D23C23124yes—
34C22×Dic23—46no—
35C22×Dic23C2316yes—
36C22×Dic23C23112yescomplemented
37C42×C23C2314yescomplemented
38C22⋊Dic23C23112yes—
39C22⋊Dic23C23112yescomplemented
40(C2×D23)⋊C4C23124yes—
41Dic23⋊C4C23124yescomplemented
42C23×C23—26no—
43C23×C23—212no—
44C23×C23—26no—
45C23×C23C2412yes—
46C23×C23C2416yes—
47C23×C23C2411yescharacteristic
48C22×D23—212no—
49C22×D23—412no—
50C22×D23—416no—
51C22×D23C2414yes—
52D4×C23—412no—
53D4×C23—412no—
54C2×C4×C23—26no—
55C2×C4×C23C2416yes—
56C22⋊D23—424no—
57C2×Dic23—212no—
58C2×Dic23—412no—
59C2×Dic23C24112yes—
60C2×#560—231nomaximal, Sylow
61C22×C23—26no—
62C22×C23—212no—
63C22×C23—26no—
64C22×C23—44no—
65C22×C23—412no—
66C22×C23H(5,𝔽2)16yes—
67C22×C23C2511yescharacteristic
68C2×D23—212no—
69C2×D23—416no—
70C2×D23—48no—
71C4×C23—26no—
72Dic23—212no—
73#560—2316no—
74C2×#127D2311yescharacteristic, complemented
75C2×#126—232no—
76C2×#123—233no—
77C2×#121—236no—
78C2×#120—233no—
79C2×C23—42no—
80C2×C23—46no—
81C2×C23#56014yescomplemented
82C2×C23C2×H(5,𝔽2)13yes—
83D23—44no—
84C25—231no—
85C22×D4—236no—
86C22×D4C2×D2313yes—
87C22×D4C2×D2313yescomplemented
88C23×C4—233no—
89#127C2×D2318yescomplemented
90#126—2316no—
91#123—2324no—
92#121—2348no—
93#120—2324no—
94C2×C4⋊C4—236no—
95C2×C22⋊C4—233no—
96C2×C22⋊C4—233no—
97C2×C22⋊C4—236no—
98C2×C42C2×D2311yescharacteristic, complemented
99C23C2×#56011yescharacteristic, complemented, Sylow
100C24—232no—
101C24—234no—
102C24—926no—
103C24C22×D2311yescharacteristic
104C24C22×D2313yes—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4—2324no—
108C2×D4—9212no—
109C2×D4C22×D23112yes—
110C2×D4C22×D23112yescomplemented
111C22×C4—236no—
112C22×C4—2312no—
113C22×C4—926no—
114C22×C4C22×D2313yes—
115C4⋊C4—2324no—
116C22⋊C4—2312no—
117C22⋊C4—2312no—
118C22⋊C4—2324no—
119C42C22×D2314yescomplemented
120C23—26no—
121C23—212no—
122C23—26no—
123C23—234no—
124C23—4612no—
125C23—9212no—
126C23—9216no—
127C23C23×D2312yes—
128C23C23×D2316yes—
129C23C23×D2311yescharacteristic
130D4—412no—
131D4—412no—
132D4—9224no—
133C2×C4—26no—
134C2×C4—2312no—
135C2×C4—4612no—
136C2×C4—9212no—
137C2×C4C23×D2316yes—
138C22—26no—
139C22—212no—
140C22—26no—
141C22—44no—
142C22—412no—
143C22—4612no—
144C22—9216no—
145C22—928no—
146C22#1062515516yes—
147C22C24×D2311yescharacteristic
148C4—26no—
149C4—4612no—
150C2—42no—
151C2—46no—
152C2—924no—
153C2#1309315414yesdirect product factor
154C2C2×#1062515513yes—
subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C23×#127C2
socleC23×C23C24
hypercenterC2×#127D23
hypocenterC23C2×#560
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #13093154C2direct (N × H)
2. C2×#10625047C2semidirect
3. C2×#10625106C2semidirect
4. C2×#10625110C2semidirect
5. C2×#10625108C2semidirect
6. C2×C23×#127C2semidirect
9. C22×D4×C23C22semidirect
11. C23×Dic23C22semidirect
12. C23×#127C22semidirect
13. C2×C42×C23C22semidirect
15. C2×C22⋊Dic23C22semidirect
16. #10625110C22semidirect
17. #10625108C22semidirect
18. #10625106C22semidirect
20. C2×Dic23⋊C4C22semidirect
21. #10625047C22semidirect
30. C2×D4×C23C23semidirect
36. C22×Dic23C23semidirect
37. C42×C23C23semidirect
39. C22⋊Dic23C23semidirect
41. Dic23⋊C4C23semidirect
74. C2×#127D23semidirect
81. C2×C23#560semidirect
87. C22×D4C2×D23semidirect
89. #127C2×D23semidirect
98. C2×C42C2×D23semidirect
99. C23C2×#560semidirect
110. C2×D4C22×D23semidirect
119. C42C22×D23semidirect
153. C2#13093154direct (N × H)

Maximal subgroups

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

subgroupindex
#130931542
C2×#106250472
C2×#106251062
C2×#106251102
C2×#106251082
C2×C23×#1272
C2×#56023