Finite Group Databasebeta

← C2×#13093158 #15687515

Subgroups — C2×#13093158 #15687515

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#13093158C2116yesmaximal, direct product factor
2C2×#10625045C211yesmaximal, characteristic, complemented
3C2×#10625047C211yesmaximal, characteristic, complemented
4C2×#10625065C213yesmaximal, complemented
5C2×#10625066C213yesmaximal, complemented
6C2×#10625055C213yesmaximal, complemented
7C2×#10625053C213yesmaximal, complemented
8C2×C23×#126C211yesmaximal, characteristic, complemented
9C24×D23C2211yescharacteristic
10C22×C22⋊D23C2213yes—
11C22×D92C2213yes—
12C22×D92C2213yes—
13C22×D92C2213yescomplemented
14C22×C4×D23C2213yescomplemented
15C23×#126C2218yescomplemented
16C2×C4⋊C4×C23C2213yescomplemented
17C2×C22⋊C4×C23C2213yes—
18C2×C42×C23C2211yescharacteristic, complemented
19C2×(C2×D23)⋊C4C2213yes—
20C2×(C2×D23)⋊C4C2213yes—
21C2×(C2×D23)⋊C4C2213yescomplemented
22C2×Dic23⋊C4C2213yescomplemented
23#10625066C22124yescomplemented
24#10625065C22124yescomplemented
25#10625055C22124yescomplemented
26#10625053C22124yescomplemented
27#10625047C2218yescomplemented
28#10625045C2218yescomplemented
29C24×C23C2311yescharacteristic
30C23×D23—46no—
31C23×D23C2311yescharacteristic
32C23×D23C2311yescharacteristic
33C23×D23C2313yes—
34C23×D23C2314yes—
35C22×C4×C23C2313yes—
36C22×C4×C23C2313yes—
37C2×C22⋊D23—46no—
38C2×C22⋊D23C23112yes—
39C22×Dic23C2313yes—
40C2×D92—46no—
41C2×D92—46no—
42C2×D92—46no—
43C2×D92C23112yes—
44C2×D92C23112yes—
45C2×D92C23112yescomplemented
46C2×C4×D23—46no—
47C2×C4×D23C23112yescomplemented
48C4⋊C4×C23C23112yescomplemented
49C22⋊C4×C23C23112yes—
50C42×C23C2314yescomplemented
51(C2×D23)⋊C4C23112yes—
52(C2×D23)⋊C4C23112yes—
53(C2×D23)⋊C4C23112yescomplemented
54Dic23⋊C4C23112yescomplemented
55C23×C23—26no—
56C23×C23C2412yes—
57C23×C23C2411yescharacteristic
58C22×D23—26no—
59C22×D23—26no—
60C22×D23—26no—
61C22×D23—26no—
62C22×D23—26no—
63C22×D23—412no—
64C22×D23—416no—
65C22×D23C2412yes—
66C22×D23C2412yes—
67C22×D23C2416yes—
68C2×C4×C23—26no—
69C2×C4×C23—26no—
70C2×C4×C23C2416yes—
71C2×C4×C23C2416yes—
72C22⋊D23—412no—
73C2×Dic23—26no—
74C2×Dic23C2416yes—
75D92—412no—
76D92—412no—
77D92—412no—
78C4×D23—412no—
79C2×#560—231nomaximal, Sylow
80C22×C23—26no—
81C22×C23—44no—
82C22×C23H(5,𝔽2)16yes—
83C22×C23C2511yescharacteristic
84C2×D23—26no—
85C2×D23—26no—
86C2×D23—26no—
87C2×D23—26no—
88C2×D23—26no—
89C2×D23—416no—
90C2×D23—412no—
91C2×D23—44no—
92C2×D23—44no—
93C4×C23—26no—
94C4×C23—26no—
95Dic23—26no—
96#560—2316no—
97C2×#127—231no—
98C2×#126—231no—
99C2×#126D2311yescharacteristic, complemented
100C2×#123—233no—
101C2×#121—233no—
102C2×#121—233no—
103C2×#120—233no—
104C2×C23—42no—
105C2×C23#56014yescomplemented
106C2×C23C2×H(5,𝔽2)13yes—
107D23—46no—
108D23—42no—
109D23—42no—
110C25—231no—
111C22×D4—233no—
112C22×D4—233no—
113C22×D4—233no—
114C22×D4—233no—
115C23×C4—233no—
116#127—238no—
117#126—238no—
118#126C2×D2318yescomplemented
119#123—2324no—
120#121—2324no—
121#121—2324no—
122#120—2324no—
123C2×C4⋊C4—233no—
124C2×C4⋊C4C2×D2313yescomplemented
125C2×C22⋊C4—233no—
126C2×C22⋊C4—233no—
127C2×C22⋊C4—233no—
128C2×C22⋊C4C2×D2313yes—
129C2×C42C2×D2311yescharacteristic, complemented
130C23C2×#56011yescharacteristic, complemented, Sylow
131C24—231no—
132C24—231no—
133C24—233no—
134C24—234no—
135C24—926no—
136C24C22×D2311yescharacteristic
137C2×D4—2312no—
138C2×D4—2312no—
139C2×D4—2312no—
140C2×D4—2312no—
141C2×D4—926no—
142C2×D4—926no—
143C2×D4—926no—
144C2×D4—926no—
145C22×C4—233no—
146C22×C4—2312no—
147C22×C4—926no—
148C22×C4C22×D2313yes—
149C22×C4C22×D2313yes—
150C4⋊C4—2312no—
151C4⋊C4C22×D23112yescomplemented
152C22⋊C4—2312no—
153C22⋊C4—2312no—
154C22⋊C4—2312no—
155C22⋊C4C22×D23112yes—
156C42C22×D2314yescomplemented
157C23—26no—
158C23—232no—
159C23—232no—
160C23—236no—
161C23—466no—
162C23—466no—
163C23—466no—
164C23—466no—
165C23—466no—
166C23—9212no—
167C23—9216no—
168C23C23×D2312yes—
169C23C23×D2311yescharacteristic
170D4—9212no—
171D4—9212no—
172D4—9212no—
173D4—9212no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—236no—
177C2×C4—466no—
178C2×C4—9212no—
179C2×C4C23×D2316yes—
180C2×C4C23×D2316yes—
181C22—26no—
182C22—44no—
183C22—466no—
184C22—466no—
185C22—466no—
186C22—466no—
187C22—466no—
188C22—9216no—
189C22—924no—
190C22—924no—
191C22—9212no—
192C22#1062516016yes—
193C22C24×D2311yescharacteristic
194C4—26no—
195C4—26no—
196C4—466no—
197C2—42no—
198C2—922no—
199C2—922no—
200C2—926no—
201C2#1309315814yesdirect product factor
202C2C2×#1062516013yes—
subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C23×#126C2
socleC23×C23C24
hypercenterC2×#126D23
hypocenterC23C2×#560
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #13093158C2direct (N × H)
2. C2×#10625045C2semidirect
3. C2×#10625047C2semidirect
4. C2×#10625065C2semidirect
5. C2×#10625066C2semidirect
6. C2×#10625055C2semidirect
7. C2×#10625053C2semidirect
8. C2×C23×#126C2semidirect
13. C22×D92C22semidirect
14. C22×C4×D23C22semidirect
15. C23×#126C22semidirect
16. C2×C4⋊C4×C23C22semidirect
18. C2×C42×C23C22semidirect
21. C2×(C2×D23)⋊C4C22semidirect
22. C2×Dic23⋊C4C22semidirect
23. #10625066C22semidirect
24. #10625065C22semidirect
25. #10625055C22semidirect
26. #10625053C22semidirect
27. #10625047C22semidirect
28. #10625045C22semidirect
45. C2×D92C23semidirect
47. C2×C4×D23C23semidirect
48. C4⋊C4×C23C23semidirect
50. C42×C23C23semidirect
53. (C2×D23)⋊C4C23semidirect
54. Dic23⋊C4C23semidirect
99. C2×#126D23semidirect
105. C2×C23#560semidirect
118. #126C2×D23semidirect
124. C2×C4⋊C4C2×D23semidirect
129. C2×C42C2×D23semidirect
130. C23C2×#560semidirect
151. C4⋊C4C22×D23semidirect
156. C42C22×D23semidirect
201. C2#13093158direct (N × H)

Maximal subgroups

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

subgroupindex
#130931582
C2×#106250452
C2×#106250472
C2×#106250652
C2×#106250662
C2×#106250552
C2×#106250532
C2×C23×#1262
C2×#56023