Finite Group Databasebeta

← C2×#13093023 #15686758

Subgroups — C2×#13093023 #15686758

Order 2944.

1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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#13093023C2116yesmaximal, direct product factor
2C2×#10625045C211yesmaximal, characteristic, complemented
3C2×#10625065C214yesmaximal, complemented
4C2×#10625066C214yesmaximal, complemented
5C2×#10625066C212yesmaximal, complemented
6C2×#10625064C212yesmaximal, complemented
7C2×#10625043C211yesmaximal, characteristic, complemented
8C2×C23×#125C211yesmaximal, characteristic, complemented
9C22×D92C2212yes—
10C22×D92C2214yes—
11C22×D92C2214yes—
12C22×C4×D23C2211yescharacteristic
13C22×C4×D23C2214yes—
14C23×#125C2218yescomplemented
15C2×C4⋊C4×C23C2212yes—
16C2×C4⋊C4×C23C2214yes—
17C2×C42×C23C2211yescharacteristic
18C2×(C2×D23)⋊C4C2212yes—
19C2×(C2×D23)⋊C4C2214yes—
20C2×(C2×D23)⋊C4C2214yes—
21C2×Dic23⋊C4C2212yes—
22C2×C4×Dic23C2211yescharacteristic
23#10625066C22132yescomplemented
24#10625066C22116yescomplemented
25#10625065C22132yescomplemented
26#10625064C22116yescomplemented
27#10625045C2218yescomplemented
28#10625043C2218yescomplemented
29C23×D23C2311yescharacteristic
30C23×D23C2314yes—
31C22×C4×C23C2312yes—
32C22×C4×C23C2314yes—
33C22×C4×C23C2311yescharacteristic
34C22×Dic23C2312yes—
35C22×Dic23C2311yescharacteristic
36C2×D92—28no—
37C2×D92—48no—
38C2×D92—48no—
39C2×D92C2318yes—
40C2×D92C23116yes—
41C2×D92C23116yes—
42C2×C4×D23—24no—
43C2×C4×D23—48no—
44C2×C4×D23C2314yes—
45C2×C4×D23C23116yes—
46C4⋊C4×C23C2318yes—
47C4⋊C4×C23C23116yes—
48C42×C23C2314yes—
49(C2×D23)⋊C4C2318yes—
50(C2×D23)⋊C4C23116yes—
51(C2×D23)⋊C4C23116yes—
52Dic23⋊C4C2318yes—
53C4×Dic23C2314yes—
54C23×C23C2411yescharacteristic
55C22×D23—22no—
56C22×D23—28no—
57C22×D23—28no—
58C22×D23—24no—
59C22×D23—28no—
60C22×D23C2412yes—
61C22×D23C2418yes—
62C2×C4×C23—28no—
63C2×C4×C23—24no—
64C2×C4×C23#4114yes—
65C2×C4×C23C2414yes—
66C2×C4×C23C2418yes—
67C2×C4×C23C2412yes—
68C2×Dic23—22no—
69C2×Dic23—24no—
70C2×Dic23C2414yes—
71C2×Dic23C2412yes—
72D92—216no—
73D92—416no—
74D92—416no—
75C4×D23—28no—
76C4×D23—416no—
77C2×#540—231nomaximal, Sylow
78C22×C23C2×#4112yes—
79C22×C23H(5,𝔽2)14yes—
80C22×C23C2511yescharacteristic
81C2×D23—22no—
82C2×D23—28no—
83C2×D23—28no—
84C2×D23—24no—
85C2×D23—28no—
86C2×D23—44no—
87C2×D23—416no—
88C4×C23—28no—
89C4×C23—24no—
90C4×C23C2×#4114yes—
91Dic23—22no—
92Dic23—24no—
93#540—2316no—
94C2×#127—231no—
95C2×#125D2311yescharacteristic, complemented
96C2×#123—234no—
97C2×#121—234no—
98C2×#121—232no—
99C2×C4×D4—232no—
100C2×#117—231no—
101C2×C23#54014yescomplemented
102C2×C23C22×#4111yescharacteristic
103C2×C23C2×H(5,𝔽2)12yes—
104D23—42no—
105D23—48no—
106C22×D4—232no—
107C22×D4—234no—
108C22×D4—234no—
109C23×C4—231no—
110C23×C4—234no—
111#127—238no—
112#125C2×D2318yescomplemented
113#123—2332no—
114#121—2332no—
115#121—2316no—
116C4×D4—2316no—
117#117—238no—
118C2×C4⋊C4—232no—
119C2×C4⋊C4C2×D2312yes—
120C2×C4⋊C4C2×D2314yes—
121C2×C22⋊C4—232no—
122C2×C22⋊C4—234no—
123C2×C22⋊C4—234no—
124C2×C42—231no—
125C2×C42C2×D2311yescharacteristic
126C23C2×#54011yescharacteristic, complemented, Sylow
127C24—231no—
128C24—234no—
129C2×D4—238no—
130C2×D4—2316no—
131C2×D4—2316no—
132C2×D4—468no—
133C2×D4—928no—
134C2×D4—928no—
135C22×C4—232no—
136C22×C4—231no—
137C22×C4—234no—
138C22×C4—2316no—
139C22×C4—464no—
140C22×C4—928no—
141C22×C4C22×D2312yes—
142C22×C4C22×D2314yes—
143C22×C4C22×D2311yescharacteristic
144C4⋊C4—238no—
145C4⋊C4C22×D2318yes—
146C4⋊C4C22×D23116yes—
147C22⋊C4—238no—
148C22⋊C4—2316no—
149C22⋊C4—2316no—
150C42—234no—
151C42C22×D2314yes—
152C23—232no—
153C23—238no—
154C23—462no—
155C23—468no—
156C23—468no—
157C23—464no—
158C23—468no—
159C23C23×D2311yescharacteristic
160D4—4616no—
161D4—9216no—
162D4—9216no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—234no—
166C2×C4—232no—
167C2×C4—462no—
168C2×C4—464no—
169C2×C4—468no—
170C2×C4—9216no—
171C2×C4#6729214yes—
172C2×C4C23×D2314yes—
173C2×C4C23×D2318yes—
174C2×C4C23×D2312yes—
175C22—462no—
176C22—468no—
177C22—468no—
178C22—464no—
179C22—468no—
180C22—924no—
181C22—9216no—
182C22C2×#6729212yes—
183C22#1062516014yes—
184C22C24×D2311yescharacteristic
185C4—28no—
186C4—24no—
187C4—462no—
188C4—464no—
189C4C2×#6729214yes—
190C2—922no—
191C2—928no—
192C2#1309302314yesdirect product factor
193C2C22×#6729211yescharacteristic
194C2C2×#1062516012yes—
subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C23×#125C2
socleC23×C23C24
hypercenterC2×#125D23
hypocenterC23C2×#540
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #13093023C2direct (N × H)
2. C2×#10625045C2semidirect
3. C2×#10625065C2semidirect
4. C2×#10625066C2semidirect
5. C2×#10625066C2semidirect
6. C2×#10625064C2semidirect
7. C2×#10625043C2semidirect
8. C2×C23×#125C2semidirect
14. C23×#125C22semidirect
23. #10625066C22semidirect
24. #10625066C22semidirect
25. #10625065C22semidirect
26. #10625064C22semidirect
27. #10625045C22semidirect
28. #10625043C22semidirect
95. C2×#125D23semidirect
101. C2×C23#540semidirect
112. #125C2×D23semidirect
126. C23C2×#540semidirect
192. C2#13093023direct (N × H)

Maximal subgroups

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

subgroupindex
#130930232
C2×#106250452
C2×#106250652
C2×#106250662
C2×#106250642
C2×#106250432
C2×C23×#1252
C2×#54023