Finite Group Databasebeta

← C2×#13092760 #15683291

Subgroups — C2×#13092760 #15683291

Order 2944.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#10625068C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic
3#13092760C218yesmaximal, direct product factor
4C2×#10624990C211yesmaximal, characteristic, complemented
5C2×#10624998C211yesmaximal, characteristic, complemented
6C2×#10624992C211yesmaximal, characteristic, complemented
7C2×(C2×D23)⋊C8C211yesmaximal, characteristic
8C2×C23×#107C211yesmaximal, characteristic, complemented
9C22×C4×D23C2211yescharacteristic
10C22×Dic46C2211yescharacteristic
11C22×C8×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×C4⋊C4×C23C2211yescharacteristic
14C2×(C2×D23)⋊C4—21no—
15C2×(C2×D23)⋊C4—21no—
16C2×C4⋊Dic23—21no—
17C2×C4⋊Dic23C2211yescharacteristic
18C2×C4×Dic23—21no—
19C22×C23⋊C8C2211yescharacteristic
20#10625068—22no—
21#10625068C2214yes—
22#10625063—22no—
23#10625063C2214yes—
24C23×#107C2214yescomplemented
25(C2×D23)⋊C8C2214yes—
26#10624998C2214yescomplemented
27#10624992C2214yescomplemented
28#10624990C2214yescomplemented
29C23×D23D411yescharacteristic
30C22×C4×C23—21no—
31C22×C4×C23—21no—
32C22×C4×C23C2311yescharacteristic
33C22×Dic23—21no—
34C22×Dic23—21no—
35C22×Dic23D411yescharacteristic
36C2×C4×D23—22no—
37C2×C4×D23—22no—
38C2×C4×D23D412yes—
39C2×C4×D23C2312yes—
40C2×Dic46—22no—
41C2×Dic46—22no—
42C2×Dic46—21no—
43C2×Dic46C2312yes—
44C2×C8×C23—22no—
45C2×C8×C23C2312yes—
46C4⋊C4×C23—21no—
47C4⋊C4×C23—21no—
48C4⋊C4×C23C2312yes—
49C4⋊C4×C23C2312yes—
50(C2×D23)⋊C4—24no—
51(C2×D23)⋊C4—24no—
52C4⋊Dic23—21no—
53C4⋊Dic23—24no—
54C4⋊Dic23C2312yes—
55C4×Dic23—24no—
56C2×C23⋊C8—22no—
57C2×C23⋊C8C2312yes—
58C23×C23C2×D411yescharacteristic
59C22×D23—22no—
60C22×D23—22no—
61C22×D23—22no—
62C22×D23C2×D412yes—
63C2×C4×C23—22no—
64C2×C4×C23—22no—
65C2×C4×C23—42no—
66C2×C4×C23—42no—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23#4112yes—
69C2×C4×C23#4112yes—
70C2×C4×C23C2411yescharacteristic
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—42no—
75C2×Dic23—42no—
76C2×Dic23C2×D412yes—
77C4×D23—24no—
78C4×D23—22no—
79C4×D23—22no—
80Dic46—22no—
81Dic46—22no—
82Dic46—42no—
83C8×C23—22no—
84C23⋊C8—22no—
85C2×#485—231nomaximal, Sylow
86C22×C23#12312yes—
87C22×C23#13512yes—
88C22×C23#13712yes—
89C22×C23C22×D411yescharacteristic
90C2×D23—22no—
91C2×D23—22no—
92C2×D23—22no—
93C2×D23—44no—
94C4×C23—42no—
95C4×C23—42no—
96C4×C23#12312yes—
97C4×C23C2×#4111yescharacteristic
98C4×C23C2×#4111yescharacteristic
99Dic23—22no—
100Dic23—42no—
101Dic23—42no—
102C2×C22⋊Q8—231no—
103C2×#117—231no—
104#485—238no—
105C2×#107D2311yescharacteristic, complemented
106C2×#106—231no—
107C2×#103—231no—
108C2×#103—231no—
109C2×C22⋊C8—231no—
110C2×C23#48514yescomplemented
111C2×C23C2×#12311yescharacteristic
112C2×C23C2×#13511yescharacteristic
113C2×C23C2×#13711yescharacteristic
114D23—42no—
115C22×Q8—231no—
116C23×C4—231no—
117C22×C8—231no—
118C22×C8C2×D2311yescharacteristic
119C22⋊Q8—234no—
120C22⋊Q8—462no—
121#117—234no—
122#117—462no—
123C2×C4⋊C4—231no—
124C2×C4⋊C4—461no—
125C2×C4⋊C4C2×D2311yescharacteristic
126C2×C4⋊C4C2×D2311yescharacteristic
127C2×C22⋊C4—461no—
128C2×C22⋊C4—461no—
129C2×C42—461no—
130#107C2×D2314yescomplemented
131#106—234no—
132#103—234no—
133#103—234no—
134C22⋊C8—234no—
135C23C2×#48511yescharacteristic, complemented, Sylow
136C24—231no—
137C2×Q8—232no—
138C2×Q8—461no—
139C2×Q8—462no—
140C2×Q8—462no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—231no—
144C22×C4—232no—
145C22×C4—232no—
146C22×C4—462no—
147C22×C4—462no—
148C22×C4—461no—
149C22×C4—461no—
150C22×C4C22×D2311yescharacteristic
151C2×C8—22no—
152C2×C8—232no—
153C2×C8—462no—
154C2×C8C22×D2312yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—232no—
158C4⋊C4—464no—
159C4⋊C4—461no—
160C4⋊C4C22×D2312yes—
161C4⋊C4C22×D2312yes—
162C22⋊C4—464no—
163C22⋊C4—464no—
164C42—464no—
165C23—232no—
166C23—462no—
167C23—462no—
168C23—462no—
169C23D4×D2311yescharacteristic
170Q8—462no—
171Q8—462no—
172Q8—922no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—232no—
178C2×C4—462no—
179C2×C4—464no—
180C2×C4—462no—
181C2×C4—462no—
182C2×C4—462no—
183C2×C4—462no—
184C2×C4—922no—
185C2×C4—922no—
186C2×C4#6728812yes—
187C2×C4D4×D2311yescharacteristic
188C2×C4#6729212yes—
189C2×C4C23×D2311yescharacteristic
190C8—22no—
191C8—462no—
192C22—462no—
193C22—462no—
194C22—462no—
195C22—924no—
196C22#1062506512yes—
197C22#1062508312yes—
198C22#1062508912yes—
199C22C2×D4×D2311yescharacteristic
200C4—42no—
201C4—42no—
202C4—462no—
203C4—922no—
204C4—922no—
205C4#1062506512yes—
206C4C2×#6728811yescharacteristic
207C4C2×#6729211yescharacteristic
208C2—922no—
209C2#1309276014yesdirect product factor
210C2C2×#1062506511yescharacteristic
211C2C2×#1062508311yescharacteristic
212C2C2×#1062508911yescharacteristic
subgroupG/H
centerC23D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#107C2
socleC23×C23C2×D4
prime radicalC23×D23D4
hypercenterC2×#107D23
hypocenterC23C2×#485
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13092760C2direct (N × H)
4. C2×#10624990C2semidirect
5. C2×#10624998C2semidirect
6. C2×#10624992C2semidirect
8. C2×C23×#107C2semidirect
24. C23×#107C22semidirect
26. #10624998C22semidirect
27. #10624992C22semidirect
28. #10624990C22semidirect
105. C2×#107D23semidirect
110. C2×C23#485semidirect
130. #107C2×D23semidirect
135. C23C2×#485semidirect
209. C2#13092760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250682
C2×#106250632
#130927602
C2×#106249902
C2×#106249982
C2×#106249922
C2×(C2×D23)⋊C82
C2×C23×#1072
C2×#48523