Finite Group Databasebeta

← C2×#13092665 #15682987

Subgroups — C2×#13092665 #15682987

Order 2944.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#67274C211yesmaximal, characteristic, complemented
2C22×#67267C211yesmaximal, characteristic, complemented
3C2×#10625101C211yesmaximal, characteristic
4#13092665C218yesmaximal, direct product factor
5C2×#10624989C211yesmaximal, characteristic, complemented
6C2×#10625017C211yesmaximal, characteristic, complemented
7C2×#10624991C211yesmaximal, characteristic, complemented
8C2×C23×C22⋊Q8C211yesmaximal, characteristic, complemented
9C22×Q8×C23C2211yescharacteristic
10C23×C4×C23C2211yescharacteristic
11C22×C22⋊D23—21no—
12C22×D92C2211yescharacteristic
13C23×C22⋊Q8—22no—
14C23×C22⋊Q8C2214yescomplemented
15C2×C4⋊C4×C23—21no—
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C22⋊C4×C23—21no—
18C2×#67274—24no—
19C2×#67274C2214yescomplemented
20#10625101—22no—
21#10625101C2214yes—
22C2×(C2×D23)⋊C4—21no—
23C2×C4⋊Dic23C2211yescharacteristic
24C2×#67267—24no—
25C2×#67267C2214yescomplemented
26C22×C23⋊C8C2211yescharacteristic
27C22×C23⋊C8C2211yescharacteristic
28#10625017C2214yescomplemented
29#10624991C2214yescomplemented
30#10624989C2214yescomplemented
31C24×C23D411yescharacteristic
32C23×D23—21no—
33C2×Q8×C23—21no—
34C2×Q8×C23—22no—
35C2×Q8×C23—22no—
36C2×Q8×C23C2312yes—
37C22×C4×C23—22no—
38C22×C4×C23—22no—
39C22×C4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23D411yescharacteristic
42C22×C4×C23D412yes—
43C22×C4×C23C2312yes—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—24no—
46C2×C22⋊D23—44no—
47C22×Dic23—21no—
48C2×D92—22no—
49C2×D92—22no—
50C2×D92—21no—
51C2×D92C2312yes—
52C4⋊C4×C23—24no—
53C4⋊C4×C23—21no—
54C4⋊C4×C23C2312yes—
55C22⋊C4×C23—24no—
56#67274—28no—
57(C2×D23)⋊C4—24no—
58C4⋊Dic23—21no—
59C4⋊Dic23C2312yes—
60#67267—28no—
61C2×C23⋊C8—22no—
62C2×C23⋊C8D414yescomplemented
63C2×C23⋊C8C2312yes—
64C2×C23⋊C8C2312yes—
65C23×C23—22no—
66C23×C23—22no—
67C23×C23—22no—
68C23×C23C2×D412yes—
69C23×C23C2×D411yescharacteristic
70C22×D23—22no—
71C22×D23—42no—
72C22×D23—42no—
73C22×D23—42no—
74Q8×C23—22no—
75Q8×C23—22no—
76Q8×C23—42no—
77C2×C4×C23—22no—
78C2×C4×C23—24no—
79C2×C4×C23—22no—
80C2×C4×C23—22no—
81C2×C4×C23—22no—
82C2×C4×C23—22no—
83C2×C4×C23—42no—
84C2×C4×C23—42no—
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D412yes—
87C2×C4×C23C2×D411yescharacteristic
88C2×C4×C23#4112yes—
89C2×C4×C23C2411yescharacteristic
90C22⋊D23—48no—
91C2×Dic23—22no—
92C2×Dic23—42no—
93D92—22no—
94D92—22no—
95D92—42no—
96C23⋊C8—22no—
97C23⋊C8C2×D414yescomplemented
98C2×#468—231nomaximal, Sylow
99C22×C23—22no—
100C22×C23—22no—
101C22×C23—22no—
102C22×C23—44no—
103C22×C23#12112yes—
104C22×C23AGL(1,ℤ/8)12yes—
105C22×C23#13712yes—
106C22×C23C22×D411yescharacteristic
107C2×D23—42no—
108C2×D23—42no—
109C2×D23—42no—
110C2×D23—84no—
111C4×C23—22no—
112C4×C23—42no—
113C4×C23—42no—
114C4×C23#12112yes—
115C4×C23C22×D411yescharacteristic
116C4×C23C2×#4111yescharacteristic
117Dic23—42no—
118C22×SD16—231no—
119C22×M16—231no—
120C2×C22⋊Q8D2311yescharacteristic, complemented
121C2×#121—231no—
122#468—238no—
123C2×#107—231no—
124C2×#103—231no—
125C2×#102—231no—
126C2×C23—42no—
127C2×C23#46814yescomplemented
128C2×C23C2×#12111yescharacteristic
129C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C23C2×#13711yescharacteristic
131D23—82no—
132C22×Q8C2×D2311yescharacteristic
133C22×D4—231no—
134C22×D4—461no—
135C23×C4C2×D2311yescharacteristic
136C2×SD16—234no—
137C2×SD16—464no—
138C2×M16—234no—
139C2×M16—464no—
140C22×C8—231no—
141C22×C8—231no—
142C22⋊Q8—22no—
143C22⋊Q8C2×D2314yescomplemented
144#121—234no—
145#121—462no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—231no—
148C2×C4⋊C4C2×D2311yescharacteristic
149C2×C22⋊C4—21no—
150C2×C22⋊C4—461no—
151#107—234no—
152#103—234no—
153#102—234no—
154C23C2×#46811yescharacteristic, complemented, Sylow
155C24—461no—
156C24C22⋊D2311yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D2312yes—
161C2×D4—232no—
162C2×D4—464no—
163C2×D4—462no—
164C2×D4—462no—
165C2×D4—461no—
166C2×D4—924no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—461no—
172C22×C4C22⋊D2312yes—
173C22×C4C22⋊D2311yescharacteristic
174C22×C4C22×D2312yes—
175C22×C4C22×D2311yescharacteristic
176SD16—468no—
177M16—468no—
178C2×C8—234no—
179C2×C8—232no—
180C2×C8—232no—
181C2×C8—462no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—232no—
185C4⋊C4—461no—
186C4⋊C4C22×D2312yes—
187C22⋊C4—24no—
188C22⋊C4—464no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—462no—
193C23—922no—
194C23—922no—
195C23—922no—
196C23C2×C22⋊D2312yes—
197C23C2×C22⋊D2311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—462no—
202D4—462no—
203D4—928no—
204D4—922no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—462no—
214C2×C4—922no—
215C2×C4D4×D2312yes—
216C2×C4#6729012yes—
217C2×C4C2×C22⋊D2312yes—
218C2×C4C2×C22⋊D2311yescharacteristic
219C2×C4C23×D2311yescharacteristic
220C8—234no—
221C8—462no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—922no—
227C22—922no—
228C22—922no—
229C22—1844no—
230C22#1062511012yes—
231C22#1062511312yes—
232C22#1062512012yes—
233C22C22×C22⋊D2311yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—922no—
238C4#1062511012yes—
239C4C2×D4×D2311yescharacteristic
240C4C2×#6729011yescharacteristic
241C2—42no—
242C2—1842no—
243C2#1309266514yesdirect product factor
244C2C2×#1062511011yescharacteristic
245C2C2×#1062512011yescharacteristic
246C2C2×#1062511311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C22⋊Q8C2
socleC23×C23C2×D4
prime radicalC2×#10625101C2
hypercenterC2×C22⋊Q8D23
hypocenterC23C2×#468
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67274C2semidirect
2. C22×#67267C2semidirect
4. #13092665C2direct (N × H)
5. C2×#10624989C2semidirect
6. C2×#10625017C2semidirect
7. C2×#10624991C2semidirect
8. C2×C23×C22⋊Q8C2semidirect
14. C23×C22⋊Q8C22semidirect
19. C2×#67274C22semidirect
25. C2×#67267C22semidirect
28. #10625017C22semidirect
29. #10624991C22semidirect
30. #10624989C22semidirect
62. C2×C23⋊C8D4semidirect
97. C23⋊C8C2×D4semidirect
120. C2×C22⋊Q8D23semidirect
127. C2×C23#468semidirect
143. C22⋊Q8C2×D23semidirect
154. C23C2×#468semidirect
243. C2#13092665direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#672742
C22×#672672
C2×#106251012
#130926652
C2×#106249892
C2×#106250172
C2×#106249912
C2×C23×C22⋊Q82
C2×#46823