Finite Group Databasebeta

← C2×#13092754 #15683304

Subgroups — C2×#13092754 #15683304

Order 2944.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4⋊C4×D23C211yesmaximal, characteristic
3#13092754C218yesmaximal, direct product factor
4C2×#10624989C211yesmaximal, characteristic, complemented
5C2×#10624998C211yesmaximal, characteristic, complemented
6C2×#10624992C211yesmaximal, characteristic, complemented
7C2×(C2×D23)⋊C8C211yesmaximal, characteristic
8C2×C23×#107C211yesmaximal, characteristic, complemented
9C22×C4×D23—21no—
10C22×C4×D23C2211yescharacteristic
11C22×Dic46C2211yescharacteristic
12C22×C8×C23C2211yescharacteristic
13C2×C4⋊C4×C23C2211yescharacteristic
14C2×C4⋊C4×C23C2211yescharacteristic
15C2×(C2×D23)⋊C4—21no—
16C2×C4⋊Dic23—21no—
17C2×C4⋊Dic23C2211yescharacteristic
18C2×Dic23⋊C4—21no—
19C22×C23⋊C8C2211yescharacteristic
20#10625068—22no—
21#10625068C2214yes—
22C4⋊C4×D23—22no—
23C4⋊C4×D23C2214yes—
24C23×#107C2214yescomplemented
25(C2×D23)⋊C8C2214yes—
26#10624998C2214yescomplemented
27#10624992C2214yescomplemented
28#10624989C2214yescomplemented
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×D23—24no—
39C2×C4×D23—44no—
40C2×C4×D23D412yes—
41C2×C4×D23C2312yes—
42C2×Dic46—22no—
43C2×Dic46—22no—
44C2×Dic46—21no—
45C2×Dic46C2312yes—
46C2×C8×C23—22no—
47C2×C8×C23C2312yes—
48C4⋊C4×C23—21no—
49C4⋊C4×C23—21no—
50C4⋊C4×C23C2312yes—
51C4⋊C4×C23C2312yes—
52(C2×D23)⋊C4—24no—
53C4⋊Dic23—21no—
54C4⋊Dic23—24no—
55C4⋊Dic23C2312yes—
56Dic23⋊C4—24no—
57C2×C23⋊C8—22no—
58C2×C23⋊C8C2312yes—
59C23×C23C2×D411yescharacteristic
60C22×D23—22no—
61C22×D23—22no—
62C22×D23Q1614yes—
63C22×D23C2×D412yes—
64C2×C4×C23—22no—
65C2×C4×C23—22no—
66C2×C4×C23—42no—
67C2×C4×C23—42no—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23#4112yes—
70C2×C4×C23#4112yes—
71C2×C4×C23C2411yescharacteristic
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—42no—
76C2×Dic23—42no—
77C2×Dic23C2×D412yes—
78C4×D23—24no—
79C4×D23—22no—
80C4×D23—22no—
81C4×D23—48no—
82Dic46—22no—
83Dic46—22no—
84Dic46—42no—
85C8×C23—22no—
86C23⋊C8—22no—
87C2×#484—231nomaximal, Sylow
88C22×C23#12312yes—
89C22×C23C2×Q1612yes—
90C22×C23AGL(1,ℤ/8)12yes—
91C22×C23C22×D411yescharacteristic
92C2×D23—22no—
93C2×D23—22no—
94C2×D23—28no—
95C2×D23C2×Q1614yes—
96C4×C23—42no—
97C4×C23—42no—
98C4×C23#12312yes—
99C4×C23C2×#4111yescharacteristic
100C4×C23C2×#4111yescharacteristic
101Dic23—22no—
102Dic23—42no—
103Dic23—42no—
104C2×C22⋊Q8—231no—
105C22×C4⋊C4—231no—
106#484—238no—
107C2×#107—231no—
108C2×#107D2311yescharacteristic, complemented
109C2×#103—231no—
110C2×#103—231no—
111C2×C22⋊C8—231no—
112C2×C23#48414yescomplemented
113C2×C23C2×#12311yescharacteristic
114C2×C23C22×Q1611yescharacteristic
115C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
116D23—24no—
117C22×Q8—231no—
118C23×C4—231no—
119C23×C4—461no—
120C22×C8—231no—
121C22×C8C2×D2311yescharacteristic
122C22⋊Q8—234no—
123C22⋊Q8—462no—
124C2×C4⋊C4—231no—
125C2×C4⋊C4—234no—
126C2×C4⋊C4—462no—
127C2×C4⋊C4—461no—
128C2×C4⋊C4—461no—
129C2×C4⋊C4C2×D2311yescharacteristic
130C2×C4⋊C4C2×D2311yescharacteristic
131C2×C22⋊C4—461no—
132#107—234no—
133#107C2×D2314yescomplemented
134#103—234no—
135#103—234no—
136C22⋊C8—234no—
137C23C2×#48411yescharacteristic, complemented, Sylow
138C24—231no—
139C2×Q8—232no—
140C2×Q8—461no—
141C2×Q8—462no—
142C2×Q8—462no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—231no—
146C22×C4—232no—
147C22×C4—232no—
148C22×C4—464no—
149C22×C4—462no—
150C22×C4—462no—
151C22×C4—461no—
152C22×C4—461no—
153C22×C4—924no—
154C22×C4C22×D2311yescharacteristic
155C2×C8—22no—
156C2×C8—232no—
157C2×C8—462no—
158C2×C8C22×D2312yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—232no—
162C4⋊C4—464no—
163C4⋊C4—464no—
164C4⋊C4—461no—
165C4⋊C4C22×D2312yes—
166C4⋊C4C22×D2312yes—
167C22⋊C4—464no—
168C23—234no—
169C23—232no—
170C23—462no—
171C23—462no—
172C23D4×D2311yescharacteristic
173Q8—462no—
174Q8—462no—
175Q8—922no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—232no—
181C2×C4—462no—
182C2×C4—464no—
183C2×C4—462no—
184C2×C4—462no—
185C2×C4—462no—
186C2×C4—462no—
187C2×C4—928no—
188C2×C4—922no—
189C2×C4—922no—
190C2×C4#6728812yes—
191C2×C4D4×D2311yescharacteristic
192C2×C4#6729212yes—
193C2×C4C23×D2311yescharacteristic
194C8—22no—
195C8—462no—
196C22—234no—
197C22—462no—
198C22—462no—
199C22—468no—
200C22#1062506512yes—
201C22#1062508212yes—
202C22Q16×D2312yes—
203C22C2×D4×D2311yescharacteristic
204C4—42no—
205C4—42no—
206C4—462no—
207C4—922no—
208C4—922no—
209C4#1062506512yes—
210C4C2×#6728811yescharacteristic
211C4C2×#6729211yescharacteristic
212C2—464no—
213C2#1309275414yesdirect product factor
214C2C2×#1062506511yescharacteristic
215C2C2×Q16×D2311yescharacteristic
216C2C2×#1062508211yescharacteristic
subgroupG/H
centerC23D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#107C2
socleC23×C23C2×D4
prime radicalC23×D23D4
hypercenterC2×#107D23
hypocenterC23C2×#484
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. #13092754C2direct (N × H)
4. C2×#10624989C2semidirect
5. C2×#10624998C2semidirect
6. C2×#10624992C2semidirect
8. C2×C23×#107C2semidirect
24. C23×#107C22semidirect
26. #10624998C22semidirect
27. #10624992C22semidirect
28. #10624989C22semidirect
108. C2×#107D23semidirect
112. C2×C23#484semidirect
133. #107C2×D23semidirect
137. C23C2×#484semidirect
213. C2#13092754direct (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×C4⋊C4×D232
#130927542
C2×#106249892
C2×#106249982
C2×#106249922
C2×(C2×D23)⋊C82
C2×C23×#1072
C2×#48423