Finite Group Databasebeta

← C2×#13092755 #15683286

Subgroups — C2×#13092755 #15683286

Order 2944.

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

normal subgroups only

This group has 416 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×#10625097C211yesmaximal, characteristic
2#13092755C218yesmaximal, direct product factor
3C2×#10624989C211yesmaximal, characteristic, complemented
4C2×#10624990C211yesmaximal, characteristic, complemented
5C2×#10625017C211yesmaximal, characteristic, complemented
6C2×#10625017C211yesmaximal, characteristic, complemented
7C2×C22⋊(C23⋊C8)C211yesmaximal, characteristic
8C2×C23×C22⋊Q8C211yesmaximal, characteristic
9C22×Q8×C23C2211yescharacteristic
10C23×C4×C23C2211yescharacteristic
11C23×C22⋊Q8—22no—
12C23×C22⋊Q8C2214yes—
13C2×C4⋊C4×C23—21no—
14C2×C4⋊C4×C23C2211yescharacteristic
15C2×C22⋊C4×C23—21no—
16C2×C22⋊Dic23—21no—
17#10625097—22no—
18#10625097C2214yes—
19C2×C4⋊Dic23C2211yescharacteristic
20C2×C4⋊Dic23C2211yescharacteristic
21C2×C4×Dic23—21no—
22C22×C23⋊C8C2211yescharacteristic
23C22×C23⋊C8C2211yescharacteristic
24#10625017C2214yescomplemented
25#10625017C2214yescomplemented
26C22⋊(C23⋊C8)C2214yes—
27#10624990C2214yescomplemented
28#10624989C2214yescomplemented
29C24×C23D411yescharacteristic
30C2×Q8×C23—21no—
31C2×Q8×C23—22no—
32C2×Q8×C23—22no—
33C2×Q8×C23C2312yes—
34C22×C4×C23—22no—
35C22×C4×C23—22no—
36C22×C4×C23—21no—
37C22×C4×C23—21no—
38C22×C4×C23D411yescharacteristic
39C22×C4×C23D412yes—
40C22×C4×C23C2312yes—
41C22×C4×C23C2311yescharacteristic
42C22×Dic23—21no—
43C22×Dic23—21no—
44C4⋊C4×C23—24no—
45C4⋊C4×C23—21no—
46C4⋊C4×C23C2312yes—
47C22⋊C4×C23—24no—
48C22⋊Dic23—24no—
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23C2312yes—
52C4⋊Dic23C2312yes—
53C4×Dic23—24no—
54C2×C23⋊C8—22no—
55C2×C23⋊C8—22no—
56C2×C23⋊C8C2312yes—
57C2×C23⋊C8C2312yes—
58C23×C23—22no—
59C23×C23—22no—
60C23×C23—22no—
61C23×C23C2×D412yes—
62C23×C23C2×D411yescharacteristic
63Q8×C23—22no—
64Q8×C23—22no—
65Q8×C23—42no—
66C2×C4×C23—22no—
67C2×C4×C23—24no—
68C2×C4×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—22no—
72C2×C4×C23—42no—
73C2×C4×C23—42no—
74C2×C4×C23C2×D412yes—
75C2×C4×C23C2×D411yescharacteristic
76C2×C4×C23#4112yes—
77C2×C4×C23#4112yes—
78C2×C4×C23C2411yescharacteristic
79C2×Dic23—22no—
80C2×Dic23—22no—
81C2×Dic23—42no—
82C2×Dic23—42no—
83C23⋊C8—22no—
84C23⋊C8—22no—
85C2×#485—231nomaximal, Sylow
86C22×C23—22no—
87C22×C23—22no—
88C22×C23—22no—
89C22×C23—44no—
90C22×C23#12312yes—
91C22×C23#13512yes—
92C22×C23#13712yes—
93C22×C23C22×D411yescharacteristic
94C4×C23—22no—
95C4×C23—42no—
96C4×C23—42no—
97C4×C23#12312yes—
98C4×C23C2×#4111yescharacteristic
99C4×C23C2×#4111yescharacteristic
100Dic23—42no—
101Dic23—42no—
102C2×C22⋊Q8D2311yescharacteristic
103C2×#117—231no—
104#485—238no—
105C2×#107—231no—
106C2×#106—231no—
107C2×#103—231no—
108C2×#103—231no—
109C2×C22⋊C8—231no—
110C2×C23—42no—
111C2×C23#48514yescomplemented
112C2×C23C2×#12311yescharacteristic
113C2×C23C2×#13511yescharacteristic
114C2×C23C2×#13711yescharacteristic
115C22×Q8C2×D2311yescharacteristic
116C23×C4C2×D2311yescharacteristic
117C22×C8—231no—
118C22×C8—231no—
119C22⋊Q8—22no—
120C22⋊Q8C2×D2314yes—
121#117—234no—
122#117—462no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—231no—
125C2×C4⋊C4—231no—
126C2×C4⋊C4C2×D2311yescharacteristic
127C2×C22⋊C4—21no—
128C2×C22⋊C4—461no—
129C2×C42—461no—
130#107—234no—
131#106—234no—
132#103—234no—
133#103—234no—
134C22⋊C8—234no—
135C23C2×#48511yescharacteristic, complemented, Sylow
136C24C22⋊D2311yescharacteristic
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D2312yes—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—461no—
146C22×C4—461no—
147C22×C4C22⋊D2312yes—
148C22×C4C22⋊D2311yescharacteristic
149C22×C4C22×D2312yes—
150C22×C4C22×D2311yescharacteristic
151C2×C8—232no—
152C2×C8—232no—
153C2×C8—462no—
154C2×C8—462no—
155C4⋊C4—24no—
156C4⋊C4—21no—
157C4⋊C4—232no—
158C4⋊C4—232no—
159C4⋊C4—461no—
160C4⋊C4—461no—
161C4⋊C4C22×D2312yes—
162C22⋊C4—24no—
163C22⋊C4—464no—
164C42—464no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D2312yes—
169C23C2×C22⋊D2311yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—462no—
182C2×C4—462no—
183C2×C4—922no—
184C2×C4—922no—
185C2×C4#6729012yes—
186C2×C4#6729012yes—
187C2×C4C2×C22⋊D2312yes—
188C2×C4C2×C22⋊D2311yescharacteristic
189C2×C4C23×D2311yescharacteristic
190C8—462no—
191C8—462no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1062510612yes—
197C22#1062511312yes—
198C22#1062512112yes—
199C22C22×C22⋊D2311yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—922no—
204C4—922no—
205C4#1062510612yes—
206C4C2×#6729011yescharacteristic
207C4C2×#6729011yescharacteristic
208C2—42no—
209C2#1309275514yesdirect product factor
210C2C2×#1062510611yescharacteristic
211C2C2×#1062512111yescharacteristic
212C2C2×#1062511311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C22⋊Q8C2
socleC23×C23C2×D4
prime radicalC24×C23D4
hypercenterC2×C22⋊Q8D23
hypocenterC23C2×#485
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
2. #13092755C2direct (N × H)
3. C2×#10624989C2semidirect
4. C2×#10624990C2semidirect
5. C2×#10625017C2semidirect
6. C2×#10625017C2semidirect
24. #10625017C22semidirect
25. #10625017C22semidirect
27. #10624990C22semidirect
28. #10624989C22semidirect
111. C2×C23#485semidirect
135. C23C2×#485semidirect
209. C2#13092755direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250972
#130927552
C2×#106249892
C2×#106249902
C2×#106250172
C2×C22⋊(C23⋊C8)2
C2×C23×C22⋊Q82
C2×#48523