Finite Group Databasebeta

← C2×#13092600 #15682739

Subgroups — C2×#13092600 #15682739

Order 2944.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10625122C212yesmaximal, complemented
2C2×#10625115C211yesmaximal, characteristic, complemented
3#13092600C218yesmaximal, direct product factor
4C2×#10625019C212yesmaximal, complemented
5C2×#10625018C211yesmaximal, characteristic, complemented
6C2×C23×2−1+4C211yesmaximal, characteristic
7C23×2−1+4—24no—
8C23×2−1+4—22no—
9C23×2−1+4C2214yes—
10C2×#41×C23—22no—
11C2×#41×C23—22no—
12C2×#41×C23C2212yes—
13C22×Q8×C23—22no—
14C22×Q8×C23C2211yescharacteristic
15C22×Dic46C2211yescharacteristic
16#10625122—24no—
17#10625122C2218yescomplemented
18#10625115—22no—
19#10625115C2214yescomplemented
20C2×#67275—22no—
21C2×#67273—22no—
22C2×Dic23⋊C4—22no—
23C2×C4×Dic23C2211yescharacteristic
24C2×#67267C2212yes—
25#10625019C2218yescomplemented
26#10625018C2214yescomplemented
27#41×C23—28no—
28#41×C23—28no—
29#41×C23—28no—
30#41×C23—28no—
31#41×C23—22no—
32#41×C23—22no—
33#41×C23D414yes—
34#41×C23C2314yes—
35C2×Q8×C23—22no—
36C2×Q8×C23—28no—
37C2×Q8×C23—28no—
38C2×Q8×C23—22no—
39C2×Q8×C23—22no—
40C2×Q8×C23D412yes—
41C2×Q8×C23D412yes—
42C2×Q8×C23C2312yes—
43C2×D4×C23—22no—
44C2×D4×C23—22no—
45C2×D4×C23D412yes—
46C22×C4×C23—24no—
47C22×C4×C23—22no—
48C22×C4×C23D412yes—
49C22×C4×C23C2311yescharacteristic
50C22×Dic23—21no—
51C22×Dic23—21no—
52C2×Dic46—22no—
53C2×Dic46—22no—
54C2×Dic46—21no—
55C2×Dic46C2312yes—
56#67275—28no—
57#67273—28no—
58Dic23⋊C4—28no—
59C4×Dic23—21no—
60C4×Dic23C2312yes—
61#67267—22no—
62#67267C2314yes—
63C2×C23⋊C8—22no—
64C23×C23—22no—
65C23×C23C2×D411yescharacteristic
66Q8×C23—28no—
67Q8×C23—22no—
68Q8×C23—24no—
69Q8×C23—24no—
70Q8×C23C2×D414yes—
71D4×C23—28no—
72D4×C23—24no—
73D4×C23—24no—
74D4×C23—22no—
75D4×C23C2×D414yes—
76C2×C4×C23—216no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—22no—
80C2×C4×C23—24no—
81C2×C4×C23—24no—
82C2×C4×C23C2×D414yes—
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2×D412yes—
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2411yescharacteristic
87C2×Dic23—24no—
88C2×Dic23—22no—
89C2×Dic23—22no—
90C2×Dic23—41no—
91C2×Dic23—41no—
92Dic46—24no—
93Dic46—42no—
94C23⋊C8—24no—
95C2×#456—231nomaximal, Sylow
96C22×C23—22no—
97C22×C23—24no—
98C22×C23—44no—
99C22×C23#12011yescharacteristic
100C22×C23#12011yescharacteristic
101C22×C23C22×D411yescharacteristic
102C4×C23—24no—
103C4×C23—24no—
104C4×C23#12012yes—
105C4×C23C22×D412yes—
106Dic23—24no—
107Dic23—42no—
108C2×2−1+4D2311yescharacteristic
109C2×#137—232no—
110C2×C4⋊Q8—231no—
111#456—238no—
112C2×#104—232no—
113C2×#101—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—44no—
117C2×C23#45612yescomplemented
118C2×C23C2×#12011yescharacteristic
1192−1+4—24no—
1202−1+4—22no—
1212−1+4C2×D2314yes—
122C2×#41—22no—
123C2×#41—22no—
124C2×#41C2×D2312yes—
125C22×Q8—22no—
126C22×Q8—231no—
127C22×Q8C2×D2311yescharacteristic
128#137—238no—
129#137—464no—
130C2×Q16—462no—
131C2×SD16—462no—
132C2×M16—232no—
133C4⋊Q8—234no—
134C4⋊Q8—462no—
135C2×C4⋊C4—462no—
136C2×C42—231no—
137#104—238no—
138#101—234no—
139C23C2×#45611yescharacteristic, complemented, Sylow
140#41—28no—
141#41—28no—
142#41—28no—
143#41—28no—
144#41—22no—
145#41—22no—
146#41C22⋊D2314yes—
147#41C22×D2314yes—
148C2×Q8—22no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—232no—
154C2×Q8—461no—
155C2×Q8—462no—
156C2×Q8—462no—
157C2×Q8C22⋊D2312yes—
158C2×Q8C22⋊D2312yes—
159C2×Q8C22×D2312yes—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4C22⋊D2312yes—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—461no—
166C22×C4—461no—
167C22×C4C22⋊D2312yes—
168C22×C4C22×D2311yescharacteristic
169Q16—468no—
170SD16—468no—
171M16—234no—
172M16—462no—
173C2×C8—462no—
174C4⋊C4—468no—
175C42—232no—
176C42—461no—
177C23—22no—
178C23C2×C22⋊D2311yescharacteristic
179Q8—28no—
180Q8—22no—
181Q8—24no—
182Q8—24no—
183Q8—464no—
184Q8—922no—
185Q8C2×C22⋊D2314yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D2314yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—464no—
198C2×C4—462no—
199C2×C4—462no—
200C2×C4—921no—
201C2×C4—921no—
202C2×C4C2×C22⋊D2314yes—
203C2×C4C2×C22⋊D2311yescharacteristic
204C2×C4C2×C22⋊D2312yes—
205C2×C4C2×C22⋊D2312yes—
206C2×C4C23×D2311yescharacteristic
207C8—464no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#1062512411yescharacteristic
212C22#1062512411yescharacteristic
213C22C22×C22⋊D2311yescharacteristic
214C4—24no—
215C4—24no—
216C4—464no—
217C4—922no—
218C4#1062512412yes—
219C4C22×C22⋊D2312yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#1309260012yesdirect product factor
224C2C2×#1062512411yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC2×C23×2−1+4C2
socleC22×C23#120
hypercenterC2×2−1+4D23
hypocenterC23C2×#456
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C2×#10625115C2semidirect
3. #13092600C2direct (N × H)
4. C2×#10625019C2semidirect
5. C2×#10625018C2semidirect
17. #10625122C22semidirect
19. #10625115C22semidirect
25. #10625019C22semidirect
26. #10625018C22semidirect
117. C2×C23#456semidirect
139. C23C2×#456semidirect
223. C2#13092600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106251222
C2×#106251152
#130926002
C2×#106250192
C2×#106250182
C2×C23×2−1+42
C2×#45623