Finite Group Databasebeta

← #15682776

Subgroups — #15682776

Order 2944.

704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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
2#13092988C211yesmaximal, characteristic, complemented
3#13092600C214yesmaximal, complemented
4#13092595C214yesmaximal, complemented
5#13092434C212yesmaximal, complemented
6#13092401C211yesmaximal, characteristic, complemented
7C23×#585C211yesmaximal, characteristic
8C23×2−1+4—22no—
9C23×2−1+4C2212yes—
10C23×H(5,𝔽2)—22no—
11C23×H(5,𝔽2)—22no—
12C23×H(5,𝔽2)C2212yes—
13C2×#41×C23—24no—
14C2×#41×C23—22no—
15C2×#41×C23C2212yes—
16C2×#41×C23C2211yescharacteristic
17C22×Dic46C2211yescharacteristic, complemented
18#10625122—24no—
19#10625122C2218yescomplemented
20#10625115C2212yescomplemented
21C2×#67275—22no—
22#10625107C2212yescomplemented
23#10625106—22no—
24C2×#67273—22no—
25#10625097C2211yescharacteristic, complemented
26#10625095—22no—
27C2×#67267C2212yescomplemented
28#10625019C2218yescomplemented
29#10625018C2212yescomplemented
30#10625015C2212yescomplemented
31#41×C23—24no—
32#41×C23—28no—
33#41×C23—24no—
34#41×C23—24no—
35#41×C23—24no—
36#41×C23—22no—
37#41×C23—22no—
38#41×C23—24no—
39#41×C23—22no—
40#41×C23—22no—
41#41×C23D414yes—
42#41×C23C2314yes—
43C2×Q8×C23—22no—
44C2×Q8×C23—24no—
45C2×Q8×C23D412yes—
46C2×Q8×C23C2311yescharacteristic
47C2×D4×C23—28no—
48C2×D4×C23—22no—
49C2×D4×C23—24no—
50C2×D4×C23—22no—
51C2×D4×C23—24no—
52C2×D4×C23D412yes—
53C2×D4×C23D412yes—
54C2×D4×C23C2311yescharacteristic
55C22×C4×C23—24no—
56C22×C4×C23—22no—
57C22×C4×C23D412yes—
58C22×C4×C23C2311yescharacteristic
59C22×Dic23—21no—
60C2×Dic46—22no—
61C2×Dic46—22no—
62C2×Dic46—21no—
63C2×Dic46C2312yes—
64C22⋊Dic23—24no—
65C22⋊Dic23—21no—
66#67275—28no—
67#67273—28no—
68C4⋊Dic23—21no—
69Dic23⋊C4—24no—
70C4×Dic23C2312yes—
71#67267—22no—
72#67267C2314yes—
73C2×C23⋊C8—22no—
74C23×C23—24no—
75C23×C23—22no—
76C23×C23C2×D412yes—
77C23×C23C2×D411yescharacteristic
78Q8×C23—24no—
79Q8×C23—22no—
80Q8×C23—22no—
81Q8×C23C2×D414yes—
82D4×C23—28no—
83D4×C23—24no—
84D4×C23—24no—
85D4×C23—24no—
86D4×C23—24no—
87D4×C23—22no—
88D4×C23—22no—
89D4×C23C2×D414yes—
90C2×C4×C23—24no—
91C2×C4×C23—28no—
92C2×C4×C23—22no—
93C2×C4×C23—24no—
94C2×C4×C23—22no—
95C2×C4×C23—22no—
96C2×C4×C23—24no—
97C2×C4×C23C2×D412yes—
98C2×C4×C23C2×D411yescharacteristic
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2×D412yes—
101C2×C4×C23C2411yescharacteristic
102C2×Dic23—22no—
103C2×Dic23—22no—
104C2×Dic23—42no—
105Dic46—24no—
106Dic46—41no—
107Dic46—41no—
108C23⋊C8—24no—
109#3022—231nomaximal, Sylow
110C22×C23—22no—
111C22×C23—24no—
112C22×C23—41no—
113C22×C23—42no—
114C22×C23—82no—
115C22×C23—84no—
116C22×C23#12012yes—
117C22×C23C22×D411yescharacteristic
118C4×C23—24no—
119C4×C23—22no—
120C4×C23#12011yescharacteristic
121C4×C23#12011yescharacteristic
122C4×C23C22×D412yes—
123Dic23—42no—
124Dic23—42no—
125#585D2311yescharacteristic
126C2×#137—232no—
127#536—231no—
128#456—234no—
129#455—234no—
130#421—232no—
131#413—231no—
132C2×C23—21no—
133C2×C23—22no—
134C2×C23—42no—
135C2×C23—44no—
136C2×C23C2×#12011yescharacteristic
1372−1+4—22no—
1382−1+4C2×D2312yes—
139H(5,𝔽2)—22no—
140H(5,𝔽2)—22no—
141H(5,𝔽2)C2×D2312yes—
142C2×#41—24no—
143C2×#41—22no—
144C2×#41C2×D2312yes—
145C2×#41C2×D2311yescharacteristic
146C22×Q8—231no—
147#137—238no—
148#137—464no—
149C2×Q16—462no—
150C2×SD16—462no—
151C2×M16—232no—
152C4⋊Q8—232no—
153#124—232no—
154#123—462no—
155C22⋊Q8—462no—
156#117—231no—
157#104—238no—
158#101—232no—
159#100—232no—
160C23#302211yescharacteristic, complemented, Sylow
161#41—24no—
162#41—28no—
163#41—24no—
164#41—24no—
165#41—24no—
166#41—22no—
167#41—22no—
168#41—24no—
169#41—22no—
170#41—22no—
171#41C22⋊D2314yes—
172#41C22×D2314yes—
173C2×Q8—22no—
174C2×Q8—24no—
175C2×Q8—232no—
176C2×Q8—461no—
177C2×Q8—462no—
178C2×Q8—462no—
179C2×Q8C22⋊D2312yes—
180C2×Q8C22×D2311yescharacteristic
181C2×D4—28no—
182C2×D4—22no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4C22⋊D2312yes—
187C2×D4C22⋊D2312yes—
188C2×D4C22×D2311yescharacteristic
189C22×C4—24no—
190C22×C4—22no—
191C22×C4—461no—
192C22×C4C22⋊D2312yes—
193C22×C4C22×D2311yescharacteristic
194Q16—468no—
195SD16—468no—
196M16—234no—
197M16—462no—
198C2×C8—462no—
199C4⋊C4—461no—
200C4⋊C4—464no—
201C22⋊C4—461no—
202C22⋊C4—464no—
203C42—232no—
204C23—24no—
205C23—22no—
206C23C2×C22⋊D2312yes—
207C23C2×C22⋊D2311yescharacteristic
208Q8—24no—
209Q8—22no—
210Q8—22no—
211Q8—464no—
212Q8—921no—
213Q8—921no—
214Q8C2×C22⋊D2314yes—
215D4—28no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—24no—
220D4—22no—
221D4—22no—
222D4C2×C22⋊D2314yes—
223C2×C4—24no—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—462no—
231C2×C4—462no—
232C2×C4—922no—
233C2×C4C2×C22⋊D2312yes—
234C2×C4C2×C22⋊D2311yescharacteristic
235C2×C4C2×C22⋊D2312yes—
236C2×C4C2×C22⋊D2312yes—
237C2×C4C23×D2311yescharacteristic
238C8—464no—
239C22—22no—
240C22—24no—
241C22—41no—
242C22—42no—
243C22—82no—
244C22—84no—
245C22#1062512412yes—
246C22C22×C22⋊D2311yescharacteristic
247C4—24no—
248C4—22no—
249C4—922no—
250C4—922no—
251C4#1062512411yescharacteristic
252C4#1062512411yescharacteristic
253C4C22×C22⋊D2312yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—44no—
258C2C2×#1062512411yescharacteristic
subgroupG/H
centerC2C2×#10625124
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#585C2
socleC2×C23C2×#120
hypercenter#585D23
hypocenterC23#3022
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. #13092988C2semidirect
3. #13092600C2semidirect
4. #13092595C2semidirect
5. #13092434C2semidirect
6. #13092401C2semidirect
17. C22×Dic46C22semidirect
19. #10625122C22semidirect
20. #10625115C22semidirect
22. #10625107C22semidirect
25. #10625097C22semidirect
27. C2×#67267C22semidirect
28. #10625019C22semidirect
29. #10625018C22semidirect
30. #10625015C22semidirect
160. C23#3022semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
#130929882
#130926002
#130925952
#130924342
#130924012
C23×#5852
#302223