Finite Group Databasebeta

← #15682753

Subgroups — #15682753

Order 2944.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10625155C211yesmaximal, characteristic, complemented
2#13093215C212yesmaximal, complemented
3#13092594C214yesmaximal, complemented
4#13092584C214yesmaximal, complemented
5#13092435C212yesmaximal, complemented
6C2×#10625015C211yesmaximal, characteristic, complemented
7C23×#535C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic, complemented
9C22×D4×C23C2211yescharacteristic
10C22×C22⋊D23—22no—
11#10625155—22no—
12#10625155—24no—
13#10625155C2214yes—
14C2×#67290—22no—
15C2×D4×D23—22no—
16C2×#67288C2212yes—
17C23×#127C2212yescomplemented
18C23×#124C2212yescomplemented
19C23×#121—22no—
20C23×#120—22no—
21C23×#117C2211yescharacteristic, complemented
22#10625122—22no—
23#10625121—24no—
24#10625120—22no—
25#10625113C2214yescomplemented
26#10625103C2214yescomplemented
27C2×#67267C2212yescomplemented
28#10625015C2214yescomplemented
29#10624987C2218yescomplemented
30C24×C23D412yes—
31C23×D23—22no—
32#41×C23—22no—
33#41×C23—22no—
34C2×Q8×C23C2311yescharacteristic, complemented
35C2×D4×C23—21no—
36C2×D4×C23—24no—
37C2×D4×C23—22no—
38C2×D4×C23—22no—
39C2×D4×C23D412yes—
40C2×D4×C23C2312yes—
41C2×D4×C23C2311yescharacteristic, complemented
42C22×C4×C23—21no—
43C22×C4×C23C2311yescharacteristic
44C2×C22⋊D23—24no—
45C2×C22⋊D23—28no—
46C2×C22⋊D23—22no—
47C2×C22⋊D23—28no—
48C22×Dic23—22no—
49#67290—28no—
50#67290—28no—
51D4×D23—28no—
52D4×D23—28no—
53#67288—22no—
54#67288—22no—
55#67288D414yescomplemented
56#67288C2314yes—
57C2×D92D412yescomplemented
58C2×C4×D23—22no—
59C2×Dic46D412yescomplemented
60C4⋊C4×C23—21no—
61C22⋊C4×C23—21no—
62C22⋊C4×C23—24no—
63C42×C23C2312yescomplemented
64#67275—24no—
65#67274—24no—
66#67273—24no—
67#67272—24no—
68#67267—22no—
69#67267C2314yescomplemented
70C2×C23⋊C8—22no—
71C23×C23—22no—
72C23×C23—22no—
73C23×C23—21no—
74C23×C23—82no—
75C23×C23C2×D414yes—
76C23×C23C2×D411yescharacteristic
77C22×D23—22no—
78C22×D23—28no—
79C22×D23—84no—
80Q8×C23—22no—
81D4×C23—24no—
82D4×C23—24no—
83D4×C23—22no—
84D4×C23—41no—
85D4×C23—41no—
86D4×C23—84no—
87C2×C4×C23—22no—
88C2×C4×C23—21no—
89C2×C4×C23—42no—
90C2×C4×C23C2×D412yes—
91C2×C4×C23C2×D412yes—
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2411yescharacteristic
94C22⋊D23—216no—
95C22⋊D23—24no—
96C22⋊D23—24no—
97C2×Dic23—28no—
98C2×Dic23—22no—
99D92—22no—
100D92C2×D414yes—
101C4×D23—24no—
102C4×D23—24no—
103Dic46—22no—
104Dic46C2×D414yes—
105C23⋊C8—24no—
106#3019—231nomaximal, Sylow
107C22×C23—24no—
108C22×C23—41no—
109C22×C23—44no—
110C22×C23—44no—
111C22×C23—42no—
112C22×C23—41no—
113C22×C23—82no—
114C22×C23#12011yescharacteristic
115C22×C23#12011yescharacteristic
116C22×C23C22×D411yescharacteristic
117C2×D23—24no—
118C2×D23—44no—
119C2×D23—88no—
120C4×C23—42no—
121C4×C23—41no—
122C4×C23#12012yes—
123C4×C23C22×D412yes—
124Dic23—24no—
125C2×H(5,𝔽2)—231no—
126#575—232no—
127#535D2311yescharacteristic, complemented
128#455—234no—
129#453—234no—
130#421—232no—
131C2×#100—231no—
132C2×C23—21no—
133C2×C23—21no—
134C2×C23—21no—
135C2×C23—44no—
136C2×C23—81no—
137C2×C23C2×#12011yescharacteristic
138D23—44no—
139H(5,𝔽2)—234no—
140H(5,𝔽2)—464no—
141H(5,𝔽2)—462no—
142C2×#41—232no—
143C2×#41—462no—
144C2×#41C2×D2311yescharacteristic, complemented
145C22×D4—462no—
146C22×D4—462no—
147C22×D4C2×D2311yescharacteristic
148#137—234no—
149#137—462no—
150AGL(1,ℤ/8)—234no—
151AGL(1,ℤ/8)—462no—
152#135—464no—
153C2×M16—232no—
154#127C2×D2312yescomplemented
155#124C2×D2312yescomplemented
156#121—22no—
157#120—22no—
158#117C2×D2311yescharacteristic, complemented
159#104—238no—
160#100—234no—
161C23#301911yescharacteristic, complemented, Sylow
162C24—462no—
163C24C22⋊D2312yes—
164#41—22no—
165#41—22no—
166#41—234no—
167#41—234no—
168#41—468no—
169#41—468no—
170#41—462no—
171#41—462no—
172C2×Q8—232no—
173C2×Q8C22×D2311yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—232no—
179C2×D4—468no—
180C2×D4—468no—
181C2×D4—464no—
182C2×D4—468no—
183C2×D4—462no—
184C2×D4—468no—
185C2×D4C22⋊D2312yes—
186C2×D4C22×D2312yes—
187C2×D4C22×D2311yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—462no—
190C22×C4—462no—
191C22×C4C22×D2311yescharacteristic
192Q16—464no—
193SD16—464no—
194SD16—464no—
195D8—464no—
196M16—234no—
197M16—462no—
198C2×C8—462no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D2312yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—468no—
208C23—462no—
209C23—1844no—
210C23C2×C22⋊D2314yes—
211C23C2×C22⋊D2311yescharacteristic
212Q8—22no—
213Q8—234no—
214Q8—462no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—234no—
222D4—4616no—
223D4—464no—
224D4—464no—
225D4—462no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—468no—
230C2×C4—462no—
231C2×C4—464no—
232C2×C4—464no—
233C2×C4D4×D2312yes—
234C2×C4D4×D2312yes—
235C2×C4C2×C22⋊D2311yescharacteristic
236C2×C4C23×D2311yescharacteristic
237C8—464no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—464no—
246C22—924no—
247C22—1848no—
248C22#1062510811yescharacteristic
249C22#1062510811yescharacteristic
250C22C22×C22⋊D2311yescharacteristic
251C4—42no—
252C4—41no—
253C4—464no—
254C4#1062510812yes—
255C4C2×D4×D2312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—924no—
262C2C2×#1062510811yescharacteristic
subgroupG/H
centerC2C2×#10625108
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#535C2
socleC2×C23C2×#120
hypercenter#535D23
hypocenterC23#3019
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. #13093215C2semidirect
3. #13092594C2semidirect
4. #13092584C2semidirect
5. #13092435C2semidirect
6. C2×#10625015C2semidirect
7. C23×#535C2semidirect
8. C2×#41×C23C22semidirect
17. C23×#127C22semidirect
18. C23×#124C22semidirect
21. C23×#117C22semidirect
25. #10625113C22semidirect
26. #10625103C22semidirect
27. C2×#67267C22semidirect
28. #10625015C22semidirect
29. #10624987C22semidirect
34. C2×Q8×C23C23semidirect
41. C2×D4×C23C23semidirect
55. #67288D4semidirect
57. C2×D92D4semidirect
59. C2×Dic46D4semidirect
63. C42×C23C23semidirect
69. #67267C23semidirect
127. #535D23semidirect
144. C2×#41C2×D23semidirect
154. #127C2×D23semidirect
155. #124C2×D23semidirect
158. #117C2×D23semidirect
161. C23#3019semidirect
173. C2×Q8C22×D23semidirect
187. C2×D4C22×D23semidirect
202. C42C22×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
#130932152
#130925942
#130925842
#130924352
C2×#106250152
C23×#5352
#301923