Finite Group Databasebeta

← #15682642

Subgroups — #15682642

Order 2944.

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

normal subgroups only

This group has 758 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
1C22×#67288C211yesmaximal, characteristic, complemented
2C2×#10625080C211yesmaximal, characteristic, complemented
3C2×#10625079C211yesmaximal, characteristic, complemented
4#13092928C211yesmaximal, characteristic, complemented
5#13092581C214yesmaximal, complemented
6#13092564C214yesmaximal, complemented
7#13092427C211yesmaximal, characteristic, complemented
8#13092423C211yesmaximal, characteristic, complemented
9C23×#407C211yesmaximal, characteristic, complemented
10C23×C4×C23C2211yescharacteristic
11C22×C22⋊D23—21no—
12C2×#67288—22no—
13C2×#67288—24no—
14C2×#67288—24no—
15C2×#67288C2211yescharacteristic
16C2×#67288C2214yes—
17C22×D92C2211yescharacteristic
18C22×C4×D23—21no—
19C22×Dic46C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic
21C2×M16×C23C2211yescharacteristic
22#10625124—21no—
23#10625101C2212yescomplemented
24#10625100—21no—
25C4×C22⋊D23—22no—
26#10625097C2211yescharacteristic
27#10625095C2212yescomplemented
28#10625080—24no—
29#10625079—24no—
30C2×Dic92C2212yescomplemented
31C2×D184C2212yescomplemented
32C2×#67263C2212yescomplemented
33C2×#67263C2212yescomplemented
34C23×C22⋊C8C2214yescomplemented
35#10625003C2214yescomplemented
36#10624998C2214yescomplemented
37C24×C23D411yescharacteristic
38C23×D23—21no—
39C22×C4×C23—22no—
40C22×C4×C23—22no—
41C22×C4×C23D412yes—
42C22×C4×C23D411yescharacteristic
43C22×C4×C23C2312yes—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—28no—
46C2×C22⋊D23—24no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—21no—
49C22×Dic23—21no—
50#67288—216no—
51#67288—28no—
52#67288—22no—
53#67288—22no—
54#67288—28no—
55C2×D92—21no—
56C2×D92—22no—
57C2×D92D414yescomplemented
58C2×D92C2311yescharacteristic
59C2×D92C2312yes—
60C2×C4×D23—28no—
61C2×C4×D23—24no—
62C2×C4×D23—21no—
63C2×Dic46—21no—
64C2×Dic46—22no—
65C2×Dic46D414yescomplemented
66C2×Dic46C2311yescharacteristic
67C2×Dic46C2312yes—
68M16×C23—22no—
69M16×C23—22no—
70C2×C8×C23C2312yes—
71C2×C8×C23C2312yes—
72C22⋊Dic23—22no—
73C22⋊Dic23—21no—
74(C2×D23)⋊C4—22no—
75C4⋊Dic23C2312yes—
76Dic23⋊C4—22no—
77C4×Dic23—21no—
78Dic92—24no—
79D184—24no—
80#67263—24no—
81#67263—24no—
82C23×C23—22no—
83C23×C23—42no—
84C23×C23C2×D412yes—
85C23×C23C2×D411yescharacteristic
86C22×D23—24no—
87C22×D23—22no—
88C22×D23—21no—
89C22×D23—44no—
90C2×C4×C23—22no—
91C2×C4×C23—24no—
92C2×C4×C23—22no—
93C2×C4×C23—22no—
94C2×C4×C23C2×D412yes—
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2×D412yes—
97C2×C4×C23C2×D412yes—
98C2×C4×C23C2411yescharacteristic
99C22⋊D23—216no—
100C22⋊D23—44no—
101C22⋊D23—42no—
102C2×Dic23—24no—
103C2×Dic23—22no—
104C2×Dic23—22no—
105C2×Dic23—21no—
106D92—24no—
107D92—22no—
108D92—21no—
109D92—21no—
110D92C2×D414yes—
111C4×D23—216no—
112C4×D23—42no—
113Dic46—24no—
114Dic46—22no—
115Dic46—21no—
116Dic46—21no—
117Dic46C2×D414yes—
118C8×C23—22no—
119C8×C23—22no—
120#3005—231nomaximal, Sylow
121C22×C23—22no—
122C22×C23—22no—
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—44no—
126C22×C23#12012yes—
127C22×C23C22×D411yescharacteristic
128C2×D23—24no—
129C2×D23—48no—
130C2×D23—44no—
131C2×D23—41no—
132C2×D23—42no—
133C4×C23—22no—
134C4×C23#12012yes—
135C4×C23C22×D411yescharacteristic
136C4×C23C22×D411yescharacteristic
137Dic23—24no—
138Dic23—41no—
139Dic23—42no—
140C22×#41—231no—
141C2×#137—231no—
142C2×AGL(1,ℤ/8)—231no—
143#525—231no—
144#452—234no—
145#449—234no—
146#419—231no—
147#418—231no—
148#407D2311yescharacteristic, complemented
149C2×C23—22no—
150C2×C23—42no—
151C2×C23C2×#12011yescharacteristic
152C2×C23#57512yes—
153D23—44no—
154D23—81no—
155C2×#41—231no—
156C2×#41—234no—
157C2×#41—464no—
158C2×#41—464no—
159C2×#41—462no—
160C22×Q8—231no—
161C22×D4—231no—
162C22×D4—461no—
163C23×C4—461no—
164C23×C4C2×D2311yescharacteristic
165#137—464no—
166AGL(1,ℤ/8)—464no—
167C2×Q16—232no—
168C2×SD16—232no—
169C2×SD16—232no—
170C2×D8—232no—
171C2×M16C2×D2311yescharacteristic
172C2×M16C2×D2311yescharacteristic
173#123—461no—
174C22⋊Q8—232no—
175#121—232no—
176#120—461no—
177C4×D4—462no—
178#117—231no—
179#103—234no—
180#102—234no—
181C22⋊C8C2×D2314yescomplemented
182C23#300511yescharacteristic, complemented, Sylow
183C24—461no—
184C24D9211yescharacteristic
185#41—468no—
186#41—468no—
187#41—4616no—
188#41—462no—
189#41—462no—
190C2×Q8—234no—
191C2×Q8—232no—
192C2×Q8—231no—
193C2×Q8—461no—
194C2×Q8—462no—
195C2×D4—234no—
196C2×D4—232no—
197C2×D4—231no—
198C2×D4—468no—
199C2×D4—464no—
200C2×D4—462no—
201C2×D4—461no—
202C2×D4—461no—
203C2×D4—462no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—468no—
207C22×C4—461no—
208C22×C4—464no—
209C22×C4—461no—
210C22×C4D9212yes—
211C22×C4D9211yescharacteristic
212C22×C4C22×D2312yes—
213C22×C4C22×D2311yescharacteristic
214Q16—464no—
215SD16—464no—
216SD16—464no—
217D8—464no—
218M16—22no—
219M16—22no—
220C2×C8C22×D2312yes—
221C2×C8C22×D2312yes—
222C4⋊C4—232no—
223C4⋊C4—462no—
224C22⋊C4—461no—
225C22⋊C4—462no—
226C22⋊C4—462no—
227C42—461no—
228C23—22no—
229C23—42no—
230C23—464no—
231C23—462no—
232C23—461no—
233C23—924no—
234C23C2×D9212yes—
235C23C2×D9211yescharacteristic
236Q8—234no—
237Q8—464no—
238Q8—462no—
239Q8—461no—
240Q8—461no—
241D4—234no—
242D4—4616no—
243D4—464no—
244D4—462no—
245D4—461no—
246D4—461no—
247D4—924no—
248D4—922no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—4616no—
254C2×C4—464no—
255C2×C4—462no—
256C2×C4—462no—
257C2×C4—461no—
258C2×C4—922no—
259C2×C4C2×D9212yes—
260C2×C4C2×D9211yescharacteristic
261C2×C4D4×D2312yes—
262C2×C4D4×D2312yes—
263C2×C4C23×D2311yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—464no—
272C22—928no—
273C22—924no—
274C22—921no—
275C22—922no—
276C22#1062505312yes—
277C22C22×D9211yescharacteristic
278C4—22no—
279C4—464no—
280C4—921no—
281C4—922no—
282C4#1062505312yes—
283C4C2×D4×D2311yescharacteristic
284C4C2×D4×D2311yescharacteristic
285C2—22no—
286C2—42no—
287C2—924no—
288C2—1841no—
289C2C2×#1062505311yescharacteristic
290C2#1309321712yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#407C2
socleC22×C23C22×D4
hypercenter#407D23
hypocenterC23#3005
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#67288C2semidirect
2. C2×#10625080C2semidirect
3. C2×#10625079C2semidirect
4. #13092928C2semidirect
5. #13092581C2semidirect
6. #13092564C2semidirect
7. #13092427C2semidirect
8. #13092423C2semidirect
9. C23×#407C2semidirect
23. #10625101C22semidirect
27. #10625095C22semidirect
30. C2×Dic92C22semidirect
31. C2×D184C22semidirect
32. C2×#67263C22semidirect
33. C2×#67263C22semidirect
34. C23×C22⋊C8C22semidirect
35. #10625003C22semidirect
36. #10624998C22semidirect
57. C2×D92D4semidirect
65. C2×Dic46D4semidirect
148. #407D23semidirect
181. C22⋊C8C2×D23semidirect
182. C23#3005semidirect

Maximal subgroups

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

subgroupindex
C22×#672882
C2×#106250802
C2×#106250792
#130929282
#130925812
#130925642
#130924272
#130924232
C23×#4072
#300523