Finite Group Databasebeta

← #15682663

Subgroups — #15682663

Order 2944.

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

normal subgroups only

This group has 784 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×#10625160C211yesmaximal, characteristic, complemented
2C2×#10625103C211yesmaximal, characteristic, complemented
3C22×#67272C211yesmaximal, characteristic, complemented
4#13092560C214yesmaximal, complemented
5#13092550C214yesmaximal, complemented
6#13092421C211yesmaximal, characteristic, complemented
7#13092411C211yesmaximal, characteristic, complemented
8#13092384C211yesmaximal, characteristic, complemented
9C23×#535C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11C22×D4×C23C2211yescharacteristic, complemented
12#10625160—24no—
13#10625160—24no—
14C2×#67292—21no—
15C2×D4×D23—21no—
16C2×D4×D23—22no—
17C2×#67288C2211yescharacteristic
18C2×#67288C2212yescomplemented
19C22×D92C2211yescharacteristic
20C22×D92C2212yescomplemented
21C23×#127—21no—
22C23×#124—21no—
23C23×#121C2214yescomplemented
24C23×#120—22no—
25C23×#117C2211yescharacteristic, complemented
26C2×#67273C2212yescomplemented
27#10625103—24no—
28C2×#67272—24no—
29C2×#67272C2214yescomplemented
30C2×#67272C2212yescomplemented
31C2×#67267C2211yescharacteristic, complemented
32C22×C23⋊C8C2211yescharacteristic, complemented
33C22⋊(C23⋊C8)C2214yescomplemented
34#10624992C2212yescomplemented
35#10624991C2212yescomplemented
36#10624991C2214yescomplemented
37C24×C23—21no—
38C23×D23—21no—
39C23×D23—22no—
40#41×C23—22no—
41#41×C23—22no—
42C2×Q8×C23D411yescharacteristic
43C2×D4×C23—24no—
44C2×D4×C23—22no—
45C2×D4×C23—22no—
46C2×D4×C23—21no—
47C2×D4×C23D412yes—
48C2×D4×C23D411yescharacteristic
49C2×D4×C23C2312yes—
50C22×C4×C23C2312yes—
51C22×C4×C23C2311yescharacteristic
52C2×C22⋊D23—21no—
53C2×C22⋊D23—22no—
54#67292—28no—
55D4×D23—216no—
56D4×D23—28no—
57#67288—22no—
58#67288—24no—
59#67288—24no—
60#67288D414yescomplemented
61C2×D92—21no—
62C2×D92—22no—
63C2×D92—22no—
64C2×D92—24no—
65C2×D92—24no—
66C2×D92D414yescomplemented
67C2×D92C2312yes—
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×C4×D23—22no—
71C2×Dic46C2311yescharacteristic
72C4⋊C4×C23C2312yes—
73C22⋊C4×C23—21no—
74C22⋊C4×C23—24no—
75C42×C23—21no—
76#67273—24no—
77#67272—28no—
78#67272—24no—
79#67267—22no—
80C2×C23⋊C8—22no—
81C2×C23⋊C8C2312yes—
82C2×C23⋊C8C2312yes—
83C23×C23—22no—
84C23×C23—42no—
85C23×C23—82no—
86C23×C23C2×D412yes—
87C23×C23C2×D411yescharacteristic
88C22×D23—21no—
89C22×D23—22no—
90C22×D23—28no—
91C22×D23—24no—
92C22×D23—82no—
93C22×D23—84no—
94Q8×C23—22no—
95D4×C23—24no—
96D4×C23—22no—
97D4×C23—22no—
98D4×C23—22no—
99D4×C23—42no—
100D4×C23—84no—
101C2×C4×C23—22no—
102C2×C4×C23—22no—
103C2×C4×C23—22no—
104C2×C4×C23C2×D412yes—
105C2×C4×C23C2×D412yes—
106C2×C4×C23C2×D412yes—
107C2×C4×C23C2×D411yescharacteristic
108C2×C4×C23C2411yescharacteristic
109C22⋊D23—28no—
110C22⋊D23—24no—
111C2×Dic23—21no—
112D92—28no—
113D92—24no—
114D92—21no—
115D92—22no—
116D92C2×D412yes—
117D92C2×D414yes—
118C4×D23—28no—
119C4×D23—24no—
120Dic46—21no—
121Dic46C2×D412yes—
122C23⋊C8—22no—
123C23⋊C8—22no—
124#3008—231nomaximal, Sylow
125C22×C23—22no—
126C22×C23—22no—
127C22×C23—24no—
128C22×C23—42no—
129C22×C23—44no—
130C22×C23—84no—
131C22×C23#12012yes—
132C22×C23C22×D411yescharacteristic
133C2×D23—24no—
134C2×D23—22no—
135C2×D23—44no—
136C2×D23—42no—
137C2×D23—84no—
138C2×D23—88no—
139C4×C23—22no—
140C4×C23—42no—
141C4×C23#12012yes—
142C4×C23C22×D411yescharacteristic
143C4×C23C22×D411yescharacteristic
144Dic23—22no—
145C2×H(5,𝔽2)—231no—
146C2×AGL(1,ℤ/8)—231no—
147C22×D8—231no—
148#535D2311yescharacteristic, complemented
149#449—234no—
150#447—234no—
151#418—231no—
152#416—231no—
153#408—231no—
154C2×C23—22no—
155C2×C23—42no—
156C2×C23—82no—
157C2×C23C2×#12011yescharacteristic
158C2×C23#57612yes—
159D23—44no—
160D23—42no—
161H(5,𝔽2)—464no—
162H(5,𝔽2)—464no—
163C2×#41—231no—
164C2×#41—232no—
165C2×#41—461no—
166C2×#41C2×D2311yescharacteristic
167C22×D4—231no—
168C22×D4—232no—
169C22×D4—462no—
170C22×D4—461no—
171C22×D4C2×D2311yescharacteristic, complemented
172AGL(1,ℤ/8)—464no—
173C2×SD16—232no—
174C2×D8—234no—
175C2×D8—232no—
176C2×D8—464no—
177C2×M16—231no—
178C22×C8—231no—
179#127—21no—
180#124—21no—
181#121C2×D2314yescomplemented
182#120—22no—
183#117C2×D2311yescharacteristic, complemented
184#103—232no—
185#102—232no—
186#102—234no—
187C22⋊C8—234no—
188C23#300811yescharacteristic, complemented, Sylow
189C24—21no—
190C24—462no—
191C24—461no—
192#41—22no—
193#41—22no—
194#41—234no—
195#41—464no—
196#41—464no—
197#41—468no—
198#41—462no—
199C2×Q8—231no—
200C2×Q8C22⋊D2311yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—234no—
206C2×D4—232no—
207C2×D4—231no—
208C2×D4—464no—
209C2×D4—464no—
210C2×D4—4616no—
211C2×D4—468no—
212C2×D4—462no—
213C2×D4—461no—
214C2×D4—462no—
215C2×D4—462no—
216C2×D4—461no—
217C2×D4C22⋊D2312yes—
218C2×D4C22⋊D2311yescharacteristic
219C2×D4C22×D2312yes—
220C22×C4—462no—
221C22×C4—461no—
222C22×C4C22×D2312yes—
223C22×C4C22×D2311yescharacteristic
224SD16—464no—
225D8—468no—
226D8—464no—
227M16—462no—
228C2×C8—232no—
229C2×C8—232no—
230C2×C8—462no—
231C4⋊C4C22×D2312yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—468no—
239C23—462no—
240C23—461no—
241C23—464no—
242C23—1842no—
243C23—1844no—
244C23C2×C22⋊D2312yes—
245C23C2×C22⋊D2311yescharacteristic
246Q8—22no—
247Q8—232no—
248Q8—461no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—234no—
256D4—232no—
257D4—468no—
258D4—468no—
259D4—464no—
260D4—464no—
261D4—461no—
262D4—462no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—468no—
267C2×C4—461no—
268C2×C4—464no—
269C2×C4D4×D2312yes—
270C2×C4D4×D2312yes—
271C2×C4C2×C22⋊D2312yes—
272C2×C4C2×C22⋊D2311yescharacteristic
273C2×C4C23×D2311yescharacteristic
274C8—462no—
275C8—462no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—464no—
283C22—462no—
284C22—924no—
285C22—922no—
286C22—1844no—
287C22—1848no—
288C22#1062510812yes—
289C22C22×C22⋊D2311yescharacteristic
290C4—22no—
291C4—42no—
292C4—462no—
293C4#1062510812yes—
294C4C2×D4×D2311yescharacteristic
295C4C2×D4×D2311yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—924no—
300C2—922no—
301C2C2×#1062510811yescharacteristic
302C2#1309322012yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#535C2
socleC22×C23C22×D4
hypercenter#535D23
hypocenterC23#3008
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#10625160C2semidirect
2. C2×#10625103C2semidirect
3. C22×#67272C2semidirect
4. #13092560C2semidirect
5. #13092550C2semidirect
6. #13092421C2semidirect
7. #13092411C2semidirect
8. #13092384C2semidirect
9. C23×#535C2semidirect
11. C22×D4×C23C22semidirect
18. C2×#67288C22semidirect
20. C22×D92C22semidirect
23. C23×#121C22semidirect
25. C23×#117C22semidirect
26. C2×#67273C22semidirect
29. C2×#67272C22semidirect
30. C2×#67272C22semidirect
31. C2×#67267C22semidirect
32. C22×C23⋊C8C22semidirect
33. C22⋊(C23⋊C8)C22semidirect
34. #10624992C22semidirect
35. #10624991C22semidirect
36. #10624991C22semidirect
60. #67288D4semidirect
66. C2×D92D4semidirect
148. #535D23semidirect
171. C22×D4C2×D23semidirect
181. #121C2×D23semidirect
183. #117C2×D23semidirect
188. C23#3008semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106251032
C22×#672722
#130925602
#130925502
#130924212
#130924112
#130923842
C23×#5352
#300823