Finite Group Databasebeta

← #19146267

Subgroups — #19146267

Order 5504.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D43C212yesmaximal, complemented
2D4×D172C211yesmaximal, characteristic, complemented
3#14583534C211yesmaximal, characteristic, complemented
4#14583275C211yesmaximal, characteristic, complemented
5#14583134C212yesmaximal, complemented
6#14583095C211yesmaximal, characteristic, complemented
7#14583034C212yesmaximal, complemented
8#14583031C212yesmaximal, complemented
9C4×#10621882C211yesmaximal, characteristic, complemented
10#14582964C211yesmaximal, characteristic, complemented
11C43×#459C211yesmaximal, characteristic, complemented
12C22×D172—21no—
13C2×D4×D43—21no—
14C2×D4×D43C2212yescomplemented
15C2×D4×D43C2212yescomplemented
16C2×D344C2212yescomplemented
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2212yescomplemented
19C2×#10621882C2212yescomplemented
20D8×D43—28no—
21C2×C8×D43C2212yescomplemented
22#13063322C2211yescharacteristic, complemented
23#13063300C2212yescomplemented
24#13063299—21no—
25#13063296—21no—
26#13063296C2212yescomplemented
27#13063295—22no—
28#13063293—22no—
29C4×D172C2211yescharacteristic
30C4×D172C2211yescharacteristic, complemented
31#13063258C2211yescharacteristic, complemented
32#13063247C2212yescomplemented
33#13063246C2211yescharacteristic, complemented
34#13063245C2211yescharacteristic, complemented
35(C2×D43)⋊C8C2212yescomplemented
36C4×C43⋊C8C2211yescharacteristic, complemented
37C2×D8×C43C2212yescomplemented
38#127×C43C2211yescharacteristic, complemented
39C4×D4×C43C2211yescharacteristic, complemented
40C4⋊C8×C43C2211yescharacteristic, complemented
41#102×C43C2212yescomplemented
42C23×D43—22no—
43C23×D43—22no—
44C2×D4×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43C2312yes—
47C2×D4×C43C2311yescharacteristic
48C22×C4×C43—21no—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52D4×D43—24no—
53D4×D43—24no—
54D4×D43—42no—
55D4×D43—42no—
56D4×D43—44no—
57C2×D172—21no—
58C2×D172—21no—
59C2×D172—22no—
60C2×D172—44no—
61C2×D172D411yescharacteristic
62C2×D172C2312yes—
63C2×D172C2311yescharacteristic
64C2×C4×D43—21no—
65C2×C4×D43C2312yes—
66D8×C43—24no—
67C2×C8×C43C2312yes—
68C4⋊C4×C43C2311yescharacteristic
69C22⋊C4×C43—21no—
70C42×C43C2311yescharacteristic
71C22⋊Dic43—22no—
72#10621882—24no—
73#10621882—42no—
74#10621882D414yescomplemented
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—22no—
77(C2×D43)⋊C4D412yes—
78C4⋊Dic43D411yescharacteristic
79C4⋊Dic43C2311yescharacteristic
80C2×C43⋊C8C2311yescharacteristic
81C2×C43⋊C8C2311yescharacteristic
82D344—24no—
83C8×D43—24no—
84C23×C43—21no—
85C23×C43—22no—
86C22×D43—21no—
87C22×D43—22no—
88C22×D43—44no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43—44no—
92C22×D43—82no—
93C22×D43—82no—
94C22×D43C2×D412yes—
95D4×C43—22no—
96D4×C43—21no—
97D4×C43—22no—
98D4×C43—42no—
99D4×C43—81no—
100D4×C43C2×D412yescomplemented
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2×D411yescharacteristic
105C2×C4×C43C2411yescharacteristic
106C22⋊D43—44no—
107C22⋊D43—44no—
108C22⋊D43—44no—
109C2×Dic43—21no—
110C2×Dic43C2×D412yes—
111D172—22no—
112D172—21no—
113D172—22no—
114D172—44no—
115D172—42no—
116D172—81no—
117D172D814yescomplemented
118D172C2×D412yescomplemented
119C4×D43—22no—
120C4×D43—22no—
121C4×D43—42no—
122C8×C43—22no—
123C43⋊C8—21no—
124C43⋊C8C2×D412yescomplemented
125C22×C43—22no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43C22×D411yescharacteristic
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—41no—
136C2×D43—41no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43—42no—
140C2×D43—88no—
141C2×D43—88no—
142C2×D43C2×D814yescomplemented
143C4×C43—21no—
144C4×C43—41no—
145C4×C43C2×D812yescomplemented
146C4×C43C22×D411yescharacteristic
147C4×C43H(5,𝔽2)11yescharacteristic
148Dic43—22no—
149Dic43—41no—
150D4×D8—431nomaximal, Sylow
151C2×C43—42no—
152C2×C43—82no—
153C2×C43D4211yescharacteristic
154C2×C43C22×D811yescharacteristic
155C2×C43#57611yescharacteristic
156D43—24no—
157D43—42no—
158D43—82no—
159C22×D8—432no—
160D42—431no—
161D42—431no—
162#493—431no—
163#466—432no—
164#459—431no—
165#459D4311yescharacteristic, complemented
166#447—432no—
167#447—432no—
168C4×D8—431no—
169C8×D4—431no—
170C43D4×D811yescharacteristic, complemented, Sylow
171C22×D4—432no—
172C22×D4—432no—
173C22×D4—861no—
174C22×D4—861no—
175C2×D8—431no—
176C2×D8—432no—
177C2×D8—432no—
178C2×D8—432no—
179C2×D8—868no—
180C2×D8C2×D4312yescomplemented
181C22×C8—432no—
182#127—431no—
183#127C2×D4311yescharacteristic, complemented
184#121—432no—
185#121—432no—
186#121—861no—
187#121—861no—
188#120—862no—
189#120—862no—
190C4×D4—431no—
191C4×D4—431no—
192C4×D4C2×D4311yescharacteristic, complemented
193#107—431no—
194C4⋊C8C2×D4311yescharacteristic, complemented
195#102—431no—
196#102—432no—
197#102—431no—
198#102C2×D4312yescomplemented
199C22⋊C8—432no—
200C4×C8—431no—
201C24—862no—
202C24—862no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—431no—
206C2×D4—431no—
207C2×D4—432no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4—862no—
211C2×D4—864no—
212C2×D4—864no—
213C2×D4—862no—
214C2×D4—861no—
215C2×D4—861no—
216C2×D4—1724no—
217C2×D4—1722no—
218C2×D4—1722no—
219C2×D4—1724no—
220C2×D4C22×D4312yes—
221C2×D4C22×D4311yescharacteristic
222C22×C4—21no—
223C22×C4—432no—
224C22×C4—861no—
225D8—24no—
226D8—434no—
227D8—864no—
228D8—864no—
229D8—1722no—
230C2×C8—431no—
231C2×C8—431no—
232C2×C8—864no—
233C2×C8C22×D4312yes—
234C4⋊C4—431no—
235C4⋊C4—431no—
236C4⋊C4C22×D4311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—432no—
239C22⋊C4—862no—
240C22⋊C4—862no—
241C22⋊C4—861no—
242C42C22×D4311yescharacteristic
243C23—21no—
244C23—22no—
245C23—432no—
246C23—861no—
247C23—862no—
248C23—3442no—
249C23—3442no—
250C23—1724no—
251C23—1724no—
252C23—1724no—
253C23—1724no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—434no—
260D4—432no—
261D4—862no—
262D4—861no—
263D4—862no—
264D4—3441no—
265D4—1724no—
266D4—1724no—
267D4—1724no—
268D4—1724no—
269D4—1722no—
270D4D4×D4312yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—432no—
274C2×C4—862no—
275C2×C4—862no—
276C2×C4—861no—
277C2×C4—1722no—
278C2×C4D4×D4311yescharacteristic
279C2×C4D4×D4311yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—22no—
282C8—432no—
283C8—861no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—434no—
291C22—862no—
292C22—862no—
293C22—862no—
294C22—3448no—
295C22—3448no—
296C22—1722no—
297C22—1722no—
298C22—1722no—
299C22—1721no—
300C22—1721no—
301C22C2×D4×D4311yescharacteristic
302C4—21no—
303C4—41no—
304C4—862no—
305C4—1721no—
306C4D8×D4312yescomplemented
307C4C2×D4×D4311yescharacteristic
308C4#1306337111yescharacteristic
309C2—42no—
310C2—82no—
311C2—864no—
312C2—3442no—
313C2—1722no—
314C2#1458353311yescharacteristic
315C2C2×D8×D4311yescharacteristic
316C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43D4×D8
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D43C2semidirect
2. D4×D172C2semidirect
3. #14583534C2semidirect
4. #14583275C2semidirect
5. #14583134C2semidirect
6. #14583095C2semidirect
7. #14583034C2semidirect
8. #14583031C2semidirect
9. C4×#10621882C2semidirect
10. #14582964C2semidirect
11. C43×#459C2semidirect
14. C2×D4×D43C22semidirect
15. C2×D4×D43C22semidirect
16. C2×D344C22semidirect
18. C2×#10621882C22semidirect
19. C2×#10621882C22semidirect
21. C2×C8×D43C22semidirect
22. #13063322C22semidirect
23. #13063300C22semidirect
26. #13063296C22semidirect
30. C4×D172C22semidirect
31. #13063258C22semidirect
32. #13063247C22semidirect
33. #13063246C22semidirect
34. #13063245C22semidirect
35. (C2×D43)⋊C8C22semidirect
36. C4×C43⋊C8C22semidirect
37. C2×D8×C43C22semidirect
38. #127×C43C22semidirect
39. C4×D4×C43C22semidirect
40. C4⋊C8×C43C22semidirect
41. #102×C43C22semidirect
74. #10621882D4semidirect
100. D4×C43C2×D4semidirect
117. D172D8semidirect
118. D172C2×D4semidirect
124. C43⋊C8C2×D4semidirect
142. C2×D43C2×D8semidirect
145. C4×C43C2×D8semidirect
165. #459D43semidirect
170. C43D4×D8semidirect
180. C2×D8C2×D43semidirect
183. #127C2×D43semidirect
192. C4×D4C2×D43semidirect
194. C4⋊C8C2×D43semidirect
198. #102C2×D43semidirect
270. D4D4×D43semidirect
306. C4D8×D43semidirect