Finite Group Databasebeta

← #19146269

Subgroups — #19146269

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
1C22×D344C211yesmaximal, characteristic, complemented
2C2×D8×D43C211yesmaximal, characteristic, complemented
3#14583533C212yesmaximal, complemented
4#14583274C211yesmaximal, characteristic, complemented
5#14583136C211yesmaximal, characteristic, complemented
6#14583093C212yesmaximal, complemented
7#14583034C212yesmaximal, complemented
8#14583032C212yesmaximal, complemented
9#14582981C211yesmaximal, characteristic, complemented
10C8×C22⋊D43C211yesmaximal, characteristic, complemented
11C43×#466C211yesmaximal, characteristic, complemented
12C22×D172C2212yescomplemented
13C2×D4×D43—22no—
14C2×D4×D43C2212yescomplemented
15C2×D344—24no—
16C2×D344C2211yescharacteristic
17C2×D344C2212yescomplemented
18C2×D344C2211yescharacteristic, complemented
19C2×#10621882C2212yescomplemented
20C2×#10621882C2212yescomplemented
21D8×D43—24no—
22C2×C8×D43C2211yescharacteristic, complemented
23#13063321C2212yescomplemented
24#13063300C2212yescomplemented
25#13063298—22no—
26#13063295—22no—
27#13063293—22no—
28#13063287C2212yescomplemented
29C4×C22⋊D43C2211yescharacteristic
30Dic43⋊C8C2211yescharacteristic, complemented
31#13063245C2212yescomplemented
32#13063245C2212yescomplemented
33C22⋊(C43⋊C8)C2211yescharacteristic, complemented
34(C2×D43)⋊C8C2211yescharacteristic, complemented
35C8×Dic43C2211yescharacteristic, complemented
36C2×D8×C43C2211yescharacteristic, complemented
37C22×C8×C43C2211yescharacteristic, complemented
38#121×C43C2212yescomplemented
39#107×C43C2211yescharacteristic, complemented
40#102×C43C2212yescomplemented
41C23×D43—22no—
42C23×D43—22no—
43C2×D4×C43—22no—
44C2×D4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43D411yescharacteristic
50D4×D43—24no—
51D4×D43—42no—
52D4×D43—48no—
53C2×D172—22no—
54C2×D172—22no—
55C2×D172—24no—
56C2×D172—42no—
57C2×D172C2312yes—
58C2×D172C2312yes—
59C2×C4×D43—22no—
60C2×C4×D43C2311yescharacteristic
61D8×C43—22no—
62C2×C8×C43—22no—
63C2×C8×C43C2311yescharacteristic
64C2×C8×C43C2311yescharacteristic
65C4⋊C4×C43C2312yes—
66C22⋊C4×C43—22no—
67C22⋊Dic43D411yescharacteristic
68#10621882—24no—
69#10621882—42no—
70(C2×D43)⋊C4—22no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4D411yescharacteristic
73Dic43⋊C4D411yescharacteristic
74C4×Dic43C2311yescharacteristic
75C2×C43⋊C8C2311yescharacteristic
76C2×C43⋊C8C2311yescharacteristic
77D344—24no—
78D344—22no—
79D344D414yescomplemented
80C8×D43—22no—
81C23×C43—22no—
82C23×C43C2×D411yescharacteristic
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—44no—
86C22×D43—44no—
87C22×D43—44no—
88C22×D43—44no—
89C22×D43—82no—
90C22×D43—82no—
91C22×D43C2×D411yescharacteristic
92D4×C43—22no—
93D4×C43—22no—
94D4×C43—44no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2411yescharacteristic
100C22⋊D43—44no—
101C22⋊D43—44no—
102C22⋊D43—82no—
103C22⋊D43D814yescomplemented
104C2×Dic43C2×D411yescharacteristic
105C2×Dic43C2×D411yescharacteristic
106C2×Dic43C2×D411yescharacteristic
107D172—22no—
108D172—22no—
109D172—22no—
110D172—44no—
111D172—44no—
112D172C2×D414yescomplemented
113C4×D43—21no—
114C4×D43—21no—
115C4×D43—44no—
116C8×C43—21no—
117C8×C43C2×D412yescomplemented
118C43⋊C8—21no—
119C43⋊C8—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43C2×D812yescomplemented
126C22×C43C22×D411yescharacteristic
127C2×D43—21no—
128C2×D43—21no—
129C2×D43—24no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—88no—
136C2×D43—88no—
137C2×D43C2×D812yescomplemented
138C4×C43—21no—
139C4×C43—42no—
140C4×C43C22×D411yescharacteristic
141C4×C43H(5,𝔽2)11yescharacteristic
142Dic43—21no—
143Dic43—21no—
144Dic43C2×D812yescomplemented
145D4×D8—431nomaximal, Sylow
146C2×C43—22no—
147C2×C43—82no—
148C2×C43D4211yescharacteristic
149C2×C43C22×D811yescharacteristic
150C2×C43#57611yescharacteristic
151D43—22no—
152D43—44no—
153D43—82no—
154C22×D8—431no—
155C22×D8—431no—
156D42—432no—
157#493—431no—
158#466—431no—
159#466D4311yescharacteristic, complemented
160#459—432no—
161#447—432no—
162#447—432no—
163C4×D8—431no—
164C8×D4—431no—
165C43D4×D811yescharacteristic, complemented, Sylow
166C22×D4—432no—
167C22×D4—432no—
168C22×D4—862no—
169C2×D8—432no—
170C2×D8—432no—
171C2×D8—431no—
172C2×D8—432no—
173C2×D8—431no—
174C2×D8—864no—
175C2×D8—864no—
176C2×D8C2×D4311yescharacteristic, complemented
177C22×C8—431no—
178C22×C8C2×D4311yescharacteristic, complemented
179#127—432no—
180#121—432no—
181#121—862no—
182#121C2×D4312yescomplemented
183#120—862no—
184#120—862no—
185C4×D4—431no—
186C4×D4—432no—
187#107C2×D4311yescharacteristic, complemented
188C4⋊C8—431no—
189#102—432no—
190#102—432no—
191#102C2×D4312yescomplemented
192C22⋊C8—431no—
193C22⋊C8—431no—
194C4×C8—431no—
195C24—862no—
196C24—862no—
197C2×D4—22no—
198C2×D4—431no—
199C2×D4—432no—
200C2×D4—432no—
201C2×D4—864no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—864no—
207C2×D4—862no—
208C2×D4—1722no—
209C2×D4—1722no—
210C2×D4—1728no—
211C2×D4C22×D4312yes—
212C22×C4—431no—
213C22×C4—862no—
214C22×C4C22×D4311yescharacteristic
215D8—22no—
216D8—434no—
217D8—864no—
218D8—864no—
219D8—862no—
220D8—1722no—
221C2×C8—22no—
222C2×C8—431no—
223C2×C8—431no—
224C2×C8—862no—
225C2×C8C22×D4311yescharacteristic
226C2×C8C22×D4311yescharacteristic
227C4⋊C4—431no—
228C4⋊C4C22×D4312yes—
229C22⋊C4—22no—
230C22⋊C4—431no—
231C22⋊C4—431no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C42—431no—
235C23—22no—
236C23—431no—
237C23—862no—
238C23—862no—
239C23—3442no—
240C23—3442no—
241C23—1724no—
242C23—1724no—
243C23—1724no—
244C23—1724no—
245C23D4×D4311yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—434no—
250D4—434no—
251D4—862no—
252D4—862no—
253D4—862no—
254D4—3442no—
255D4—1724no—
256D4—1724no—
257D4—1724no—
258D4—1724no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—431no—
263C2×C4—431no—
264C2×C4—431no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—1724no—
268C2×C4D4×D4311yescharacteristic
269C2×C4C23×D4311yescharacteristic
270C8—21no—
271C8—861no—
272C8—861no—
273C8D4×D4312yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—432no—
280C22—861no—
281C22—861no—
282C22—864no—
283C22—3448no—
284C22—3448no—
285C22—1722no—
286C22—1722no—
287C22—1722no—
288C22—1722no—
289C22—1722no—
290C22D8×D4312yescomplemented
291C22C2×D4×D4311yescharacteristic
292C4—21no—
293C4—42no—
294C4—432no—
295C4—861no—
296C4—861no—
297C4C2×D4×D4311yescharacteristic
298C4#1306337111yescharacteristic
299C2—22no—
300C2—82no—
301C2—862no—
302C2—3442no—
303C2—1724no—
304C2#1458353311yescharacteristic
305C2C2×D8×D4311yescharacteristic
306C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#466C2
socleC22×C43C22×D4
hypercenter#466D43
hypocenterC43D4×D8
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D344C2semidirect
2. C2×D8×D43C2semidirect
3. #14583533C2semidirect
4. #14583274C2semidirect
5. #14583136C2semidirect
6. #14583093C2semidirect
7. #14583034C2semidirect
8. #14583032C2semidirect
9. #14582981C2semidirect
10. C8×C22⋊D43C2semidirect
11. C43×#466C2semidirect
12. C22×D172C22semidirect
14. C2×D4×D43C22semidirect
17. C2×D344C22semidirect
18. C2×D344C22semidirect
19. C2×#10621882C22semidirect
20. C2×#10621882C22semidirect
22. C2×C8×D43C22semidirect
23. #13063321C22semidirect
24. #13063300C22semidirect
28. #13063287C22semidirect
30. Dic43⋊C8C22semidirect
31. #13063245C22semidirect
32. #13063245C22semidirect
33. C22⋊(C43⋊C8)C22semidirect
34. (C2×D43)⋊C8C22semidirect
35. C8×Dic43C22semidirect
36. C2×D8×C43C22semidirect
37. C22×C8×C43C22semidirect
38. #121×C43C22semidirect
39. #107×C43C22semidirect
40. #102×C43C22semidirect
79. D344D4semidirect
103. C22⋊D43D8semidirect
112. D172C2×D4semidirect
117. C8×C43C2×D4semidirect
125. C22×C43C2×D8semidirect
137. C2×D43C2×D8semidirect
144. Dic43C2×D8semidirect
159. #466D43semidirect
165. C43D4×D8semidirect
176. C2×D8C2×D43semidirect
178. C22×C8C2×D43semidirect
182. #121C2×D43semidirect
187. #107C2×D43semidirect
191. #102C2×D43semidirect
273. C8D4×D43semidirect
290. C22D8×D43semidirect