Finite Group Databasebeta

← #19145365

Subgroups — #19145365

Order 5504.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#14583412C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic, complemented
3#14583226C212yesmaximal, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583136C212yesmaximal, complemented
6#14583131C212yesmaximal, complemented
7#14583049C211yesmaximal, characteristic, complemented
8#14583047C212yesmaximal, complemented
9#14583035C211yesmaximal, characteristic, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#484C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic, complemented
13C22×D172—21no—
14C22×D172C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16C2×#10621884C2212yescomplemented
17C2×D344C2212yescomplemented
18C2×C8×D43C2212yescomplemented
19#13063310—21no—
20#13063301C2211yescharacteristic, complemented
21#13063300—21no—
22#13063300—21no—
23#13063300C2212yes—
24#13063300C2212yes—
25#13063300C2211yescharacteristic, complemented
26#13063299C2211yescharacteristic
27#13063295—21no—
28#13063287—21no—
29(C22⋊D43)⋊C4—21no—
30#13063283C2211yescharacteristic, complemented
31C2×(C2×D43)⋊C4—21no—
32#13063256C2212yescomplemented
33#13063247C2212yescomplemented
34#13063245C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yescomplemented
38C22⋊Q8×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43—21no—
44C23×D43D411yescharacteristic
45C2×Q8×C43C2311yescharacteristic
46C22×C4×C43—21no—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—21no—
49C22×Dic43D411yescharacteristic
50#10621902—42no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172—21no—
54C2×D172—22no—
55C2×D172—22no—
56C2×D172—44no—
57C2×D172—42no—
58C2×D172C2311yescharacteristic
59C2×D172C2312yes—
60C2×C4×D43—21no—
61C2×C4×D43—42no—
62C2×C4×D43D411yescharacteristic
63C2×C4×D43D411yescharacteristic
64C2×C4×D43C2311yescharacteristic
65C2×C4×D43C2311yescharacteristic
66C2×C8×C43C2312yes—
67C4⋊C4×C43—21no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43C2312yes—
70C4⋊C4×C43C2311yescharacteristic
71C22⋊C4×C43—21no—
72#10621884—42no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4—22no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—21no—
79C4⋊Dic43C2311yescharacteristic
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82C2×C43⋊C8C2312yes—
83D344—42no—
84C8×D43—42no—
85C23×C43C2×D411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—21no—
89C22×D43—22no—
90C22×D43—41no—
91C22×D43—42no—
92C22×D43—42no—
93C22×D43—42no—
94C22×D43C2×D411yescharacteristic
95C22×D43C2×D411yescharacteristic
96Q8×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—42no—
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—42no—
105C2×Dic43—21no—
106C2×Dic43—41no—
107C2×Dic43C2×D411yescharacteristic
108C2×Dic43C2×D411yescharacteristic
109D172—22no—
110D172—22no—
111D172—22no—
112D172—42no—
113D172—44no—
114D172—42no—
115D172—42no—
116D172—44no—
117C4×D43—22no—
118C4×D43—22no—
119C4×D43—41no—
120C4×D43—41no—
121C4×D43—42no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43#13512yes—
127C22×C43C22×D411yescharacteristic
128C2×D43—21no—
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—44no—
134C2×D43—42no—
135C2×D43—41no—
136C2×D43—42no—
137C2×D43—41no—
138C2×D43—42no—
139C2×D43—41no—
140C2×D43—84no—
141C2×D43AGL(1,ℤ/8)12yes—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—42no—
145C4×C43—41no—
146C4×C43H(5,𝔽2)12yes—
147Dic43—21no—
148Dic43—21no—
149Dic43—41no—
150#3188—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43#53411yescharacteristic
153C2×C43C2×#13511yescharacteristic
154C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
155D43—22no—
156D43—41no—
157D43—81no—
158D43—82no—
159#525—431no—
160C2×#121—431no—
161#484D4311yescharacteristic, complemented
162#482—432no—
163#481—431no—
164#466—432no—
165#465—432no—
166#450—431no—
167#449—432no—
168#447—431no—
169C2×C22⋊C8—431no—
170C43#318811yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C22×D4—431no—
173C22×D4—861no—
174C23×C4—431no—
175C2×SD16—432no—
176C2×D8—432no—
177C22×C8—432no—
178#123—861no—
179C22⋊Q8—431no—
180C22⋊Q8C2×D4311yescharacteristic
181#121—431no—
182#121—432no—
183#121—432no—
184#121—431no—
185#121—861no—
186#121—861no—
187#120—861no—
188C4×D4—861no—
189C4×D4—861no—
190#117—431no—
191C2×C4⋊C4C2×D4311yescharacteristic
192C2×C22⋊C4—861no—
193#107C2×D4312yescomplemented
194#106—432no—
195#103C2×D4312yescomplemented
196#102—432no—
197#102—432no—
198#102—432no—
199C22⋊C8—431no—
200C22⋊C8—432no—
201C22⋊C8C2×D4311yescharacteristic
202C24—431no—
203C24—861no—
204#41—1722no—
205C2×Q8C22×D4311yescharacteristic
206C2×D4—431no—
207C2×D4—432no—
208C2×D4—861no—
209C2×D4—861no—
210C2×D4—862no—
211C2×D4—862no—
212C2×D4—861no—
213C2×D4—861no—
214C2×D4—1722no—
215C2×D4—1724no—
216C22×C4—21no—
217C22×C4—431no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—431no—
222C22×C4—861no—
223C22×C4—1722no—
224C22×C4C22×D4311yescharacteristic
225SD16—1722no—
226D8—1722no—
227C2×C8—432no—
228C2×C8—1722no—
229C2×C8C22×D4312yes—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—431no—
233C4⋊C4—861no—
234C4⋊C4C22×D4311yescharacteristic
235C4⋊C4C22×D4312yes—
236C22⋊C4—21no—
237C22⋊C4—862no—
238C22⋊C4—862no—
239C22⋊C4—861no—
240C22⋊C4—861no—
241C22⋊C4—861no—
242C22⋊C4—861no—
243C42—861no—
244C23—431no—
245C23—431no—
246C23—862no—
247C23—862no—
248C23—861no—
249C23—862no—
250C23—1721no—
251C23—1722no—
252C23—1722no—
253C23—1722no—
254C23D4×D4311yescharacteristic
255Q8—22no—
256D4—862no—
257D4—862no—
258D4—862no—
259D4—1722no—
260D4—1724no—
261D4—1722no—
262D4—1724no—
263D4—1722no—
264D4—1722no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—431no—
271C2×C4—431no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—861no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1722no—
278C2×C4—1721no—
279C2×C4D4×D4311yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—22no—
282C8—862no—
283C22—21no—
284C22—21no—
285C22—432no—
286C22—861no—
287C22—861no—
288C22—861no—
289C22—861no—
290C22—861no—
291C22—3444no—
292C22—1724no—
293C22—1721no—
294C22—1722no—
295C22—1722no—
296C22—1721no—
297C22—1721no—
298C22—1722no—
299C22#1306334812yes—
300C22C2×D4×D4311yescharacteristic
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—861no—
306C4—861no—
307C4—1721no—
308C4#1306337112yes—
309C2—22no—
310C2—862no—
311C2—3442no—
312C2—3441no—
313C2—1721no—
314C2#1458346011yescharacteristic
315C2C2×#1306334811yescharacteristic
316C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3188
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14583412C2semidirect
2. C2×#13063300C2semidirect
3. #14583226C2semidirect
4. #14583217C2semidirect
5. #14583136C2semidirect
6. #14583131C2semidirect
7. #14583049C2semidirect
8. #14583047C2semidirect
9. #14583035C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#484C2semidirect
12. C2×#10621902C22semidirect
16. C2×#10621884C22semidirect
17. C2×D344C22semidirect
18. C2×C8×D43C22semidirect
20. #13063301C22semidirect
25. #13063300C22semidirect
30. #13063283C22semidirect
32. #13063256C22semidirect
33. #13063247C22semidirect
34. #13063245C22semidirect
35. #13063245C22semidirect
37. (C2×D43)⋊C8C22semidirect
40. #107×C43C22semidirect
41. #103×C43C22semidirect
161. #484D43semidirect
170. C43#3188semidirect
193. #107C2×D43semidirect
195. #103C2×D43semidirect