Finite Group Databasebeta

← #19145363

Subgroups — #19145363

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×#13063296C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583222C212yesmaximal, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583134C212yesmaximal, complemented
7#14583125C212yesmaximal, complemented
8#14583043C212yesmaximal, complemented
9#14583033C211yesmaximal, characteristic, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#450C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic, complemented
13C22×C22⋊D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×#10621882C2212yescomplemented
16C2×C8×D43C2212yescomplemented
17#13063310—21no—
18#13063301C2211yescharacteristic, complemented
19#13063300C2211yescharacteristic, complemented
20#13063299C2211yescharacteristic
21#13063296—21no—
22#13063296—21no—
23#13063296C2212yes—
24#13063296C2212yes—
25#13063295—21no—
26#13063287—21no—
27(C22⋊D43)⋊C4—21no—
28#13063283C2211yescharacteristic, complemented
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43—21no—
31#13063258C2212yescomplemented
32#13063257C2212yescomplemented
33#13063249C2212yescomplemented
34#13063247C2212yescomplemented
35#13063246C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yescomplemented
38C22×D4×C43C2211yescharacteristic
39C2×SD16×C43C2212yescomplemented
40C22⋊Q8×C43C2211yescharacteristic
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C24×C43—21no—
44C23×D43D411yescharacteristic
45C2×Q8×C43C2311yescharacteristic
46C2×D4×C43—21no—
47C2×D4×C43—42no—
48C2×D4×C43C2312yes—
49C22×C4×C43C2311yescharacteristic
50C2×C22⋊D43—21no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—44no—
54C22×Dic43—21no—
55C22×Dic43D411yescharacteristic
56#10621902—42no—
57C2×D172—21no—
58C2×D172—21no—
59C2×D172C2311yescharacteristic
60C2×C4×D43—21no—
61C2×C4×D43—42no—
62C2×C4×D43D411yescharacteristic
63C2×C4×D43D411yescharacteristic
64C2×C4×D43C2311yescharacteristic
65C2×C4×D43C2311yescharacteristic
66SD16×C43—42no—
67C2×C8×C43C2312yes—
68C4⋊C4×C43—21no—
69C4⋊C4×C43C2311yescharacteristic
70C22⋊C4×C43—21no—
71C22⋊Dic43—22no—
72C22⋊Dic43—22no—
73#10621882—42no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43C2311yescharacteristic
80C4⋊Dic43C2312yes—
81Dic43⋊C4—21no—
82C4×Dic43—21no—
83C2×C43⋊C8C2312yes—
84C8×D43—42no—
85C23×C43—22no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43C2×D411yescharacteristic
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—21no—
93C22×D43—41no—
94C22×D43C2×D411yescharacteristic
95C22×D43C2×D411yescharacteristic
96Q8×C43—22no—
97D4×C43—22no—
98D4×C43—22no—
99D4×C43—42no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2411yescharacteristic
105C22⋊D43—44no—
106C22⋊D43—42no—
107C22⋊D43—44no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—41no—
111C2×Dic43—42no—
112C2×Dic43C2×D411yescharacteristic
113C2×Dic43C2×D411yescharacteristic
114D172—22no—
115D172—42no—
116D172—42no—
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—42no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—84no—
130C22×C43#13512yes—
131C22×C43C22×D411yescharacteristic
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—21no—
136C2×D43—21no—
137C2×D43—44no—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—41no—
141C2×D43AGL(1,ℤ/8)12yes—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43H(5,𝔽2)12yes—
146Dic43—21no—
147Dic43—21no—
148Dic43—41no—
149Dic43—42no—
150#3188—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—82no—
153C2×C43#53411yescharacteristic
154C2×C43C2×#13511yescharacteristic
155C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
156D43—22no—
157D43—41no—
158D43—81no—
159#525—431no—
160C2×#121—431no—
161#484—431no—
162#482—432no—
163#481—431no—
164#466—432no—
165#465—432no—
166#450D4311yescharacteristic, complemented
167#449—432no—
168#447—431no—
169C2×C22⋊C8—431no—
170C43#318811yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C22×D4—861no—
173C22×D4C2×D4311yescharacteristic
174C23×C4—431no—
175C2×SD16C2×D4312yescomplemented
176C2×D8—432no—
177C22×C8—432no—
178#123—861no—
179C22⋊Q8—431no—
180C22⋊Q8C2×D4311yescharacteristic
181#121—432no—
182#121—432no—
183#121—431no—
184#121—431no—
185#121—861no—
186#121—861no—
187#120—861no—
188C4×D4—861no—
189C4×D4—861no—
190#117—431no—
191C2×C4⋊C4—431no—
192C2×C22⋊C4—861no—
193#107—432no—
194#106—432no—
195#103—432no—
196#102—432no—
197#102—432no—
198#102C2×D4312yescomplemented
199C22⋊C8—431no—
200C22⋊C8—432no—
201C22⋊C8C2×D4311yescharacteristic
202C24—21no—
203C24—431no—
204#41—1722no—
205C2×Q8C22×D4311yescharacteristic
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—431no—
209C2×D4—861no—
210C2×D4—861no—
211C2×D4—862no—
212C2×D4—862no—
213C2×D4—861no—
214C2×D4—1724no—
215C2×D4C22×D4312yes—
216C22×C4—431no—
217C22×C4—431no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—1722no—
224C22×C4C22×D4311yescharacteristic
225SD16—42no—
226D8—1722no—
227C2×C8—432no—
228C2×C8—1722no—
229C2×C8C22×D4312yes—
230C4⋊C4—21no—
231C4⋊C4—431no—
232C4⋊C4—432no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4C22×D4311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C22⋊C4—862no—
241C22⋊C4—862no—
242C22⋊C4—861no—
243C42—861no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—431no—
249C23—431no—
250C23—862no—
251C23—862no—
252C23—861no—
253C23—1721no—
254C23D4×D4311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—862no—
260D4—1722no—
261D4—1722no—
262D4—1724no—
263D4—1724no—
264D4—1722no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—431no—
269C2×C4—431no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—861no—
273C2×C4—862no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1722no—
277C2×C4—1721no—
278C2×C4—1722no—
279C2×C4D4×D4311yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—22no—
282C8—862no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—432no—
290C22—861no—
291C22—861no—
292C22—861no—
293C22—861no—
294C22—861no—
295C22—1724no—
296C22—1721no—
297C22—1721no—
298C22—1721no—
299C22#1306334612yes—
300C22C2×D4×D4311yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—861no—
305C4—861no—
306C4—1721no—
307C4—1722no—
308C4#1306337012yes—
309C2—22no—
310C2—82no—
311C2—862no—
312C2—3441no—
313C2—1721no—
314C2#1458345911yescharacteristic
315C2C2×#1306334611yescharacteristic
316C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3188
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583412C2semidirect
2. C2×#13063296C2semidirect
3. #14583232C2semidirect
4. #14583222C2semidirect
5. #14583218C2semidirect
6. #14583134C2semidirect
7. #14583125C2semidirect
8. #14583043C2semidirect
9. #14583033C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#450C2semidirect
12. C2×#10621902C22semidirect
15. C2×#10621882C22semidirect
16. C2×C8×D43C22semidirect
18. #13063301C22semidirect
19. #13063300C22semidirect
28. #13063283C22semidirect
31. #13063258C22semidirect
32. #13063257C22semidirect
33. #13063249C22semidirect
34. #13063247C22semidirect
35. #13063246C22semidirect
37. (C2×D43)⋊C8C22semidirect
39. C2×SD16×C43C22semidirect
41. #102×C43C22semidirect
166. #450D43semidirect
170. C43#3188semidirect
175. C2×SD16C2×D43semidirect
198. #102C2×D43semidirect