Finite Group Databasebeta

← #19145399

Subgroups — #19145399

Order 5504.

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

normal subgroups only

This group has 462 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
1C2×#13063301C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic
3#14583233C212yesmaximal, complemented
4#14583213C211yesmaximal, characteristic, complemented
5#14583210C211yesmaximal, characteristic, complemented
6#14583148C212yesmaximal, complemented
7#14583142C212yesmaximal, complemented
8#14583048C212yesmaximal, complemented
9#14583038C211yesmaximal, characteristic, complemented
10#14582861C211yesmaximal, characteristic, complemented
11C43×#448C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C2×#10621884C2212yescomplemented
16C2×#10621872C2212yescomplemented
17#13063301—21no—
18#13063301—21no—
19#13063301C2212yes—
20#13063301C2212yescomplemented
21#13063300C2211yescharacteristic
22#13063299C2211yescharacteristic
23#13063298—21no—
24#13063297—21no—
25#13063296C2211yescharacteristic
26C2×C4⋊Dic43C2211yescharacteristic, complemented
27C2×Dic43⋊C4—21no—
28C4⋊C4×D43C2211yescharacteristic
29C2×(C2×D43)⋊C4—21no—
30C22⋊C4×D43—21no—
31#13063259C2212yescomplemented
32#13063258C2212yescomplemented
33#13063249C2212yescomplemented
34#13063247C2212yescomplemented
35#13063246C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37(C2×D43)⋊C8C2212yes—
38C22×Q8×C43C2211yescharacteristic, complemented
39C2×SD16×C43C2212yescomplemented
40#121×C43C2211yescharacteristic
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C23×D43D411yescharacteristic
45C2×Q8×C43—21no—
46C2×Q8×C43—42no—
47C2×Q8×C43C2312yes—
48C2×D4×C43—21no—
49C2×D4×C43C2311yescharacteristic
50C22×C4×C43—21no—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C2×C22⋊D43—21no—
55C22×Dic43—21no—
56C22×Dic43D411yescharacteristic
57D4×D43—44no—
58D4×D43—42no—
59C2×D172—21no—
60C2×D172C2311yescharacteristic
61C2×C4×D43—21no—
62C2×C4×D43—42no—
63C2×C4×D43D411yescharacteristic
64C2×C4×D43D411yescharacteristic
65C2×C4×D43C2311yescharacteristic
66C2×C4×D43C2311yescharacteristic
67SD16×C43—42no—
68C2×C8×C43C2312yes—
69C4⋊C4×C43C2311yescharacteristic
70C22⋊C4×C43—21no—
71C22⋊Dic43—21no—
72#10621884—42no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—22no—
76(C2×D43)⋊C4—22no—
77C4⋊Dic43—21no—
78C4⋊Dic43C2312yes—
79C4⋊Dic43C2311yescharacteristic
80Dic43⋊C4—21no—
81Dic43⋊C4—22no—
82Dic43⋊C4—22no—
83C2×C43⋊C8C2312yes—
84#10621872—42no—
85C23×C43—21no—
86C23×C43C2×D411yescharacteristic
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—21no—
90C22×D43—41no—
91C22×D43—42no—
92C22×D43—42no—
93C22×D43—42no—
94C22×D43C2×D411yescharacteristic
95C22×D43C2×D411yescharacteristic
96Q8×C43—22no—
97Q8×C43—22no—
98Q8×C43—42no—
99D4×C43—22no—
100D4×C43—42no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2411yescharacteristic
107C22⋊D43—42no—
108C22⋊D43—42no—
109C22⋊D43—42no—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43—41no—
113C2×Dic43—42no—
114C2×Dic43C2×D411yescharacteristic
115C2×Dic43C2×D411yescharacteristic
116D172—22no—
117D172—42no—
118C4×D43—22no—
119C4×D43—22no—
120C4×D43—41no—
121C4×D43—41no—
122C4×D43—42no—
123C8×C43—22no—
124C43⋊C8—22no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43AGL(1,ℤ/8)12yes—
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×D43—84no—
142C2×D43#13712yes—
143C4×C43—21no—
144C4×C43—42no—
145C4×C43—41no—
146C4×C43H(5,𝔽2)12yes—
147Dic43—21no—
148Dic43—21no—
149Dic43—41no—
150Dic43—42no—
151#3193—431nomaximal, Sylow
152C2×C43—22no—
153C2×C43—81no—
154C2×C43#53411yescharacteristic
155C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C43C2×#13711yescharacteristic
157D43—22no—
158D43—41no—
159D43—81no—
160C2×C22⋊Q8—431no—
161C2×#121—431no—
162#484—432no—
163#480—431no—
164#480—431no—
165#468—432no—
166#468—432no—
167#450—432no—
168#448—431no—
169#448D4311yescharacteristic, complemented
170#407—431no—
171C43#319311yescharacteristic, complemented, Sylow
172C22×Q8C2×D4311yescharacteristic, complemented
173C22×D4—431no—
174C22×D4—861no—
175C23×C4—431no—
176C2×SD16—432no—
177C2×SD16C2×D4312yescomplemented
178C2×M16—432no—
179C22⋊Q8—432no—
180C22⋊Q8—432no—
181C22⋊Q8—861no—
182C22⋊Q8—861no—
183#121—431no—
184#121—431no—
185#121—431no—
186#121—861no—
187#121—861no—
188#121C2×D4311yescharacteristic
189C2×C4⋊C4—431no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—861no—
192C2×C22⋊C4—861no—
193C2×C22⋊C4—861no—
194#107—432no—
195#107—432no—
196#103—432no—
197#103C2×D4312yescomplemented
198#102—432no—
199#102—432no—
200C22⋊C8—431no—
201C22⋊C8—432no—
202C22⋊C8C2×D4311yescharacteristic, complemented
203C24—431no—
204C24—861no—
205C2×Q8—21no—
206C2×Q8—42no—
207C2×Q8C22×D4312yes—
208C2×D4—21no—
209C2×D4—431no—
210C2×D4—861no—
211C2×D4—861no—
212C2×D4—861no—
213C2×D4—861no—
214C2×D4—1722no—
215C2×D4—1724no—
216C2×D4C22×D4311yescharacteristic
217C22×C4—21no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—431no—
222C22×C4—431no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—1722no—
226C22×C4C22×D4311yescharacteristic
227SD16—42no—
228SD16—1722no—
229M16—1722no—
230C2×C8—432no—
231C2×C8C22×D4312yes—
232C4⋊C4—432no—
233C4⋊C4—431no—
234C4⋊C4—861no—
235C4⋊C4—862no—
236C4⋊C4—862no—
237C4⋊C4—861no—
238C4⋊C4C22×D4311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—861no—
241C22⋊C4—862no—
242C22⋊C4—862no—
243C22⋊C4—861no—
244C22⋊C4—861no—
245C23—21no—
246C23—431no—
247C23—431no—
248C23—862no—
249C23—862no—
250C23—861no—
251C23—1721no—
252C23—1722no—
253C23—1722no—
254C23—1722no—
255C23D4×D4311yescharacteristic
256Q8—22no—
257Q8—22no—
258Q8—42no—
259D4—22no—
260D4—42no—
261D4—862no—
262D4—1722no—
263D4—1722no—
264D4—1722no—
265D4—1722no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—431no—
271C2×C4—431no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—862no—
275C2×C4—861no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1722no—
279C2×C4—1721no—
280C2×C4—1722no—
281C2×C4D4×D4311yescharacteristic
282C2×C4C23×D4311yescharacteristic
283C8—22no—
284C8—862no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—432no—
291C22—861no—
292C22—861no—
293C22—861no—
294C22—861no—
295C22—861no—
296C22—3444no—
297C22—1724no—
298C22—1721no—
299C22—1721no—
300C22—1721no—
301C22#1306335212yes—
302C22C2×D4×D4311yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—861no—
307C4—861no—
308C4—1721no—
309C4—1722no—
310C4#1306337012yes—
311C2—22no—
312C2—81no—
313C2—862no—
314C2—3441no—
315C2—1721no—
316C2#1458345911yescharacteristic
317C2C2×#1306335211yescharacteristic
318C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3193
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#13063301C2semidirect
3. #14583233C2semidirect
4. #14583213C2semidirect
5. #14583210C2semidirect
6. #14583148C2semidirect
7. #14583142C2semidirect
8. #14583048C2semidirect
9. #14583038C2semidirect
10. #14582861C2semidirect
11. C43×#448C2semidirect
15. C2×#10621884C22semidirect
16. C2×#10621872C22semidirect
20. #13063301C22semidirect
26. C2×C4⋊Dic43C22semidirect
31. #13063259C22semidirect
32. #13063258C22semidirect
33. #13063249C22semidirect
34. #13063247C22semidirect
35. #13063246C22semidirect
36. C22⋊(C43⋊C8)C22semidirect
38. C22×Q8×C43C22semidirect
39. C2×SD16×C43C22semidirect
41. #103×C43C22semidirect
42. C22⋊C8×C43C22semidirect
169. #448D43semidirect
171. C43#3193semidirect
172. C22×Q8C2×D43semidirect
177. C2×SD16C2×D43semidirect
197. #103C2×D43semidirect
202. C22⋊C8C2×D43semidirect