Finite Group Databasebeta

← #19145411

Subgroups — #19145411

Order 5504.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583410C211yesmaximal, characteristic, complemented
2C2×#13063299C211yesmaximal, characteristic, complemented
3#14583230C211yesmaximal, characteristic, complemented
4#14583224C212yesmaximal, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583152C212yesmaximal, complemented
7#14583145C212yesmaximal, complemented
8#14583052C211yesmaximal, characteristic, complemented
9#14583046C212yesmaximal, complemented
10#14583035C211yesmaximal, characteristic, complemented
11C43×#407C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic, complemented
13C22×D172C2211yescharacteristic
14C22×C22⋊D43—21no—
15C2×#10621873C2212yescomplemented
16C2×D344C2212yescomplemented
17#13063308—21no—
18#13063304C2211yescharacteristic
19#13063304C2211yescharacteristic, complemented
20#13063299—21no—
21#13063299—21no—
22#13063299C2212yes—
23#13063299C2212yes—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic, complemented
26#13063294—21no—
27C4×C22⋊D43—21no—
28C4×C22⋊D43—21no—
29#13063284C2211yescharacteristic, complemented
30C2×C4⋊Dic43C2211yescharacteristic
31C2×(C2×D43)⋊C4—21no—
32#13063259C2212yescomplemented
33#13063257C2212yescomplemented
34#13063250C2212yescomplemented
35#13063247C2212yescomplemented
36#13063247C2212yescomplemented
37#13063247C2212yescomplemented
38C23×C4×C43C2211yescharacteristic
39C2×M16×C43C2212yescomplemented
40C22⋊C8×C43C2211yescharacteristic
41C22⋊C8×C43C2211yescharacteristic
42C22⋊C8×C43C2212yescomplemented
43C24×C43D411yescharacteristic
44C23×D43—21no—
45C22×C4×C43—42no—
46C22×C4×C43D411yescharacteristic
47C22×C4×C43D411yescharacteristic
48C22×C4×C43D411yescharacteristic
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C2×C22⋊D43—21no—
55C2×C22⋊D43—22no—
56C2×C22⋊D43—22no—
57C2×C22⋊D43—44no—
58C22×Dic43—21no—
59#10621898—42no—
60C2×D172—21no—
61C2×D172—42no—
62C2×D172C2312yes—
63C2×D172C2311yescharacteristic
64C2×C4×D43—21no—
65C2×Dic86C2311yescharacteristic
66M16×C43—42no—
67C2×C8×C43C2312yes—
68C2×C8×C43C2312yes—
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76C4⋊Dic43—21no—
77C4⋊Dic43C2311yescharacteristic
78C4⋊Dic43C2311yescharacteristic
79C4⋊Dic43C2312yes—
80Dic43⋊C4—21no—
81Dic43⋊C4—21no—
82C4×Dic43—21no—
83D344—42no—
84#10621873—42no—
85C23×C43—22no—
86C23×C43—41no—
87C23×C43—41no—
88C23×C43C2×D411yescharacteristic
89C23×C43C2×D411yescharacteristic
90C23×C43C2×D411yescharacteristic
91C22×D43—21no—
92C22×D43—22no—
93C22×D43—42no—
94C22×D43—42no—
95C22×D43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2×D411yescharacteristic
105C2×C4×C43C2411yescharacteristic
106C22⋊D43—42no—
107C22⋊D43—42no—
108C22⋊D43—44no—
109C22⋊D43—44no—
110C22⋊D43—42no—
111C2×Dic43—21no—
112C2×Dic43—21no—
113C2×Dic43—21no—
114C2×Dic43—22no—
115C2×Dic43—42no—
116D172—22no—
117D172—22no—
118D172—22no—
119D172—42no—
120C4×D43—42no—
121Dic86—22no—
122C8×C43—22no—
123C8×C43—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—44no—
133C22×C43AGL(1,ℤ/8)12yes—
134C22×C43C22×D411yescharacteristic
135C2×D43—42no—
136C2×D43—41no—
137C2×D43—42no—
138C2×D43—41no—
139C2×D43—42no—
140C2×D43—41no—
141C2×D43—84no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43H(5,𝔽2)12yes—
146Dic43—41no—
147Dic43—42no—
148Dic43—41no—
149Dic43—41no—
150#3194—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—41no—
153C2×C43—41no—
154C2×C43#53411yescharacteristic
155C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C43#57511yescharacteristic
157D43—81no—
158D43—82no—
159#525—431no—
160C2×#121—431no—
161#483—431no—
162#482—432no—
163#480—431no—
164#469—432no—
165#468—432no—
166#450—431no—
167#449—432no—
168#447—431no—
169#407D4311yescharacteristic, complemented
170C43#319411yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C22×D4—431no—
173C22×D4—861no—
174C23×C4C2×D4311yescharacteristic
175C2×SD16—432no—
176C2×D8—432no—
177C2×M16C2×D4312yescomplemented
178#123—861no—
179C22⋊Q8—431no—
180C22⋊Q8—431no—
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#102—432no—
199C22⋊C8C2×D4311yescharacteristic
200C22⋊C8C2×D4311yescharacteristic
201C22⋊C8C2×D4312yescomplemented
202C24—861no—
203C24D17211yescharacteristic
204#41—1722no—
205C2×Q8—431no—
206C2×D4—431no—
207C2×D4—432no—
208C2×D4—861no—
209C2×D4—861no—
210C2×D4—861no—
211C2×D4—862no—
212C2×D4—862no—
213C2×D4—861no—
214C2×D4—1722no—
215C2×D4—1724no—
216C22×C4—42no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4D17211yescharacteristic
220C22×C4D17211yescharacteristic
221C22×C4D17211yescharacteristic
222C22×C4C22×D4311yescharacteristic
223C22×C4C22×D4311yescharacteristic
224C22×C4C22×D4311yescharacteristic
225SD16—1722no—
226D8—1722no—
227M16—42no—
228C2×C8C22×D4312yes—
229C2×C8C22×D4312yes—
230C4⋊C4—431no—
231C4⋊C4—431no—
232C4⋊C4—432no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4—861no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—862no—
240C22⋊C4—862no—
241C22⋊C4—861no—
242C22⋊C4—861no—
243C42—861no—
244C23—22no—
245C23—41no—
246C23—41no—
247C23—861no—
248C23—862no—
249C23—1722no—
250C23—1722no—
251C23—1722no—
252C23C2×D17211yescharacteristic
253C23C2×D17211yescharacteristic
254C23C2×D17211yescharacteristic
255Q8—862no—
256D4—862no—
257D4—862no—
258D4—862no—
259D4—1722no—
260D4—1724no—
261D4—1724no—
262D4—1722no—
263D4—1722no—
264D4—1722no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—862no—
274C2×C4—861no—
275C2×C4—1722no—
276C2×C4—1722no—
277C2×C4C2×D17211yescharacteristic
278C2×C4C2×D17211yescharacteristic
279C2×C4C2×D17211yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—3444no—
293C22—1722no—
294C22—1721no—
295C22—1721no—
296C22—1722no—
297C22—1721no—
298C22—1722no—
299C22#1306335312yes—
300C22C22×D17211yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—1722no—
305C4—1721no—
306C4—1721no—
307C4—1721no—
308C4#1306337012yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—3442no—
313C2—3441no—
314C2#1458346111yescharacteristic
315C2C2×#1306335311yescharacteristic
316C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3194
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14583410C2semidirect
2. C2×#13063299C2semidirect
3. #14583230C2semidirect
4. #14583224C2semidirect
5. #14583213C2semidirect
6. #14583152C2semidirect
7. #14583145C2semidirect
8. #14583052C2semidirect
9. #14583046C2semidirect
10. #14583035C2semidirect
11. C43×#407C2semidirect
12. C2×#10621898C22semidirect
15. C2×#10621873C22semidirect
16. C2×D344C22semidirect
19. #13063304C22semidirect
25. #13063299C22semidirect
29. #13063284C22semidirect
32. #13063259C22semidirect
33. #13063257C22semidirect
34. #13063250C22semidirect
35. #13063247C22semidirect
36. #13063247C22semidirect
37. #13063247C22semidirect
39. C2×M16×C43C22semidirect
42. C22⋊C8×C43C22semidirect
169. #407D43semidirect
170. C43#3194semidirect
177. C2×M16C2×D43semidirect
201. C22⋊C8C2×D43semidirect