Finite Group Databasebeta

← #19144387

Subgroups — #19144387

Order 5504.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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#14583454C211yesmaximal, characteristic, complemented
2C4×D4×D43C211yesmaximal, characteristic
3#14583202C212yesmaximal, complemented
4#14583201C212yesmaximal, complemented
5#14583190C211yesmaximal, characteristic, complemented
6#14583189C211yesmaximal, characteristic, complemented
7#14583176C211yesmaximal, characteristic, complemented
8#14582940C212yesmaximal, complemented
9#14582921C211yesmaximal, characteristic, complemented
10#14582902C212yesmaximal
11C43×#474C211yesmaximal, characteristic, complemented
12C2×D4×D43C2211yescharacteristic
13C22×C4×D43—21no—
14C2×#10621872C2212yes—
15#13063325C2211yescharacteristic, complemented
16#13063316C2212yescomplemented
17#13063305—21no—
18#13063301—21no—
19Q8×Dic43—21no—
20#13063290—21no—
21C4×D172C2211yescharacteristic
22D4×Dic43C2211yescharacteristic
23#13063287C2211yescharacteristic
24C4×C22⋊D43—21no—
25(C22⋊D43)⋊C4—21no—
26#13063283C2212yes—
27C4⋊C4×D43C2211yescharacteristic
28C22⋊C4×D43—21no—
29C42×D43C2211yescharacteristic
30#13063258C2212yescomplemented
31#13063257C2212yescomplemented
32#13063256C2212yescomplemented
33C4⋊(C43⋊C8)C2211yescharacteristic, complemented
34Dic43⋊C8C2212yescomplemented
35#13063247C2212yes—
36#13063246C2212yes—
37#13063245C2212yes—
38C4⋊Q8×C43C2211yescharacteristic, complemented
39C4×D4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41C4⋊C8×C43C2211yescharacteristic, complemented
42#102×C43C2212yes—
43C23×D43—21no—
44C2×Q8×C43—21no—
45C2×D4×C43C2311yescharacteristic
46C22×C4×C43—21no—
47C2×C22⋊D43—21no—
48C22×Dic43—21no—
49D4×D43—22no—
50D4×D43Q814yescomplemented
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×C4×D43—21no—
54C2×C4×D43—21no—
55C2×C4×D43—44no—
56C2×C4×D43D411yescharacteristic
57C2×C4×D43D411yescharacteristic
58C2×C4×D43C2311yescharacteristic
59C2×Dic86—21no—
60C2×C8×C43C2312yes—
61C4⋊C4×C43—21no—
62C4⋊C4×C43C2312yes—
63C4⋊C4×C43C2311yescharacteristic
64C22⋊C4×C43—21no—
65C42×C43C2311yescharacteristic
66C22⋊Dic43—21no—
67(C2×D43)⋊C4—21no—
68(C2×D43)⋊C4—21no—
69(C2×D43)⋊C4—22no—
70C4⋊Dic43—21no—
71C4⋊Dic43—22no—
72C4⋊Dic43C2312yes—
73C4⋊Dic43C2311yescharacteristic
74Dic43⋊C4—21no—
75Dic43⋊C4—22no—
76C4×Dic43—22no—
77C4×Dic43D411yescharacteristic
78C4×Dic43D411yescharacteristic
79C4×Dic43C2311yescharacteristic
80C2×C43⋊C8C2312yes—
81#10621872—24no—
82C23×C43—21no—
83C22×D43—21no—
84C22×D43—24no—
85C22×D43—42no—
86C22×D43—42no—
87C22×D43C2×D411yescharacteristic
88Q8×C43—42no—
89D4×C43—21no—
90D4×C43C2×Q812yes—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—42no—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—24no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—42no—
101C2×Dic43C2×D411yescharacteristic
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D411yescharacteristic
104D172—21no—
105D172C2×Q812yes—
106C4×D43—22no—
107C4×D43—41no—
108C4×D43—42no—
109C4×D43—42no—
110C4×D43—42no—
111C4×D43C2×Q812yes—
112C4×D43#4112yes—
113Dic86—42no—
114C8×C43—22no—
115C43⋊C8—22no—
116C22×C43—22no—
117C22×C43—41no—
118C22×C43—41no—
119C22×C43C22×D411yescharacteristic
120C2×D43—21no—
121C2×D43—21no—
122C2×D43—22no—
123C2×D43—48no—
124C2×D43—41no—
125C2×D43—41no—
126C2×D43C22⋊Q812yes—
127C4×C43—21no—
128C4×C43—41no—
129C4×C43—42no—
130C4×C43AGL(1,ℤ/8)12yes—
131C4×C43C22×Q811yescharacteristic
132C4×C43C2×#4111yescharacteristic
133Dic43—21no—
134Dic43—21no—
135Dic43—41no—
136Dic43—42no—
137Dic43C22⋊Q812yes—
138#3077—431nomaximal, Sylow
139C2×C43—42no—
140C2×C43C2×C22⋊Q811yescharacteristic
141C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C43#57511yescharacteristic
143D43—22no—
144D43—42no—
145#533—431no—
146C2×C4×D4—431no—
147#478—432no—
148#478—432no—
149#476—431no—
150#476—431no—
151#474—431no—
152#474D4311yescharacteristic, complemented
153#428—432no—
154#423—431no—
155#418—432no—
156C43#307711yescharacteristic, complemented, Sylow
157C22×D4—431no—
158C23×C4—861no—
159C2×M16—432no—
160C4⋊Q8—431no—
161C4⋊Q8C2×D4311yescharacteristic, complemented
162#125—432no—
163C22⋊Q8—861no—
164C22⋊Q8—861no—
165C4×Q8—861no—
166C4×Q8—861no—
167C4×D4—431no—
168C4×D4—431no—
169C4×D4—431no—
170C4×D4—861no—
171C4×D4—861no—
172C4×D4C2×D4311yescharacteristic
173#117—432no—
174C2×C4⋊C4—431no—
175C2×C22⋊C4—861no—
176C2×C42—431no—
177#107—432no—
178#107C2×D4312yescomplemented
179#106—432no—
180#106—432no—
181C4⋊C8—432no—
182C4⋊C8—431no—
183C4⋊C8C2×D4311yescharacteristic, complemented
184#102—432no—
185#102—432no—
186#102—432no—
187#102C2×D4312yes—
188C24—861no—
189C2×Q8—21no—
190C2×Q8—861no—
191C2×D4—434no—
192C2×D4—431no—
193C2×D4—862no—
194C2×D4—861no—
195C2×D4C22×D4311yescharacteristic
196C22×C4—21no—
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—861no—
201C22×C4—861no—
202C22×C4—861no—
203C22×C4—861no—
204C22×C4—1724no—
205M16—864no—
206C2×C8—432no—
207C2×C8C22×D4312yes—
208C4⋊C4—21no—
209C4⋊C4—432no—
210C4⋊C4—431no—
211C4⋊C4—861no—
212C4⋊C4—862no—
213C4⋊C4—862no—
214C4⋊C4—861no—
215C4⋊C4C22×D4312yes—
216C4⋊C4C22×D4311yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—861no—
219C22⋊C4—862no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C42—431no—
223C42—431no—
224C42—431no—
225C42—862no—
226C42C22×D4311yescharacteristic
227C23—21no—
228C23—431no—
229C23—864no—
230C23—861no—
231C23—1722no—
232C23—1722no—
233Q8—42no—
234Q8—1722no—
235D4—21no—
236D4—432no—
237D4—864no—
238D4—861no—
239D4Q8×D4312yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—431no—
244C2×C4—432no—
245C2×C4—432no—
246C2×C4—431no—
247C2×C4—431no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—1721no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4D4×D4311yescharacteristic
257C2×C4D4×D4311yescharacteristic
258C2×C4C23×D4311yescharacteristic
259C8—22no—
260C8—862no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—432no—
265C22—861no—
266C22—861no—
267C22—862no—
268C22—1728no—
269C22—1721no—
270C22—1721no—
271C22C2×D4×D4311yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—432no—
276C4—861no—
277C4—861no—
278C4—1721no—
279C4—1722no—
280C4#1306334912yes—
281C4C2×Q8×D4311yescharacteristic
282C4#41×D4311yescharacteristic
283C2—42no—
284C2—862no—
285C2—1722no—
286C2C22⋊Q8×D4311yescharacteristic
287C2C2×#1306334911yescharacteristic
288C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3077
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583202C2semidirect
4. #14583201C2semidirect
5. #14583190C2semidirect
6. #14583189C2semidirect
7. #14583176C2semidirect
8. #14582940C2semidirect
9. #14582921C2semidirect
11. C43×#474C2semidirect
15. #13063325C22semidirect
16. #13063316C22semidirect
30. #13063258C22semidirect
31. #13063257C22semidirect
32. #13063256C22semidirect
33. C4⋊(C43⋊C8)C22semidirect
34. Dic43⋊C8C22semidirect
38. C4⋊Q8×C43C22semidirect
40. #107×C43C22semidirect
41. C4⋊C8×C43C22semidirect
50. D4×D43Q8semidirect
152. #474D43semidirect
156. C43#3077semidirect
161. C4⋊Q8C2×D43semidirect
178. #107C2×D43semidirect
183. C4⋊C8C2×D43semidirect