Finite Group Databasebeta

← #19145611

Subgroups — #19145611

Order 5504.

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

normal subgroups only

This group has 490 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×#13063321C211yesmaximal, characteristic, complemented
2#14583430C211yesmaximal, characteristic, complemented
3#14583287C212yesmaximal, complemented
4#14583262C212yesmaximal, complemented
5#14583098C212yesmaximal, complemented
6#14583092C212yesmaximal, complemented
7#14583052C211yesmaximal, characteristic, complemented
8#14583050C211yesmaximal, characteristic, complemented
9#14583032C211yesmaximal, characteristic, complemented
10#14582953C211yesmaximal, characteristic, complemented
11C43×#447C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43—21no—
14C22×C22⋊D43—21no—
15C2×#10621873C2212yescomplemented
16C2×#10621883C2212yescomplemented
17C2×#10621882C2212yescomplemented
18#13063321—21no—
19#13063321—21no—
20#13063321C2212yes—
21#13063321C2212yes—
22#13063318—21no—
23#13063316C2211yescharacteristic, complemented
24#13063312C2211yescharacteristic, complemented
25#13063306—21no—
26#13063304C2211yescharacteristic
27#13063290C2211yescharacteristic, complemented
28D4×Dic43—21no—
29D4×Dic43C2211yescharacteristic, complemented
30#13063281—21no—
31C2×C4×Dic43C2211yescharacteristic
32Dic43⋊C8C2212yescomplemented
33#13063247C2212yescomplemented
34#13063246C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37#13063235C2212yescomplemented
38C22×D4×C43C2211yescharacteristic
39C2×D8×C43C2212yescomplemented
40#121×C43C2211yescharacteristic
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C24×C43—21no—
44C23×D43—21no—
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—42no—
48C2×D4×C43C2312yes—
49C2×D4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—44no—
56C2×C22⋊D43—44no—
57C22×Dic43—21no—
58C22×Dic43D411yescharacteristic
59C22×Dic43D411yescharacteristic
60C2×D172—21no—
61C2×D172—42no—
62C2×D172C2312yes—
63C2×Dic86C2311yescharacteristic
64D8×C43—42no—
65C2×C8×C43C2312yes—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C22⋊Dic43—21no—
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72#10621883—42no—
73#10621882—42no—
74C4⋊Dic43—21no—
75C4⋊Dic43C2311yescharacteristic
76Dic43⋊C4—21no—
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80C4×Dic43D411yescharacteristic
81C4×Dic43D411yescharacteristic
82C4×Dic43C2311yescharacteristic
83C4×Dic43C2311yescharacteristic
84C2×C43⋊C8C2312yes—
85#10621873—42no—
86C23×C43—21no—
87C23×C43—22no—
88C23×C43—42no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43C2×D411yescharacteristic
92C22×D43—22no—
93C22×D43—42no—
94C22×D43—42no—
95C22×D43—42no—
96D4×C43—22no—
97D4×C43—22no—
98D4×C43—22no—
99D4×C43—42no—
100D4×C43—42no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2411yescharacteristic
105C22⋊D43—44no—
106C22⋊D43—44no—
107C22⋊D43—44no—
108C22⋊D43—44no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43—21no—
113C2×Dic43—42no—
114C2×Dic43C2×D411yescharacteristic
115C2×Dic43C2×D411yescharacteristic
116C2×Dic43C2×D411yescharacteristic
117C2×Dic43C2×D411yescharacteristic
118D172—22no—
119D172—22no—
120D172—42no—
121Dic86—22no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—41no—
131C22×C43—41no—
132C22×C43—84no—
133C22×C43AGL(1,ℤ/8)12yes—
134C22×C43C22×D411yescharacteristic
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—42no—
138C2×D43—84no—
139C4×C43—21no—
140C4×C43—41no—
141C4×C43H(5,𝔽2)12yes—
142Dic43—21no—
143Dic43—21no—
144Dic43—21no—
145Dic43—41no—
146Dic43—41no—
147Dic43AGL(1,ℤ/8)12yes—
148#3217—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43—81no—
151C2×C43—82no—
152C2×C43#53511yescharacteristic
153C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
155D43—82no—
156C2×#127—431no—
157#529—431no—
158#496—432no—
159#490—432no—
160#460—432no—
161#459—432no—
162#450—431no—
163#450—431no—
164#447—431no—
165#447D4311yescharacteristic, complemented
166#432—431no—
167C43#321711yescharacteristic, complemented, Sylow
168C22×D4—431no—
169C22×D4—861no—
170C22×D4—861no—
171C22×D4C2×D4311yescharacteristic
172C2×SD16—432no—
173C2×SD16—432no—
174C2×D8—432no—
175C2×D8C2×D4312yescomplemented
176#127—432no—
177#127—432no—
178#127—861no—
179#127—861no—
180#126—861no—
181#125—431no—
182#124—431no—
183#123—861no—
184C22⋊Q8—431no—
185#121C2×D4311yescharacteristic
186C4×Q8—431no—
187C4×D4—431no—
188C4×D4—861no—
189#117—861no—
190C2×C42—431no—
191C4⋊C8—432no—
192#102—432no—
193#102—432no—
194#102—432no—
195#102C2×D4312yescomplemented
196C22⋊C8—431no—
197C22⋊C8C2×D4311yescharacteristic
198#97—432no—
199C24—21no—
200C24—861no—
201C2×Q8—431no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—42no—
205C2×D4—432no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4—861no—
211C2×D4—1722no—
212C2×D4—1724no—
213C2×D4—1724no—
214C2×D4C22×D4312yes—
215C2×D4C22×D4311yescharacteristic
216C22×C4—431no—
217C22×C4—431no—
218C22×C4—861no—
219C22×C4C22×D4311yescharacteristic
220SD16—1722no—
221SD16—1722no—
222D8—42no—
223D8—1722no—
224C2×C8—432no—
225C2×C8C22×D4312yes—
226C4⋊C4—431no—
227C4⋊C4—861no—
228C4⋊C4—861no—
229C4⋊C4—861no—
230C4⋊C4—861no—
231C4⋊C4C22×D4311yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—861no—
234C22⋊C4—861no—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C42—431no—
238C42—431no—
239C42—431no—
240C42—431no—
241C42—861no—
242C23—21no—
243C23—22no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—862no—
248C23—1722no—
249C23—1722no—
250C23—1722no—
251C23D4×D4311yescharacteristic
252Q8—862no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—862no—
259D4—862no—
260D4—1722no—
261D4—1724no—
262D4—1724no—
263D4—1724no—
264D4—1724no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—431no—
268C2×C4—431no—
269C2×C4—431no—
270C2×C4—431no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—1722no—
276C2×C4D4×D4311yescharacteristic
277C2×C4C23×D4311yescharacteristic
278C8—22no—
279C8—862no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—84no—
289C22—3444no—
290C22—1722no—
291C22—1722no—
292C22—1722no—
293C22#1306334912yes—
294C22C2×D4×D4311yescharacteristic
295C4—21no—
296C4—41no—
297C4—432no—
298C4—861no—
299C4—861no—
300C4—861no—
301C4—1721no—
302C4—1721no—
303C4#1306337012yes—
304C2—22no—
305C2—82no—
306C2—81no—
307C2—3442no—
308C2#1458346411yescharacteristic
309C2AGL(1,ℤ/8)×D4311yescharacteristic
310C2C2×#1306334911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3217
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13063321C2semidirect
2. #14583430C2semidirect
3. #14583287C2semidirect
4. #14583262C2semidirect
5. #14583098C2semidirect
6. #14583092C2semidirect
7. #14583052C2semidirect
8. #14583050C2semidirect
9. #14583032C2semidirect
10. #14582953C2semidirect
11. C43×#447C2semidirect
15. C2×#10621873C22semidirect
16. C2×#10621883C22semidirect
17. C2×#10621882C22semidirect
23. #13063316C22semidirect
24. #13063312C22semidirect
27. #13063290C22semidirect
29. D4×Dic43C22semidirect
32. Dic43⋊C8C22semidirect
33. #13063247C22semidirect
34. #13063246C22semidirect
35. #13063245C22semidirect
37. #13063235C22semidirect
39. C2×D8×C43C22semidirect
41. #102×C43C22semidirect
165. #447D43semidirect
167. C43#3217semidirect
175. C2×D8C2×D43semidirect
195. #102C2×D43semidirect