Finite Group Databasebeta

← #19145849

Subgroups — #19145849

Order 5504.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583526C211yesmaximal, characteristic, complemented
2#14583505C211yesmaximal, characteristic
3#14583298C211yesmaximal, characteristic, complemented
4#14583264C211yesmaximal, characteristic, complemented
5#14583247C211yesmaximal, characteristic, complemented
6#14583226C211yesmaximal, characteristic, complemented
7#14583225C211yesmaximal, characteristic, complemented
8#14583219C211yesmaximal, characteristic, complemented
9#14583214C211yesmaximal, characteristic, complemented
10#14583202C211yesmaximal, characteristic, complemented
11#14583198C211yesmaximal, characteristic, complemented
12#14583188C211yesmaximal, characteristic, complemented
13#14583178C211yesmaximal, characteristic, complemented
14#14582961C211yesmaximal, characteristic, complemented
15C43×#501C211yesmaximal, characteristic, complemented
16#13063324C2211yescharacteristic
17#13063323—21no—
18#13063322C2211yescharacteristic
19#13063317C2211yescharacteristic
20#13063316C2211yescharacteristic
21#13063315—21no—
22#13063310—21no—
23#13063310—21no—
24#13063303—21no—
25#13063301—21no—
26#13063300—21no—
27#13063300—21no—
28#13063300C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063287C2211yescharacteristic
31#13063287C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063282C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35#13063258C2211yescharacteristic
36#13063258C2211yescharacteristic
37#13063256C2211yescharacteristic
38#13063256C2211yescharacteristic
39Dic43⋊C8C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063247C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D172—21no—
61C2×D172—21no—
62C2×D172—21no—
63C2×D172—21no—
64C2×D172C2311yescharacteristic
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43C2311yescharacteristic
70C2×Dic86—21no—
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C42×C43C2311yescharacteristic
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4D411yescharacteristic
87(C2×D43)⋊C4D411yescharacteristic
88C4⋊Dic43—21no—
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97Dic43⋊C4D411yescharacteristic
98C4×Dic43—21no—
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C22×D43—21no—
103C22×D43—21no—
104C22×D43C2×D411yescharacteristic
105Q8×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43C2×D411yescharacteristic
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2411yescharacteristic
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43C2×D411yescharacteristic
116C2×Dic43C2×D411yescharacteristic
117C2×Dic43C2×D411yescharacteristic
118D172—21no—
119D172—21no—
120D172—21no—
121D172—21no—
122D172—81no—
123D172—81no—
124D172—81no—
125D172—81no—
126C4×D43—21no—
127C4×D43—21no—
128C4×D43—81no—
129C4×D43—81no—
130C4×D43—81no—
131Dic86—81no—
132C8×C43—21no—
133C8×C43—21no—
134C43⋊C8—21no—
135C43⋊C8—21no—
136C22×C43C22×D411yescharacteristic
137C2×D43—21no—
138C2×D43—21no—
139C2×D43—21no—
140C2×D43—41no—
141C2×D43—41no—
142C2×D43—41no—
143C2×D43—41no—
144C2×D43—41no—
145C2×D43—41no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C432−1+411yescharacteristic
153C4×C432−1+411yescharacteristic
154Dic43—21no—
155Dic43—21no—
156Dic43—21no—
157Dic43—41no—
158Dic43—41no—
159#3241—431nomaximal, Sylow
160C2×C43#53611yescharacteristic
161C2×C43#57611yescharacteristic
162C2×C43#57711yescharacteristic
163D43—41no—
164D43—81no—
165D43—81no—
166#544—431no—
167#540—431no—
168#501D4311yescharacteristic, complemented
169#499—431no—
170#490—431no—
171#486—431no—
172#482—431no—
173#482—431no—
174#481—431no—
175#480—431no—
176#478—431no—
177#478—431no—
178#476—431no—
179#474—431no—
180#433—431no—
181C43#324111yescharacteristic, complemented, Sylow
182C4⋊Q8—431no—
183C4⋊Q8—861no—
184C4⋊Q8C2×D4311yescharacteristic
185#127—431no—
186#125—431no—
187#125—431no—
188#125—861no—
189#125C2×D4311yescharacteristic
190#123—861no—
191#123—861no—
192C22⋊Q8—861no—
193C22⋊Q8—861no—
194#121—431no—
195#121—431no—
196#121—861no—
197#121—861no—
198C4×D4—431no—
199C4×D4—431no—
200#117—431no—
201#117—431no—
202C2×C4⋊C4—431no—
203#107—431no—
204#107—431no—
205#107C2×D4311yescharacteristic
206#107C2×D4311yescharacteristic
207#106—431no—
208#106—431no—
209#106C2×D4311yescharacteristic
210#106C2×D4311yescharacteristic
211C4⋊C8—431no—
212C4⋊C8—431no—
213#102—431no—
214#102—431no—
215#102—431no—
216#102—431no—
217#102—431no—
218#102—431no—
219#102—431no—
220#102—431no—
221C22⋊C8—431no—
222C22⋊C8—431no—
223#97C2×D4311yescharacteristic
224C4×C8—431no—
225C2×Q8—21no—
226C2×Q8—861no—
227C2×D4—431no—
228C2×D4—431no—
229C2×D4—861no—
230C2×D4—861no—
231C2×D4—861no—
232C2×D4—861no—
233C22×C4—431no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C2×C8—431no—
238C2×C8—431no—
239C2×C8C22×D4311yescharacteristic
240C2×C8C22×D4311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—431no—
245C4⋊C4—431no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4C22×D4311yescharacteristic
255C4⋊C4C22×D4311yescharacteristic
256C4⋊C4C22×D4311yescharacteristic
257C4⋊C4C22×D4311yescharacteristic
258C22⋊C4—431no—
259C22⋊C4—431no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C42—431no—
266C42—861no—
267C42C22×D4311yescharacteristic
268C23—431no—
269C23—861no—
270C23—861no—
271Q8—81no—
272Q8—3441no—
273D4—861no—
274D4—861no—
275D4—861no—
276D4—861no—
277D4—3441no—
278D4—3441no—
279D4—3441no—
280D4—3441no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—431no—
286C2×C4—431no—
287C2×C4—431no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—3441no—
293C2×C4—3441no—
294C2×C4—3441no—
295C2×C4D4×D4311yescharacteristic
296C2×C4D4×D4311yescharacteristic
297C2×C4C23×D4311yescharacteristic
298C8—21no—
299C8—21no—
300C8—861no—
301C8—861no—
302C22—861no—
303C22—861no—
304C22—861no—
305C22—1721no—
306C22—1721no—
307C22—1721no—
308C22—1721no—
309C22—1721no—
310C22—1721no—
311C22C2×D4×D4311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—861no—
319C4—861no—
320C4—861no—
321C4—1721no—
322C4—1721no—
323C4#1306337311yescharacteristic
324C4#1306337311yescharacteristic
325C2—3441no—
326C2—3441no—
327C2—1721no—
328C2#1458347411yescharacteristic
329C2#1458370311yescharacteristic
330C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3241
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14583526C2semidirect
3. #14583298C2semidirect
4. #14583264C2semidirect
5. #14583247C2semidirect
6. #14583226C2semidirect
7. #14583225C2semidirect
8. #14583219C2semidirect
9. #14583214C2semidirect
10. #14583202C2semidirect
11. #14583198C2semidirect
12. #14583188C2semidirect
13. #14583178C2semidirect
14. #14582961C2semidirect
15. C43×#501C2semidirect
168. #501D43semidirect
181. C43#3241semidirect