Finite Group Databasebeta

← #19145841

Subgroups — #19145841

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#14583503C211yesmaximal, characteristic
3#14583305C211yesmaximal, characteristic, complemented
4#14583301C211yesmaximal, characteristic, complemented
5#14583263C211yesmaximal, characteristic, complemented
6#14583222C211yesmaximal, characteristic, complemented
7#14583221C211yesmaximal, characteristic, complemented
8#14583216C211yesmaximal, characteristic, complemented
9#14583211C211yesmaximal, characteristic, complemented
10#14583201C211yesmaximal, characteristic, complemented
11#14583197C211yesmaximal, characteristic, complemented
12#14583187C211yesmaximal, characteristic, complemented
13#14583177C211yesmaximal, characteristic, complemented
14#14582958C211yesmaximal, characteristic, complemented
15C43×#486C211yesmaximal, characteristic, complemented
16#13063324C2211yescharacteristic
17#13063323—21no—
18#13063317C2211yescharacteristic
19#13063317C2211yescharacteristic
20#13063316C2211yescharacteristic
21#13063315—21no—
22#13063306—21no—
23#13063306—21no—
24#13063303—21no—
25#13063301—21no—
26#13063297—21no—
27#13063297—21no—
28#13063296C2211yescharacteristic
29#13063296C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063282C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35#13063259C2211yescharacteristic
36#13063259C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#127×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68C2×C4×D43—21no—
69C2×C4×D43C2311yescharacteristic
70C2×Dic86—21no—
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C42×C43C2311yescharacteristic
77C22⋊Dic43—21no—
78C22⋊Dic43—21no—
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4D411yescharacteristic
83(C2×D43)⋊C4D411yescharacteristic
84C4⋊Dic43—21no—
85C4⋊Dic43C2311yescharacteristic
86C4⋊Dic43C2311yescharacteristic
87C4⋊Dic43C2311yescharacteristic
88C4⋊Dic43C2311yescharacteristic
89Dic43⋊C4—21no—
90Dic43⋊C4—21no—
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
102C23×C43—21no—
103C23×C43—21no—
104C22×D43C2×D411yescharacteristic
105Q8×C43—81no—
106D4×C43—21no—
107D4×C43—21no—
108D4×C43—21no—
109D4×C43—21no—
110D4×C43—81no—
111D4×C43—81no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2411yescharacteristic
117C22⋊D43—81no—
118C22⋊D43—81no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—81no—
124C2×Dic43—81no—
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C4×D43—21no—
129C4×D43—21no—
130C4×D43—81no—
131Dic86—81no—
132C8×C43—21no—
133C8×C43—21no—
134C43⋊C8—21no—
135C43⋊C8—21no—
136C22×C43—41no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43C22×D411yescharacteristic
143C2×D43—21no—
144C2×D43—21no—
145C2×D43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C432−1+411yescharacteristic
151C4×C432−1+411yescharacteristic
152Dic43—21no—
153Dic43—21no—
154Dic43—21no—
155Dic43—41no—
156Dic43—41no—
157Dic43—41no—
158Dic43—41no—
159#3241—431nomaximal, Sylow
160C2×C43—81no—
161C2×C43—81no—
162C2×C43#53611yescharacteristic
163C2×C43#57611yescharacteristic
164C2×C43#57711yescharacteristic
165D43—41no—
166#544—431no—
167#540—431no—
168#501—431no—
169#499—431no—
170#490—431no—
171#486D4311yescharacteristic, complemented
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#127C2×D4311yescharacteristic
186#125—431no—
187#125—431no—
188#125—431no—
189#125—861no—
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#107—431no—
206#107—431no—
207#106—431no—
208#106—431no—
209#106—431no—
210#106—431no—
211C4⋊C8—431no—
212C4⋊C8—431no—
213#102—431no—
214#102—431no—
215#102—431no—
216#102—431no—
217#102C2×D4311yescharacteristic
218#102C2×D4311yescharacteristic
219#102C2×D4311yescharacteristic
220#102C2×D4311yescharacteristic
221C22⋊C8—431no—
222C22⋊C8—431no—
223#97—431no—
224C4×C8C2×D4311yescharacteristic
225C2×Q8—21no—
226C2×Q8—861no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—861no—
230C2×D4—861no—
231C2×D4C22×D4311yescharacteristic
232C2×D4C22×D4311yescharacteristic
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—431no—
243C4⋊C4—431no—
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⋊C4—861no—
255C4⋊C4—861no—
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—21no—
269C23—21no—
270C23—431no—
271Q8—81no—
272Q8—3441no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—3441no—
280D4—3441no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—431no—
284C2×C4—431no—
285C2×C4—431no—
286C2×C4—861no—
287C2×C4—861no—
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—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—861no—
309C22—861no—
310C22—861no—
311C22C2×D4×D4311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—861no—
317C4—861no—
318C4—861no—
319C4—1721no—
320C4—1721no—
321C4—1721no—
322C4—1721no—
323C4#1306337211yescharacteristic
324C4#1306337211yescharacteristic
325C2—81no—
326C2—81no—
327C2—1721no—
328C2#1458346911yescharacteristic
329C2#1458370011yescharacteristic
330C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3241
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583526C2semidirect
3. #14583305C2semidirect
4. #14583301C2semidirect
5. #14583263C2semidirect
6. #14583222C2semidirect
7. #14583221C2semidirect
8. #14583216C2semidirect
9. #14583211C2semidirect
10. #14583201C2semidirect
11. #14583197C2semidirect
12. #14583187C2semidirect
13. #14583177C2semidirect
14. #14582958C2semidirect
15. C43×#486C2semidirect
171. #486D43semidirect
181. C43#3241semidirect