Finite Group Databasebeta

← #19145884

Subgroups — #19145884

Order 5504.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583527C211yesmaximal, characteristic, complemented
2#14583522C211yesmaximal, characteristic
3#14583306C211yesmaximal, characteristic, complemented
4#14583303C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583255C211yesmaximal, characteristic, complemented
7#14583232C211yesmaximal, characteristic, complemented
8#14583223C211yesmaximal, characteristic
9#14583213C211yesmaximal, characteristic
10#14583208C211yesmaximal, characteristic, complemented
11#14583198C211yesmaximal, characteristic, complemented
12#14583192C211yesmaximal, characteristic, complemented
13#14583178C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#485C211yesmaximal, characteristic, complemented
16#13063325—21no—
17#13063324C2211yescharacteristic
18#13063324C2211yescharacteristic
19#13063324C2211yescharacteristic
20#13063320—21no—
21#13063317—21no—
22#13063316C2211yescharacteristic
23#13063316C2211yescharacteristic
24#13063314C2211yescharacteristic
25#13063311—21no—
26#13063307—21no—
27#13063305—21no—
28#13063302—21no—
29#13063302—21no—
30#13063299C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063284C2211yescharacteristic
34C2×C4⋊Dic43C2211yescharacteristic
35#13063259C2211yescharacteristic
36#13063259C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C22×Dic43—21no—
63C2×D172C2311yescharacteristic
64C2×C4×D43—21no—
65C2×Dic86—21no—
66C2×Dic86—21no—
67C2×Dic86—21no—
68C2×C8×C43C2311yescharacteristic
69C2×C8×C43C2311yescharacteristic
70C4⋊C4×C43—21no—
71C4⋊C4×C43C2311yescharacteristic
72C4⋊C4×C43C2311yescharacteristic
73C4⋊C4×C43C2311yescharacteristic
74C22⋊C4×C43—21no—
75C22⋊C4×C43—21no—
76C42×C43—21no—
77C22⋊Dic43D411yescharacteristic
78C22⋊Dic43D411yescharacteristic
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43D411yescharacteristic
88C4⋊Dic43D411yescharacteristic
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97C4×Dic43—21no—
98C4×Dic43C2311yescharacteristic
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C23×C43C2×D411yescharacteristic
103C22×D43—21no—
104Q8×C43—21no—
105Q8×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43C2×D411yescharacteristic
113C2×C4×C43C2411yescharacteristic
114C22⋊D43—81no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—81no—
119C2×Dic43C2×D411yescharacteristic
120C2×Dic43C2×D411yescharacteristic
121C2×Dic43C2×D411yescharacteristic
122C2×Dic43C2×D411yescharacteristic
123D172—21no—
124D172—21no—
125C4×D43—81no—
126Dic86—81no—
127Dic86—81no—
128Dic86—81no—
129C8×C43—21no—
130C8×C43—21no—
131C43⋊C8—21no—
132C43⋊C8—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43C22×D411yescharacteristic
137C2×D43—41no—
138C2×D43—41no—
139C2×D43—41no—
140C4×C43—21no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C432−1+411yescharacteristic
146C4×C432−1+411yescharacteristic
147Dic43—21no—
148Dic43—21no—
149Dic43—21no—
150Dic43—21no—
151Dic43—41no—
152Dic43—41no—
153Dic43—41no—
154#3243—431nomaximal, Sylow
155C2×C43—41no—
156C2×C43#53611yescharacteristic
157C2×C43#57611yescharacteristic
158C2×C43#57811yescharacteristic
159D43—81no—
160#544—431no—
161#542—431no—
162#501—431no—
163#500—431no—
164#489—431no—
165#488—431no—
166#485D4311yescharacteristic, complemented
167#484—431no—
168#482—431no—
169#480—431no—
170#479—431no—
171#478—431no—
172#477—431no—
173#474—431no—
174#433—431no—
175C43#324311yescharacteristic, complemented, Sylow
176C4⋊Q8—431no—
177C4⋊Q8—431no—
178C4⋊Q8—431no—
179C4⋊Q8—861no—
180#126—861no—
181#125—431no—
182#125—431no—
183#125—861no—
184#124—431no—
185#124—861no—
186#123—861no—
187C22⋊Q8—861no—
188C22⋊Q8—861no—
189C22⋊Q8—861no—
190C22⋊Q8C2×D4311yescharacteristic
191#121—431no—
192C4×Q8—431no—
193C4×D4—431no—
194#117—431no—
195#117C2×D4311yescharacteristic
196C2×C4⋊C4—431no—
197#107—431no—
198#107—431no—
199#107—431no—
200#107—431no—
201#107—431no—
202#107C2×D4311yescharacteristic
203#106—431no—
204#106C2×D4311yescharacteristic
205C4⋊C8—431no—
206C4⋊C8—431no—
207#103—431no—
208#103—431no—
209#103C2×D4311yescharacteristic
210#103C2×D4311yescharacteristic
211#102—431no—
212#102—431no—
213#102—431no—
214#102—431no—
215C22⋊C8—431no—
216C22⋊C8C2×D4311yescharacteristic
217#97—431no—
218C4×C8—431no—
219C2×Q8—861no—
220C2×Q8—861no—
221C2×Q8—861no—
222C2×Q8C22×D4311yescharacteristic
223C2×D4—431no—
224C2×D4—861no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4C22×D4311yescharacteristic
228C2×C8—431no—
229C2×C8—431no—
230C2×C8C22×D4311yescharacteristic
231C2×C8C22×D4311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—431no—
234C4⋊C4—431no—
235C4⋊C4—431no—
236C4⋊C4—431no—
237C4⋊C4—431no—
238C4⋊C4—861no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4—861no—
246C4⋊C4—861no—
247C4⋊C4C22×D4311yescharacteristic
248C4⋊C4C22×D4311yescharacteristic
249C4⋊C4C22×D4311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—431no—
253C22⋊C4—431no—
254C22⋊C4—861no—
255C22⋊C4—861no—
256C22⋊C4—861no—
257C22⋊C4—861no—
258C42—21no—
259C42—431no—
260C42—431no—
261C42—861no—
262C23—861no—
263C23D4×D4311yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—3441no—
267Q8—3441no—
268Q8—3441no—
269D4—861no—
270D4—861no—
271D4—3441no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—431no—
279C2×C4—431no—
280C2×C4—431no—
281C2×C4—431no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4D4×D4311yescharacteristic
288C2×C4C23×D4311yescharacteristic
289C8—21no—
290C8—21no—
291C8—861no—
292C8—861no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—1721no—
297C22—1721no—
298C22—1721no—
299C22C2×D4×D4311yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—861no—
306C4—861no—
307C4—861no—
308C4—861no—
309C4—1721no—
310C4—1721no—
311C4—1721no—
312C4#1306337211yescharacteristic
313C4#1306337211yescharacteristic
314C2—41no—
315C2—3441no—
316C2#1458347111yescharacteristic
317C2#1458370111yescharacteristic
318C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3243
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14583527C2semidirect
3. #14583306C2semidirect
4. #14583303C2semidirect
5. #14583260C2semidirect
6. #14583255C2semidirect
7. #14583232C2semidirect
10. #14583208C2semidirect
11. #14583198C2semidirect
12. #14583192C2semidirect
13. #14583178C2semidirect
14. #14582957C2semidirect
15. C43×#485C2semidirect
166. #485D43semidirect
175. C43#3243semidirect