Finite Group Databasebeta

← #19145870

Subgroups — #19145870

Order 5504.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583526C211yesmaximal, characteristic
2#14583507C211yesmaximal, characteristic
3#14583306C211yesmaximal, characteristic, complemented
4#14583299C211yesmaximal, characteristic, complemented
5#14583266C211yesmaximal, characteristic, complemented
6#14583248C211yesmaximal, characteristic, complemented
7#14583243C211yesmaximal, characteristic
8#14583238C211yesmaximal, characteristic
9#14583233C211yesmaximal, characteristic
10#14583231C211yesmaximal, characteristic
11#14583207C211yesmaximal, characteristic, complemented
12#14583206C211yesmaximal, characteristic, complemented
13#14583191C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic
15C43×#475C211yesmaximal, characteristic, complemented
16#13063324C2211yescharacteristic
17#13063323—21no—
18#13063323C2211yescharacteristic
19#13063320—21no—
20#13063319—21no—
21#13063317—21no—
22#13063317C2211yescharacteristic
23#13063316C2211yescharacteristic
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063315—21no—
27#13063305C2211yescharacteristic
28#13063303—21no—
29#13063301—21no—
30#13063301C2211yescharacteristic
31C4×Dic86C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063282C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35#13063259C2211yescharacteristic
36#13063258C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×C4×D43—21no—
62C2×C4×D43C2311yescharacteristic
63C2×Dic86—21no—
64C2×Dic86C2311yescharacteristic
65C2×C8×C43C2311yescharacteristic
66C2×C8×C43C2311yescharacteristic
67C4⋊C4×C43—21no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43C2311yescharacteristic
70C4⋊C4×C43C2311yescharacteristic
71C4⋊C4×C43C2311yescharacteristic
72C42×C43—21no—
73C42×C43C2311yescharacteristic
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4D411yescharacteristic
78(C2×D43)⋊C4D411yescharacteristic
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43C2311yescharacteristic
83C4⋊Dic43C2311yescharacteristic
84C4⋊Dic43C2311yescharacteristic
85Dic43⋊C4—21no—
86Dic43⋊C4—21no—
87Dic43⋊C4—21no—
88Dic43⋊C4—21no—
89Dic43⋊C4—21no—
90Dic43⋊C4—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4D411yescharacteristic
96Dic43⋊C4D411yescharacteristic
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C22×D43C2×D411yescharacteristic
103Q8×C43—21no—
104Q8×C43—21no—
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×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43C2×D411yescharacteristic
118C2×Dic43C2×D411yescharacteristic
119C2×Dic43C2×D411yescharacteristic
120C4×D43—21no—
121C4×D43—21no—
122C4×D43—81no—
123Dic86—21no—
124Dic86—21no—
125Dic86—81no—
126C8×C43—21no—
127C8×C43—21no—
128C43⋊C8—21no—
129C43⋊C8—21no—
130C22×C43C22×D411yescharacteristic
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—21no—
134C4×C43—21no—
135C4×C43—21no—
136C4×C43—41no—
137C4×C43—41no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C432−1+411yescharacteristic
141C4×C432−1+411yescharacteristic
142Dic43—21no—
143Dic43—21no—
144Dic43—21no—
145Dic43—41no—
146Dic43—41no—
147Dic43—41no—
148Dic43—41no—
149#3242—431nomaximal, Sylow
150C2×C43#53611yescharacteristic
151C2×C43#57711yescharacteristic
152C2×C43#57811yescharacteristic
153D43—41no—
154#544—431no—
155#541—431no—
156#501—431no—
157#499—431no—
158#491—431no—
159#487—431no—
160#485—431no—
161#485—431no—
162#484—431no—
163#483—431no—
164#479—431no—
165#479—431no—
166#477—431no—
167#475D4311yescharacteristic, complemented
168#433—431no—
169C43#324211yescharacteristic, complemented, Sylow
170C4⋊Q8—431no—
171C4⋊Q8—431no—
172C4⋊Q8—861no—
173C4⋊Q8C2×D4311yescharacteristic
174#126—861no—
175#126—861no—
176#125—431no—
177#125—431no—
178#125—431no—
179#125—861no—
180#125—861no—
181#125—861no—
182C22⋊Q8—431no—
183C22⋊Q8—431no—
184C22⋊Q8—861no—
185C22⋊Q8—861no—
186C4×Q8—431no—
187C4×Q8C2×D4311yescharacteristic
188#117—431no—
189#117—431no—
190C2×C4⋊C4—431no—
191#107—431no—
192#107—431no—
193#107—431no—
194#107—431no—
195#106—431no—
196#106—431no—
197#106C2×D4311yescharacteristic
198#106C2×D4311yescharacteristic
199C4⋊C8—431no—
200C4⋊C8C2×D4311yescharacteristic
201#103—431no—
202#103—431no—
203#103—431no—
204#103—431no—
205#103—431no—
206#103—431no—
207#103C2×D4311yescharacteristic
208#103C2×D4311yescharacteristic
209C22⋊C8—431no—
210C22⋊C8—431no—
211#97—431no—
212C4×C8—431no—
213C2×Q8—21no—
214C2×Q8—431no—
215C2×Q8—861no—
216C2×Q8C22×D4311yescharacteristic
217C22×C4—431no—
218C22×C4—861no—
219C2×C8—431no—
220C2×C8—431no—
221C2×C8C22×D4311yescharacteristic
222C2×C8C22×D4311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—431no—
226C4⋊C4—431no—
227C4⋊C4—431no—
228C4⋊C4—431no—
229C4⋊C4—431no—
230C4⋊C4—861no—
231C4⋊C4—861no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4—861no—
236C4⋊C4—861no—
237C4⋊C4—861no—
238C4⋊C4—861no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4C22×D4311yescharacteristic
244C4⋊C4C22×D4311yescharacteristic
245C4⋊C4C22×D4311yescharacteristic
246C22⋊C4—431no—
247C22⋊C4—431no—
248C22⋊C4—861no—
249C22⋊C4—861no—
250C22⋊C4—861no—
251C42—21no—
252C42—431no—
253C42—861no—
254C42—861no—
255C42C22×D4311yescharacteristic
256C23—431no—
257Q8—21no—
258Q8—21no—
259Q8—81no—
260Q8—861no—
261Q8—861no—
262Q8—3441no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—431no—
268C2×C4—431no—
269C2×C4—431no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—861no—
276C2×C4—3441no—
277C2×C4D4×D4311yescharacteristic
278C2×C4D4×D4311yescharacteristic
279C2×C4C23×D4311yescharacteristic
280C8—21no—
281C8—21no—
282C8—861no—
283C8—861no—
284C22—861no—
285C22—861no—
286C22—861no—
287C22C2×D4×D4311yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—861no—
295C4—861no—
296C4—861no—
297C4—1721no—
298C4—1721no—
299C4—1721no—
300C4—1721no—
301C4#1306337211yescharacteristic
302C4#1306337311yescharacteristic
303C2—1721no—
304C2#1458347211yescharacteristic
305C2#1458370511yescharacteristic
306C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3242
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #14583306C2semidirect
4. #14583299C2semidirect
5. #14583266C2semidirect
6. #14583248C2semidirect
11. #14583207C2semidirect
12. #14583206C2semidirect
13. #14583191C2semidirect
15. C43×#475C2semidirect
167. #475D43semidirect
169. C43#3242semidirect