Finite Group Databasebeta

← #19147170

Subgroups — #19147170

Order 5504.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic
2#14583583C211yesmaximal, characteristic
3#14583300C211yesmaximal, characteristic, complemented
4#14583241C211yesmaximal, characteristic, complemented
5#14583239C211yesmaximal, characteristic, complemented
6#14583236C211yesmaximal, characteristic, complemented
7#14583205C211yesmaximal, characteristic, complemented
8#14583204C211yesmaximal, characteristic, complemented
9#14583156C211yesmaximal, characteristic, complemented
10#14583155C211yesmaximal, characteristic, complemented
11#14582991C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic
13#14582940C211yesmaximal, characteristic, complemented
14#14582939C211yesmaximal, characteristic, complemented
15C43×#484C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19#13063320—21no—
20#13063318—21no—
21#13063316C2211yescharacteristic
22#13063316C2211yescharacteristic
23#13063315—21no—
24#13063315—21no—
25#13063308—21no—
26#13063307—21no—
27#13063305C2211yescharacteristic
28#13063304C2211yescharacteristic
29#13063301C2211yescharacteristic
30Q8×Dic43C2211yescharacteristic
31#13063290C2211yescharacteristic
32C4×C22⋊D43C2211yescharacteristic
33#13063284—21no—
34#13063284C2211yescharacteristic
35#13063283—21no—
36#13063283C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063249C2211yescharacteristic
49#13063248C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43D411yescharacteristic
63C2×C4×D43—21no—
64C2×C4×D43C2311yescharacteristic
65C2×Dic86C2311yescharacteristic
66C2×C8×C43C2311yescharacteristic
67C2×C8×C43C2311yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43C2311yescharacteristic
71C4⋊C4×C43C2311yescharacteristic
72C4⋊C4×C43C2311yescharacteristic
73C22⋊C4×C43—21no—
74C22⋊Dic43—21no—
75C22⋊Dic43—21no—
76C22⋊Dic43D411yescharacteristic
77#10621885—22no—
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4D411yescharacteristic
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
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⋊C4D411yescharacteristic
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43C2311yescharacteristic
101#10621877—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104#10621872—22no—
105C23×C43C2×D411yescharacteristic
106C22×D43C2×D411yescharacteristic
107Q8×C43—21no—
108Q8×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—42no—
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—41no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43C2×D411yescharacteristic
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126C4×D43—21no—
127C4×D43—21no—
128C4×D43—42no—
129Dic86—21no—
130Dic86—21no—
131C8×C43—21no—
132C8×C43—21no—
133C43⋊C8—21no—
134C43⋊C8#4112yes—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43C22×D411yescharacteristic
139C2×D43—21no—
140C2×D43—21no—
141C2×D43—21no—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43C2×#4111yescharacteristic
148C4×C432−1+411yescharacteristic
149Dic43—21no—
150Dic43—21no—
151Dic43—21no—
152Dic43—41no—
153Dic43—41no—
154Dic43—41no—
155Dic43—41no—
156#3352—431nomaximal, Sylow
157C2×C43—41no—
158C2×C43#54711yescharacteristic
159C2×C43#57511yescharacteristic
160C2×C43#57811yescharacteristic
161D43—41no—
162#552—431no—
163#552—431no—
164#499—431no—
165#485—431no—
166#485—431no—
167#484—431no—
168#484D4311yescharacteristic, complemented
169#479—431no—
170#479—431no—
171#470—431no—
172#470—431no—
173C4×Q16—431no—
174#436—431no—
175#428—431no—
176#428—431no—
177C43#335211yescharacteristic, complemented, Sylow
178C2×Q16—431no—
179C2×M16—431no—
180C2×M16—431no—
181#126—861no—
182#126—861no—
183#125—431no—
184#125—431no—
185#125—861no—
186#125—861no—
187#123—861no—
188#123—861no—
189C22⋊Q8—431no—
190C22⋊Q8—431no—
191C22⋊Q8—431no—
192C22⋊Q8C2×D4311yescharacteristic
193C4×Q8—431no—
194C4×Q8—431no—
195C4×D4—431no—
196#117—431no—
197#117—431no—
198#117—861no—
199#117—861no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4C2×D4311yescharacteristic
202#107—431no—
203#107—431no—
204#107—431no—
205#107C2×D4311yescharacteristic
206#107C2×D4311yescharacteristic
207#106—431no—
208#106—431no—
209#106—431no—
210#106—431no—
211C4⋊C8—431no—
212#103—431no—
213#103—431no—
214#103—431no—
215#103—431no—
216#103C2×D4311yescharacteristic
217#103C2×D4311yescharacteristic
218C22⋊C8—431no—
219C22⋊C8C2×D4311yescharacteristic
220C4×C8—431no—
221C2×Q8—431no—
222C2×Q8C22×D4311yescharacteristic
223C2×D4—431no—
224C22×C4—21no—
225C22×C4—431no—
226C22×C4—861no—
227C22×C4C22×D4311yescharacteristic
228Q16—862no—
229M16—862no—
230M16—862no—
231C2×C8—431no—
232C2×C8—431no—
233C2×C8C22×D4311yescharacteristic
234C2×C8C22×D4311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—431no—
238C4⋊C4—431no—
239C4⋊C4—431no—
240C4⋊C4—431no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4—861no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4C22×D4311yescharacteristic
252C4⋊C4C22×D4311yescharacteristic
253C4⋊C4C22×D4311yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—431no—
256C22⋊C4—431no—
257C22⋊C4—861no—
258C22⋊C4—861no—
259C22⋊C4—861no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C42—431no—
263C42—861no—
264C42—861no—
265C42—861no—
266C42—861no—
267C23—431no—
268C23D4×D4311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—861no—
272Q8—861no—
273D4—1721no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—431no—
282C2×C4—431no—
283C2×C4—431no—
284C2×C4—861no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—1722no—
291C2×C4D4×D4311yescharacteristic
292C2×C4C23×D4311yescharacteristic
293C8—21no—
294C8—21no—
295C8—432no—
296C8—861no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—861no—
301C22—861no—
302C22—861no—
303C22C2×D4×D4311yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—861no—
310C4—861no—
311C4—861no—
312C4—1721no—
313C4—1721no—
314C4—1721no—
315C4—1721no—
316C4#41×D4311yescharacteristic
317C4#1306337211yescharacteristic
318C2—41no—
319C2—1721no—
320C2#1458354711yescharacteristic
321C2#1458369511yescharacteristic
322C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3352
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #14583300C2semidirect
4. #14583241C2semidirect
5. #14583239C2semidirect
6. #14583236C2semidirect
7. #14583205C2semidirect
8. #14583204C2semidirect
9. #14583156C2semidirect
10. #14583155C2semidirect
11. #14582991C2semidirect
13. #14582940C2semidirect
14. #14582939C2semidirect
15. C43×#484C2semidirect
168. #484D43semidirect
177. C43#3352semidirect