Finite Group Databasebeta

← #19145564

Subgroups — #19145564

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583436C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic, complemented
3#14583284C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583255C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583111C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14583039C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic
14#14582951C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic, complemented
20C2×#10621884C2211yescharacteristic
21C2×#10621884C2211yescharacteristic, complemented
22C2×D344C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24#13063320—21no—
25#13063316C2211yescharacteristic, complemented
26#13063314C2211yescharacteristic
27#13063314C2211yescharacteristic, complemented
28#13063313C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063311—21no—
31#13063311—21no—
32#13063310—21no—
33#13063301C2211yescharacteristic
34#13063300C2211yescharacteristic
35C4×D172—21no—
36C4×D172C2211yescharacteristic, complemented
37#13063282—21no—
38C22⋊C4×D43—21no—
39C22⋊C4×D43—21no—
40C42×D43C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50C8×Dic43C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×Q16×C43C2211yescharacteristic, complemented
53C2×SD16×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64Q8×D43—41no—
65Q8×D43—41no—
66D4×D43—41no—
67D4×D43—41no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43D411yescharacteristic
74C2×C4×D43D411yescharacteristic
75C2×C4×D43C2311yescharacteristic
76C2×Dic86—21no—
77C2×Dic86C2311yescharacteristic
78Q16×C43—41no—
79SD16×C43—41no—
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621885—41no—
91#10621884—41no—
92#10621884—41no—
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43D411yescharacteristic
108C4×Dic43D411yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112D344—41no—
113#10621873—41no—
114C23×C43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43C2×D411yescharacteristic
121Q8×C43—21no—
122Q8×C43—21no—
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—42no—
144C4×D43—22no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—41no—
148C4×D43—42no—
149C4×D43—42no—
150Dic86—21no—
151Dic86—21no—
152Dic86—42no—
153C8×C43—21no—
154C8×C43—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—84no—
170C2×D43#13512yes—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43H(5,𝔽2)11yescharacteristic
177C4×C43H(5,𝔽2)11yescharacteristic
178Dic43—21no—
179Dic43—21no—
180Dic43—21no—
181Dic43—41no—
182Dic43—41no—
183#3211—431nomaximal, Sylow
184C2×C43—81no—
185C2×C43#53511yescharacteristic
186C2×C43C2×#13511yescharacteristic
187C2×C43#57511yescharacteristic
188D43—22no—
189D43—81no—
190D43—81no—
191#529—431no—
192C2×#124—431no—
193#495—431no—
194#495—431no—
195#488—431no—
196#488—431no—
197#464—431no—
198#464D4311yescharacteristic, complemented
199#463—431no—
200#463—431no—
201#451—431no—
202#450—431no—
203#448—431no—
204#447—431no—
205#431—431no—
206C43#321111yescharacteristic, complemented, Sylow
207C22×Q8—431no—
208C22×D4—431no—
209C2×Q16—431no—
210C2×Q16C2×D4311yescharacteristic, complemented
211C2×SD16—431no—
212C2×SD16—431no—
213C2×SD16—431no—
214C2×SD16C2×D4311yescharacteristic
215C2×D8—431no—
216C2×D8—431no—
217#126—861no—
218#125—431no—
219#124—431no—
220#124—431no—
221#124—431no—
222#124—431no—
223#124—861no—
224#124—861no—
225#124C2×D4311yescharacteristic
226#123—861no—
227C22⋊Q8—431no—
228#121—431no—
229C4×Q8C2×D4311yescharacteristic, complemented
230C4×D4—431no—
231C4×D4—861no—
232#117—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C42—431no—
236C4⋊C8—431no—
237C4⋊C8C2×D4311yescharacteristic, complemented
238#103—431no—
239#103—431no—
240#103—431no—
241#103C2×D4311yescharacteristic, complemented
242#102—431no—
243#102—431no—
244#102—431no—
245#102C2×D4311yescharacteristic
246C22⋊C8—431no—
247C22⋊C8—431no—
248C4×C8—431no—
249C4×C8—431no—
250C24—861no—
251C2×Q8—431no—
252C2×Q8—861no—
253C2×Q8—1721no—
254C2×Q8—1721no—
255C2×Q8C22×D4311yescharacteristic
256C2×Q8C22×D4311yescharacteristic
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—1721no—
262C2×D4—1721no—
263C2×D4C22×D4311yescharacteristic
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269Q16—41no—
270Q16—1721no—
271SD16—41no—
272SD16—1721no—
273SD16—1721no—
274SD16—1721no—
275D8—1721no—
276D8—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C42—21no—
301C42—431no—
302C42—431no—
303C42—431no—
304C42C22×D4311yescharacteristic
305C23—21no—
306C23—431no—
307C23—861no—
308C23—861no—
309C23—1722no—
310C23—1722no—
311C23—1722no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—861no—
317Q8—861no—
318Q8—1722no—
319D4—21no—
320D4—21no—
321D4—861no—
322D4—861no—
323D4—861no—
324D4—861no—
325D4—1722no—
326D4—1722no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—862no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4D4×D4311yescharacteristic
343C2×C4C23×D4311yescharacteristic
344C8—21no—
345C8—21no—
346C8—861no—
347C8—861no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—432no—
352C22—861no—
353C22—861no—
354C22—3444no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—861no—
368C4—861no—
369C4—861no—
370C4—1721no—
371C4—1721no—
372C4#1306337011yescharacteristic
373C4#1306337111yescharacteristic
374C2—81no—
375C2—862no—
376C2—3441no—
377C2—3441no—
378C2#1458346511yescharacteristic
379C2#135×D4311yescharacteristic
380C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3211
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14583436C2semidirect
2. #124×D43C2semidirect
3. #14583284C2semidirect
4. #14583280C2semidirect
5. #14583255C2semidirect
6. #14583252C2semidirect
7. #14583121C2semidirect
8. #14583115C2semidirect
9. #14583111C2semidirect
10. #14583053C2semidirect
11. #14583048C2semidirect
12. #14583039C2semidirect
14. #14582951C2semidirect
15. C43×#464C2semidirect
18. C2×#10621885C22semidirect
19. C2×#10621873C22semidirect
21. C2×#10621884C22semidirect
25. #13063316C22semidirect
27. #13063314C22semidirect
36. C4×D172C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063249C22semidirect
44. #13063248C22semidirect
50. C8×Dic43C22semidirect
51. C8×Dic43C22semidirect
52. C2×Q16×C43C22semidirect
55. C4×Q8×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
198. #464D43semidirect
206. C43#3211semidirect
210. C2×Q16C2×D43semidirect
229. C4×Q8C2×D43semidirect
237. C4⋊C8C2×D43semidirect
241. #103C2×D43semidirect