Finite Group Databasebeta

← #19146436

Subgroups — #19146436

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583591C211yesmaximal, characteristic, complemented
2#14583540C211yesmaximal, characteristic
3#14583255C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583226C211yesmaximal, characteristic, complemented
6#14583202C211yesmaximal, characteristic, complemented
7#14583131C211yesmaximal, characteristic, complemented
8#14583123C211yesmaximal, characteristic, complemented
9#14583060C211yesmaximal, characteristic, complemented
10#14583049C211yesmaximal, characteristic, complemented
11#14582984C211yesmaximal, characteristic, complemented
12C8×C22⋊D43C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#467C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic, complemented
21#13063320—21no—
22#13063316—21no—
23#13063316C2211yescharacteristic, complemented
24#13063314C2211yescharacteristic
25#13063310—21no—
26#13063309—21no—
27#13063301C2211yescharacteristic, complemented
28#13063300—21no—
29#13063300C2211yescharacteristic
30#13063295—21no—
31Q8×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34#13063283C2211yescharacteristic, complemented
35#13063281—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C22⋊C4×D43—21no—
38#13063256C2211yescharacteristic, complemented
39#13063256C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×Q16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#103×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43D411yescharacteristic
64C22×Dic43—21no—
65#10621902—22no—
66#10621902—41no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77Q16×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621884—22no—
89#10621884—41no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—22no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172—21no—
139D172—21no—
140D172—42no—
141D172—42no—
142D172—81no—
143D172#4112yes—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—42no—
147C4×D43—81no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43#13512yes—
155C22×C43C22×D411yescharacteristic
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43#54611yescharacteristic
181C2×C43C2×#13511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—42no—
185D43—81no—
186#552—431no—
187#546—431no—
188#488—431no—
189#483—431no—
190#482—431no—
191#478—431no—
192#467D4311yescharacteristic, complemented
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102—431no—
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16C2×D4311yescharacteristic, complemented
205C2×SD16—431no—
206C2×SD16—431no—
207C22×C8—431no—
208C22×C8C2×D4311yescharacteristic
209#126—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8C2×D4311yescharacteristic
217C22⋊Q8C2×D4311yescharacteristic
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—861no—
228#107C2×D4311yescharacteristic, complemented
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic, complemented
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—1721no—
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—41no—
264SD16—862no—
265SD16—1721no—
266C2×C8—41no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—431no—
287C22⋊C4—431no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—431no—
298C23—861no—
299C23—861no—
300C23—3441no—
301C23—1722no—
302C23—1722no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—432no—
309D4—862no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22—862no—
344C22—3444no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22—1721no—
350C22#1306334812yes—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—861no—
360C4—1721no—
361C4—1721no—
362C4#41×D4311yescharacteristic
363C4#1306337011yescharacteristic
364C2—22no—
365C2—3441no—
366C2—1721no—
367C2—1722no—
368C2#1458353811yescharacteristic
369C2C2×#1306334811yescharacteristic
370C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#467C2
socleC22×C43C22×D4
hypercenter#467D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #14583591C2semidirect
3. #14583255C2semidirect
4. #14583227C2semidirect
5. #14583226C2semidirect
6. #14583202C2semidirect
7. #14583131C2semidirect
8. #14583123C2semidirect
9. #14583060C2semidirect
10. #14583049C2semidirect
11. #14582984C2semidirect
12. C8×C22⋊D43C2semidirect
13. #14582894C2semidirect
14. C2×#13063247C2semidirect
15. C43×#467C2semidirect
20. C2×C8×D43C22semidirect
23. #13063316C22semidirect
27. #13063301C22semidirect
31. Q8×Dic43C22semidirect
34. #13063283C22semidirect
38. #13063256C22semidirect
39. #13063256C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
52. C2×Q16×C43C22semidirect
56. #107×C43C22semidirect
57. #103×C43C22semidirect
58. #103×C43C22semidirect
192. #467D43semidirect
201. C43#3296semidirect
204. C2×Q16C2×D43semidirect
228. #107C2×D43semidirect
234. #103C2×D43semidirect
235. #103C2×D43semidirect