Finite Group Databasebeta

← #19145361

Subgroups — #19145361

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583412C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic, complemented
3#14583233C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583221C211yesmaximal, characteristic, complemented
6#14583219C211yesmaximal, characteristic, complemented
7#14583135C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14583047C211yesmaximal, characteristic, complemented
12#14583043C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic, complemented
17C2×D4×D43—21no—
18C2×D4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C2×#10621884C2211yescharacteristic, complemented
21C2×D344C2211yescharacteristic, complemented
22C2×#10621882C2211yescharacteristic, complemented
23C22×C43⋊C8C2211yescharacteristic, complemented
24#13063310—21no—
25#13063301C2211yescharacteristic
26#13063300C2211yescharacteristic
27#13063300C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic, complemented
30#13063298—21no—
31#13063297—21no—
32#13063296C2211yescharacteristic
33#13063295—21no—
34#13063287—21no—
35(C22⋊D43)⋊C4—21no—
36#13063283C2211yescharacteristic, complemented
37C4⋊C4×D43C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43C2211yescharacteristic, complemented
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43D411yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43D411yescharacteristic
70#10621902—41no—
71#10621902—41no—
72D4×D43—44no—
73D4×D43—41no—
74D4×D43—41no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172C2311yescharacteristic
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43D411yescharacteristic
85C2×C4×D43D411yescharacteristic
86C2×C4×D43C2311yescharacteristic
87C2×C4×D43C2311yescharacteristic
88SD16×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊Dic43—21no—
98#10621884—41no—
99#10621882—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106C4⋊Dic43C2311yescharacteristic
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110C4×Dic43—21no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114D344—41no—
115C23×C43—21no—
116C23×C43C2×D411yescharacteristic
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—41no—
122C22×D43—42no—
123C22×D43—42no—
124C22×D43—42no—
125C22×D43C2×D411yescharacteristic
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43—21no—
129D4×C43—21no—
130D4×C43—21no—
131D4×C43—42no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C22⋊D43—42no—
140C22⋊D43—42no—
141C22⋊D43—42no—
142C22⋊D43—42no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—41no—
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148D172—21no—
149D172—21no—
150D172—21no—
151D172—21no—
152D172—42no—
153D172—42no—
154D172—42no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—42no—
162C4×D43—42no—
163C8×C43—21no—
164C8×C43—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43AGL(1,ℤ/8)12yes—
173C22×C43C22×D411yescharacteristic
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—44no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—84no—
187C2×D43#13512yes—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43H(5,𝔽2)11yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—21no—
195Dic43—21no—
196Dic43—41no—
197Dic43—41no—
198#3188—431nomaximal, Sylow
199C2×C43—22no—
200C2×C43—81no—
201C2×C43#53411yescharacteristic
202C2×C43C2×#13511yescharacteristic
203C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
204D43—22no—
205D43—41no—
206D43—81no—
207D43—81no—
208#525—431no—
209C2×#121—431no—
210#484—431no—
211#482—431no—
212#482—431no—
213#481—431no—
214#466—431no—
215#466—431no—
216#465—431no—
217#465D4311yescharacteristic, complemented
218#450—431no—
219#449—431no—
220#449—431no—
221#447—431no—
222C2×C22⋊C8—431no—
223C43#318811yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C22×D4—431no—
226C22×D4—861no—
227C23×C4—431no—
228C2×SD16—431no—
229C2×SD16C2×D4311yescharacteristic, complemented
230C2×D8—431no—
231C2×D8—431no—
232C22×C8—431no—
233C22×C8C2×D4311yescharacteristic, complemented
234#123—861no—
235C22⋊Q8—431no—
236C22⋊Q8C2×D4311yescharacteristic, complemented
237#121—431no—
238#121—431no—
239#121—431no—
240#121—431no—
241#121—431no—
242#121—861no—
243#121—861no—
244#121C2×D4311yescharacteristic
245#120—861no—
246C4×D4—861no—
247C4×D4—861no—
248#117—431no—
249C2×C4⋊C4—431no—
250C2×C22⋊C4—861no—
251#107—431no—
252#107—431no—
253#106—431no—
254#106C2×D4311yescharacteristic, complemented
255#103—431no—
256#103C2×D4311yescharacteristic, complemented
257#102—431no—
258#102—431no—
259#102—431no—
260#102—431no—
261#102—431no—
262#102C2×D4311yescharacteristic, complemented
263C22⋊C8—431no—
264C22⋊C8—431no—
265C22⋊C8—431no—
266C22⋊C8—431no—
267C24—431no—
268C24—861no—
269#41—1721no—
270#41—1721no—
271C2×Q8C22×D4311yescharacteristic
272C2×D4—21no—
273C2×D4—431no—
274C2×D4—431no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4—1721no—
284C2×D4—1724no—
285C2×D4C22×D4311yescharacteristic
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4C22×D4311yescharacteristic
296SD16—41no—
297SD16—1721no—
298D8—1721no—
299D8—1721no—
300C2×C8—41no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8—1721no—
304C2×C8C22×D4311yescharacteristic
305C2×C8C22×D4311yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—431no—
308C4⋊C4—431no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4C22×D4311yescharacteristic
312C4⋊C4C22×D4311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C42—861no—
323C23—21no—
324C23—431no—
325C23—431no—
326C23—862no—
327C23—862no—
328C23—861no—
329C23—861no—
330C23—1721no—
331C23—1722no—
332C23—1722no—
333C23—1722no—
334C23D4×D4311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—861no—
341D4—861no—
342D4—861no—
343D4—861no—
344D4—1722no—
345D4—1722no—
346D4—1722no—
347D4—1722no—
348D4—1722no—
349D4—1722no—
350D4—1722no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—431no—
357C2×C4—431no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1721no—
369C2×C4D4×D4311yescharacteristic
370C2×C4C23×D4311yescharacteristic
371C8—21no—
372C8—21no—
373C8—861no—
374C8—861no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—432no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—861no—
385C22—861no—
386C22—3444no—
387C22—1724no—
388C22—1721no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22#1306335212yes—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—861no—
401C4—861no—
402C4—1721no—
403C4—1721no—
404C4#1306337011yescharacteristic
405C4#1306337111yescharacteristic
406C2—22no—
407C2—81no—
408C2—862no—
409C2—3441no—
410C2—3441no—
411C2—1721no—
412C2#1458345711yescharacteristic
413C2#135×D4311yescharacteristic
414C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3188
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14583412C2semidirect
2. #121×D43C2semidirect
3. #14583233C2semidirect
4. #14583225C2semidirect
5. #14583221C2semidirect
6. #14583219C2semidirect
7. #14583135C2semidirect
8. #14583133C2semidirect
9. #14583130C2semidirect
10. #14583048C2semidirect
11. #14583047C2semidirect
12. #14583043C2semidirect
13. #14583034C2semidirect
14. C2×(C2×D43)⋊C8C2semidirect
15. C43×#465C2semidirect
16. C2×#10621902C22semidirect
20. C2×#10621884C22semidirect
21. C2×D344C22semidirect
22. C2×#10621882C22semidirect
23. C22×C43⋊C8C22semidirect
29. #13063299C22semidirect
36. #13063283C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. #13063256C22semidirect
42. #13063249C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
45. #13063246C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
52. C2×SD16×C43C22semidirect
53. C22×C8×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
217. #465D43semidirect
223. C43#3188semidirect
229. C2×SD16C2×D43semidirect
233. C22×C8C2×D43semidirect
236. C22⋊Q8C2×D43semidirect
254. #106C2×D43semidirect
256. #103C2×D43semidirect
262. #102C2×D43semidirect