Finite Group Databasebeta

← #19145644

Subgroups — #19145644

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583500C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic, complemented
3#14583287C211yesmaximal, characteristic, complemented
4#14583274C211yesmaximal, characteristic, complemented
5#14583262C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583115C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583091C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic, complemented
11#14583041C211yesmaximal, characteristic, complemented
12#14583034C211yesmaximal, characteristic, complemented
13#14583031C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic, complemented
19C2×#10621883C2211yescharacteristic, complemented
20C2×D344C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic, complemented
24#13063321C2211yescharacteristic
25#13063321C2211yescharacteristic, complemented
26#13063316C2211yescharacteristic, complemented
27#13063313C2211yescharacteristic
28#13063312C2211yescharacteristic
29#13063308—21no—
30#13063307—21no—
31#13063300C2211yescharacteristic
32#13063299—21no—
33#13063298—21no—
34#13063297—21no—
35#13063297—21no—
36#13063296C2211yescharacteristic
37#13063293—21no—
38#13063293—21no—
39C4×D172C2211yescharacteristic, complemented
40#13063282C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic, complemented
54#127×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C22×Dic43—21no—
74#10621900—41no—
75#10621900—41no—
76D4×D43—41no—
77D4×D43—41no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86C2311yescharacteristic
84D8×C43—41no—
85D8×C43—41no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94#10621883—41no—
95#10621882—41no—
96#10621882—41no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4D411yescharacteristic
103(C2×D43)⋊C4D411yescharacteristic
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4D411yescharacteristic
108Dic43⋊C4D411yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112D344—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43C2×D411yescharacteristic
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—81no—
130D4×C43—81no—
131C2×C4×C43—21no—
132C2×C4×C43—81no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2411yescharacteristic
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149D172—21no—
150D172—21no—
151D172—21no—
152D172—21no—
153D172—81no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—81no—
157Dic86—21no—
158Dic86—21no—
159C8×C43—21no—
160C8×C43—21no—
161C43⋊C8—21no—
162C43⋊C8—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43C22×D411yescharacteristic
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—84no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43H(5,𝔽2)11yescharacteristic
187C4×C43H(5,𝔽2)11yescharacteristic
188Dic43—21no—
189Dic43—21no—
190Dic43—21no—
191Dic43—41no—
192Dic43—41no—
193#3220—431nomaximal, Sylow
194C2×C43—81no—
195C2×C43—81no—
196C2×C43—81no—
197C2×C43#53511yescharacteristic
198C2×C43#57611yescharacteristic
199C2×C43#57611yescharacteristic
200D43—41no—
201D43—81no—
202D43—81no—
203#540—431no—
204#535—431no—
205#496—431no—
206#493—431no—
207#490—431no—
208#488—431no—
209#463—431no—
210#463—431no—
211#459—431no—
212#459D4311yescharacteristic, complemented
213#449—431no—
214#449—431no—
215#447—431no—
216#447—431no—
217#433—431no—
218C43#322011yescharacteristic, complemented, Sylow
219C2×#41—431no—
220C22×D4—431no—
221C2×SD16—431no—
222C2×SD16—431no—
223C2×D8—431no—
224C2×D8—431no—
225C2×D8—431no—
226C2×D8—431no—
227C2×D8C2×D4311yescharacteristic
228C2×D8C2×D4311yescharacteristic, complemented
229#127—431no—
230#127—431no—
231#127C2×D4311yescharacteristic
232#125—431no—
233#124—431no—
234#124—431no—
235#123—861no—
236#123—861no—
237#121—431no—
238#121—431no—
239#121—861no—
240#121—861no—
241#121—861no—
242#121—861no—
243#120—861no—
244#120—861no—
245C4×D4—431no—
246C4×D4C2×D4311yescharacteristic, complemented
247#117—431no—
248C4⋊C8—431no—
249C4⋊C8C2×D4311yescharacteristic, complemented
250#103—431no—
251#103—431no—
252#102—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102C2×D4311yescharacteristic
257#102C2×D4311yescharacteristic, complemented
258C22⋊C8—431no—
259C22⋊C8—431no—
260#97—431no—
261C4×C8—431no—
262C24—861no—
263#41—1721no—
264#41—1721no—
265C2×Q8—431no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4C22×D4311yescharacteristic
281C2×D4C22×D4311yescharacteristic
282C2×D4C22×D4311yescharacteristic
283C22×C4—21no—
284C22×C4—431no—
285C22×C4—861no—
286C22×C4—861no—
287SD16—1721no—
288SD16—1721no—
289D8—41no—
290D8—41no—
291D8—1721no—
292D8—1721no—
293D8—1721no—
294D8—1721no—
295C2×C8—431no—
296C2×C8—431no—
297C2×C8C22×D4311yescharacteristic
298C2×C8C22×D4311yescharacteristic
299C4⋊C4—431no—
300C4⋊C4—431no—
301C4⋊C4—431no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4C22×D4311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—431no—
307C22⋊C4—431no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C42—431no—
316C42C22×D4311yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—431no—
321C23—861no—
322C23—861no—
323C23—3441no—
324C23—3441no—
325C23—1722no—
326Q8—861no—
327Q8—861no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—861no—
337D4—861no—
338D4—861no—
339D4—861no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343D4—3441no—
344D4—3441no—
345D4—3441no—
346D4—1722no—
347D4—1722no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—431no—
351C2×C4—431no—
352C2×C4—431no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—1722no—
359C2×C4D4×D4311yescharacteristic
360C2×C4D4×D4311yescharacteristic
361C2×C4C23×D4311yescharacteristic
362C8—21no—
363C8—21no—
364C8—861no—
365C8—861no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—861no—
376C22—861no—
377C22—861no—
378C22—3444no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22C2×D4×D4311yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—861no—
390C4—861no—
391C4—861no—
392C4—1721no—
393C4—1721no—
394C4#1306337011yescharacteristic
395C4#1306337111yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—3441no—
400C2—3441no—
401C2—1721no—
402C2#1458346511yescharacteristic
403C2#1458370011yescharacteristic
404C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14583500C2semidirect
2. #14583462C2semidirect
3. #14583287C2semidirect
4. #14583274C2semidirect
5. #14583262C2semidirect
6. #14583252C2semidirect
7. #14583115C2semidirect
8. #14583114C2semidirect
9. #14583091C2semidirect
10. #14583045C2semidirect
11. #14583041C2semidirect
12. #14583034C2semidirect
13. #14583031C2semidirect
14. #14582959C2semidirect
15. C43×#459C2semidirect
18. C2×#10621873C22semidirect
19. C2×#10621883C22semidirect
23. C2×#10621882C22semidirect
25. #13063321C22semidirect
26. #13063316C22semidirect
39. C4×D172C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
46. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
53. C2×D8×C43C22semidirect
55. C4×D4×C43C22semidirect
56. C4⋊C8×C43C22semidirect
58. #102×C43C22semidirect
212. #459D43semidirect
218. C43#3220semidirect
228. C2×D8C2×D43semidirect
246. C4×D4C2×D43semidirect
249. C4⋊C8C2×D43semidirect
257. #102C2×D43semidirect