Finite Group Databasebeta

← #21435145

Subgroups — #21435145

Order 7552.

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#16838003C211yesmaximal, characteristic, complemented
2#16837965C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837777C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837755C211yesmaximal, characteristic, complemented
7#16837618C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837594C211yesmaximal, characteristic, complemented
10#16837548C211yesmaximal, characteristic, complemented
11#16837544C211yesmaximal, characteristic, complemented
12#16837537C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#459C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745660C2211yescharacteristic, complemented
19C2×#11745670C2211yescharacteristic, complemented
20C2×D472C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic, complemented
24#14273723C2211yescharacteristic
25#14273723C2211yescharacteristic, complemented
26#14273718C2211yescharacteristic, complemented
27#14273715C2211yescharacteristic
28#14273714C2211yescharacteristic
29#14273710—21no—
30#14273709—21no—
31#14273702C2211yescharacteristic
32#14273701—21no—
33#14273700—21no—
34#14273699—21no—
35#14273699—21no—
36#14273698C2211yescharacteristic
37#14273695—21no—
38#14273695—21no—
39C4×D236C2211yescharacteristic, complemented
40#14273684C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic
53C2×D8×C59C2211yescharacteristic, complemented
54#127×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C22×Dic59—21no—
74#11745687—41no—
75#11745687—41no—
76D4×D59—41no—
77D4×D59—41no—
78C2×D236—21no—
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×Dic118C2311yescharacteristic
84D8×C59—41no—
85D8×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94#11745670—41no—
95#11745669—41no—
96#11745669—41no—
97#11745669—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4D411yescharacteristic
103(C2×D59)⋊C4D411yescharacteristic
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4D411yescharacteristic
108Dic59⋊C4D411yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112D472—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—81no—
130D4×C59—81no—
131C2×C4×C59—21no—
132C2×C4×C59—81no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2411yescharacteristic
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C22⋊D59—81no—
141C22⋊D59—81no—
142C22⋊D59—81no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149D236—21no—
150D236—21no—
151D236—21no—
152D236—21no—
153D236—81no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—81no—
157Dic118—21no—
158Dic118—21no—
159C8×C59—21no—
160C8×C59—21no—
161C59⋊C8—21no—
162C59⋊C8—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59C22×D411yescharacteristic
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—84no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59H(5,𝔽2)11yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—21no—
189Dic59—21no—
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193#3220—591nomaximal, Sylow
194C2×C59—81no—
195C2×C59—81no—
196C2×C59—81no—
197C2×C59#53511yescharacteristic
198C2×C59#57611yescharacteristic
199C2×C59#57611yescharacteristic
200D59—41no—
201D59—81no—
202D59—81no—
203#540—591no—
204#535—591no—
205#496—591no—
206#493—591no—
207#490—591no—
208#488—591no—
209#463—591no—
210#463—591no—
211#459—591no—
212#459D5911yescharacteristic, complemented
213#449—591no—
214#449—591no—
215#447—591no—
216#447—591no—
217#433—591no—
218C59#322011yescharacteristic, complemented, Sylow
219C2×#41—591no—
220C22×D4—591no—
221C2×SD16—591no—
222C2×SD16—591no—
223C2×D8—591no—
224C2×D8—591no—
225C2×D8—591no—
226C2×D8—591no—
227C2×D8C2×D5911yescharacteristic
228C2×D8C2×D5911yescharacteristic, complemented
229#127—591no—
230#127—591no—
231#127C2×D5911yescharacteristic
232#125—591no—
233#124—591no—
234#124—591no—
235#123—1181no—
236#123—1181no—
237#121—591no—
238#121—591no—
239#121—1181no—
240#121—1181no—
241#121—1181no—
242#121—1181no—
243#120—1181no—
244#120—1181no—
245C4×D4—591no—
246C4×D4C2×D5911yescharacteristic, complemented
247#117—591no—
248C4⋊C8—591no—
249C4⋊C8C2×D5911yescharacteristic, complemented
250#103—591no—
251#103—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102C2×D5911yescharacteristic
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8—591no—
260#97—591no—
261C4×C8—591no—
262C24—1181no—
263#41—2361no—
264#41—2361no—
265C2×Q8—591no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—591no—
269C2×D4—591no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—2361no—
279C2×D4—2361no—
280C2×D4C22×D5911yescharacteristic
281C2×D4C22×D5911yescharacteristic
282C2×D4C22×D5911yescharacteristic
283C22×C4—21no—
284C22×C4—591no—
285C22×C4—1181no—
286C22×C4—1181no—
287SD16—2361no—
288SD16—2361no—
289D8—41no—
290D8—41no—
291D8—2361no—
292D8—2361no—
293D8—2361no—
294D8—2361no—
295C2×C8—591no—
296C2×C8—591no—
297C2×C8C22×D5911yescharacteristic
298C2×C8C22×D5911yescharacteristic
299C4⋊C4—591no—
300C4⋊C4—591no—
301C4⋊C4—591no—
302C4⋊C4—1181no—
303C4⋊C4—1181no—
304C4⋊C4C22×D5911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—591no—
307C22⋊C4—591no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C42—591no—
316C42C22×D5911yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—591no—
321C23—1181no—
322C23—1181no—
323C23—4721no—
324C23—4721no—
325C23—2362no—
326Q8—1181no—
327Q8—1181no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—1181no—
337D4—1181no—
338D4—1181no—
339D4—1181no—
340D4—4721no—
341D4—4721no—
342D4—4721no—
343D4—4721no—
344D4—4721no—
345D4—4721no—
346D4—2362no—
347D4—2362no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—591no—
351C2×C4—591no—
352C2×C4—591no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—4721no—
358C2×C4—2362no—
359C2×C4D4×D5911yescharacteristic
360C2×C4D4×D5911yescharacteristic
361C2×C4C23×D5911yescharacteristic
362C8—21no—
363C8—21no—
364C8—1181no—
365C8—1181no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—1181no—
376C22—1181no—
377C22—1181no—
378C22—4724no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22C2×D4×D5911yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—1181no—
390C4—1181no—
391C4—1181no—
392C4—2361no—
393C4—2361no—
394C4#1427377211yescharacteristic
395C4#1427377311yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—4721no—
400C2—4721no—
401C2—2361no—
402C2#1683796811yescharacteristic
403C2#1683820311yescharacteristic
404C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3220
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838003C2semidirect
2. #16837965C2semidirect
3. #16837790C2semidirect
4. #16837777C2semidirect
5. #16837765C2semidirect
6. #16837755C2semidirect
7. #16837618C2semidirect
8. #16837617C2semidirect
9. #16837594C2semidirect
10. #16837548C2semidirect
11. #16837544C2semidirect
12. #16837537C2semidirect
13. #16837534C2semidirect
14. #16837462C2semidirect
15. C59×#459C2semidirect
18. C2×#11745660C22semidirect
19. C2×#11745670C22semidirect
23. C2×#11745669C22semidirect
25. #14273723C22semidirect
26. #14273718C22semidirect
39. C4×D236C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273650C22semidirect
46. #14273648C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
53. C2×D8×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
58. #102×C59C22semidirect
212. #459D59semidirect
218. C59#3220semidirect
228. C2×D8C2×D59semidirect
246. C4×D4C2×D59semidirect
249. C4⋊C8C2×D59semidirect
257. #102C2×D59semidirect