Finite Group Databasebeta

← #21435142

Subgroups — #21435142

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#16838005C211yesmaximal, characteristic, complemented
2#16837969C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837777C211yesmaximal, characteristic, complemented
5#16837765C211yesmaximal, characteristic, complemented
6#16837755C211yesmaximal, characteristic, complemented
7#16837616C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837596C211yesmaximal, characteristic, complemented
10#16837595C211yesmaximal, characteristic, complemented
11#16837549C211yesmaximal, characteristic, complemented
12#16837545C211yesmaximal, characteristic, complemented
13#16837536C211yesmaximal, characteristic, complemented
14#16837460C211yesmaximal, characteristic, complemented
15C59×#447C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745660C2211yescharacteristic, complemented
18C2×#11745670C2211yescharacteristic, complemented
19C2×D472C2211yescharacteristic, complemented
20C2×#11745669C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22C2×#11745669C2211yescharacteristic, complemented
23#14273723C2211yescharacteristic
24#14273723C2211yescharacteristic
25#14273723C2211yescharacteristic, complemented
26#14273718C2211yescharacteristic, complemented
27#14273714C2211yescharacteristic
28#14273714C2211yescharacteristic
29#14273711—21no—
30#14273709—21no—
31#14273701C2211yescharacteristic
32#14273699—21no—
33#14273698—21no—
34#14273698—21no—
35#14273698—21no—
36#14273696—21no—
37#14273696—21no—
38D4×Dic59C2211yescharacteristic, complemented
39#14273689C2211yescharacteristic, complemented
40#14273686C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×D8×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C24×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—41no—
63C2×D4×C59—41no—
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C22×Dic59—21no—
77#11745685—41no—
78#11745685—41no—
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×Dic118C2311yescharacteristic
84D8×C59—41no—
85D8×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59D411yescharacteristic
96C22⋊Dic59D411yescharacteristic
97#11745670—41no—
98#11745669—41no—
99#11745669—41no—
100#11745669—41no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59D411yescharacteristic
105C4⋊Dic59D411yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108C4×Dic59C2311yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112D472—41no—
113#11745660—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—42no—
118C23×C59—81no—
119C23×C59—81no—
120C23×C59C2×D411yescharacteristic
121C22×D59—21no—
122C22×D59—21no—
123D4×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—42no—
130D4×C59—81no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2411yescharacteristic
136C22⋊D59—42no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C22⋊D59—81no—
140C22⋊D59—81no—
141C22⋊D59—81no—
142C22⋊D59—81no—
143C22⋊D59—81no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—81no—
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—21no—
152D236—21no—
153D236—21no—
154D236—21no—
155C4×D59—42no—
156C4×D59—81no—
157Dic118—21no—
158Dic118—21no—
159C8×C59—21no—
160C8×C59—21no—
161C59⋊C8—21no—
162C59⋊C8—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—84no—
176C22×C59C22×D411yescharacteristic
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C4×C59—21no—
184C4×C59—41no—
185C4×C59H(5,𝔽2)11yescharacteristic
186C4×C59H(5,𝔽2)11yescharacteristic
187Dic59—21no—
188Dic59—21no—
189Dic59—21no—
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193#3220—591nomaximal, Sylow
194C2×C59—41no—
195C2×C59—81no—
196C2×C59—81no—
197C2×C59—81no—
198C2×C59#53511yescharacteristic
199C2×C59#57611yescharacteristic
200C2×C59#57611yescharacteristic
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#459—591no—
213#449—591no—
214#449—591no—
215#447—591no—
216#447D5911yescharacteristic, complemented
217#433—591no—
218C59#322011yescharacteristic, complemented, Sylow
219C2×#41—591no—
220C22×D4C2×D5911yescharacteristic
221C2×SD16—591no—
222C2×SD16—591no—
223C2×D8—591no—
224C2×D8—591no—
225C2×D8—591no—
226C2×D8—591no—
227C2×D8C2×D5911yescharacteristic
228C2×D8C2×D5911yescharacteristic
229#127—591no—
230#127—591no—
231#127—591no—
232#125—591no—
233#124—591no—
234#124—591no—
235#123—1181no—
236#123—1181no—
237#121—591no—
238#121—1181no—
239#121—1181no—
240#121—1181no—
241#121—1181no—
242#121C2×D5911yescharacteristic
243#120—1181no—
244#120—1181no—
245C4×D4—591no—
246C4×D4—591no—
247#117—591no—
248C4⋊C8—591no—
249C4⋊C8—591no—
250#103—591no—
251#103—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102C2×D5911yescharacteristic
257#102C2×D5911yescharacteristic
258C22⋊C8—591no—
259C22⋊C8C2×D5911yescharacteristic
260#97—591no—
261C4×C8—591no—
262C24—21no—
263#41—2361no—
264#41—2361no—
265C2×Q8—591no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—591no—
271C2×D4—591no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4C22×D5911yescharacteristic
281C2×D4C22×D5911yescharacteristic
282C2×D4C22×D5911yescharacteristic
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4C22×D5911yescharacteristic
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—
316C42—591no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1181no—
324C23—1181no—
325C23D4×D5911yescharacteristic
326Q8—1181no—
327Q8—1181no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—1181no—
337D4—1181no—
338D4—1181no—
339D4—1181no—
340D4—4721no—
341D4—4721no—
342D4—4721no—
343D4—4721no—
344D4—4721no—
345D4—4721no—
346D4—4721no—
347D4—2362no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—591no—
352C2×C4—591no—
353C2×C4—591no—
354C2×C4—591no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—4721no—
358C2×C4—4721no—
359C2×C4—2362no—
360C2×C4D4×D5911yescharacteristic
361C2×C4C23×D5911yescharacteristic
362C8—21no—
363C8—21no—
364C8—1181no—
365C8—1181no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22—2361no—
384C22—2361no—
385C22C2×D4×D5911yescharacteristic
386C4—21no—
387C4—41no—
388C4—1181no—
389C4—1181no—
390C4—1181no—
391C4—1181no—
392C4—2361no—
393C4—2361no—
394C4#1427377211yescharacteristic
395C4#1427377211yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—4721no—
401C2—4721no—
402C2#1683796711yescharacteristic
403C2#1683820311yescharacteristic
404C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#447C2
socleC22×C59C22×D4
hypercenter#447D59
hypocenterC59#3220
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16838005C2semidirect
2. #16837969C2semidirect
3. #16837790C2semidirect
4. #16837777C2semidirect
5. #16837765C2semidirect
6. #16837755C2semidirect
7. #16837616C2semidirect
8. #16837615C2semidirect
9. #16837596C2semidirect
10. #16837595C2semidirect
11. #16837549C2semidirect
12. #16837545C2semidirect
13. #16837536C2semidirect
14. #16837460C2semidirect
15. C59×#447C2semidirect
17. C2×#11745660C22semidirect
18. C2×#11745670C22semidirect
19. C2×D472C22semidirect
22. C2×#11745669C22semidirect
25. #14273723C22semidirect
26. #14273718C22semidirect
38. D4×Dic59C22semidirect
39. #14273689C22semidirect
41. Dic59⋊C8C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
45. #14273649C22semidirect
48. #14273647C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
216. #447D59semidirect
218. C59#3220semidirect