Finite Group Databasebeta

← #21434959

Subgroups — #21434959

Order 7552.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837969C211yesmaximal, characteristic, complemented
2#16837968C211yesmaximal, characteristic, complemented
3#16837727C211yesmaximal, characteristic, complemented
4#16837725C211yesmaximal, characteristic, complemented
5#16837724C211yesmaximal, characteristic, complemented
6#16837723C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837652C211yesmaximal, characteristic, complemented
9#16837637C211yesmaximal, characteristic, complemented
10#16837635C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837534C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#447C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic, complemented
18C2×#11745669C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22#14273723—21no—
23#14273723—21no—
24#14273714—21no—
25#14273713—21no—
26#14273702C2211yescharacteristic, complemented
27#14273701C2211yescharacteristic
28#14273698C2211yescharacteristic
29#14273698C2211yescharacteristic
30#14273698C2211yescharacteristic, complemented
31#14273698C2211yescharacteristic, complemented
32#14273698C2211yescharacteristic, complemented
33#14273697—21no—
34#14273696—21no—
35#14273696—21no—
36#14273695—21no—
37#14273686C2211yescharacteristic, complemented
38#14273685C2211yescharacteristic, complemented
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic, complemented
53C2×D8×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C24×C59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59—41no—
64C2×D4×C59—41no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C2×D4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
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—
76C2×C22⋊D59D411yescharacteristic
77C2×C22⋊D59D411yescharacteristic
78D4×D59—41no—
79D4×D59—41no—
80#11745685—41no—
81#11745685—41no—
82C2×D236—21no—
83C2×D236D411yescharacteristic
84C2×D236C2311yescharacteristic
85C2×C4×D59C2311yescharacteristic
86C2×C4×D59C2311yescharacteristic
87C2×Dic118D411yescharacteristic
88D8×C59—41no—
89D8×C59—41no—
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100#11745669—41no—
101#11745669—41no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107C4⋊Dic59C2311yescharacteristic
108C4×Dic59—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113C8×D59—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—42no—
123C22×D59—81no—
124C22×D59—81no—
125C22×D59C2×D411yescharacteristic
126C22×D59C2×D411yescharacteristic
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—21no—
131D4×C59—21no—
132D4×C59—21no—
133D4×C59—42no—
134D4×C59—81no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—41no—
141C22⋊D59—41no—
142C22⋊D59—42no—
143C22⋊D59—81no—
144C22⋊D59—81no—
145C22⋊D59—81no—
146C22⋊D59—81no—
147C22⋊D59—81no—
148C22⋊D59—81no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59C2×D411yescharacteristic
153C2×Dic59C2×D411yescharacteristic
154D236—21no—
155D236—21no—
156D236—41no—
157D236—81no—
158C4×D59—21no—
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—21no—
162Dic118—41no—
163C8×C59—21no—
164C8×C59—21no—
165C59⋊C8—21no—
166C59⋊C8—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—84no—
180C22×C59C22×D411yescharacteristic
181C2×D59—21no—
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—21no—
185C2×D59—21no—
186C2×D59—21no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—84no—
191C4×C59—21no—
192C4×C59—41no—
193C4×C59H(5,𝔽2)11yescharacteristic
194C4×C59H(5,𝔽2)11yescharacteristic
195Dic59—21no—
196Dic59—21no—
197Dic59—41no—
198Dic59—41no—
199Dic59—41no—
200#3199—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—81no—
203C2×C59—81no—
204C2×C59—81no—
205C2×C59#53411yescharacteristic
206C2×C59#57611yescharacteristic
207C2×C59#57611yescharacteristic
208D59—41no—
209D59—41no—
210D59—81no—
211#535—591no—
212#535—591no—
213#482—591no—
214#482—591no—
215#482—591no—
216#482—591no—
217#469—591no—
218#469—591no—
219#466—591no—
220#466—591no—
221#447—591no—
222#447—591no—
223#447—591no—
224#447D5911yescharacteristic, complemented
225#408—591no—
226C59#319911yescharacteristic, complemented, Sylow
227C2×#41—591no—
228C22×D4—591no—
229C22×D4C2×D5911yescharacteristic, complemented
230C2×D8—591no—
231C2×D8—591no—
232C2×D8C2×D5911yescharacteristic
233C2×D8C2×D5911yescharacteristic
234C2×M16—591no—
235C22×C8—591no—
236#127—1181no—
237#127—1181no—
238#124—1181no—
239#124—1181no—
240#121—591no—
241#121—591no—
242#121—591no—
243#121—591no—
244#121—591no—
245#121—591no—
246#121—591no—
247#121C2×D5911yescharacteristic
248#120—1181no—
249#120—1181no—
250#120—1181no—
251#120—1181no—
252#117—591no—
253#117—591no—
254#107—591no—
255#107—591no—
256#106—591no—
257#106—591no—
258#102—591no—
259#102—591no—
260#102—591no—
261#102—591no—
262#102—591no—
263#102—591no—
264#102C2×D5911yescharacteristic, complemented
265#102C2×D5911yescharacteristic, complemented
266C22⋊C8—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269C22⋊C8C2×D5911yescharacteristic, complemented
270C24—21no—
271C24—1181no—
272#41—2361no—
273#41—2361no—
274C2×Q8—591no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—591no—
280C2×D4—591no—
281C2×D4—591no—
282C2×D4—591no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4—1181no—
290C2×D4—1181no—
291C2×D4—2361no—
292C2×D4—2361no—
293C2×D4C22×D5911yescharacteristic
294C2×D4C22×D5911yescharacteristic
295C2×D4C22×D5911yescharacteristic
296C22×C4—591no—
297C22×C4—591no—
298C22×C4C22×D5911yescharacteristic
299D8—41no—
300D8—41no—
301D8—2361no—
302D8—2361no—
303M16—2361no—
304C2×C8—591no—
305C2×C8—591no—
306C2×C8—2361no—
307C2×C8C22×D5911yescharacteristic
308C2×C8C22×D5911yescharacteristic
309C4⋊C4—591no—
310C4⋊C4—591no—
311C4⋊C4—591no—
312C4⋊C4C22×D5911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C42—1181no—
324C42—1181no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—591no—
332C23—591no—
333C23—1181no—
334C23—4721no—
335C23—4721no—
336C23—2362no—
337C23D4×D5911yescharacteristic
338Q8—2361no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—1181no—
348D4—1181no—
349D4—4721no—
350D4—4721no—
351D4—4721no—
352D4—4721no—
353D4—4721no—
354D4—4721no—
355D4—4721no—
356D4—2361no—
357D4—2361no—
358D4—2361no—
359D4—2362no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—591no—
364C2×C4—591no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4D4×D5911yescharacteristic
373C2×C4C23×D5911yescharacteristic
374C8—21no—
375C8—21no—
376C8—1181no—
377C8—1181no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—1181no—
392C22—1181no—
393C22—1181no—
394C22—1181no—
395C22—1181no—
396C22—1181no—
397C22—4724no—
398C22—2361no—
399C22—2361no—
400C22—2361no—
401C22C2×D4×D5911yescharacteristic
402C4—21no—
403C4—41no—
404C4—1181no—
405C4—1181no—
406C4—2361no—
407C4—2361no—
408C4—2361no—
409C4#1427377211yescharacteristic
410C4#1427377211yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—4721no—
416C2—2361no—
417C2—2361no—
418C2#1683796211yescharacteristic
419C2#1683820311yescharacteristic
420C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#447C2
socleC22×C59C22×D4
hypercenter#447D59
hypocenterC59#3199
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. #16837969C2semidirect
2. #16837968C2semidirect
3. #16837727C2semidirect
4. #16837725C2semidirect
5. #16837724C2semidirect
6. #16837723C2semidirect
7. #16837654C2semidirect
8. #16837652C2semidirect
9. #16837637C2semidirect
10. #16837635C2semidirect
11. #16837536C2semidirect
12. #16837534C2semidirect
13. #16837534C2semidirect
14. #16837367C2semidirect
15. C59×#447C2semidirect
17. C2×D4×D59C22semidirect
20. C2×#11745659C22semidirect
21. C2×C8×D59C22semidirect
26. #14273702C22semidirect
30. #14273698C22semidirect
31. #14273698C22semidirect
32. #14273698C22semidirect
37. #14273686C22semidirect
38. #14273685C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
45. #14273648C22semidirect
46. #14273648C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C22×D4×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
224. #447D59semidirect
226. C59#3199semidirect
229. C22×D4C2×D59semidirect
264. #102C2×D59semidirect
265. #102C2×D59semidirect
269. C22⋊C8C2×D59semidirect