Finite Group Databasebeta

← #21434859

Subgroups — #21434859

Order 7552.

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#16837909C211yesmaximal, characteristic, complemented
2#121×D59C211yesmaximal, characteristic, complemented
3#16837736C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837723C211yesmaximal, characteristic, complemented
6#16837719C211yesmaximal, characteristic, complemented
7#16837637C211yesmaximal, characteristic, complemented
8#16837635C211yesmaximal, characteristic, complemented
9#16837634C211yesmaximal, characteristic, complemented
10#16837628C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14C22⋊C8×D59C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×D4×D59—21no—
17C2×D4×D59C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19C2×#11745671C2211yescharacteristic, complemented
20C2×#11745669C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22C2×C8×D59C2211yescharacteristic, complemented
23#14273708—21no—
24#14273703C2211yescharacteristic
25#14273703C2211yescharacteristic, complemented
26#14273702C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273700—21no—
29#14273699—21no—
30#14273698C2211yescharacteristic
31#14273698C2211yescharacteristic
32#14273698C2211yescharacteristic, complemented
33#14273695—21no—
34C4×C22⋊D59—21no—
35C4×C22⋊D59—21no—
36#14273686C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273661C2211yescharacteristic, complemented
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic, complemented
53C2×SD16×C59C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic, complemented
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59D411yescharacteristic
61#41×C59—41no—
62#41×C59—41no—
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59C2311yescharacteristic
67C2×D4×C59C2311yescharacteristic
68C22×C4×C59—21no—
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—21no—
74C2×C22⋊D59—21no—
75C22×Dic59D411yescharacteristic
76D4×D59—41no—
77D4×D59—41no—
78D4×D59—44no—
79C2×D236—21no—
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59—41no—
83C2×C4×D59—41no—
84C2×C4×D59D411yescharacteristic
85C2×C4×D59D411yescharacteristic
86C2×C4×D59C2311yescharacteristic
87C2×C4×D59C2311yescharacteristic
88SD16×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—
98#11745671—41no—
99#11745669—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
110C4×Dic59—21no—
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C8×D59—41no—
114C8×D59—41no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59C2×D411yescharacteristic
118C22×D59—22no—
119C22×D59—22no—
120C22×D59—21no—
121C22×D59—41no—
122C22×D59—42no—
123C22×D59—42no—
124C22×D59—42no—
125C22×D59C2×D411yescharacteristic
126C22×D59C2×D411yescharacteristic
127Q8×C59—21no—
128Q8×C59—21no—
129D4×C59—21no—
130D4×C59—21no—
131D4×C59—21no—
132D4×C59—21no—
133D4×C59—42no—
134D4×C59—42no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—42no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2411yescharacteristic
142C22⋊D59—42no—
143C22⋊D59—42no—
144C22⋊D59—42no—
145C22⋊D59—42no—
146C22⋊D59—42no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—41no—
151C2×Dic59C2×D411yescharacteristic
152C2×Dic59C2×D411yescharacteristic
153D236—21no—
154D236—21no—
155D236—42no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—21no—
159C4×D59—21no—
160C4×D59—41no—
161C4×D59—41no—
162C4×D59—42no—
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×C59C22×D411yescharacteristic
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—21no—
181C2×D59—44no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—41no—
185C2×D59—84no—
186C2×D59#13512yes—
187C2×D59AGL(1,ℤ/8)12yes—
188C4×C59—21no—
189C4×C59—41no—
190C4×C59—41no—
191C4×C59H(5,𝔽2)11yescharacteristic
192C4×C59H(5,𝔽2)11yescharacteristic
193Dic59—21no—
194Dic59—21no—
195Dic59—41no—
196Dic59—41no—
197Dic59—41no—
198#3188—591nomaximal, Sylow
199C2×C59—41no—
200C2×C59—81no—
201C2×C59—81no—
202C2×C59#53411yescharacteristic
203C2×C59C2×#13511yescharacteristic
204C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
205D59—22no—
206D59—22no—
207D59—81no—
208#525—591no—
209C2×#121—591no—
210#484—591no—
211#482—591no—
212#482—591no—
213#481—591no—
214#466—591no—
215#466—591no—
216#465—591no—
217#465—591no—
218#450—591no—
219#449—591no—
220#449D5911yescharacteristic, complemented
221#447—591no—
222C2×C22⋊C8—591no—
223C59#318811yescharacteristic, complemented, Sylow
224C2×#41C2×D5911yescharacteristic, complemented
225C22×D4—591no—
226C22×D4—1181no—
227C23×C4—591no—
228C2×SD16—591no—
229C2×SD16C2×D5911yescharacteristic, complemented
230C2×D8—591no—
231C2×D8C2×D5911yescharacteristic, complemented
232C22×C8—591no—
233C22×C8—591no—
234#123—1181no—
235C22⋊Q8—591no—
236C22⋊Q8—591no—
237#121—591no—
238#121—591no—
239#121—591no—
240#121—591no—
241#121—591no—
242#121—1181no—
243#121—1181no—
244#121C2×D5911yescharacteristic
245#120—1181no—
246C4×D4—1181no—
247C4×D4—1181no—
248#117—591no—
249C2×C4⋊C4—591no—
250C2×C22⋊C4—1181no—
251#107—591no—
252#107—591no—
253#106—591no—
254#106—591no—
255#103—591no—
256#103C2×D5911yescharacteristic, complemented
257#102—591no—
258#102—591no—
259#102—591no—
260#102—591no—
261#102—591no—
262#102C2×D5911yescharacteristic, complemented
263C22⋊C8—591no—
264C22⋊C8—591no—
265C22⋊C8—591no—
266C22⋊C8C2×D5911yescharacteristic, complemented
267C24—591no—
268C24—1181no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D5911yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—591no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—2361no—
282C2×D4—2361no—
283C2×D4—2364no—
284C2×D4C22×D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—21no—
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—591no—
292C22×C4—1181no—
293C22×C4—2361no—
294C22×C4—2361no—
295C22×C4C22×D5911yescharacteristic
296SD16—41no—
297SD16—2361no—
298D8—41no—
299D8—2361no—
300C2×C8—591no—
301C2×C8—591no—
302C2×C8—2361no—
303C2×C8—2361no—
304C2×C8C22×D5911yescharacteristic
305C2×C8C22×D5911yescharacteristic
306C4⋊C4—591no—
307C4⋊C4—591no—
308C4⋊C4—591no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
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—
322C42—1181no—
323C23—21no—
324C23—21no—
325C23—591no—
326C23—591no—
327C23—1182no—
328C23—1182no—
329C23—1181no—
330C23—2361no—
331C23—2362no—
332C23—2362no—
333C23—2362no—
334C23D4×D5911yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—1181no—
344D4—1181no—
345D4—2362no—
346D4—2362no—
347D4—2362no—
348D4—2362no—
349D4—2362no—
350D4—2362no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—591no—
357C2×C4—591no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—2361no—
366C2×C4—2361no—
367C2×C4—2362no—
368C2×C4—2361no—
369C2×C4D4×D5911yescharacteristic
370C2×C4C23×D5911yescharacteristic
371C8—21no—
372C8—21no—
373C8—1181no—
374C8—1181no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—592no—
385C22—592no—
386C22—1181no—
387C22—1181no—
388C22—1181no—
389C22—1181no—
390C22—4724no—
391C22—2364no—
392C22—2361no—
393C22—2361no—
394C22—2361no—
395C22C2×D4×D5911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—1181no—
400C4—1181no—
401C4—2361no—
402C4—2361no—
403C4—2361no—
404C4#1427377211yescharacteristic
405C4#1427377211yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—1182no—
410C2—1182no—
411C2—4721no—
412C2#1683796211yescharacteristic
413C2#135×D5911yescharacteristic
414C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3188
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16837909C2semidirect
2. #121×D59C2semidirect
3. #16837736C2semidirect
4. #16837727C2semidirect
5. #16837723C2semidirect
6. #16837719C2semidirect
7. #16837637C2semidirect
8. #16837635C2semidirect
9. #16837634C2semidirect
10. #16837628C2semidirect
11. #16837551C2semidirect
12. #16837547C2semidirect
13. #16837534C2semidirect
14. C22⋊C8×D59C2semidirect
15. C59×#449C2semidirect
19. C2×#11745671C22semidirect
20. C2×#11745669C22semidirect
21. C2×C8×D59C22semidirect
22. C2×C8×D59C22semidirect
25. #14273703C22semidirect
32. #14273698C22semidirect
36. #14273686C22semidirect
39. #14273661C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. #14273651C22semidirect
44. #14273649C22semidirect
45. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
52. C2×#41×C59C22semidirect
53. C2×SD16×C59C22semidirect
54. C2×D8×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
220. #449D59semidirect
223. C59#3188semidirect
224. C2×#41C2×D59semidirect
229. C2×SD16C2×D59semidirect
231. C2×D8C2×D59semidirect
256. #103C2×D59semidirect
262. #102C2×D59semidirect
266. C22⋊C8C2×D59semidirect