Finite Group Databasebeta

← #21434945

Subgroups — #21434945

Order 7552.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837980C211yesmaximal, characteristic, complemented
2#16837968C211yesmaximal, characteristic, complemented
3#16837742C211yesmaximal, characteristic, complemented
4#16837724C211yesmaximal, characteristic, complemented
5#16837718C211yesmaximal, characteristic, complemented
6#16837716C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837645C211yesmaximal, characteristic, complemented
9#16837635C211yesmaximal, characteristic, complemented
10#16837634C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#449C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22#14273723—21no—
23#14273713—21no—
24#14273706—21no—
25#14273703C2211yescharacteristic
26#14273703C2211yescharacteristic, complemented
27#14273702C2211yescharacteristic
28#14273701—21no—
29#14273701C2211yescharacteristic
30#14273699—21no—
31#14273699—21no—
32#14273698C2211yescharacteristic
33#14273698C2211yescharacteristic
34#14273698C2211yescharacteristic, complemented
35#14273697—21no—
36#14273695—21no—
37#14273685C2211yescharacteristic
38C2×C4⋊Dic59C2211yescharacteristic, complemented
39#14273661C2211yescharacteristic, complemented
40#14273661C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×#41×C59C2211yescharacteristic, complemented
53C2×SD16×C59C2211yescharacteristic
54C2×D8×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60#41×C59—41no—
61#41×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59—21no—
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⋊D59D411yescharacteristic
75C2×C22⋊D59D411yescharacteristic
76C22×Dic59—21no—
77D4×D59—41no—
78D4×D59—41no—
79#11745685—41no—
80#11745685—41no—
81C2×D236—21no—
82C2×D236D411yescharacteristic
83C2×D236C2311yescharacteristic
84C2×C4×D59C2311yescharacteristic
85C2×C4×D59C2311yescharacteristic
86C2×Dic118D411yescharacteristic
87SD16×C59—41no—
88D8×C59—41no—
89C2×C8×C59C2311yescharacteristic
90C2×C8×C59C2311yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96#11745671—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)⋊C4—21no—
103C4⋊Dic59—21no—
104C4⋊Dic59C2311yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109C4×Dic59—21no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112#11745659—41no—
113C8×D59—41no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59C2×D411yescharacteristic
117C22×D59—21no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121C22×D59C2×D411yescharacteristic
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×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×C59—21no—
135C2×C4×C59—42no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C22⋊D59—41no—
139C22⋊D59—41no—
140C22⋊D59—42no—
141C22⋊D59—81no—
142C22⋊D59—81no—
143C22⋊D59—81no—
144C22⋊D59—81no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—81no—
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—21no—
152D236—21no—
153D236—41no—
154D236—81no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—21no—
159Dic118—41no—
160C8×C59—21no—
161C8×C59—21no—
162C59⋊C8—21no—
163C59⋊C8—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59C22×D411yescharacteristic
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—84no—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59—41no—
187C4×C59H(5,𝔽2)11yescharacteristic
188C4×C59H(5,𝔽2)11yescharacteristic
189Dic59—21no—
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194#3198—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59—81no—
197C2×C59—81no—
198C2×C59#53411yescharacteristic
199C2×C59#57611yescharacteristic
200C2×C59#57711yescharacteristic
201D59—41no—
202D59—41no—
203D59—81no—
204#537—591no—
205#535—591no—
206#485—591no—
207#482—591no—
208#481—591no—
209#480—591no—
210#469—591no—
211#468—591no—
212#466—591no—
213#465—591no—
214#450—591no—
215#449—591no—
216#449D5911yescharacteristic, complemented
217#447—591no—
218#408—591no—
219C59#319811yescharacteristic, complemented, Sylow
220C2×#41—591no—
221C2×#41C2×D5911yescharacteristic, complemented
222C22×D4—591no—
223C2×SD16—591no—
224C2×SD16C2×D5911yescharacteristic
225C2×D8—591no—
226C2×D8C2×D5911yescharacteristic
227C2×M16—591no—
228C22×C8—591no—
229#127—1181no—
230#124—1181no—
231C22⋊Q8—591no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—591no—
235#121—591no—
236#121—591no—
237#121—591no—
238#121—591no—
239#121—1181no—
240#121—1181no—
241#121—1181no—
242#121C2×D5911yescharacteristic
243#120—1181no—
244#120—1181no—
245#117—591no—
246C2×C4⋊C4—591no—
247#107—591no—
248#107—591no—
249#106—591no—
250#106—591no—
251#103—591no—
252#103C2×D5911yescharacteristic, complemented
253#102—591no—
254#102—591no—
255#102—591no—
256#102—591no—
257#102—591no—
258#102C2×D5911yescharacteristic, complemented
259C22⋊C8—591no—
260C22⋊C8—591no—
261C22⋊C8—591no—
262C22⋊C8C2×D5911yescharacteristic, complemented
263C24—1181no—
264#41—41no—
265#41—41no—
266#41—2361no—
267#41—2361no—
268C2×Q8—591no—
269C2×Q8C22×D5911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—591no—
273C2×D4—591no—
274C2×D4—591no—
275C2×D4—591no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—1181no—
282C2×D4—2361no—
283C2×D4—2361no—
284C2×D4C22×D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—21no—
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—1181no—
290C22×C4C22×D5911yescharacteristic
291SD16—41no—
292SD16—2361no—
293D8—41no—
294D8—2361no—
295M16—2361no—
296C2×C8—591no—
297C2×C8—591no—
298C2×C8—2361no—
299C2×C8C22×D5911yescharacteristic
300C2×C8C22×D5911yescharacteristic
301C4⋊C4—591no—
302C4⋊C4—591no—
303C4⋊C4—591no—
304C4⋊C4—1181no—
305C4⋊C4—1181no—
306C4⋊C4—1181no—
307C4⋊C4C22×D5911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—1181no—
318C23—21no—
319C23—21no—
320C23—591no—
321C23—591no—
322C23—1181no—
323C23—4721no—
324C23—4721no—
325C23—2362no—
326C23D4×D5911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2361no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—1181no—
337D4—1181no—
338D4—4721no—
339D4—4721no—
340D4—4721no—
341D4—4721no—
342D4—4721no—
343D4—2361no—
344D4—2361no—
345D4—2361no—
346D4—2362no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—591no—
353C2×C4—591no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—4721no—
362C2×C4D4×D5911yescharacteristic
363C2×C4C23×D5911yescharacteristic
364C8—21no—
365C8—21no—
366C8—1181no—
367C8—1181no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—1181no—
378C22—1181no—
379C22—1181no—
380C22—1181no—
381C22—1181no—
382C22—1181no—
383C22—4724no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C2×D4×D5911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—1181no—
392C4—1181no—
393C4—2361no—
394C4—2361no—
395C4—2361no—
396C4#1427377211yescharacteristic
397C4#1427377211yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—4721no—
402C2—2361no—
403C2—2361no—
404C2#1683796211yescharacteristic
405C2#1683820411yescharacteristic
406C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#449C2
socleC22×C59C22×D4
hypercenter#449D59
hypocenterC59#3198
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. #16837980C2semidirect
2. #16837968C2semidirect
3. #16837742C2semidirect
4. #16837724C2semidirect
5. #16837718C2semidirect
6. #16837716C2semidirect
7. #16837654C2semidirect
8. #16837645C2semidirect
9. #16837635C2semidirect
10. #16837634C2semidirect
11. #16837551C2semidirect
12. #16837547C2semidirect
13. #16837534C2semidirect
14. #16837367C2semidirect
15. C59×#449C2semidirect
20. C2×#11745659C22semidirect
21. C2×C8×D59C22semidirect
26. #14273703C22semidirect
34. #14273698C22semidirect
38. C2×C4⋊Dic59C22semidirect
39. #14273661C22semidirect
40. #14273661C22semidirect
41. #14273658C22semidirect
42. #14273658C22semidirect
43. #14273651C22semidirect
48. #14273648C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
52. C2×#41×C59C22semidirect
56. #103×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
216. #449D59semidirect
219. C59#3198semidirect
221. C2×#41C2×D59semidirect
252. #103C2×D59semidirect
258. #102C2×D59semidirect
262. C22⋊C8C2×D59semidirect