Finite Group Databasebeta

← #21435185

Subgroups — #21435185

Order 7552.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838021C211yesmaximal, characteristic, complemented
2#16837965C211yesmaximal, characteristic, complemented
3#16837784C211yesmaximal, characteristic, complemented
4#16837762C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837622C211yesmaximal, characteristic, complemented
7#16837615C211yesmaximal, characteristic, complemented
8#16837600C211yesmaximal, characteristic, complemented
9#16837595C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837544C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837464C211yesmaximal, characteristic, complemented
15C59×#496C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745671C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22#14273727C2211yescharacteristic, complemented
23#14273723C2211yescharacteristic
24#14273720—21no—
25#14273715C2211yescharacteristic
26#14273714C2211yescharacteristic
27#14273713—21no—
28#14273711—21no—
29#14273704—21no—
30#14273703C2211yescharacteristic
31#14273699—21no—
32#14273699—21no—
33#14273698C2211yescharacteristic
34#14273695—21no—
35#14273695—21no—
36Q8×Dic59C2211yescharacteristic, complemented
37D4×Dic59C2211yescharacteristic, complemented
38#14273684C2211yescharacteristic
39Dic59⋊C8C2211yescharacteristic, complemented
40Dic59⋊C8C2211yescharacteristic, complemented
41#14273652C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic
44#14273649C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C4×C59⋊C8C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic, complemented
54C2×D8×C59C2211yescharacteristic
55C2×D8×C59C2211yescharacteristic, complemented
56#127×C59C2211yescharacteristic
57#124×C59C2211yescharacteristic, complemented
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73#11745687—41no—
74#11745687—41no—
75D4×D59—41no—
76D4×D59—41no—
77C2×D236C2311yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×Dic118—21no—
80C2×Dic118C2311yescharacteristic
81SD16×C59—41no—
82SD16×C59—41no—
83D8×C59—41no—
84D8×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C42×C59C2311yescharacteristic
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94#11745672—41no—
95#11745671—41no—
96#11745670—41no—
97#11745669—41no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4D411yescharacteristic
102(C2×D59)⋊C4D411yescharacteristic
103C4⋊Dic59—21no—
104C4⋊Dic59—21no—
105C4⋊Dic59C2311yescharacteristic
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108Dic59⋊C4D411yescharacteristic
109Dic59⋊C4D411yescharacteristic
110C4×Dic59—21no—
111C4×Dic59C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C22×D59—21no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121C22×D59C2×D411yescharacteristic
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—81no—
131D4×C59—81no—
132C2×C4×C59—21no—
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—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—42no—
145C2×Dic59—81no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149D236—21no—
150D236—21no—
151C4×D59—21no—
152C4×D59—21no—
153Dic118—21no—
154Dic118—21no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59C22×D411yescharacteristic
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—84no—
177C4×C59—21no—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59H(5,𝔽2)11yescharacteristic
181C4×C59H(5,𝔽2)11yescharacteristic
182Dic59—21no—
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188#3224—591nomaximal, Sylow
189C2×C59—81no—
190C2×C59—81no—
191C2×C59—81no—
192C2×C59#53511yescharacteristic
193C2×C59#57611yescharacteristic
194C2×C59#57711yescharacteristic
195D59—41no—
196D59—81no—
197#542—591no—
198#535—591no—
199#496D5911yescharacteristic, complemented
200#495—591no—
201#489—591no—
202#486—591no—
203#464—591no—
204#463—591no—
205#460—591no—
206#459—591no—
207#452—591no—
208#450—591no—
209#449—591no—
210#447—591no—
211#433—591no—
212C59#322411yescharacteristic, complemented, Sylow
213C2×#41—591no—
214C22×D4—591no—
215C2×Q16—591no—
216C2×SD16—591no—
217C2×SD16—591no—
218C2×SD16C2×D5911yescharacteristic
219C2×SD16C2×D5911yescharacteristic, complemented
220C2×D8—591no—
221C2×D8C2×D5911yescharacteristic
222C2×D8C2×D5911yescharacteristic, complemented
223C4⋊Q8—591no—
224#127—591no—
225#127C2×D5911yescharacteristic
226#126—1181no—
227#124—591no—
228#124—591no—
229#124—1181no—
230#124C2×D5911yescharacteristic, complemented
231#123—1181no—
232C22⋊Q8—591no—
233C22⋊Q8—1181no—
234#121—591no—
235#121—1181no—
236#121—1181no—
237#120—1181no—
238#120—1181no—
239C4×Q8—591no—
240C4×D4—591no—
241#117—591no—
242C4⋊C8—591no—
243C4⋊C8—591no—
244#103—591no—
245#103—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97C2×D5911yescharacteristic, complemented
255C4×C8—591no—
256C24—1181no—
257#41—2361no—
258#41—2361no—
259C2×Q8—591no—
260C2×Q8—1181no—
261C2×Q8C22×D5911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—591no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—2361no—
271C2×D4—2361no—
272C2×D4C22×D5911yescharacteristic
273C2×D4C22×D5911yescharacteristic
274C2×D4C22×D5911yescharacteristic
275C22×C4—591no—
276C22×C4—1181no—
277C22×C4—1181no—
278Q16—2361no—
279SD16—41no—
280SD16—41no—
281SD16—2361no—
282SD16—2361no—
283D8—41no—
284D8—41no—
285D8—2361no—
286C2×C8—591no—
287C2×C8—591no—
288C2×C8C22×D5911yescharacteristic
289C2×C8C22×D5911yescharacteristic
290C4⋊C4—591no—
291C4⋊C4—591no—
292C4⋊C4—591no—
293C4⋊C4—591no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—591no—
300C22⋊C4—591no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C42—591no—
309C42—1181no—
310C42C22×D5911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—591no—
315C23—1181no—
316C23—4721no—
317C23—4721no—
318C23—2362no—
319Q8—21no—
320Q8—21no—
321Q8—1181no—
322Q8—1181no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—1181no—
333D4—1181no—
334D4—4721no—
335D4—4721no—
336D4—4721no—
337D4—2362no—
338D4—2362no—
339C2×C4—21no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—591no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—4721no—
349C2×C4—2362no—
350C2×C4D4×D5911yescharacteristic
351C2×C4D4×D5911yescharacteristic
352C2×C4C23×D5911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1181no—
356C8—1181no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—1181no—
367C22—1181no—
368C22—1181no—
369C22—4724no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22C2×D4×D5911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1181no—
378C4—1181no—
379C4—1181no—
380C4—2361no—
381C4—2361no—
382C4—2361no—
383C4#1427377211yescharacteristic
384C4#1427377211yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—4721no—
389C2—2361no—
390C2#1683796511yescharacteristic
391C2#1683820611yescharacteristic
392C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16838021C2semidirect
2. #16837965C2semidirect
3. #16837784C2semidirect
4. #16837762C2semidirect
5. #16837748C2semidirect
6. #16837622C2semidirect
7. #16837615C2semidirect
8. #16837600C2semidirect
9. #16837595C2semidirect
10. #16837561C2semidirect
11. #16837551C2semidirect
12. #16837544C2semidirect
13. #16837534C2semidirect
14. #16837464C2semidirect
15. C59×#496C2semidirect
18. C2×#11745672C22semidirect
19. C2×#11745670C22semidirect
22. #14273727C22semidirect
36. Q8×Dic59C22semidirect
37. D4×Dic59C22semidirect
39. Dic59⋊C8C22semidirect
40. Dic59⋊C8C22semidirect
41. #14273652C22semidirect
42. #14273652C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
51. C4×C59⋊C8C22semidirect
53. C2×SD16×C59C22semidirect
55. C2×D8×C59C22semidirect
57. #124×C59C22semidirect
58. #97×C59C22semidirect
199. #496D59semidirect
212. C59#3224semidirect
219. C2×SD16C2×D59semidirect
222. C2×D8C2×D59semidirect
230. #124C2×D59semidirect
254. #97C2×D59semidirect