Finite Group Databasebeta

← #21436244

Subgroups — #21436244

Order 7552.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838102C211yesmaximal, characteristic, complemented
2#16838037C211yesmaximal, characteristic, complemented
3#16837766C211yesmaximal, characteristic, complemented
4#16837724C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837703C211yesmaximal, characteristic, complemented
7#16837652C211yesmaximal, characteristic, complemented
8#16837635C211yesmaximal, characteristic, complemented
9#16837534C211yesmaximal, characteristic, complemented
10#16837534C211yesmaximal, characteristic, complemented
11#16837512C211yesmaximal, characteristic, complemented
12#16837472C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#459C211yesmaximal, characteristic, complemented
16C2×D4×D59—21no—
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic, complemented
21C2×C8×D59C2211yescharacteristic, complemented
22#14273720—21no—
23#14273719C2211yescharacteristic, complemented
24#14273710—21no—
25#14273700—21no—
26#14273698—21no—
27#14273698C2211yescharacteristic
28#14273698C2211yescharacteristic
29#14273698C2211yescharacteristic, complemented
30#14273698C2211yescharacteristic, complemented
31#14273695—21no—
32#14273695—21no—
33C4×D236C2211yescharacteristic
34C4×D236C2211yescharacteristic
35C4×C22⋊D59—21no—
36#14273685C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic, complemented
38#14273661C2211yescharacteristic, complemented
39#14273659C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41#14273649C2211yescharacteristic
42#14273649C2211yescharacteristic
43#14273648C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51#14273638C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic, complemented
53C2×D8×C59C2211yescharacteristic, complemented
54#127×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73D4×D59—22no—
74D4×D59—22no—
75D4×D59—41no—
76D4×D59—41no—
77D4×D59—44no—
78C2×D236D411yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84D8×C59—41no—
85D8×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C42×C59C2311yescharacteristic
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95#11745669—22no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4D411yescharacteristic
99(C2×D59)⋊C4D411yescharacteristic
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123C22×D59C2×D411yescharacteristic
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129D4×C59—21no—
130D4×C59—42no—
131D4×C59—81no—
132C2×C4×C59—21no—
133C2×C4×C59—81no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—42no—
141C22⋊D59—42no—
142C22⋊D59—81no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148D236—22no—
149D236—21no—
150D236#4112yes—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—21no—
155C4×D59—42no—
156C4×D59—81no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
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×C59—41no—
170C22×C59C22×D411yescharacteristic
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—22no—
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—84no—
180C2×D59—84no—
181C2×D59AGL(1,ℤ/8)12yes—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—41no—
185C4×C59C2×#4111yescharacteristic
186C4×C59H(5,𝔽2)11yescharacteristic
187Dic59—21no—
188Dic59—21no—
189Dic59—41no—
190Dic59—41no—
191Dic59—41no—
192#3318—591nomaximal, Sylow
193C2×C59—81no—
194C2×C59—81no—
195C2×C59—81no—
196C2×C59#54611yescharacteristic
197C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C59#57611yescharacteristic
199D59—22no—
200D59—41no—
201D59—42no—
202#553—591no—
203D42—591no—
204#490—591no—
205#482—591no—
206#481—591no—
207#478—591no—
208#469—591no—
209#466—591no—
210#459D5911yescharacteristic, complemented
211#447—591no—
212#447—591no—
213#442—591no—
214#435—591no—
215#418—591no—
216C2×#102—591no—
217C59#331811yescharacteristic, complemented, Sylow
218C22×D4—591no—
219C22×D4—591no—
220C22×D4—1181no—
221C2×D8—591no—
222C2×D8C2×D5911yescharacteristic, complemented
223C2×D8C2×D5911yescharacteristic, complemented
224C2×M16—591no—
225C22×C8—591no—
226#127C2×D5911yescharacteristic
227#126—1181no—
228#125—591no—
229#123—1181no—
230#121—591no—
231#121—591no—
232#121—591no—
233#121—591no—
234#121—1181no—
235#121—1181no—
236#120—1181no—
237#120—1181no—
238C4×D4—591no—
239C4×D4—591no—
240C4×D4—1181no—
241C4×D4C2×D5911yescharacteristic, complemented
242#117—591no—
243C2×C4⋊C4—591no—
244#107—591no—
245#106—591no—
246#106—591no—
247C4⋊C8C2×D5911yescharacteristic, complemented
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102C2×D5911yescharacteristic, complemented
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8—591no—
260#97—591no—
261C24—1181no—
262C24—1181no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—591no—
266C2×D4—591no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1182no—
270C2×D4—1182no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—2361no—
276C2×D4—2361no—
277C2×D4—2364no—
278C2×D4C22×D5911yescharacteristic
279C2×D4C22×D5911yescharacteristic
280C2×D4C22×D5911yescharacteristic
281C22×C4—21no—
282C22×C4—591no—
283C22×C4—591no—
284C22×C4—1181no—
285C22×C4—1181no—
286D8—41no—
287D8—41no—
288D8—1182no—
289M16—2361no—
290C2×C8—591no—
291C2×C8—591no—
292C2×C8—2361no—
293C2×C8C22×D5911yescharacteristic
294C2×C8C22×D5911yescharacteristic
295C4⋊C4—591no—
296C4⋊C4—591no—
297C4⋊C4—591no—
298C4⋊C4—591no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4—1181no—
302C4⋊C4C22×D5911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—591no—
305C22⋊C4—591no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C42—1181no—
313C42C22×D5911yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—591no—
318C23—591no—
319C23—1181no—
320C23—4721no—
321C23—4721no—
322C23—2362no—
323C23—2362no—
324C23—2362no—
325C23—2362no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—592no—
335D4—1182no—
336D4—1181no—
337D4—4721no—
338D4—2362no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—591no—
346C2×C4—591no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—4721no—
355C2×C4—2362no—
356C2×C4D4×D5911yescharacteristic
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—592no—
373C22—1181no—
374C22—1181no—
375C22—1181no—
376C22—1181no—
377C22—1181no—
378C22—1182no—
379C22—4724no—
380C22—4724no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—1181no—
388C4—1181no—
389C4—2361no—
390C4—2361no—
391C4—2361no—
392C4#41×D5911yescharacteristic
393C4#1427377211yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—1182no—
398C2—2361no—
399C2—2362no—
400C2#1683804911yescharacteristic
401C2AGL(1,ℤ/8)×D5911yescharacteristic
402C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3318
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838102C2semidirect
2. #16838037C2semidirect
3. #16837766C2semidirect
4. #16837724C2semidirect
5. #16837719C2semidirect
6. #16837703C2semidirect
7. #16837652C2semidirect
8. #16837635C2semidirect
9. #16837534C2semidirect
10. #16837534C2semidirect
11. #16837512C2semidirect
12. #16837472C2semidirect
13. #16837405C2semidirect
14. #102×D59C2semidirect
15. C59×#459C2semidirect
20. C2×#11745659C22semidirect
21. C2×C8×D59C22semidirect
23. #14273719C22semidirect
29. #14273698C22semidirect
30. #14273698C22semidirect
36. #14273685C22semidirect
37. C4⋊C4×D59C22semidirect
38. #14273661C22semidirect
39. #14273659C22semidirect
40. #14273658C22semidirect
43. #14273648C22semidirect
44. #14273648C22semidirect
45. #14273648C22semidirect
46. #14273648C22semidirect
47. #14273648C22semidirect
49. (C2×D59)⋊C8C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. #14273638C22semidirect
52. C2×D8×C59C22semidirect
53. C2×D8×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #102×C59C22semidirect
58. #102×C59C22semidirect
210. #459D59semidirect
217. C59#3318semidirect
222. C2×D8C2×D59semidirect
223. C2×D8C2×D59semidirect
241. C4×D4C2×D59semidirect
247. C4⋊C8C2×D59semidirect
256. #102C2×D59semidirect
257. #102C2×D59semidirect