Finite Group Databasebeta

← #21436334

Subgroups — #21436334

Order 7552.

460 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#16838115C211yesmaximal, characteristic, complemented
2D4×C22⋊D59C211yesmaximal, characteristic, complemented
3#16837747C211yesmaximal, characteristic, complemented
4#16837726C211yesmaximal, characteristic, complemented
5#16837725C211yesmaximal, characteristic, complemented
6#16837690C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837654C211yesmaximal, characteristic, complemented
9#16837596C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837482C211yesmaximal, characteristic, complemented
13#16837478C211yesmaximal, characteristic, complemented
14#16837405C211yesmaximal, characteristic, complemented
15C59×#418C211yesmaximal, characteristic, complemented
16C22×C22⋊D59—21no—
17C2×D4×D59C2211yescharacteristic
18C2×D472C2211yescharacteristic, complemented
19C2×#11745669C2211yescharacteristic
20C2×#11745669C2211yescharacteristic, complemented
21C2×#11745659C2211yescharacteristic, complemented
22#14273726C2211yescharacteristic, complemented
23#14273723C2211yescharacteristic
24#14273715—21no—
25#14273713—21no—
26#14273702C2211yescharacteristic, complemented
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic, complemented
29#14273700—21no—
30#14273699—21no—
31#14273698C2211yescharacteristic
32#14273696—21no—
33#14273695—21no—
34D4×Dic59C2211yescharacteristic
35#14273689C2211yescharacteristic, complemented
36C4×C22⋊D59C2211yescharacteristic
37#14273685C2211yescharacteristic, complemented
38#14273684—21no—
39#14273660C2211yescharacteristic, complemented
40#14273659C2211yescharacteristic, complemented
41#14273658C2211yescharacteristic, complemented
42Dic59⋊C8C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49C22⋊(C59⋊C8)C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×M16×C59C2211yescharacteristic, complemented
54#117×C59C2211yescharacteristic, complemented
55#102×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic, complemented
59C24×C59—21no—
60C23×D59—21no—
61C2×D4×C59—22no—
62C2×D4×C59—21no—
63C2×D4×C59—41no—
64C2×D4×C59C2311yescharacteristic
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C2×C22⋊D59—21no—
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C2×C22⋊D59—44no—
74C2×C22⋊D59D411yescharacteristic
75C22×Dic59—21no—
76D4×D59—22no—
77D4×D59—41no—
78C2×D236—21no—
79C2×D236C2311yescharacteristic
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×Dic118—21no—
84M16×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C42×C59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59D411yescharacteristic
94#11745669—22no—
95#11745669—41no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4D411yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103C4⋊Dic59C2311yescharacteristic
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110D472—41no—
111#11745659—41no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—42no—
115C23×C59—42no—
116C23×C59—81no—
117C23×C59C2×D411yescharacteristic
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—42no—
121C22×D59—42no—
122C22×D59—81no—
123C22×D59C2×D411yescharacteristic
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—42no—
128D4×C59#4112yes—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—22no—
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—81no—
141C22⋊D59—81no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—42no—
145C2×Dic59C2×D411yescharacteristic
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148D236—21no—
149D236—21no—
150D236—21no—
151D236—21no—
152D236—81no—
153C4×D59—21no—
154C4×D59—21no—
155C4×D59—42no—
156Dic118—81no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—22no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59—84no—
171C22×C59C22×D411yescharacteristic
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—84no—
182C4×C59—21no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59C2×#4111yescharacteristic
186C4×C59H(5,𝔽2)11yescharacteristic
187Dic59—21no—
188Dic59—21no—
189Dic59—41no—
190Dic59—41no—
191Dic59AGL(1,ℤ/8)12yes—
192#3325—591nomaximal, Sylow
193C2×C59—42no—
194C2×C59—41no—
195C2×C59—81no—
196C2×C59#54611yescharacteristic
197C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C59#57611yescharacteristic
199D59—41no—
200D59—81no—
201D59—81no—
202#555—591no—
203D42—591no—
204#486—591no—
205#482—591no—
206#482—591no—
207#476—591no—
208#469—591no—
209#469—591no—
210#459—591no—
211#447—591no—
212#447—591no—
213C4×D8—591no—
214#436—591no—
215#418—591no—
216#418D5911yescharacteristic, complemented
217C59#332511yescharacteristic, complemented, Sylow
218C22×D4—591no—
219C22×D4—1181no—
220C22×D4C2×D5911yescharacteristic
221C2×D8—591no—
222C2×D8—591no—
223C2×D8—591no—
224C2×M16—591no—
225C2×M16C2×D5911yescharacteristic, complemented
226C4⋊Q8—591no—
227#127—591no—
228#124—1181no—
229#124—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—591no—
241#117—591no—
242#117—1181no—
243#117C2×D5911yescharacteristic, complemented
244#107—591no—
245#106—591no—
246#106—591no—
247C4⋊C8—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102C2×D5911yescharacteristic
255#102C2×D5911yescharacteristic
256#102C2×D5911yescharacteristic, complemented
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8—591no—
260C4×C8—591no—
261C24—21no—
262C24—1181no—
263C2×Q8—1181no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—591no—
268C2×D4—591no—
269C2×D4—591no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1182no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—2361no—
279C2×D4—2364no—
280C2×D4C22×D5911yescharacteristic
281C2×D4C22×D5911yescharacteristic
282C22×C4—591no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4C22×D5911yescharacteristic
286D8—1182no—
287D8—2361no—
288D8—2361no—
289M16—41no—
290M16—2361no—
291C2×C8—591no—
292C2×C8—591no—
293C2×C8C22×D5911yescharacteristic
294C2×C8C22×D5911yescharacteristic
295C4⋊C4—591no—
296C4⋊C4—591no—
297C4⋊C4—591no—
298C4⋊C4—1181no—
299C4⋊C4C22×D5911yescharacteristic
300C4⋊C4C22×D5911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—591no—
303C22⋊C4—591no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C42—21no—
312C42—591no—
313C42—1181no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—591no—
320C23—1181no—
321C23—1181no—
322C23—4721no—
323C23—2362no—
324C23—2362no—
325C23D4×D5911yescharacteristic
326Q8—4721no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—1182no—
332D4—1181no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—4721no—
337D4—4721no—
338D4—4721no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343D4#1174568512yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—591no—
349C2×C4—591no—
350C2×C4—591no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22—1181no—
374C22—1181no—
375C22—1181no—
376C22—4724no—
377C22—2361no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—592no—
388C4—1181no—
389C4—1181no—
390C4—2361no—
391C4—2361no—
392C4C2×#1174568511yescharacteristic
393C4#1427377211yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—4721no—
398C2—4721no—
399C2—2361no—
400C2#1683804211yescharacteristic
401C2AGL(1,ℤ/8)×D5911yescharacteristic
402C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#418C2
socleC22×C59C22×D4
hypercenter#418D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16838115C2semidirect
2. D4×C22⋊D59C2semidirect
3. #16837747C2semidirect
4. #16837726C2semidirect
5. #16837725C2semidirect
6. #16837690C2semidirect
7. #16837655C2semidirect
8. #16837654C2semidirect
9. #16837596C2semidirect
10. #16837537C2semidirect
11. #16837536C2semidirect
12. #16837482C2semidirect
13. #16837478C2semidirect
14. #16837405C2semidirect
15. C59×#418C2semidirect
18. C2×D472C22semidirect
20. C2×#11745669C22semidirect
21. C2×#11745659C22semidirect
22. #14273726C22semidirect
26. #14273702C22semidirect
28. #14273701C22semidirect
35. #14273689C22semidirect
37. #14273685C22semidirect
39. #14273660C22semidirect
40. #14273659C22semidirect
41. #14273658C22semidirect
42. Dic59⋊C8C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
46. #14273648C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
49. C22⋊(C59⋊C8)C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
53. C2×M16×C59C22semidirect
54. #117×C59C22semidirect
57. #102×C59C22semidirect
58. #102×C59C22semidirect
216. #418D59semidirect
217. C59#3325semidirect
225. C2×M16C2×D59semidirect
243. #117C2×D59semidirect
256. #102C2×D59semidirect
257. #102C2×D59semidirect