Finite Group Databasebeta

← #21436320

Subgroups — #21436320

Order 7552.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838123C211yesmaximal, characteristic, complemented
2D4×C22⋊D59C211yesmaximal, characteristic
3#16837747C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837725C211yesmaximal, characteristic, complemented
6#16837680C211yesmaximal, characteristic, complemented
7#16837650C211yesmaximal, characteristic, complemented
8#16837645C211yesmaximal, characteristic, complemented
9#16837600C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837407C211yesmaximal, characteristic, complemented
14#16837405C211yesmaximal, characteristic, complemented
15C59×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D59—21no—
17C2×D4×D59C2211yescharacteristic
18C2×#11745671C2211yescharacteristic, complemented
19C2×#11745664C2211yescharacteristic, complemented
20C2×#11745659C2211yescharacteristic, complemented
21#14273726C2211yescharacteristic, complemented
22#14273723C2211yescharacteristic
23#14273722—21no—
24#14273720—21no—
25#14273713—21no—
26#14273703C2211yescharacteristic, complemented
27#14273701C2211yescharacteristic
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273696—21no—
31#14273695—21no—
32Q8×Dic59C2211yescharacteristic, complemented
33#14273692—21no—
34D4×Dic59C2211yescharacteristic
35C4×C22⋊D59C2211yescharacteristic
36#14273686C2211yescharacteristic, complemented
37#14273685C2211yescharacteristic, complemented
38#14273661C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273659C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273648C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic, complemented
55C22⋊Q8×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C24×C59—21no—
60C23×D59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59—22no—
63C2×D4×C59—21no—
64C2×D4×C59—41no—
65C2×D4×C59C2311yescharacteristic
66C2×D4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
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×D236C2311yescharacteristic
79C2×C4×D59C2311yescharacteristic
80C2×Dic118—21no—
81SD16×C59—22no—
82SD16×C59—41no—
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59D411yescharacteristic
92#11745671—41no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108#11745664—41no—
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
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—42no—
120C22×D59—42no—
121C22×D59—81no—
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—42no—
129D4×C59#4112yes—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2411yescharacteristic
136C22⋊D59—22no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—42no—
141C22⋊D59—81no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146C2×Dic59C2×D411yescharacteristic
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149D236—21no—
150D236—21no—
151C4×D59—21no—
152C4×D59—21no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—22no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—84no—
168C22×C59C22×D411yescharacteristic
169C2×D59—21no—
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—84no—
176C4×C59—21no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59C2×#4111yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—21no—
182Dic59—21no—
183Dic59—41no—
184Dic59—41no—
185Dic59—41no—
186Dic59AGL(1,ℤ/8)12yes—
187#3324—591nomaximal, Sylow
188C2×C59—42no—
189C2×C59—41no—
190C2×C59—81no—
191C2×C59#54611yescharacteristic
192C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C59#57711yescharacteristic
194D59—41no—
195D59—81no—
196#556—591no—
197D42—591no—
198#486—591no—
199#482—591no—
200#482—591no—
201#474—591no—
202#468—591no—
203#468—591no—
204#460—591no—
205#450—591no—
206#450D5911yescharacteristic, complemented
207C4×SD16—591no—
208#436—591no—
209#418—591no—
210#418—591no—
211C59#332411yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—1181no—
214C22×D4C2×D5911yescharacteristic
215C2×SD16—591no—
216C2×SD16C2×D5911yescharacteristic
217C2×SD16C2×D5911yescharacteristic, complemented
218C2×M16—591no—
219C2×M16—591no—
220C4⋊Q8—591no—
221#127—591no—
222#126—1181no—
223#126—1181no—
224#124—1181no—
225C22⋊Q8—591no—
226C22⋊Q8C2×D5911yescharacteristic, complemented
227#121—591no—
228#121—591no—
229#121—1181no—
230#120—1181no—
231#120—1181no—
232C4×Q8—591no—
233C4×Q8—1181no—
234C4×D4—591no—
235C4×D4—591no—
236#117—591no—
237#117—591no—
238#107—591no—
239#107—591no—
240#106—591no—
241C4⋊C8—591no—
242#103—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102C2×D5911yescharacteristic
251#102C2×D5911yescharacteristic, complemented
252C22⋊C8—591no—
253C22⋊C8C2×D5911yescharacteristic, complemented
254C4×C8—591no—
255C24—21no—
256C24—1181no—
257C2×Q8—1181no—
258C2×Q8C22×D5911yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1181no—
267C2×D4—1182no—
268C2×D4—1181no—
269C2×D4—1181no—
270C2×D4—2361no—
271C2×D4—2364no—
272C2×D4C22×D5911yescharacteristic
273C2×D4C22×D5911yescharacteristic
274C22×C4—591no—
275C22×C4—1181no—
276C22×C4C22×D5911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—2361no—
280M16—2361no—
281M16—2361no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—591no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4C22×D5911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—591no—
297C22⋊C4—591no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C42—591no—
305C42—1181no—
306C42—1181no—
307C42—1181no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—591no—
314C23—1181no—
315C23—4721no—
316C23—2362no—
317C23—2362no—
318C23D4×D5911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2362no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—1182no—
327D4—1181no—
328D4—1181no—
329D4—4721no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4—2362no—
334D4#1174568712yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—591no—
340C2×C4—591no—
341C2×C4—591no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—2362no—
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—1181no—
365C22—1181no—
366C22—1181no—
367C22—4724no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22C2×D4×D5911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—592no—
376C4—1181no—
377C4—1181no—
378C4—2361no—
379C4—2361no—
380C4—2361no—
381C4C2×#1174568711yescharacteristic
382C4#1427377211yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—4721no—
387C2—2361no—
388C2#1683803911yescharacteristic
389C2AGL(1,ℤ/8)×D5911yescharacteristic
390C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#450C2
socleC22×C59C22×D4
hypercenter#450D59
hypocenterC59#3324
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16838123C2semidirect
3. #16837747C2semidirect
4. #16837727C2semidirect
5. #16837725C2semidirect
6. #16837680C2semidirect
7. #16837650C2semidirect
8. #16837645C2semidirect
9. #16837600C2semidirect
10. #16837551C2semidirect
11. SD16×Dic59C2semidirect
12. #16837477C2semidirect
13. #16837407C2semidirect
14. #16837405C2semidirect
15. C59×#450C2semidirect
18. C2×#11745671C22semidirect
19. C2×#11745664C22semidirect
20. C2×#11745659C22semidirect
21. #14273726C22semidirect
26. #14273703C22semidirect
32. Q8×Dic59C22semidirect
36. #14273686C22semidirect
37. #14273685C22semidirect
38. #14273661C22semidirect
39. #14273660C22semidirect
40. #14273659C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273651C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
47. #14273648C22semidirect
48. #14273648C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
54. C2×SD16×C59C22semidirect
55. C22⋊Q8×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
206. #450D59semidirect
211. C59#3324semidirect
217. C2×SD16C2×D59semidirect
226. C22⋊Q8C2×D59semidirect
251. #102C2×D59semidirect
253. C22⋊C8C2×D59semidirect