Finite Group Databasebeta

← #21435913

Subgroups — #21435913

Order 7552.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838110C211yesmaximal, characteristic, complemented
2D4×C22⋊D59C211yesmaximal, characteristic
3#16837747C211yesmaximal, characteristic, complemented
4#16837721C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837690C211yesmaximal, characteristic, complemented
7#16837633C211yesmaximal, characteristic, complemented
8#16837628C211yesmaximal, characteristic, complemented
9#16837600C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14273648C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D59—21no—
17C2×D4×D59C2211yescharacteristic
18C2×#11745671C2211yescharacteristic, complemented
19C22×C59⋊C8C2211yescharacteristic, complemented
20C2×C8×D59C2211yescharacteristic, complemented
21#14273726C2211yescharacteristic, complemented
22#14273723C2211yescharacteristic
23#14273717—21no—
24#14273707—21no—
25#14273704—21no—
26#14273703C2211yescharacteristic, complemented
27#14273701C2211yescharacteristic
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273696—21no—
31#14273695—21no—
32Q8×Dic59C2211yescharacteristic, complemented
33D4×Dic59C2211yescharacteristic
34C4×C22⋊D59C2211yescharacteristic
35(C22⋊D59)⋊C4—21no—
36C2×C4⋊Dic59C2211yescharacteristic, complemented
37C4⋊C4×D59C2211yescharacteristic, complemented
38#14273659C2211yescharacteristic, complemented
39#14273659C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, 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—
76C22×Dic59—21no—
77D4×D59—22no—
78D4×D59—41no—
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59C2311yescharacteristic
82C2×Dic118—21no—
83SD16×C59—22no—
84SD16×C59—41no—
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C4⋊C4×C59—21no—
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92C22⋊Dic59D411yescharacteristic
93#11745671—41no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4D411yescharacteristic
106C4×Dic59—21no—
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8—41no—
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C8×D59—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—42no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C22⋊D59—81no—
141C22⋊D59SD1614yescomplemented
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146C2×Dic59—81no—
147C2×Dic59C2×D411yescharacteristic
148C2×Dic59C2×D411yescharacteristic
149C2×Dic59C2×D411yescharacteristic
150D236—21no—
151D236—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—81no—
155Dic118—81no—
156C8×C59—21no—
157C8×C59—21no—
158C59⋊C8—21no—
159C59⋊C8—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—22no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—84no—
169C22×C59C2×SD1612yes—
170C22×C59C22×D411yescharacteristic
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—84no—
177C2×D59C2×SD1612yes—
178C4×C59—21no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59C2×#4111yescharacteristic
182C4×C59H(5,𝔽2)11yescharacteristic
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187Dic59—41no—
188Dic59C2×SD1612yes—
189#3295—591nomaximal, Sylow
190C2×C59—22no—
191C2×C59—42no—
192C2×C59—81no—
193C2×C59#54611yescharacteristic
194C2×C59C22×SD1611yescharacteristic
195C2×C59#57611yescharacteristic
196D59—22no—
197D59—81no—
198#554—591no—
199D42—591no—
200#486—591no—
201#481—591no—
202#481—591no—
203#476—591no—
204#465—591no—
205#465—591no—
206#460—591no—
207#450—591no—
208#450D5911yescharacteristic, complemented
209C4×SD16—591no—
210C8×D4—591no—
211C2×#102—591no—
212C2×#102—591no—
213C59#329511yescharacteristic, complemented, Sylow
214C22×D4—591no—
215C22×D4—1181no—
216C22×D4C2×D5911yescharacteristic
217C2×SD16—591no—
218C2×SD16C2×D5911yescharacteristic
219C2×SD16C2×D5911yescharacteristic, complemented
220C22×C8—591no—
221C22×C8—591no—
222C4⋊Q8—591no—
223#127—591no—
224#125—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—1181no—
227C22⋊Q8—1181no—
228C22⋊Q8C2×D5911yescharacteristic, complemented
229#121—591no—
230#121—591no—
231#121—1181no—
232#120—1181no—
233#120—1181no—
234C4×Q8—591no—
235C4×D4—591no—
236C4×D4—591no—
237C4×D4—1181no—
238C2×C4⋊C4—591no—
239C2×C4⋊C4—591no—
240#106—591no—
241#106—591no—
242#106—591no—
243C4⋊C8—591no—
244#103—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102C2×D5911yescharacteristic
253#102C2×D5911yescharacteristic, complemented
254C22⋊C8—591no—
255C22⋊C8C2×D5911yescharacteristic, complemented
256C4×C8—591no—
257C24—21no—
258C24—1181no—
259C2×Q8—1181no—
260C2×Q8C22×D5911yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—591no—
265C2×D4—591no—
266C2×D4—1181no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—1182no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—2361no—
273C2×D4—2364no—
274C2×D4C22×D5911yescharacteristic
275C2×D4C22×D5911yescharacteristic
276C22×C4—591no—
277C22×C4—1181no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4C22×D5911yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—2361no—
284C2×C8—591no—
285C2×C8—591no—
286C2×C8—2361no—
287C2×C8—2361no—
288C2×C8C22×D5911yescharacteristic
289C2×C8C22×D5911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—591no—
292C4⋊C4—591no—
293C4⋊C4—591no—
294C4⋊C4—591no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C4⋊C4—1181no—
298C4⋊C4—1181no—
299C4⋊C4—1181no—
300C4⋊C4C22×D5911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—591no—
303C22⋊C4—591no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C42—591no—
309C42—1181no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—591no—
316C23—1181no—
317C23—4721no—
318C23—2362no—
319C23—2362no—
320C23D4×D5911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—4721no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—594no—
329D4—1181no—
330D4—1181no—
331D4—4721no—
332D4—2362no—
333D4—2362no—
334D4—2362no—
335D4—2362no—
336D4#1174568712yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—591no—
342C2×C4—591no—
343C2×C4—591no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—4721no—
350C2×C4—4721no—
351C2×C4—2362no—
352C2×C4D4×D5911yescharacteristic
353C2×C4C23×D5911yescharacteristic
354C8—21no—
355C8—21no—
356C8—1181no—
357C8—1181no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—592no—
368C22—1181no—
369C22—1181no—
370C22—4724no—
371C22—2361no—
372C22—2361no—
373C22—2361no—
374C22SD16×D5912yes—
375C22C2×D4×D5911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—592no—
380C4—1181no—
381C4—1181no—
382C4—2361no—
383C4—2361no—
384C4—2361no—
385C4C2×#1174568711yescharacteristic
386C4#1427377211yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—1182no—
391C2—4721no—
392C2#1683803911yescharacteristic
393C2C2×SD16×D5911yescharacteristic
394C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#450C2
socleC22×C59C22×D4
hypercenter#450D59
hypocenterC59#3295
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. #16838110C2semidirect
3. #16837747C2semidirect
4. #16837721C2semidirect
5. #16837719C2semidirect
6. #16837690C2semidirect
7. #16837633C2semidirect
8. #16837628C2semidirect
9. #16837600C2semidirect
10. #16837551C2semidirect
11. SD16×Dic59C2semidirect
12. (C22⋊D59)⋊C8C2semidirect
13. C2×#14273648C2semidirect
14. #102×D59C2semidirect
15. C59×#450C2semidirect
18. C2×#11745671C22semidirect
19. C22×C59⋊C8C22semidirect
20. C2×C8×D59C22semidirect
21. #14273726C22semidirect
26. #14273703C22semidirect
32. Q8×Dic59C22semidirect
36. C2×C4⋊Dic59C22semidirect
37. C4⋊C4×D59C22semidirect
38. #14273659C22semidirect
39. #14273659C22semidirect
40. #14273658C22semidirect
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
141. C22⋊D59SD16semidirect
208. #450D59semidirect
213. C59#3295semidirect
219. C2×SD16C2×D59semidirect
228. C22⋊Q8C2×D59semidirect
253. #102C2×D59semidirect
255. C22⋊C8C2×D59semidirect