Finite Group Databasebeta

← #21436316

Subgroups — #21436316

Order 7552.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838086C211yesmaximal, characteristic, complemented
2#16838046C211yesmaximal, characteristic
3#16837755C211yesmaximal, characteristic, complemented
4#16837744C211yesmaximal, characteristic, complemented
5#16837719C211yesmaximal, characteristic, complemented
6#16837700C211yesmaximal, characteristic, complemented
7#16837658C211yesmaximal, characteristic, complemented
8#16837645C211yesmaximal, characteristic, complemented
9#16837622C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837407C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C59×#450C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745664C2211yescharacteristic
19C2×#11745659C2211yescharacteristic, complemented
20#14273720—21no—
21#14273718C2211yescharacteristic, complemented
22#14273717—21no—
23#14273714C2211yescharacteristic
24#14273709—21no—
25#14273708—21no—
26#14273706C2211yescharacteristic
27#14273703C2211yescharacteristic, complemented
28#14273699—21no—
29#14273698C2211yescharacteristic
30#14273696—21no—
31Q8×Dic59C2211yescharacteristic, complemented
32D4×Dic59C2211yescharacteristic
33C4×C22⋊D59C2211yescharacteristic
34#14273686C2211yescharacteristic
35#14273685—21no—
36C4⋊C4×D59C2211yescharacteristic, complemented
37C2×C22⋊Dic59—21no—
38#14273661C2211yescharacteristic, complemented
39#14273659C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273651C2211yescharacteristic, complemented
45#14273650C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C22×D4×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C22⋊Q8×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C24×C59—21no—
60C2×Q8×C59C2311yescharacteristic
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⋊D59D411yescharacteristic
70C22×Dic59—21no—
71C22×Dic59—21no—
72#11745687—22no—
73#11745687—41no—
74C2×C4×D59—21no—
75C2×C4×D59C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77SD16×C59—22no—
78SD16×C59—41no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59D411yescharacteristic
91#11745672—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4D411yescharacteristic
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107#11745664—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—42no—
114C23×C59—42no—
115C23×C59—81no—
116C23×C59C2×D411yescharacteristic
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—42no—
124D4×C59#4112yes—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—41no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—42no—
139C2×Dic59—81no—
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—42no—
146Dic118—21no—
147Dic118—21no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—22no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—84no—
162C22×C59C22×D411yescharacteristic
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—21no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59H(5,𝔽2)11yescharacteristic
171Dic59—21no—
172Dic59—21no—
173Dic59—21no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178#3323—591nomaximal, Sylow
179C2×C59—41no—
180C2×C59—42no—
181C2×C59—81no—
182C2×C59#54611yescharacteristic
183C2×C59#57511yescharacteristic
184C2×C59#57711yescharacteristic
185D59—41no—
186#552—591no—
187#546—591no—
188#488—591no—
189#485—591no—
190#481—591no—
191#478—591no—
192#470—591no—
193#468—591no—
194#464—591no—
195#452—591no—
196#450D5911yescharacteristic, complemented
197C4×SD16—591no—
198#436—591no—
199#418—591no—
200#417—591no—
201C59#332311yescharacteristic, complemented, Sylow
202C2×#41—591no—
203C22×D4C2×D5911yescharacteristic
204C2×Q16—591no—
205C2×SD16C2×D5911yescharacteristic
206C2×SD16C2×D5911yescharacteristic
207C2×M16—591no—
208C2×M16—591no—
209#126—1181no—
210#125—591no—
211#125—1181no—
212#124—591no—
213#123—1181no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8C2×D5911yescharacteristic
218#121—591no—
219#121—1181no—
220#120—1181no—
221C4×Q8—591no—
222C4×D4—591no—
223C4×D4—591no—
224#117—591no—
225#117—1181no—
226C2×C4⋊C4—591no—
227C2×C22⋊C4—1181no—
228#107—591no—
229#106—591no—
230#106—591no—
231C4⋊C8—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241#102C2×D5911yescharacteristic
242C22⋊C8—591no—
243C22⋊C8C2×D5911yescharacteristic
244C4×C8—591no—
245C24—21no—
246#41—1182no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4C22×D5911yescharacteristic
257C2×D4C22×D5911yescharacteristic
258C22×C4—591no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263Q16—2361no—
264SD16—22no—
265SD16—41no—
266M16—2361no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8C22×D5911yescharacteristic
271C2×C8C22×D5911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—591no—
286C22⋊C4—591no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—591no—
295C42—1181no—
296C42—1181no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—591no—
303C23D4×D5911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—4721no—
313D4—2361no—
314D4—2362no—
315D4#1174568712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—591no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4—2362no—
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—1181no—
349C22—1181no—
350C22—1181no—
351C22C2×D4×D5911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—1181no—
356C4—1181no—
357C4—1181no—
358C4—2361no—
359C4—2361no—
360C4—2361no—
361C4—2361no—
362C4C2×#1174568711yescharacteristic
363C4#1427377211yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—2361no—
368C2#1683803911yescharacteristic
369C2#1683819811yescharacteristic
370C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#450C2
socleC22×C59C22×D4
hypercenter#450D59
hypocenterC59#3323
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. #16838086C2semidirect
3. #16837755C2semidirect
4. #16837744C2semidirect
5. #16837719C2semidirect
6. #16837700C2semidirect
7. #16837658C2semidirect
8. #16837645C2semidirect
9. #16837622C2semidirect
10. #16837561C2semidirect
11. SD16×Dic59C2semidirect
12. #16837477C2semidirect
13. #16837407C2semidirect
14. #16837400C2semidirect
15. C59×#450C2semidirect
17. C2×#11745672C22semidirect
19. C2×#11745659C22semidirect
21. #14273718C22semidirect
27. #14273703C22semidirect
31. Q8×Dic59C22semidirect
36. C4⋊C4×D59C22semidirect
38. #14273661C22semidirect
39. #14273659C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273651C22semidirect
45. #14273650C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
196. #450D59semidirect
201. C59#3323semidirect