Finite Group Databasebeta

← #21435930

Subgroups — #21435930

Order 7552.

408 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#16838090C211yesmaximal, characteristic, complemented
2#16838045C211yesmaximal, characteristic
3#16837731C211yesmaximal, characteristic, complemented
4#16837725C211yesmaximal, characteristic, complemented
5#16837699C211yesmaximal, characteristic, complemented
6#16837642C211yesmaximal, characteristic, complemented
7#16837630C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837567C211yesmaximal, characteristic, complemented
10#16837554C211yesmaximal, characteristic, complemented
11C4×#11745660C211yesmaximal, characteristic, complemented
12C8×D236C211yesmaximal, characteristic, complemented
13#16837397C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#488C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic, complemented
19C2×#11745660C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22C2×C8×D59C2211yescharacteristic, complemented
23#14273722—21no—
24#14273718—21no—
25#14273712—21no—
26#14273709—21no—
27#14273707C2211yescharacteristic
28#14273707C2211yescharacteristic, complemented
29#14273703C2211yescharacteristic
30#14273700—21no—
31#14273698C2211yescharacteristic
32#14273697—21no—
33C4×Dic118C2211yescharacteristic, complemented
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic
36#14273685—21no—
37#14273685C2211yescharacteristic, complemented
38C4⋊C4×D59C2211yescharacteristic
39C22⋊C4×D59—21no—
40#14273660C2211yescharacteristic, complemented
41#14273659C2211yescharacteristic, complemented
42#14273658C2211yescharacteristic, complemented
43C4⋊(C59⋊C8)C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273651C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52#125×C59C2211yescharacteristic, complemented
53#124×C59C2211yescharacteristic
54#103×C59C2211yescharacteristic, complemented
55#103×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64#11745689—22no—
65#11745689—41no—
66D4×D59—22no—
67D4×D59—41no—
68C2×D236—21no—
69C2×D236D411yescharacteristic
70C2×D236C2311yescharacteristic
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59C2311yescharacteristic
75C2×C4×D59C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59C2311yescharacteristic
86C22⋊Dic59—21no—
87#11745672—41no—
88#11745670—41no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59D411yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
109C8×D59—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59—21no—
113C22×D59—42no—
114C22×D59—42no—
115C22×D59—81no—
116C22×D59C2×D411yescharacteristic
117C22×D59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2411yescharacteristic
128C22⋊D59—42no—
129C22⋊D59—81no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—22no—
136D236—21no—
137D236—42no—
138D236#4112yes—
139C4×D59—21no—
140C4×D59—21no—
141C4×D59—21no—
142C4×D59—21no—
143C4×D59—42no—
144C4×D59—42no—
145C4×D59—81no—
146Dic118—21no—
147Dic118—21no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—22no—
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—84no—
165C2×D59#13512yes—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59C2×#4111yescharacteristic
172C4×C59H(5,𝔽2)11yescharacteristic
173Dic59—21no—
174Dic59—21no—
175Dic59—41no—
176Dic59—41no—
177Dic59—41no—
178#3296—591nomaximal, Sylow
179C2×C59—81no—
180C2×C59#54611yescharacteristic
181C2×C59C2×#13511yescharacteristic
182C2×C59#57711yescharacteristic
183D59—22no—
184D59—41no—
185D59—42no—
186#552—591no—
187#546—591no—
188#488D5911yescharacteristic, complemented
189#483—591no—
190#482—591no—
191#478—591no—
192#467—591no—
193#465—591no—
194#464—591no—
195#452—591no—
196#450—591no—
197C4×SD16—591no—
198C8×D4—591no—
199#416—591no—
200C2×#102—591no—
201C59#329611yescharacteristic, complemented, Sylow
202C2×#41—591no—
203C22×D4—591no—
204C2×Q16—591no—
205C2×SD16—591no—
206C2×SD16—591no—
207C22×C8—591no—
208C22×C8—591no—
209#126—1181no—
210#125—1181no—
211#125C2×D5911yescharacteristic, complemented
212#124C2×D5911yescharacteristic
213#123—1181no—
214#123—1181no—
215C22⋊Q8—591no—
216C22⋊Q8—591no—
217C22⋊Q8—591no—
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#103C2×D5911yescharacteristic, complemented
235#103C2×D5911yescharacteristic, complemented
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102C2×D5911yescharacteristic
241#102C2×D5911yescharacteristic
242C22⋊C8—591no—
243C22⋊C8—591no—
244C4×C8C2×D5911yescharacteristic, complemented
245C24—1181no—
246#41—1182no—
247#41—2361no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—591no—
251C2×D4—591no—
252C2×D4—1181no—
253C2×D4—1181no—
254C2×D4—1182no—
255C2×D4—1181no—
256C2×D4—2361no—
257C2×D4C22×D5911yescharacteristic
258C22×C4—591no—
259C22×C4—591no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263Q16—2361no—
264SD16—1182no—
265SD16—2361no—
266C2×C8—591no—
267C2×C8—591no—
268C2×C8—2361no—
269C2×C8—2361no—
270C2×C8C22×D5911yescharacteristic
271C2×C8C22×D5911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
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⋊C4C22×D5911yescharacteristic
283C4⋊C4C22×D5911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—591no—
287C22⋊C4—591no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C42—1181no—
295C42—1181no—
296C42C22×D5911yescharacteristic
297C23—21no—
298C23—591no—
299C23—591no—
300C23—1181no—
301C23—4721no—
302C23—2362no—
303C23—2362no—
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—21no—
309D4—21no—
310D4—592no—
311D4—1182no—
312D4—1181no—
313D4—4721no—
314D4—2362no—
315D4—2362no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—591no—
320C2×C4—591no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—4721no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4D4×D5911yescharacteristic
333C2×C4C23×D5911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1181no—
337C8—1181no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—592no—
342C22—1181no—
343C22—1181no—
344C22—1181no—
345C22—1181no—
346C22—1181no—
347C22—1182no—
348C22—4724no—
349C22—2361no—
350C22—2361no—
351C22C2×D4×D5911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1181no—
358C4—1181no—
359C4—2361no—
360C4—2361no—
361C4—2361no—
362C4#41×D5911yescharacteristic
363C4#1427377311yescharacteristic
364C2—81no—
365C2—1182no—
366C2—2361no—
367C2—2362no—
368C2#1683804511yescharacteristic
369C2#135×D5911yescharacteristic
370C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#488C2
socleC22×C59C22×D4
hypercenter#488D59
hypocenterC59#3296
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16838090C2semidirect
3. #16837731C2semidirect
4. #16837725C2semidirect
5. #16837699C2semidirect
6. #16837642C2semidirect
7. #16837630C2semidirect
8. #16837621C2semidirect
9. #16837567C2semidirect
10. #16837554C2semidirect
11. C4×#11745660C2semidirect
12. C8×D236C2semidirect
13. #16837397C2semidirect
14. #102×D59C2semidirect
15. C59×#488C2semidirect
18. C2×#11745672C22semidirect
22. C2×C8×D59C22semidirect
28. #14273707C22semidirect
33. C4×Dic118C22semidirect
37. #14273685C22semidirect
40. #14273660C22semidirect
41. #14273659C22semidirect
42. #14273658C22semidirect
43. C4⋊(C59⋊C8)C22semidirect
44. #14273652C22semidirect
45. #14273651C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. #125×C59C22semidirect
54. #103×C59C22semidirect
55. #103×C59C22semidirect
58. C4×C8×C59C22semidirect
188. #488D59semidirect
201. C59#3296semidirect
211. #125C2×D59semidirect
234. #103C2×D59semidirect
235. #103C2×D59semidirect
244. C4×C8C2×D59semidirect