Finite Group Databasebeta

← #21435097

Subgroups — #21435097

Order 7552.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837956C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic
3#16837795C211yesmaximal, characteristic, complemented
4#16837793C211yesmaximal, characteristic, complemented
5#16837763C211yesmaximal, characteristic, complemented
6#16837760C211yesmaximal, characteristic, complemented
7#16837625C211yesmaximal, characteristic, complemented
8#16837624C211yesmaximal, characteristic, complemented
9#16837621C211yesmaximal, characteristic, complemented
10#16837559C211yesmaximal, characteristic, complemented
11#16837556C211yesmaximal, characteristic, complemented
12#16837554C211yesmaximal, characteristic
13#16837551C211yesmaximal, characteristic
14#16837458C211yesmaximal, characteristic, complemented
15C59×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×Dic236C2211yescharacteristic, complemented
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745660C2211yescharacteristic
22C2×#11745670C2211yescharacteristic
23C2×#11745671C2211yescharacteristic
24#14273726C2211yescharacteristic, complemented
25#14273725C2211yescharacteristic, complemented
26#14273717—21no—
27#14273716C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273714C2211yescharacteristic
30#14273713—21no—
31#14273713—21no—
32#14273707C2211yescharacteristic
33#14273705—21no—
34#14273703C2211yescharacteristic
35C4×Dic118—21no—
36C4×Dic118C2211yescharacteristic, complemented
37#14273684—21no—
38C22⋊C4×D59—21no—
39C22⋊C4×D59—21no—
40C42×D59C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51#14273637C2211yescharacteristic, complemented
52C2×Q16×C59C2211yescharacteristic, complemented
53C2×SD16×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×Q8×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64Q8×D59—41no—
65Q8×D59—41no—
66D4×D59—41no—
67D4×D59—41no—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59D411yescharacteristic
71C2×C4×D59D411yescharacteristic
72C2×C4×D59C2311yescharacteristic
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77Q16×C59—41no—
78SD16×C59—41no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745672—41no—
90#11745672—41no—
91#11745671—41no—
92#11745670—41no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C4×Dic59D411yescharacteristic
108C4×Dic59D411yescharacteristic
109C4×Dic59C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112Dic236—41no—
113#11745660—41no—
114C23×C59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59C2×D411yescharacteristic
120Q8×C59—21no—
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—21no—
124D4×C59—21no—
125D4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2411yescharacteristic
132C22⋊D59—42no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139D236—21no—
140D236—21no—
141C4×D59—22no—
142C4×D59—21no—
143C4×D59—21no—
144C4×D59—41no—
145C4×D59—42no—
146Dic118—21no—
147Dic118—21no—
148Dic118—21no—
149Dic118—21no—
150Dic118—42no—
151Dic118—42no—
152C8×C59—21no—
153C8×C59—21no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59C22×D411yescharacteristic
160C2×D59—21no—
161C2×D59—21no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—84no—
166C2×D59#13712yes—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59H(5,𝔽2)11yescharacteristic
173C4×C59H(5,𝔽2)11yescharacteristic
174Dic59—21no—
175Dic59—21no—
176Dic59—21no—
177Dic59—41no—
178Dic59—41no—
179Dic59—41no—
180#3215—591nomaximal, Sylow
181C2×C59—81no—
182C2×C59#53511yescharacteristic
183C2×C59C2×#13711yescharacteristic
184C2×C59#57511yescharacteristic
185D59—22no—
186D59—81no—
187#533—591no—
188C2×#124—591no—
189#497—591no—
190#497—591no—
191#489—591no—
192#489—591no—
193#464—591no—
194#464—591no—
195#464—591no—
196#464D5911yescharacteristic, complemented
197#451—591no—
198#451—591no—
199#450—591no—
200#450—591no—
201#432—591no—
202C59#321511yescharacteristic, complemented, Sylow
203C22×Q8—591no—
204C22×D4—591no—
205C2×Q16—591no—
206C2×Q16—591no—
207C2×Q16—591no—
208C2×Q16C2×D5911yescharacteristic, complemented
209C2×SD16—591no—
210C2×SD16—591no—
211C2×SD16—591no—
212C2×SD16C2×D5911yescharacteristic
213C4⋊Q8—591no—
214C4⋊Q8—591no—
215#125—1181no—
216#124—591no—
217#124—591no—
218#124—591no—
219#124—1181no—
220#124—1181no—
221#124C2×D5911yescharacteristic
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—1181no—
225C4×Q8—591no—
226C4×Q8—1181no—
227C4×Q8C2×D5911yescharacteristic, complemented
228#117—1181no—
229C2×C22⋊C4—1181no—
230C2×C22⋊C4—1181no—
231C2×C42—591no—
232C4⋊C8—591no—
233C4⋊C8C2×D5911yescharacteristic, complemented
234#103—591no—
235#103—591no—
236#103—591no—
237#103C2×D5911yescharacteristic, complemented
238#102—591no—
239#102—591no—
240#102—591no—
241#102C2×D5911yescharacteristic
242C22⋊C8—591no—
243C22⋊C8—591no—
244#97—591no—
245#97—591no—
246C24—1181no—
247C2×Q8—591no—
248C2×Q8—591no—
249C2×Q8—1181no—
250C2×Q8—1181no—
251C2×Q8—2361no—
252C2×Q8—2361no—
253C2×Q8C22×D5911yescharacteristic
254C2×Q8C22×D5911yescharacteristic
255C2×D4—591no—
256C2×D4—1181no—
257C2×D4—2361no—
258C2×D4—2361no—
259C2×D4C22×D5911yescharacteristic
260C22×C4—591no—
261C22×C4—591no—
262C22×C4—591no—
263C22×C4—1181no—
264Q16—41no—
265Q16—2361no—
266Q16—2361no—
267Q16—2361no—
268SD16—41no—
269SD16—2361no—
270SD16—2361no—
271SD16—2361no—
272C2×C8—591no—
273C2×C8—591no—
274C2×C8C22×D5911yescharacteristic
275C2×C8C22×D5911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—591no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C42—21no—
296C42—591no—
297C42—591no—
298C42—591no—
299C42—1181no—
300C42C22×D5911yescharacteristic
301C23—21no—
302C23—591no—
303C23—1181no—
304C23—2362no—
305C23—2362no—
306C23—2362no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—1181no—
312Q8—1181no—
313Q8—1181no—
314Q8—1181no—
315Q8—2362no—
316Q8—2362no—
317D4—21no—
318D4—21no—
319D4—1181no—
320D4—1181no—
321D4—2362no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—591no—
326C2×C4—591no—
327C2×C4—591no—
328C2×C4—1182no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—2361no—
335C2×C4—2362no—
336C2×C4D4×D5911yescharacteristic
337C2×C4D4×D5911yescharacteristic
338C2×C4C23×D5911yescharacteristic
339C8—21no—
340C8—21no—
341C8—1181no—
342C8—1181no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—592no—
347C22—1181no—
348C22—1181no—
349C22—4724no—
350C22—2361no—
351C22—2361no—
352C22—2361no—
353C22C2×D4×D5911yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—1181no—
360C4—1181no—
361C4—1181no—
362C4—2361no—
363C4—2361no—
364C4—2361no—
365C4#1427377211yescharacteristic
366C4#1427377311yescharacteristic
367C2—81no—
368C2—1182no—
369C2—4721no—
370C2#1683796811yescharacteristic
371C2#137×D5911yescharacteristic
372C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#464C2
socleC22×C59C22×D4
hypercenter#464D59
hypocenterC59#3215
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #16837956C2semidirect
3. #16837795C2semidirect
4. #16837793C2semidirect
5. #16837763C2semidirect
6. #16837760C2semidirect
7. #16837625C2semidirect
8. #16837624C2semidirect
9. #16837621C2semidirect
10. #16837559C2semidirect
11. #16837556C2semidirect
14. #16837458C2semidirect
15. C59×#464C2semidirect
18. C2×Dic236C22semidirect
19. C2×#11745672C22semidirect
20. C2×#11745672C22semidirect
24. #14273726C22semidirect
25. #14273725C22semidirect
36. C4×Dic118C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273651C22semidirect
44. #14273650C22semidirect
50. #14273637C22semidirect
51. #14273637C22semidirect
52. C2×Q16×C59C22semidirect
55. C4×Q8×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
196. #464D59semidirect
202. C59#3215semidirect
208. C2×Q16C2×D59semidirect
227. C4×Q8C2×D59semidirect
233. C4⋊C8C2×D59semidirect
237. #103C2×D59semidirect