Finite Group Databasebeta

← #21434449

Subgroups — #21434449

Order 7552.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838032C211yesmaximal, characteristic, complemented
2#16837970C211yesmaximal, characteristic
3#16837768C211yesmaximal, characteristic, complemented
4#16837765C211yesmaximal, characteristic, complemented
5#16837763C211yesmaximal, characteristic, complemented
6#16837761C211yesmaximal, characteristic, complemented
7#16837758C211yesmaximal, characteristic, complemented
8#16837749C211yesmaximal, characteristic, complemented
9#16837747C211yesmaximal, characteristic, complemented
10#16837405C211yesmaximal, characteristic, complemented
11#16837402C211yesmaximal, characteristic, complemented
12#16837397C211yesmaximal, characteristic, complemented
13#102×D59C211yesmaximal, characteristic, complemented
14#16837356C211yesmaximal, characteristic, complemented
15C59×#488C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273727C2211yescharacteristic, complemented
21#14273726—21no—
22#14273726C2211yescharacteristic, complemented
23#14273724C2211yescharacteristic
24#14273723C2211yescharacteristic
25#14273718C2211yescharacteristic, complemented
26#14273717—21no—
27#14273716C2211yescharacteristic
28#14273707—21no—
29#14273705—21no—
30#14273700—21no—
31#14273700—21no—
32#14273697—21no—
33#14273697—21no—
34#14273685C2211yescharacteristic
35#14273684C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37#14273651C2211yescharacteristic, complemented
38#14273651C2211yescharacteristic, complemented
39#14273649C2211yescharacteristic
40#14273649C2211yescharacteristic
41#14273649C2211yescharacteristic, complemented
42#14273649C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, 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—
64C2×C22⋊D59—21no—
65#11745689—22no—
66#11745689—22no—
67D4×D59—22no—
68D4×D59—22no—
69C2×D236—21no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236C2311yescharacteristic
73C2×D236C2311yescharacteristic
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×Dic118—21no—
78C2×Dic118—21no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C42×C59C2311yescharacteristic
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4D411yescharacteristic
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—42no—
112C22×D59—81no—
113C22×D59—81no—
114C22×D59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59—21no—
117D4×C59—21no—
118D4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—42no—
126C22⋊D59—81no—
127C22⋊D59—81no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59C2×D411yescharacteristic
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—21no—
134D236—21no—
135D236—21no—
136D236—21no—
137D236—42no—
138D236—81no—
139D236—81no—
140C4×D59—42no—
141C4×D59—81no—
142C4×D59#4112yes—
143C4×D59#4112yes—
144Dic118—81no—
145Dic118—81no—
146C8×C59—21no—
147C8×C59—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59C22×D411yescharacteristic
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—84no—
163C2×D59#12412yes—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59C2×#4111yescharacteristic
170C4×C59C2×#4111yescharacteristic
171Dic59—21no—
172Dic59—21no—
173Dic59—41no—
174Dic59—41no—
175Dic59#12412yes—
176#3136—591nomaximal, Sylow
177C2×C59—81no—
178C2×C59C2×#12411yescharacteristic
179C2×C59#57611yescharacteristic
180C2×C59#57711yescharacteristic
181D59—22no—
182D59—81no—
183D59—81no—
184#544—591no—
185#535—591no—
186#490—591no—
187#490—591no—
188#489—591no—
189#489—591no—
190#488—591no—
191#488D5911yescharacteristic, complemented
192#486—591no—
193#486—591no—
194#418—591no—
195#417—591no—
196#416—591no—
197C2×#102—591no—
198#405—591no—
199C59#313611yescharacteristic, complemented, Sylow
200C2×#41—591no—
201C22×D4—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—591no—
205C4⋊Q8—591no—
206C4⋊Q8—1181no—
207#127—591no—
208#127—591no—
209#125—591no—
210#125—1181no—
211#125C2×D5911yescharacteristic, complemented
212#124—591no—
213#124C2×D5911yescharacteristic
214C22⋊Q8—1181no—
215C22⋊Q8—1181no—
216#121—1181no—
217#121—1181no—
218#120—1181no—
219#120—1181no—
220#117—591no—
221#117—591no—
222C2×C4⋊C4—591no—
223#103—591no—
224#103—591no—
225#103C2×D5911yescharacteristic, complemented
226#103C2×D5911yescharacteristic, complemented
227#102—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#102—591no—
235#102—591no—
236#102—591no—
237#102C2×D5911yescharacteristic
238#102C2×D5911yescharacteristic
239#97—591no—
240#97—591no—
241C4×C8—591no—
242C4×C8C2×D5911yescharacteristic, complemented
243C24—1181no—
244#41—1182no—
245#41—1182no—
246C2×Q8—1181no—
247C2×Q8—1181no—
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—591no—
251C2×D4—1181no—
252C2×D4—1182no—
253C2×D4—1182no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4C22×D5911yescharacteristic
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4—1181no—
263M16—1182no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8—1182no—
267C2×C8C22×D5911yescharacteristic
268C2×C8C22×D5911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—591no—
272C4⋊C4—591no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4C22×D5911yescharacteristic
281C4⋊C4C22×D5911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—591no—
285C22⋊C4—591no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C42—591no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—21no—
293C23—591no—
294C23—1181no—
295C23—1181no—
296C23—4721no—
297C23—4721no—
298C23—2362no—
299Q8—21no—
300Q8—21no—
301Q8—4721no—
302Q8—4721no—
303D4—21no—
304D4—21no—
305D4—1181no—
306D4—1181no—
307D4—1181no—
308D4—1181no—
309D4—4721no—
310D4—4721no—
311D4—4721no—
312D4—4721no—
313D4—2362no—
314D4—2362no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—591no—
319C2×C4—592no—
320C2×C4—592no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—4721no—
326C2×C4—2362no—
327C2×C4D4×D5911yescharacteristic
328C2×C4D4×D5911yescharacteristic
329C2×C4C23×D5911yescharacteristic
330C8—21no—
331C8—21no—
332C8—1181no—
333C8—1181no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—592no—
338C22—1181no—
339C22—1181no—
340C22—4724no—
341C22—2361no—
342C22—2361no—
343C22—2361no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22C2×D4×D5911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—592no—
354C4—1181no—
355C4—1181no—
356C4—2361no—
357C4—2361no—
358C4#41×D5911yescharacteristic
359C4#41×D5911yescharacteristic
360C2—81no—
361C2—1182no—
362C2—4721no—
363C2—4721no—
364C2#124×D5911yescharacteristic
365C2#1683820411yescharacteristic
366C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#488C2
socleC22×C59C22×D4
hypercenter#488D59
hypocenterC59#3136
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. #16838032C2semidirect
3. #16837768C2semidirect
4. #16837765C2semidirect
5. #16837763C2semidirect
6. #16837761C2semidirect
7. #16837758C2semidirect
8. #16837749C2semidirect
9. #16837747C2semidirect
10. #16837405C2semidirect
11. #16837402C2semidirect
12. #16837397C2semidirect
13. #102×D59C2semidirect
14. #16837356C2semidirect
15. C59×#488C2semidirect
20. #14273727C22semidirect
22. #14273726C22semidirect
25. #14273718C22semidirect
37. #14273651C22semidirect
38. #14273651C22semidirect
41. #14273649C22semidirect
42. #14273649C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
49. #14273638C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
52. #125×C59C22semidirect
54. #103×C59C22semidirect
55. #103×C59C22semidirect
58. C4×C8×C59C22semidirect
191. #488D59semidirect
199. C59#3136semidirect
211. #125C2×D59semidirect
225. #103C2×D59semidirect
226. #103C2×D59semidirect
242. C4×C8C2×D59semidirect