Finite Group Databasebeta

← #21435081

Subgroups — #21435081

Order 7552.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837949C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic, complemented
3#16837790C211yesmaximal, characteristic, complemented
4#16837788C211yesmaximal, characteristic, complemented
5#16837763C211yesmaximal, characteristic, complemented
6#16837760C211yesmaximal, characteristic, complemented
7#16837618C211yesmaximal, characteristic, complemented
8#16837617C211yesmaximal, characteristic, complemented
9#16837614C211yesmaximal, characteristic, complemented
10#16837542C211yesmaximal, characteristic, complemented
11#16837539C211yesmaximal, characteristic, complemented
12#16837537C211yesmaximal, characteristic, complemented
13#16837534C211yesmaximal, characteristic, complemented
14#16837458C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×Q8×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745660C2211yescharacteristic, complemented
20C2×#11745670C2211yescharacteristic, complemented
21C2×#11745671C2211yescharacteristic, complemented
22C2×D472C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25#14273726C2211yescharacteristic, complemented
26#14273723C2211yescharacteristic, complemented
27#14273716C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273714C2211yescharacteristic
30#14273713—21no—
31#14273713—21no—
32#14273713—21no—
33#14273702C2211yescharacteristic
34#14273700—21no—
35#14273698C2211yescharacteristic
36C4×D236C2211yescharacteristic, complemented
37C4×C22⋊D59—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×SD16×C59C2211yescharacteristic, complemented
53C2×D8×C59C2211yescharacteristic
54#124×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic, complemented
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#102×C59C2211yescharacteristic
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68Q8×D59—41no—
69Q8×D59—41no—
70D4×D59—41no—
71D4×D59—41no—
72#11745685—44no—
73C2×D236—21no—
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59D411yescharacteristic
79C2×C4×D59D411yescharacteristic
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×Dic118—21no—
83C2×Dic118C2311yescharacteristic
84SD16×C59—41no—
85D8×C59—41no—
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96#11745671—41no—
97#11745670—41no—
98#11745669—41no—
99#11745669—41no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106C4⋊Dic59C2311yescharacteristic
107Dic59⋊C4—21no—
108C4×Dic59D411yescharacteristic
109C4×Dic59D411yescharacteristic
110C4×Dic59C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113D472—41no—
114#11745660—41no—
115C23×C59—21no—
116C23×C59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—42no—
121C22×D59—42no—
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—42no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—42no—
136C22⋊D59—42no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—21no—
145D236—21no—
146D236—21no—
147D236—21no—
148D236—42no—
149C4×D59—22no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—41no—
153C4×D59—42no—
154C4×D59—42no—
155Dic118—21no—
156Dic118—21no—
157Dic118—42no—
158Dic118—42no—
159C8×C59—21no—
160C8×C59—21no—
161C59⋊C8—21no—
162C59⋊C8—21no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59C22×D411yescharacteristic
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—84no—
179C2×D59AGL(1,ℤ/8)12yes—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59H(5,𝔽2)11yescharacteristic
185C4×C59H(5,𝔽2)11yescharacteristic
186Dic59—21no—
187Dic59—21no—
188Dic59—21no—
189Dic59—41no—
190Dic59—41no—
191#3213—591nomaximal, Sylow
192C2×C59—81no—
193C2×C59—81no—
194C2×C59#53511yescharacteristic
195C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C59#57511yescharacteristic
197D59—22no—
198D59—81no—
199D59—81no—
200#532—591no—
201C2×#124—591no—
202#496—591no—
203#496—591no—
204#489—591no—
205#489—591no—
206#463—591no—
207#463—591no—
208#463—591no—
209#463D5911yescharacteristic, complemented
210#448—591no—
211#448—591no—
212#447—591no—
213#447—591no—
214#432—591no—
215C59#321311yescharacteristic, complemented, Sylow
216C2×#41—1181no—
217C22×Q8—591no—
218C22×D4—591no—
219C2×SD16—591no—
220C2×SD16—591no—
221C2×SD16—591no—
222C2×SD16C2×D5911yescharacteristic, complemented
223C2×D8—591no—
224C2×D8—591no—
225C2×D8—591no—
226C2×D8C2×D5911yescharacteristic
227C4⋊Q8—591no—
228#127—591no—
229#124—591no—
230#124—591no—
231#124—591no—
232#124—1181no—
233#124—1181no—
234#124—1181no—
235#124C2×D5911yescharacteristic
236#121—591no—
237#121—591no—
238#121—1181no—
239C4×D4—591no—
240C4×D4—1181no—
241C4×D4C2×D5911yescharacteristic, complemented
242C2×C22⋊C4—1181no—
243C2×C22⋊C4—1181no—
244C2×C42—591no—
245C4⋊C8—591no—
246C4⋊C8C2×D5911yescharacteristic, complemented
247#103—591no—
248#103—591no—
249#103—591no—
250#103C2×D5911yescharacteristic, complemented
251#102—591no—
252#102—591no—
253#102—591no—
254#102C2×D5911yescharacteristic
255C22⋊C8—591no—
256C22⋊C8—591no—
257#97—591no—
258#97—591no—
259C24—1181no—
260#41—2364no—
261C2×Q8—591no—
262C2×Q8—1181no—
263C2×Q8—1181no—
264C2×Q8—2361no—
265C2×Q8—2361no—
266C2×Q8C22×D5911yescharacteristic
267C2×D4—591no—
268C2×D4—591no—
269C2×D4—1181no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—2361no—
275C2×D4—2361no—
276C2×D4C22×D5911yescharacteristic
277C2×D4C22×D5911yescharacteristic
278C22×C4—21no—
279C22×C4—591no—
280C22×C4—591no—
281C22×C4—591no—
282C22×C4—1181no—
283C22×C4—1181no—
284SD16—41no—
285SD16—2361no—
286SD16—2361no—
287SD16—2361no—
288D8—41no—
289D8—2361no—
290D8—2361no—
291D8—2361no—
292C2×C8—591no—
293C2×C8—591no—
294C2×C8C22×D5911yescharacteristic
295C2×C8C22×D5911yescharacteristic
296C4⋊C4—591no—
297C4⋊C4—1181no—
298C4⋊C4C22×D5911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C42—591no—
312C42—591no—
313C42—591no—
314C42C22×D5911yescharacteristic
315C23—21no—
316C23—21no—
317C23—591no—
318C23—1181no—
319C23—1181no—
320C23—2362no—
321C23—2362no—
322C23—2362no—
323Q8—21no—
324Q8—21no—
325Q8—1181no—
326Q8—1181no—
327Q8—2362no—
328Q8—2362no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—1181no—
337D4—2362no—
338D4—2362no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—591no—
346C2×C4—591no—
347C2×C4—591no—
348C2×C4—1182no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—2361no—
354C2×C4—2362no—
355C2×C4—2362no—
356C2×C4D4×D5911yescharacteristic
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—592no—
370C22—1181no—
371C22—1181no—
372C22—4724no—
373C22—2361no—
374C22—2361no—
375C22—2361no—
376C22—2361no—
377C22—2361no—
378C22—2361no—
379C22C2×D4×D5911yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—1181no—
385C4—1181no—
386C4—1181no—
387C4—2361no—
388C4—2361no—
389C4#1427377211yescharacteristic
390C4#1427377311yescharacteristic
391C2—81no—
392C2—81no—
393C2—1182no—
394C2—4721no—
395C2—4721no—
396C2#1683796811yescharacteristic
397C2AGL(1,ℤ/8)×D5911yescharacteristic
398C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3213
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16837949C2semidirect
2. #124×D59C2semidirect
3. #16837790C2semidirect
4. #16837788C2semidirect
5. #16837763C2semidirect
6. #16837760C2semidirect
7. #16837618C2semidirect
8. #16837617C2semidirect
9. #16837614C2semidirect
10. #16837542C2semidirect
11. #16837539C2semidirect
12. #16837537C2semidirect
13. #16837534C2semidirect
14. #16837458C2semidirect
15. C59×#463C2semidirect
19. C2×#11745660C22semidirect
20. C2×#11745670C22semidirect
21. C2×#11745671C22semidirect
25. #14273726C22semidirect
26. #14273723C22semidirect
36. C4×D236C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273651C22semidirect
44. #14273650C22semidirect
50. #14273637C22semidirect
51. #14273637C22semidirect
52. C2×SD16×C59C22semidirect
55. C4×D4×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
209. #463D59semidirect
215. C59#3213semidirect
222. C2×SD16C2×D59semidirect
241. C4×D4C2×D59semidirect
246. C4⋊C8C2×D59semidirect
250. #103C2×D59semidirect