Finite Group Databasebeta

← #21436336

Subgroups — #21436336

Order 7552.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838115C211yesmaximal, characteristic, complemented
2#16838036C211yesmaximal, characteristic, complemented
3#16837747C211yesmaximal, characteristic, complemented
4#16837729C211yesmaximal, characteristic, complemented
5#16837691C211yesmaximal, characteristic, complemented
6#16837656C211yesmaximal, characteristic, complemented
7#16837653C211yesmaximal, characteristic, complemented
8#16837596C211yesmaximal, characteristic, complemented
9#16837538C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11#16837484C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837406C211yesmaximal, characteristic, complemented
14#16837405C211yesmaximal, characteristic, complemented
15C59×#482C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C2×D4×D59—21no—
18C2×D4×D59C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic, complemented
21C2×#11745669C2211yescharacteristic, complemented
22C2×#11745664C2211yescharacteristic, complemented
23C2×#11745659C2211yescharacteristic, complemented
24#14273726C2211yescharacteristic, complemented
25#14273723C2211yescharacteristic
26#14273715—21no—
27#14273713—21no—
28#14273702C2211yescharacteristic
29#14273702C2211yescharacteristic, complemented
30#14273701C2211yescharacteristic, complemented
31#14273700—21no—
32#14273700—21no—
33#14273697—21no—
34#14273695—21no—
35#14273689C2211yescharacteristic
36#14273689C2211yescharacteristic, complemented
37C4×C22⋊D59C2211yescharacteristic
38#14273685C2211yescharacteristic, complemented
39#14273684—21no—
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273649C2211yescharacteristic
43#14273649C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic, complemented
48#14273647C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53#117×C59C2211yescharacteristic, complemented
54#107×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×D4×C59—21no—
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59D411yescharacteristic
69D4×D59—22no—
70D4×D59—41no—
71D4×D59—44no—
72C2×D236—22no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—41no—
77C2×D236C2311yescharacteristic
78C2×D236C2311yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×Dic118—21no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C42×C59—21no—
92C22⋊Dic59D411yescharacteristic
93#11745669—41no—
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—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59C2311yescharacteristic
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—22no—
110D472—41no—
111#11745659—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59—42no—
121C22×D59—81no—
122C22×D59—81no—
123C22×D59C2×D411yescharacteristic
124D4×C59—21no—
125D4×C59—21no—
126D4×C59—42no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—22no—
135C22⋊D59—42no—
136C22⋊D59—42no—
137C22⋊D59—81no—
138C22⋊D59—81no—
139C2×Dic59—21no—
140C2×Dic59C2×D411yescharacteristic
141C2×Dic59C2×D411yescharacteristic
142C2×Dic59C2×D411yescharacteristic
143D236—21no—
144D236—21no—
145D236—21no—
146D236—21no—
147D236—21no—
148D236—42no—
149D236—42no—
150D236—81no—
151D236#4112yes—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—42no—
155C4×D59—42no—
156Dic118—81no—
157C8×C59—21no—
158C8×C59—21no—
159C59⋊C8—21no—
160C59⋊C8—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—41no—
165C22×C59—41no—
166C22×C59—41no—
167C22×C59C22×D411yescharacteristic
168C2×D59—21no—
169C2×D59—22no—
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—41no—
179C2×D59—41no—
180C2×D59—84no—
181C2×D59—84no—
182C4×C59—21no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59C2×#4111yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—21no—
189Dic59—21no—
190Dic59—41no—
191Dic59AGL(1,ℤ/8)12yes—
192#3325—591nomaximal, Sylow
193C2×C59—41no—
194C2×C59—81no—
195C2×C59#54611yescharacteristic
196C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C59#57611yescharacteristic
198D59—41no—
199D59—42no—
200D59—81no—
201D59—81no—
202#555—591no—
203D42—591no—
204#486—591no—
205#482—591no—
206#482D5911yescharacteristic, complemented
207#476—591no—
208#469—591no—
209#469—591no—
210#459—591no—
211#447—591no—
212#447—591no—
213C4×D8—591no—
214#436—591no—
215#418—591no—
216#418—591no—
217C59#332511yescharacteristic, complemented, Sylow
218C22×D4—591no—
219C22×D4—591no—
220C22×D4—1181no—
221C2×D8—591no—
222C2×D8—591no—
223C2×D8—591no—
224C2×M16—591no—
225C2×M16—591no—
226C4⋊Q8—591no—
227#127—591no—
228#124—1181no—
229#124—1181no—
230#121—591no—
231#121—591no—
232#121—591no—
233#121—1181no—
234#121—1181no—
235#121C2×D5911yescharacteristic
236#120—1181no—
237#120—1181no—
238C4×D4—591no—
239C4×D4—591no—
240C4×D4—591no—
241#117—591no—
242#117—1181no—
243#117C2×D5911yescharacteristic, complemented
244#107C2×D5911yescharacteristic, complemented
245#106—591no—
246#106C2×D5911yescharacteristic, complemented
247C4⋊C8—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102—591no—
252#102—591no—
253#102—591no—
254#102—591no—
255#102—591no—
256#102C2×D5911yescharacteristic, complemented
257#102C2×D5911yescharacteristic, complemented
258C22⋊C8—591no—
259C22⋊C8C2×D5911yescharacteristic, complemented
260C4×C8—591no—
261C24—1181no—
262C24—1181no—
263C2×Q8—1181no—
264C2×D4—21no—
265C2×D4—591no—
266C2×D4—591no—
267C2×D4—591no—
268C2×D4—591no—
269C2×D4—1182no—
270C2×D4—1181no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1182no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4—2361no—
279C2×D4—2361no—
280C2×D4—2364no—
281C2×D4C22×D5911yescharacteristic
282C22×C4—591no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4C22×D5911yescharacteristic
286D8—1182no—
287D8—2361no—
288D8—2361no—
289M16—2361no—
290M16—2361no—
291C2×C8—591no—
292C2×C8—591no—
293C2×C8C22×D5911yescharacteristic
294C2×C8C22×D5911yescharacteristic
295C4⋊C4—591no—
296C4⋊C4—591no—
297C4⋊C4—1181no—
298C4⋊C4C22×D5911yescharacteristic
299C4⋊C4C22×D5911yescharacteristic
300C4⋊C4C22×D5911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—591no—
304C22⋊C4—591no—
305C22⋊C4—1181no—
306C22⋊C4—1181no—
307C22⋊C4—1181no—
308C22⋊C4—1181no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C42—21no—
312C42—591no—
313C42—1181no—
314C23—21no—
315C23—591no—
316C23—1181no—
317C23—1181no—
318C23—1181no—
319C23—4721no—
320C23—4721no—
321C23—2362no—
322C23—2362no—
323C23—2362no—
324C23—2362no—
325C23D4×D5911yescharacteristic
326Q8—4721no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—592no—
331D4—1182no—
332D4—1181no—
333D4—1181no—
334D4—1181no—
335D4—1181no—
336D4—1181no—
337D4—4721no—
338D4—4721no—
339D4—4721no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343D4—2362no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—591no—
350C2×C4—591no—
351C2×C4—591no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4D4×D5911yescharacteristic
358C2×C4C23×D5911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1181no—
362C8—1181no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—1181no—
370C22—1181no—
371C22—1181no—
372C22—1182no—
373C22—4724no—
374C22—4724no—
375C22—2361no—
376C22—2361no—
377C22—2361no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—592no—
389C4—1181no—
390C4—1181no—
391C4—2361no—
392C4#41×D5911yescharacteristic
393C4#1427377311yescharacteristic
394C2—41no—
395C2—81no—
396C2—4721no—
397C2—4721no—
398C2—2361no—
399C2—2362no—
400C2#1683804411yescharacteristic
401C2AGL(1,ℤ/8)×D5911yescharacteristic
402C2#1683820411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#482C2
socleC22×C59C22×D4
hypercenter#482D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16838115C2semidirect
2. #16838036C2semidirect
3. #16837747C2semidirect
4. #16837729C2semidirect
5. #16837691C2semidirect
6. #16837656C2semidirect
7. #16837653C2semidirect
8. #16837596C2semidirect
9. #16837538C2semidirect
10. #16837537C2semidirect
11. #16837484C2semidirect
12. #16837477C2semidirect
13. #16837406C2semidirect
14. #16837405C2semidirect
15. C59×#482C2semidirect
20. C2×D472C22semidirect
21. C2×#11745669C22semidirect
22. C2×#11745664C22semidirect
23. C2×#11745659C22semidirect
24. #14273726C22semidirect
29. #14273702C22semidirect
30. #14273701C22semidirect
36. #14273689C22semidirect
38. #14273685C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
43. #14273649C22semidirect
44. #14273648C22semidirect
47. #14273647C22semidirect
48. #14273647C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. C8×Dic59C22semidirect
53. #117×C59C22semidirect
54. #107×C59C22semidirect
55. #106×C59C22semidirect
56. #102×C59C22semidirect
57. #102×C59C22semidirect
58. C22⋊C8×C59C22semidirect
206. #482D59semidirect
217. C59#3325semidirect
243. #117C2×D59semidirect
244. #107C2×D59semidirect
246. #106C2×D59semidirect
256. #102C2×D59semidirect
257. #102C2×D59semidirect
259. C22⋊C8C2×D59semidirect