Finite Group Databasebeta

← #21435062

Subgroups — #21435062

Order 7552.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837937C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic, complemented
3#16837786C211yesmaximal, characteristic, complemented
4#16837784C211yesmaximal, characteristic, complemented
5#16837759C211yesmaximal, characteristic, complemented
6#16837627C211yesmaximal, characteristic, complemented
7#16837623C211yesmaximal, characteristic, complemented
8#16837620C211yesmaximal, characteristic, complemented
9#16837616C211yesmaximal, characteristic, complemented
10#16837559C211yesmaximal, characteristic, complemented
11#16837554C211yesmaximal, characteristic, complemented
12#16837542C211yesmaximal, characteristic, complemented
13#16837537C211yesmaximal, characteristic
14#16837453C211yesmaximal, characteristic, complemented
15C59×#488C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×Dic236C2211yescharacteristic, complemented
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745660C2211yescharacteristic
21C2×#11745660C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic
23C2×#11745671C2211yescharacteristic, complemented
24C2×D472C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26#14273722—21no—
27#14273716C2211yescharacteristic
28#14273715C2211yescharacteristic
29#14273715C2211yescharacteristic, complemented
30#14273714C2211yescharacteristic
31#14273713—21no—
32#14273713—21no—
33#14273712—21no—
34#14273707C2211yescharacteristic
35#14273702C2211yescharacteristic
36#14273692C2211yescharacteristic, complemented
37#14273689—21no—
38#14273689C2211yescharacteristic, complemented
39#14273685—21no—
40C22⋊C4×D59—21no—
41C22⋊C4×D59—21no—
42C42×D59C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic, complemented
44Dic59⋊C8C2211yescharacteristic, complemented
45#14273650C2211yescharacteristic, complemented
46#14273650C2211yescharacteristic, complemented
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C4×C59⋊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—
63Q8×D59—41no—
64Q8×D59—41no—
65D4×D59—41no—
66D4×D59—41no—
67C2×D236—21no—
68C2×D236C2311yescharacteristic
69C2×D236C2311yescharacteristic
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59D411yescharacteristic
73C2×C4×D59D411yescharacteristic
74C2×C4×D59C2311yescharacteristic
75C2×Dic118—21no—
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745672—41no—
90#11745671—41no—
91#11745670—41no—
92#11745669—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—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102C4⋊Dic59—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59D411yescharacteristic
106C4×Dic59D411yescharacteristic
107C4×Dic59C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110Dic236—41no—
111D472—41no—
112#11745660—41no—
113#11745660—41no—
114C23×C59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—42no—
120C22×D59C2×D411yescharacteristic
121Q8×C59—21no—
122Q8×C59—21no—
123D4×C59—21no—
124D4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—42no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59C2×D411yescharacteristic
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137D236—21no—
138D236—21no—
139D236—21no—
140D236—21no—
141D236—42no—
142C4×D59—22no—
143C4×D59—21no—
144C4×D59—21no—
145C4×D59—41no—
146C4×D59—42no—
147C4×D59—42no—
148Dic118—21no—
149Dic118—21no—
150Dic118—21no—
151Dic118—21no—
152Dic118—42no—
153C8×C59—21no—
154C8×C59—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59C22×D411yescharacteristic
161C2×D59—21no—
162C2×D59—21no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—84no—
170C2×D59#13512yes—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59H(5,𝔽2)11yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—21no—
179Dic59—21no—
180Dic59—21no—
181Dic59—41no—
182Dic59—41no—
183#3211—591nomaximal, Sylow
184C2×C59—81no—
185C2×C59#53511yescharacteristic
186C2×C59C2×#13511yescharacteristic
187C2×C59#57511yescharacteristic
188D59—22no—
189D59—81no—
190D59—81no—
191#529—591no—
192C2×#124—591no—
193#495—591no—
194#495—591no—
195#488—591no—
196#488D5911yescharacteristic, complemented
197#464—591no—
198#464—591no—
199#463—591no—
200#463—591no—
201#451—591no—
202#450—591no—
203#448—591no—
204#447—591no—
205#431—591no—
206C59#321111yescharacteristic, complemented, Sylow
207C22×Q8—591no—
208C22×D4—591no—
209C2×Q16—591no—
210C2×Q16—591no—
211C2×SD16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×SD16—591no—
215C2×D8—591no—
216C2×D8—591no—
217#126—1181no—
218#125C2×D5911yescharacteristic, complemented
219#124—591no—
220#124—591no—
221#124—591no—
222#124—591no—
223#124—1181no—
224#124—1181no—
225#124C2×D5911yescharacteristic
226#123—1181no—
227C22⋊Q8—591no—
228#121—591no—
229C4×Q8—591no—
230C4×D4—591no—
231C4×D4—1181no—
232#117—1181no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1181no—
235C2×C42—591no—
236C4⋊C8—591no—
237C4⋊C8—591no—
238#103—591no—
239#103—591no—
240#103C2×D5911yescharacteristic, complemented
241#103C2×D5911yescharacteristic, complemented
242#102—591no—
243#102—591no—
244#102C2×D5911yescharacteristic
245#102C2×D5911yescharacteristic
246C22⋊C8—591no—
247C22⋊C8—591no—
248C4×C8—591no—
249C4×C8C2×D5911yescharacteristic, complemented
250C24—1181no—
251C2×Q8—591no—
252C2×Q8—591no—
253C2×Q8—1181no—
254C2×Q8—2361no—
255C2×Q8—2361no—
256C2×Q8C22×D5911yescharacteristic
257C2×D4—591no—
258C2×D4—591no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—2361no—
262C2×D4—2361no—
263C2×D4C22×D5911yescharacteristic
264C22×C4—591no—
265C22×C4—591no—
266C22×C4—591no—
267C22×C4—1181no—
268C22×C4—1181no—
269Q16—2361no—
270Q16—2361no—
271SD16—2361no—
272SD16—2361no—
273SD16—2361no—
274SD16—2361no—
275D8—2361no—
276D8—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4C22×D5911yescharacteristic
286C4⋊C4C22×D5911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C42—591no—
301C42—591no—
302C42—591no—
303C42—1181no—
304C42C22×D5911yescharacteristic
305C23—21no—
306C23—591no—
307C23—1181no—
308C23—1181no—
309C23—2362no—
310C23—2362no—
311C23—2362no—
312Q8—21no—
313Q8—21no—
314Q8—1181no—
315Q8—1181no—
316Q8—1181no—
317Q8—1181no—
318Q8—2362no—
319D4—21no—
320D4—21no—
321D4—1181no—
322D4—1181no—
323D4—1181no—
324D4—1181no—
325D4—2362no—
326D4—2362no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—591no—
331C2×C4—591no—
332C2×C4—591no—
333C2×C4—1182no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—2361no—
339C2×C4—2362no—
340C2×C4—2362no—
341C2×C4D4×D5911yescharacteristic
342C2×C4D4×D5911yescharacteristic
343C2×C4C23×D5911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1181no—
347C8—1181no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—592no—
352C22—1181no—
353C22—1181no—
354C22—4724no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C2×D4×D5911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1181no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4#1427377311yescharacteristic
373C4#1427377311yescharacteristic
374C2—81no—
375C2—1182no—
376C2—4721no—
377C2—4721no—
378C2#1683797011yescharacteristic
379C2#135×D5911yescharacteristic
380C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#488C2
socleC22×C59C22×D4
hypercenter#488D59
hypocenterC59#3211
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. #16837937C2semidirect
2. #124×D59C2semidirect
3. #16837786C2semidirect
4. #16837784C2semidirect
5. #16837759C2semidirect
6. #16837627C2semidirect
7. #16837623C2semidirect
8. #16837620C2semidirect
9. #16837616C2semidirect
10. #16837559C2semidirect
11. #16837554C2semidirect
12. #16837542C2semidirect
14. #16837453C2semidirect
15. C59×#488C2semidirect
18. C2×Dic236C22semidirect
19. C2×#11745672C22semidirect
21. C2×#11745660C22semidirect
23. C2×#11745671C22semidirect
29. #14273715C22semidirect
36. #14273692C22semidirect
38. #14273689C22semidirect
43. Dic59⋊C8C22semidirect
44. Dic59⋊C8C22semidirect
45. #14273650C22semidirect
46. #14273650C22semidirect
51. C4×C59⋊C8C22semidirect
52. #125×C59C22semidirect
54. #103×C59C22semidirect
55. #103×C59C22semidirect
58. C4×C8×C59C22semidirect
196. #488D59semidirect
206. C59#3211semidirect
218. #125C2×D59semidirect
240. #103C2×D59semidirect
241. #103C2×D59semidirect
249. C4×C8C2×D59semidirect