Finite Group Databasebeta

← #21436060

Subgroups — #21436060

Order 7552.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838053C211yesmaximal, characteristic, complemented
2#16838049C211yesmaximal, characteristic, complemented
3#16837760C211yesmaximal, characteristic, complemented
4#16837734C211yesmaximal, characteristic, complemented
5#16837691C211yesmaximal, characteristic, complemented
6#16837653C211yesmaximal, characteristic, complemented
7#16837632C211yesmaximal, characteristic, complemented
8#16837616C211yesmaximal, characteristic, complemented
9#16837549C211yesmaximal, characteristic, complemented
10#16837537C211yesmaximal, characteristic, complemented
11#16837513C211yesmaximal, characteristic, complemented
12#16837476C211yesmaximal, characteristic, complemented
13#16837401C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#481C211yesmaximal, characteristic, complemented
16C2×#11745685—21no—
17C2×#11745685C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745660C2211yescharacteristic, complemented
20C2×D472C2211yescharacteristic
21C2×#11745669C2211yescharacteristic
22C2×#11745664C2211yescharacteristic, complemented
23C2×C8×D59C2211yescharacteristic
24#14273726C2211yescharacteristic, complemented
25#14273714C2211yescharacteristic
26#14273712—21no—
27#14273710—21no—
28#14273709—21no—
29#14273707C2211yescharacteristic
30#14273705—21no—
31#14273702C2211yescharacteristic
32#14273701C2211yescharacteristic, complemented
33#14273698—21no—
34#14273695—21no—
35#14273689C2211yescharacteristic
36#14273689C2211yescharacteristic, complemented
37C4×C22⋊D59C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic
39C22⋊C4×D59—21no—
40#14273658C2211yescharacteristic, complemented
41Dic59⋊C8C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic, complemented
52#121×C59C2211yescharacteristic
53C2×C4⋊C4×C59C2211yescharacteristic, complemented
54#106×C59C2211yescharacteristic, complemented
55#106×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59—21no—
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59D411yescharacteristic
68D4×D59—22no—
69D4×D59—41no—
70#11745685—22no—
71#11745685—41no—
72#11745685—44no—
73C2×D236—21no—
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59C2311yescharacteristic
81C2×Dic118—21no—
82C2×Dic118C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C2×C8×C59C2311yescharacteristic
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91C22⋊Dic59—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)⋊C4D411yescharacteristic
100C4⋊Dic59—21no—
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4D411yescharacteristic
105C4×Dic59C2311yescharacteristic
106#11745664—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—22no—
110#11745660—41no—
111C8×D59—41no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—81no—
119C22×D59C2×D411yescharacteristic
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—81no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—42no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2411yescharacteristic
131C22⋊D59—22no—
132C22⋊D59—42no—
133C22⋊D59—42no—
134C22⋊D59—42no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—21no—
141D236—21no—
142D236—21no—
143D236—42no—
144D236#4112yescomplemented
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—42no—
148C4×D59—42no—
149C4×D59—42no—
150C4×D59—81no—
151Dic118—21no—
152Dic118—21no—
153Dic118—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—22no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—84no—
174C2×D59AGL(1,ℤ/8)12yes—
175C4×C59—21no—
176C4×C59—41no—
177C4×C59—41no—
178C4×C59—41no—
179C4×C59C2×#4111yescharacteristic
180C4×C59H(5,𝔽2)11yescharacteristic
181Dic59—21no—
182Dic59—21no—
183Dic59—21no—
184Dic59—41no—
185Dic59—41no—
186#3306—591nomaximal, Sylow
187C2×C59—41no—
188C2×C59—81no—
189C2×C59#54611yescharacteristic
190C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C59#57711yescharacteristic
192D59—22no—
193D59—42no—
194D59—81no—
195#547—591no—
196#546—591no—
197#489—591no—
198#483—591no—
199#481D5911yescharacteristic, complemented
200#476—591no—
201#469—591no—
202#465—591no—
203#463—591no—
204#449—591no—
205#447—591no—
206#442—591no—
207#435—591no—
208#417—591no—
209C2×#102—591no—
210C59#330611yescharacteristic, complemented, Sylow
211C2×#41—591no—
212C2×#41—1181no—
213C22×D4—591no—
214C2×SD16—591no—
215C2×D8—591no—
216C2×D8—591no—
217C2×M16—591no—
218C22×C8—591no—
219C4⋊Q8—591no—
220#124—591no—
221#123—1181no—
222#123—1181no—
223#123—1181no—
224C22⋊Q8—591no—
225C22⋊Q8—1181no—
226#121—591no—
227#121—591no—
228#121—1181no—
229#121C2×D5911yescharacteristic
230#120—1181no—
231C4×D4—591no—
232C4×D4—591no—
233C4×D4—591no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4C2×D5911yescharacteristic, complemented
236C2×C22⋊C4—1181no—
237#106—591no—
238#106C2×D5911yescharacteristic, complemented
239#106C2×D5911yescharacteristic, complemented
240C4⋊C8—591no—
241#103—591no—
242#103—591no—
243#103—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102C2×D5911yescharacteristic
250#102C2×D5911yescharacteristic
251C22⋊C8—591no—
252C22⋊C8C2×D5911yescharacteristic, complemented
253#97—591no—
254C24—1181no—
255#41—1182no—
256#41—2361no—
257#41—2364no—
258C2×Q8—591no—
259C2×Q8—1181no—
260C2×D4—21no—
261C2×D4—591no—
262C2×D4—591no—
263C2×D4—591no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4—1182no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—2361no—
270C2×D4C22×D5911yescharacteristic
271C22×C4—21no—
272C22×C4—591no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4C22×D5911yescharacteristic
278SD16—2361no—
279D8—1182no—
280D8—2361no—
281M16—2361no—
282C2×C8—591no—
283C2×C8—591no—
284C2×C8—2361no—
285C2×C8C22×D5911yescharacteristic
286C2×C8C22×D5911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4C22×D5911yescharacteristic
294C4⋊C4C22×D5911yescharacteristic
295C4⋊C4C22×D5911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—591no—
298C22⋊C4—591no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C22⋊C4—1181no—
306C42—591no—
307C23—21no—
308C23—591no—
309C23—1181no—
310C23—1181no—
311C23—4721no—
312C23—2362no—
313C23—2362no—
314C23D4×D5911yescharacteristic
315Q8—1181no—
316Q8—1181no—
317Q8—2362no—
318D4—21no—
319D4—21no—
320D4—81no—
321D4—592no—
322D4—1182no—
323D4—1181no—
324D4—1181no—
325D4—1181no—
326D4—2362no—
327D4—2362no—
328D4—2362no—
329D4—2362no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—591no—
337C2×C4—591no—
338C2×C4—591no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—4721no—
344C2×C4—2362no—
345C2×C4—2362no—
346C2×C4—2362no—
347C2×C4D4×D5911yescharacteristic
348C2×C4C23×D5911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1181no—
352C8—1181no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—592no—
360C22—1181no—
361C22—1181no—
362C22—1182no—
363C22—4724no—
364C22—2361no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22C2×D4×D5911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—1181no—
375C4—1181no—
376C4—1181no—
377C4—2361no—
378C4—2361no—
379C4#41×D5911yescharacteristic
380C4#1427377311yescharacteristic
381C2—41no—
382C2—81no—
383C2—1182no—
384C2—4721no—
385C2—2362no—
386C2#1683804411yescharacteristic
387C2AGL(1,ℤ/8)×D5911yescharacteristic
388C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#481C2
socleC22×C59C22×D4
hypercenter#481D59
hypocenterC59#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #16838053C2semidirect
2. #16838049C2semidirect
3. #16837760C2semidirect
4. #16837734C2semidirect
5. #16837691C2semidirect
6. #16837653C2semidirect
7. #16837632C2semidirect
8. #16837616C2semidirect
9. #16837549C2semidirect
10. #16837537C2semidirect
11. #16837513C2semidirect
12. #16837476C2semidirect
13. #16837401C2semidirect
14. #102×D59C2semidirect
15. C59×#481C2semidirect
19. C2×#11745660C22semidirect
22. C2×#11745664C22semidirect
24. #14273726C22semidirect
32. #14273701C22semidirect
36. #14273689C22semidirect
40. #14273658C22semidirect
41. Dic59⋊C8C22semidirect
42. #14273652C22semidirect
43. #14273650C22semidirect
44. #14273650C22semidirect
49. #14273647C22semidirect
51. #14273637C22semidirect
53. C2×C4⋊C4×C59C22semidirect
54. #106×C59C22semidirect
55. #106×C59C22semidirect
58. C22⋊C8×C59C22semidirect
144. D236#41semidirect
199. #481D59semidirect
210. C59#3306semidirect
235. C2×C4⋊C4C2×D59semidirect
238. #106C2×D59semidirect
239. #106C2×D59semidirect
252. C22⋊C8C2×D59semidirect