Finite Group Databasebeta

← #21434034

Subgroups — #21434034

Order 7552.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273698C211yesmaximal, characteristic
2#117×D59C211yesmaximal, characteristic, complemented
3#16837725C212yesmaximal, complemented
4#16837724C212yesmaximal, complemented
5#16837719C212yesmaximal, complemented
6#16837714C212yesmaximal, complemented
7#16837445C211yesmaximal, characteristic, complemented
8#16837444C211yesmaximal, characteristic, complemented
9#16837407C211yesmaximal, characteristic, complemented
10#16837365C211yesmaximal, characteristic, complemented
11C59×#418C211yesmaximal, characteristic, complemented
12C22×C22⋊D59—21no—
13C22×C4×D59C2211yescharacteristic
14C2×#11745664C2211yescharacteristic
15#14273698—21no—
16#14273698—21no—
17#14273698C2212yes—
18#14273698C2212yes—
19#14273686C2211yescharacteristic
20#14273685C2211yescharacteristic, complemented
21#14273685C2211yescharacteristic, complemented
22#14273684—21no—
23#14273683—21no—
24C2×C4⋊Dic59C2211yescharacteristic
25C4⋊C4×D59C2211yescharacteristic, complemented
26C4⋊C4×D59C2211yescharacteristic, complemented
27C2×C22⋊Dic59—21no—
28C22⋊C4×D59—21no—
29C42×D59—21no—
30#14273661C2212yescomplemented
31#14273660C2212yescomplemented
32#14273659C2212yescomplemented
33#14273658C2212yescomplemented
34#14273648C2212yescomplemented
35#14273648C2212yescomplemented
36(C2×D59)⋊C8C2212yescomplemented
37(C2×D59)⋊C8C2212yescomplemented
38C22×D4×C59C2211yescharacteristic
39C2×M16×C59C2211yescharacteristic
40#117×C59C2211yescharacteristic
41#102×C59C2212yescomplemented
42#102×C59C2212yescomplemented
43C24×C59—21no—
44C23×D59D411yescharacteristic
45C2×D4×C59—21no—
46C2×D4×C59—22no—
47C2×D4×C59—22no—
48C2×D4×C59C2312yes—
49C22×C4×C59C2311yescharacteristic
50C2×C22⋊D59—22no—
51C2×C22⋊D59—22no—
52C2×C22⋊D59—44no—
53C22×Dic59—21no—
54C22×Dic59D411yescharacteristic
55C2×C4×D59—22no—
56C2×C4×D59—22no—
57C2×C4×D59—21no—
58C2×C4×D59—21no—
59C2×C4×D59D411yescharacteristic
60C2×C4×D59D411yescharacteristic
61C2×C4×D59C2311yescharacteristic
62C2×C4×D59C2311yescharacteristic
63M16×C59—22no—
64C2×C8×C59C2312yes—
65C4⋊C4×C59C2311yescharacteristic
66C4⋊C4×C59C2311yescharacteristic
67C22⋊C4×C59—21no—
68C42×C59—21no—
69C22⋊Dic59—21no—
70C22⋊Dic59—22no—
71C22⋊Dic59—22no—
72(C2×D59)⋊C4—21no—
73(C2×D59)⋊C4—21no—
74C4⋊Dic59—21no—
75C4⋊Dic59C2311yescharacteristic
76C4⋊Dic59C2311yescharacteristic
77C4⋊Dic59C2312yes—
78Dic59⋊C4—21no—
79Dic59⋊C4—21no—
80C4×Dic59—21no—
81C4×Dic59—21no—
82C4×Dic59—21no—
83#11745664—22no—
84C2×C59⋊C8C2312yes—
85C23×C59—22no—
86C23×C59—42no—
87C23×C59—42no—
88C23×C59—42no—
89C23×C59C2×D411yescharacteristic
90C22×D59—22no—
91C22×D59—22no—
92C22×D59—41no—
93C22×D59C2×D411yescharacteristic
94C22×D59C2×D411yescharacteristic
95D4×C59—22no—
96D4×C59—22no—
97D4×C59—42no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59#4112yes—
102C2×C4×C59#4112yes—
103C2×C4×C59C2411yescharacteristic
104C22⋊D59—44no—
105C22⋊D59—44no—
106C2×Dic59—22no—
107C2×Dic59—21no—
108C2×Dic59—21no—
109C2×Dic59—22no—
110C2×Dic59—42no—
111C2×Dic59C2×D411yescharacteristic
112C2×Dic59C2×D411yescharacteristic
113C4×D59—22no—
114C4×D59—22no—
115C4×D59—21no—
116C4×D59—21no—
117C4×D59—21no—
118C4×D59—21no—
119C4×D59—42no—
120C4×D59—42no—
121C8×C59—22no—
122C59⋊C8—22no—
123C22×C59—21no—
124C22×C59—21no—
125C22×C59—42no—
126C22×C59—42no—
127C22×C59—42no—
128C22×C59—84no—
129C22×C59#12312yes—
130C22×C59C22×D411yescharacteristic
131C2×D59—21no—
132C2×D59—21no—
133C2×D59—21no—
134C2×D59—21no—
135C2×D59—21no—
136C2×D59—44no—
137C2×D59AGL(1,ℤ/8)12yes—
138C4×C59—41no—
139C4×C59—41no—
140C4×C59#12312yes—
141C4×C59C2×#4111yescharacteristic
142C4×C59C2×#4111yescharacteristic
143Dic59—21no—
144Dic59—21no—
145Dic59—41no—
146Dic59—42no—
147Dic59—41no—
148#3094—591nomaximal, Sylow
149C2×C59—22no—
150C2×C59—82no—
151C2×C59C2×#12311yescharacteristic
152C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C59#57511yescharacteristic
154D59—22no—
155D59—41no—
156C2×#121—591no—
157C2×#117—591no—
158#482—592no—
159#482—592no—
160#481—592no—
161#480—592no—
162#428—591no—
163#428—591no—
164#418—591no—
165#418D5911yescharacteristic, complemented
166#407—591no—
167C59#309411yescharacteristic, complemented, Sylow
168C22×D4—1181no—
169C22×D4C2×D5911yescharacteristic
170C23×C4—591no—
171C2×M16—591no—
172C2×M16C2×D5911yescharacteristic
173#121—592no—
174#121—592no—
175#121—1181no—
176#121—1181no—
177#117—591no—
178#117—591no—
179#117—591no—
180#117—1181no—
181#117—1181no—
182#117C2×D5911yescharacteristic
183C2×C4⋊C4—591no—
184C2×C4⋊C4—591no—
185C2×C4⋊C4—591no—
186C2×C22⋊C4—1181no—
187C2×C22⋊C4—1181no—
188C2×C42—1181no—
189#107—592no—
190#107—592no—
191#106—592no—
192#106—592no—
193#102—592no—
194#102—592no—
195#102C2×D5912yescomplemented
196#102C2×D5912yescomplemented
197C22⋊C8—592no—
198C22⋊C8—592no—
199C24—21no—
200C24—591no—
201C2×D4—22no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—1182no—
205C2×D4—1182no—
206C2×D4—2364no—
207C2×D4C22×D5912yes—
208C22×C4—591no—
209C22×C4—591no—
210C22×C4—591no—
211C22×C4—591no—
212C22×C4—591no—
213C22×C4—1181no—
214C22×C4—1181no—
215C22×C4—1182no—
216C22×C4—1182no—
217C22×C4—1181no—
218C22×C4C22×D5911yescharacteristic
219M16—22no—
220M16—1182no—
221C2×C8—592no—
222C2×C8C22×D5912yes—
223C4⋊C4—591no—
224C4⋊C4—591no—
225C4⋊C4—592no—
226C4⋊C4—1181no—
227C4⋊C4—1181no—
228C4⋊C4—1181no—
229C4⋊C4C22×D5911yescharacteristic
230C4⋊C4C22×D5911yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—1181no—
233C22⋊C4—1181no—
234C22⋊C4—1182no—
235C22⋊C4—1182no—
236C22⋊C4—1181no—
237C42—21no—
238C42—1181no—
239C42—1181no—
240C42—1181no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—591no—
246C23—591no—
247C23—1182no—
248C23—1182no—
249C23—2361no—
250C23D4×D5911yescharacteristic
251D4—22no—
252D4—22no—
253D4—42no—
254D4—2364no—
255D4—2364no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—591no—
259C2×C4—591no—
260C2×C4—1182no—
261C2×C4—1182no—
262C2×C4—1182no—
263C2×C4—1181no—
264C2×C4—1181no—
265C2×C4—1181no—
266C2×C4—1181no—
267C2×C4—1181no—
268C2×C4—1181no—
269C2×C4—1182no—
270C2×C4—2362no—
271C2×C4—2362no—
272C2×C4—2362no—
273C2×C4#1174568512yes—
274C2×C4D4×D5911yescharacteristic
275C2×C4#1174568712yes—
276C2×C4C23×D5911yescharacteristic
277C8—22no—
278C8—1182no—
279C22—21no—
280C22—21no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—592no—
286C22—1181no—
287C22—1181no—
288C22—1181no—
289C22—1181no—
290C22—1181no—
291C22—2364no—
292C22#1427370912yes—
293C22C2×D4×D5911yescharacteristic
294C4—41no—
295C4—41no—
296C4—1181no—
297C4—1181no—
298C4—2362no—
299C4—2361no—
300C4—2361no—
301C4#1427370912yes—
302C4C2×#1174568711yescharacteristic
303C4C2×#1174568511yescharacteristic
304C2—22no—
305C2—82no—
306C2—1182no—
307C2—2361no—
308C2C2×#1427370911yescharacteristic
309C2AGL(1,ℤ/8)×D5911yescharacteristic
310C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#418C2
socleC22×C59C22×D4
hypercenter#418D59
hypocenterC59#3094
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #117×D59C2semidirect
3. #16837725C2semidirect
4. #16837724C2semidirect
5. #16837719C2semidirect
6. #16837714C2semidirect
7. #16837445C2semidirect
8. #16837444C2semidirect
9. #16837407C2semidirect
10. #16837365C2semidirect
11. C59×#418C2semidirect
20. #14273685C22semidirect
21. #14273685C22semidirect
25. C4⋊C4×D59C22semidirect
26. C4⋊C4×D59C22semidirect
30. #14273661C22semidirect
31. #14273660C22semidirect
32. #14273659C22semidirect
33. #14273658C22semidirect
34. #14273648C22semidirect
35. #14273648C22semidirect
36. (C2×D59)⋊C8C22semidirect
37. (C2×D59)⋊C8C22semidirect
41. #102×C59C22semidirect
42. #102×C59C22semidirect
165. #418D59semidirect
167. C59#3094semidirect
195. #102C2×D59semidirect
196. #102C2×D59semidirect