Finite Group Databasebeta

← #21434038

Subgroups — #21434038

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×#14273702C211yesmaximal, characteristic
2#117×D59C211yesmaximal, characteristic, complemented
3#16837729C212yesmaximal, complemented
4#16837728C212yesmaximal, complemented
5#16837722C212yesmaximal, complemented
6#16837717C212yesmaximal, complemented
7#16837442C211yesmaximal, characteristic, complemented
8#16837408C211yesmaximal, characteristic, complemented
9#16837406C211yesmaximal, characteristic, complemented
10#16837365C211yesmaximal, characteristic, complemented
11C59×#428C211yesmaximal, characteristic, complemented
12C22×D236—21no—
13C22×D236C2211yescharacteristic
14C22×C4×D59C2211yescharacteristic
15C2×#11745664C2211yescharacteristic
16#14273702—21no—
17#14273702—21no—
18#14273702C2212yes—
19#14273702C2212yes—
20#14273686C2211yescharacteristic
21#14273685C2211yescharacteristic, complemented
22#14273685C2211yescharacteristic, complemented
23#14273684—21no—
24#14273683—21no—
25C4⋊C4×D59C2211yescharacteristic, complemented
26C4⋊C4×D59C2211yescharacteristic, complemented
27C2×(C2×D59)⋊C4—21no—
28C22⋊C4×D59—21no—
29C42×D59—21no—
30#14273660C2212yescomplemented
31#14273658C2212yescomplemented
32#14273649C2212yescomplemented
33#14273649C2212yescomplemented
34#14273647C2212yescomplemented
35#14273647C2212yescomplemented
36(C2×D59)⋊C8C2212yescomplemented
37(C2×D59)⋊C8C2212yescomplemented
38C2×M16×C59C2211yescharacteristic
39#117×C59C2211yescharacteristic
40C2×C4⋊C4×C59C2211yescharacteristic
41#107×C59C2212yescomplemented
42#106×C59C2212yescomplemented
43C23×D59—21no—
44C23×D59D411yescharacteristic
45C22×C4×C59—21no—
46C22×C4×C59C2311yescharacteristic
47C22×Dic59D411yescharacteristic
48C2×D236—22no—
49C2×D236—22no—
50C2×D236—22no—
51C2×D236—22no—
52C2×D236—21no—
53C2×D236—44no—
54C2×D236C2312yes—
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×C59—21no—
66C4⋊C4×C59C2311yescharacteristic
67C4⋊C4×C59C2312yes—
68C4⋊C4×C59C2311yescharacteristic
69C22⋊C4×C59—21no—
70C42×C59—21no—
71C22⋊Dic59—21no—
72(C2×D59)⋊C4—21no—
73(C2×D59)⋊C4—21no—
74(C2×D59)⋊C4—22no—
75(C2×D59)⋊C4—22no—
76C4⋊Dic59C2311yescharacteristic
77C4⋊Dic59C2311yescharacteristic
78Dic59⋊C4—21no—
79Dic59⋊C4—21no—
80C4×Dic59—21no—
81C4×Dic59—21no—
82C4×Dic59—21no—
83#11745664—22no—
84C2×C59⋊C8C2312yes—
85C23×C59C2×D411yescharacteristic
86C22×D59—22no—
87C22×D59—22no—
88C22×D59—22no—
89C22×D59—41no—
90C22×D59—42no—
91C22×D59—42no—
92C22×D59—42no—
93C22×D59C2×D411yescharacteristic
94C22×D59C2×D411yescharacteristic
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—22no—
98C2×C4×C59—42no—
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59#4112yes—
101C2×C4×C59#4112yes—
102C2×C4×C59C2411yescharacteristic
103C2×Dic59—22no—
104C2×Dic59—21no—
105C2×Dic59—21no—
106C2×Dic59C2×D411yescharacteristic
107C2×Dic59C2×D411yescharacteristic
108D236—22no—
109D236—22no—
110D236—44no—
111D236—44no—
112D236—42no—
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#12312yes—
126C22×C59C22×D411yescharacteristic
127C2×D59—21no—
128C2×D59—21no—
129C2×D59—21no—
130C2×D59—21no—
131C2×D59—21no—
132C2×D59—44no—
133C2×D59—42no—
134C2×D59—42no—
135C2×D59—42no—
136C2×D59—84no—
137C2×D59AGL(1,ℤ/8)12yes—
138C4×C59—41no—
139C4×C59—42no—
140C4×C59—41no—
141C4×C59#12312yes—
142C4×C59C2×#4111yescharacteristic
143C4×C59C2×#4111yescharacteristic
144Dic59—21no—
145Dic59—21no—
146Dic59—41no—
147Dic59—41no—
148#3094—591nomaximal, Sylow
149C2×C59—22no—
150C2×C59C2×#12311yescharacteristic
151C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C59#57511yescharacteristic
153D59—22no—
154D59—41no—
155D59—82no—
156C2×#121—591no—
157C2×#117—591no—
158#482—592no—
159#482—592no—
160#481—592no—
161#480—592no—
162#428—591no—
163#428D5911yescharacteristic, complemented
164#418—591no—
165#418—591no—
166#407—591no—
167C59#309411yescharacteristic, complemented, Sylow
168C22×D4—591no—
169C22×D4—1181no—
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⋊C4C2×D5911yescharacteristic
186C2×C22⋊C4—1181no—
187C2×C22⋊C4—1181no—
188C2×C42—1181no—
189#107—592no—
190#107C2×D5912yescomplemented
191#106—592no—
192#106C2×D5912yescomplemented
193#102—592no—
194#102—592no—
195#102—592no—
196#102—592no—
197C22⋊C8—592no—
198C22⋊C8—592no—
199C24—591no—
200C24—1181no—
201C2×D4—592no—
202C2×D4—1182no—
203C2×D4—1182no—
204C2×D4—1182no—
205C2×D4—1181no—
206C2×D4—1182no—
207C2×D4—2364no—
208C22×C4—21no—
209C22×C4—591no—
210C22×C4—591no—
211C22×C4—591no—
212C22×C4—591no—
213C22×C4—591no—
214C22×C4—1181no—
215C22×C4—1181no—
216C22×C4—1182no—
217C22×C4—1182no—
218C22×C4C22×D5911yescharacteristic
219M16—22no—
220M16—1182no—
221C2×C8—592no—
222C2×C8C22×D5912yes—
223C4⋊C4—21no—
224C4⋊C4—591no—
225C4⋊C4—591no—
226C4⋊C4—1181no—
227C4⋊C4—1181no—
228C4⋊C4C22×D5911yescharacteristic
229C4⋊C4C22×D5911yescharacteristic
230C4⋊C4C22×D5912yes—
231C22⋊C4—21no—
232C22⋊C4—1182no—
233C22⋊C4—1182no—
234C22⋊C4—1181no—
235C22⋊C4—1181no—
236C22⋊C4—1181no—
237C42—21no—
238C42—1181no—
239C42—1181no—
240C42—1181no—
241C23—591no—
242C23—591no—
243C23—1182no—
244C23—1182no—
245C23—1182no—
246C23—2361no—
247C23—2362no—
248C23—2362no—
249C23—2362no—
250C23D4×D5911yescharacteristic
251D4—1182no—
252D4—1182no—
253D4—2364no—
254D4—2364no—
255D4—2362no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—591no—
261C2×C4—591no—
262C2×C4—1182no—
263C2×C4—1182no—
264C2×C4—1182no—
265C2×C4—1181no—
266C2×C4—1181no—
267C2×C4—1181no—
268C2×C4—1181no—
269C2×C4—1181no—
270C2×C4—1181no—
271C2×C4—2362no—
272C2×C4—2362no—
273C2×C4#1174568512yes—
274C2×C4D4×D5911yescharacteristic
275C2×C4#1174568912yes—
276C2×C4C23×D5911yescharacteristic
277C8—22no—
278C8—1182no—
279C22—21no—
280C22—21no—
281C22—592no—
282C22—1181no—
283C22—1181no—
284C22—1181no—
285C22—1181no—
286C22—1181no—
287C22—4724no—
288C22—2364no—
289C22—2362no—
290C22—2362no—
291C22—2362no—
292C22#1427371212yes—
293C22C2×D4×D5911yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—1181no—
298C4—1181no—
299C4—2361no—
300C4—2361no—
301C4#1427371212yes—
302C4C2×#1174568511yescharacteristic
303C4C2×#1174568911yescharacteristic
304C2—22no—
305C2—1182no—
306C2—4722no—
307C2—2361no—
308C2C2×#1427371211yescharacteristic
309C2AGL(1,ℤ/8)×D5911yescharacteristic
310C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#428C2
socleC22×C59C22×D4
hypercenter#428D59
hypocenterC59#3094
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #117×D59C2semidirect
3. #16837729C2semidirect
4. #16837728C2semidirect
5. #16837722C2semidirect
6. #16837717C2semidirect
7. #16837442C2semidirect
8. #16837408C2semidirect
9. #16837406C2semidirect
10. #16837365C2semidirect
11. C59×#428C2semidirect
21. #14273685C22semidirect
22. #14273685C22semidirect
25. C4⋊C4×D59C22semidirect
26. C4⋊C4×D59C22semidirect
30. #14273660C22semidirect
31. #14273658C22semidirect
32. #14273649C22semidirect
33. #14273649C22semidirect
34. #14273647C22semidirect
35. #14273647C22semidirect
36. (C2×D59)⋊C8C22semidirect
37. (C2×D59)⋊C8C22semidirect
41. #107×C59C22semidirect
42. #106×C59C22semidirect
163. #428D59semidirect
167. C59#3094semidirect
190. #107C2×D59semidirect
192. #106C2×D59semidirect