Finite Group Databasebeta

← #21433729

Subgroups — #21433729

Order 7552.

496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14273757C211yesmaximal, characteristic, complemented
2C2×M16×D59C211yesmaximal, characteristic, complemented
3#16837909C211yesmaximal, characteristic
4C2×#14273707C211yesmaximal, characteristic, complemented
5#16837659C212yesmaximal, complemented
6#16837647C212yesmaximal, complemented
7#16837642C212yesmaximal, complemented
8#16837630C212yesmaximal, complemented
9#16837442C211yesmaximal, characteristic, complemented
10#16837412C211yesmaximal, characteristic, complemented
11C59×#417C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C4×D59C2211yescharacteristic
14#14273757—24no—
15C2×#11745672C2212yescomplemented
16C2×#11745670C2212yescomplemented
17C2×#11745664C2211yescharacteristic
18C2×#11745659C2212yes—
19M16×D59—24no—
20C2×C8×D59C2212yes—
21#14273708—21no—
22#14273707—21no—
23#14273707—21no—
24#14273707C2212yes—
25#14273707C2212yes—
26#14273703C2211yescharacteristic
27#14273703C2211yescharacteristic
28#14273698C2211yescharacteristic
29#14273698C2211yescharacteristic
30#14273695—21no—
31C4×C22⋊D59—21no—
32C4×C22⋊D59—21no—
33#14273686C2211yescharacteristic
34C2×C4⋊Dic59—21no—
35C2×(C2×D59)⋊C4—21no—
36#14273660C2212yescomplemented
37#14273658C2212yescomplemented
38#14273652C2212yescomplemented
39#14273652C2212yescomplemented
40C2×#41×C59C2211yescharacteristic
41C2×M16×C59C2211yescharacteristic
42C2×C4⋊C4×C59C2211yescharacteristic
43#103×C59C2212yescomplemented
44#102×C59C2212yescomplemented
45C23×D59D411yescharacteristic
46#41×C59—22no—
47#41×C59—22no—
48C2×Q8×C59C2311yescharacteristic
49C2×D4×C59—21no—
50C2×D4×C59C2311yescharacteristic
51C22×C4×C59—21no—
52C22×C4×C59—21no—
53C22×C4×C59C2311yescharacteristic
54C2×C22⋊D59—21no—
55C2×C22⋊D59—21no—
56C22×Dic59—21no—
57C22×Dic59D411yescharacteristic
58C2×C4×D59—22no—
59C2×C4×D59—22no—
60C2×C4×D59D411yescharacteristic
61C2×C4×D59D411yescharacteristic
62C2×C4×D59C2311yescharacteristic
63C2×C4×D59C2311yescharacteristic
64C2×Dic118—22no—
65C2×Dic118—22no—
66C2×Dic118—21no—
67C2×Dic118C2312yes—
68M16×C59—22no—
69C2×C8×C59C2312yes—
70C4⋊C4×C59—21no—
71C4⋊C4×C59C2312yes—
72C22⋊Dic59—21no—
73C22⋊Dic59—21no—
74C22⋊Dic59—21no—
75#11745672—24no—
76#11745670—24no—
77(C2×D59)⋊C4—22no—
78(C2×D59)⋊C4—22no—
79(C2×D59)⋊C4—21no—
80(C2×D59)⋊C4—21no—
81C4⋊Dic59—22no—
82C4⋊Dic59—22no—
83C4⋊Dic59C2311yescharacteristic
84C4⋊Dic59C2311yescharacteristic
85Dic59⋊C4—21no—
86Dic59⋊C4—21no—
87C4×Dic59—21no—
88#11745664D414yescomplemented
89C2×C59⋊C8C2312yes—
90#11745659—24no—
91C8×D59—24no—
92C23×C59—21no—
93C23×C59C2×D411yescharacteristic
94C22×D59—22no—
95C22×D59—22no—
96C22×D59—41no—
97C22×D59C2×D411yescharacteristic
98C22×D59C2×D411yescharacteristic
99Q8×C59—21no—
100Q8×C59—21no—
101D4×C59—21no—
102D4×C59—21no—
103D4×C59—42no—
104C2×C4×C59—21no—
105C2×C4×C59—22no—
106C2×C4×C59—42no—
107C2×C4×C59—42no—
108C2×C4×C59C2×D411yescharacteristic
109C2×C4×C59C2×D412yes—
110C2×C4×C59#4112yes—
111C2×C4×C59C2411yescharacteristic
112C22⋊D59—42no—
113C22⋊D59—42no—
114C2×Dic59—22no—
115C2×Dic59—21no—
116C2×Dic59—21no—
117C2×Dic59—22no—
118C2×Dic59—42no—
119C2×Dic59C2×D411yescharacteristic
120C2×Dic59C2×D411yescharacteristic
121C4×D59—22no—
122C4×D59—22no—
123C4×D59—21no—
124C4×D59—21no—
125C4×D59—21no—
126C4×D59—21no—
127Dic118—22no—
128Dic118—22no—
129Dic118—42no—
130C8×C59—22no—
131C59⋊C8C2×D414yes—
132C22×C59—21no—
133C22×C59—21no—
134C22×C59—41no—
135C22×C59—41no—
136C22×C59—41no—
137C22×C59#12112yes—
138C22×C59C22×D411yescharacteristic
139C2×D59—21no—
140C2×D59—21no—
141C2×D59—21no—
142C2×D59—21no—
143C2×D59—21no—
144C2×D59—44no—
145C2×D59#13712yescomplemented
146C4×C59—41no—
147C4×C59—42no—
148C4×C59#12112yes—
149C4×C59C22×D411yescharacteristic
150C4×C59C2×#4111yescharacteristic
151Dic59—21no—
152Dic59—21no—
153Dic59—42no—
154Dic59—41no—
155Dic59—41no—
156#3056—591nomaximal, Sylow
157C2×C59—22no—
158C2×C59—81no—
159C2×C59C2×#12111yescharacteristic
160C2×C59C2×#13711yescharacteristic
161C2×C59#57511yescharacteristic
162D59—22no—
163D59—41no—
164C2×#137—591no—
165C22×M16—591no—
166#525—591no—
167C2×C22⋊Q8—591no—
168#470—592no—
169#468—592no—
170#467—592no—
171#465—592no—
172#428—591no—
173#419—591no—
174#417D5911yescharacteristic, complemented
175C59#305611yescharacteristic, complemented, Sylow
176C2×#41C2×D5911yescharacteristic
177C22×Q8—591no—
178C23×C4—591no—
179#137—1184no—
180C2×Q16—592no—
181C2×SD16—592no—
182C2×M16—591no—
183C2×M16—592no—
184C2×M16—1184no—
185C2×M16C2×D5911yescharacteristic
186C22×C8—592no—
187#123—1181no—
188C22⋊Q8—591no—
189C22⋊Q8—591no—
190C22⋊Q8—592no—
191C22⋊Q8—592no—
192C22⋊Q8—1181no—
193C22⋊Q8—1181no—
194#121—591no—
195#121—591no—
196#120—1181no—
197C4×D4—1181no—
198C4×D4—1181no—
199#117—591no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4C2×D5911yescharacteristic
202C2×C22⋊C4—1181no—
203#107—592no—
204#106—592no—
205#103—592no—
206#103—592no—
207#103C2×D5912yescomplemented
208#102C2×D5912yescomplemented
209C24—591no—
210#41—22no—
211#41—22no—
212C2×Q8—592no—
213C2×Q8—1181no—
214C2×Q8—1182no—
215C2×Q8—1182no—
216C2×Q8C22×D5911yescharacteristic
217C2×D4—21no—
218C2×D4—1181no—
219C2×D4—1181no—
220C2×D4C22×D5911yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—591no—
224C22×C4—591no—
225C22×C4—591no—
226C22×C4—591no—
227C22×C4—591no—
228C22×C4—1182no—
229C22×C4—1182no—
230C22×C4—1181no—
231C22×C4C22×D5911yescharacteristic
232Q16—1184no—
233SD16—1184no—
234M16—22no—
235M16—594no—
236M16—1184no—
237C2×C8—592no—
238C2×C8—1184no—
239C2×C8C22×D5912yes—
240C4⋊C4—21no—
241C4⋊C4—591no—
242C4⋊C4—591no—
243C4⋊C4—1182no—
244C4⋊C4—1182no—
245C4⋊C4—1181no—
246C4⋊C4—1181no—
247C4⋊C4C22×D5912yes—
248C22⋊C4—1182no—
249C22⋊C4—1182no—
250C22⋊C4—1181no—
251C22⋊C4—1181no—
252C22⋊C4—1181no—
253C22⋊C4—1181no—
254C22⋊C4—1181no—
255C42—1181no—
256C23—21no—
257C23—591no—
258C23—591no—
259C23—1182no—
260C23—1182no—
261C23—2361no—
262C23D4×D5911yescharacteristic
263Q8—21no—
264Q8—21no—
265Q8—1182no—
266Q8—1182no—
267Q8—2362no—
268D4—21no—
269D4—21no—
270D4—42no—
271D4—2362no—
272D4—2362no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—591no—
278C2×C4—591no—
279C2×C4—1182no—
280C2×C4—1182no—
281C2×C4—1182no—
282C2×C4—1181no—
283C2×C4—1181no—
284C2×C4—1181no—
285C2×C4—1181no—
286C2×C4—1181no—
287C2×C4—1181no—
288C2×C4—1182no—
289C2×C4—2362no—
290C2×C4#1174568512yes—
291C2×C4D4×D5911yescharacteristic
292C2×C4D4×D5912yes—
293C2×C4C23×D5911yescharacteristic
294C8—22no—
295C8—594no—
296C22—21no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—592no—
302C22—1181no—
303C22—1181no—
304C22—1181no—
305C22—1181no—
306C22—1181no—
307C22—2364no—
308C22#1427370012yes—
309C22C2×D4×D5911yescharacteristic
310C4—41no—
311C4—42no—
312C4—1181no—
313C4—1181no—
314C4—2362no—
315C4—2361no—
316C4—2361no—
317C4#1427370012yes—
318C4C2×D4×D5911yescharacteristic
319C4C2×#1174568511yescharacteristic
320C2—22no—
321C2—81no—
322C2—1182no—
323C2—2361no—
324C2C2×#1427370011yescharacteristic
325C2#137×D5911yescharacteristic
326C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#417C2
socleC22×C59C22×D4
hypercenter#417D59
hypocenterC59#3056
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14273757C2semidirect
2. C2×M16×D59C2semidirect
4. C2×#14273707C2semidirect
5. #16837659C2semidirect
6. #16837647C2semidirect
7. #16837642C2semidirect
8. #16837630C2semidirect
9. #16837442C2semidirect
10. #16837412C2semidirect
11. C59×#417C2semidirect
15. C2×#11745672C22semidirect
16. C2×#11745670C22semidirect
36. #14273660C22semidirect
37. #14273658C22semidirect
38. #14273652C22semidirect
39. #14273652C22semidirect
43. #103×C59C22semidirect
44. #102×C59C22semidirect
88. #11745664D4semidirect
145. C2×D59#137semidirect
174. #417D59semidirect
175. C59#3056semidirect
207. #103C2×D59semidirect
208. #102C2×D59semidirect