Finite Group Databasebeta

← #21433720

Subgroups — #21433720

Order 7552.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D59C211yesmaximal, characteristic, complemented
2#16837909C211yesmaximal, characteristic
3C2×#14273703C211yesmaximal, characteristic, complemented
4#16837657C212yesmaximal, complemented
5#16837645C212yesmaximal, complemented
6#16837640C212yesmaximal, complemented
7#16837628C212yesmaximal, complemented
8#16837444C211yesmaximal, characteristic, complemented
9#16837411C211yesmaximal, characteristic, complemented
10#16837403C211yesmaximal, characteristic, complemented
11C2×#137×C59C211yesmaximal, characteristic, complemented
12C22×C4×D59C2211yescharacteristic
13C2×#11745664C2211yescharacteristic
14C2×#11745659C2212yes—
15M16×D59—24no—
16C2×C8×D59C2212yes—
17#14273708—21no—
18#14273703—21no—
19#14273703—21no—
20#14273703C2211yescharacteristic
21#14273703C2212yes—
22#14273703C2212yes—
23#14273703C2211yescharacteristic
24#14273698C2211yescharacteristic
25#14273698C2211yescharacteristic
26#14273695—21no—
27C4×C22⋊D59—21no—
28C4×C22⋊D59—21no—
29#14273686C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×(C2×D59)⋊C4—21no—
33#14273661C2212yescomplemented
34#14273659C2212yescomplemented
35#14273651C2212yescomplemented
36#14273651C2212yescomplemented
37#14273651C2212yescomplemented
38#14273648C2212yescomplemented
39C2×#41×C59C2211yescharacteristic
40C22×Q8×C59C2211yescharacteristic
41#137×C59—24no—
42C2×Q16×C59C2212yescomplemented
43C2×SD16×C59C2212yescomplemented
44C2×M16×C59C2211yescharacteristic
45C23×D59D411yescharacteristic
46#41×C59—22no—
47#41×C59—22no—
48C2×Q8×C59—21no—
49C2×Q8×C59—22no—
50C2×Q8×C59—22no—
51C2×Q8×C59C2312yes—
52C2×Q8×C59C2311yescharacteristic
53C2×D4×C59—21no—
54C2×D4×C59C2311yescharacteristic
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59C2311yescharacteristic
58C2×C22⋊D59—21no—
59C2×C22⋊D59—21no—
60C22×Dic59—21no—
61C22×Dic59D411yescharacteristic
62C2×C4×D59—22no—
63C2×C4×D59—22no—
64C2×C4×D59D411yescharacteristic
65C2×C4×D59D411yescharacteristic
66C2×C4×D59C2311yescharacteristic
67C2×C4×D59C2311yescharacteristic
68Q16×C59—24no—
69SD16×C59—24no—
70M16×C59D414yescomplemented
71C2×C8×C59C2312yes—
72C22⋊Dic59—21no—
73C22⋊Dic59—21no—
74C22⋊Dic59—21no—
75(C2×D59)⋊C4—22no—
76(C2×D59)⋊C4—22no—
77(C2×D59)⋊C4—21no—
78(C2×D59)⋊C4—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59C2312yes—
81C4⋊Dic59C2311yescharacteristic
82C4⋊Dic59C2311yescharacteristic
83Dic59⋊C4—22no—
84Dic59⋊C4—22no—
85Dic59⋊C4—21no—
86Dic59⋊C4—21no—
87C4×Dic59—21no—
88#11745664—22no—
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—22no—
100Q8×C59—21no—
101Q8×C59—22no—
102Q8×C59—21no—
103Q8×C59—42no—
104D4×C59—21no—
105D4×C59—21no—
106D4×C59—42no—
107C2×C4×C59—21no—
108C2×C4×C59—22no—
109C2×C4×C59—42no—
110C2×C4×C59—42no—
111C2×C4×C59C2×D411yescharacteristic
112C2×C4×C59C2×D412yes—
113C2×C4×C59#4112yes—
114C2×C4×C59C2411yescharacteristic
115C22⋊D59—42no—
116C22⋊D59—42no—
117C2×Dic59—22no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—22no—
121C2×Dic59—42no—
122C2×Dic59C2×D411yescharacteristic
123C2×Dic59C2×D411yescharacteristic
124C4×D59—22no—
125C4×D59—22no—
126C4×D59—21no—
127C4×D59—21no—
128C4×D59—21no—
129C4×D59—21no—
130C8×C59C2×D414yes—
131C59⋊C8—22no—
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—41no—
154Dic59—42no—
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×#137D5911yescharacteristic, complemented
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#417—591no—
175C59#305611yescharacteristic, complemented, Sylow
176C2×#41C2×D5911yescharacteristic
177C22×Q8C2×D5911yescharacteristic
178C23×C4—591no—
179#137—24no—
180C2×Q16C2×D5912yescomplemented
181C2×SD16C2×D5912yescomplemented
182C2×M16—591no—
183C2×M16—592no—
184C2×M16—1184no—
185C2×M16C2×D5911yescharacteristic
186C22×C8—592no—
187#123—1181no—
188C22⋊Q8—592no—
189C22⋊Q8—592no—
190C22⋊Q8—591no—
191C22⋊Q8—591no—
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—591no—
201C2×C4⋊C4—1181no—
202C2×C22⋊C4—1181no—
203#107—592no—
204#106—592no—
205#103—592no—
206#103—592no—
207#103—592no—
208#102—592no—
209C24—591no—
210#41—22no—
211#41—22no—
212C2×Q8—21no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8C22×D5912yes—
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—24no—
233SD16—24no—
234M16—1182no—
235M16—1184no—
236M16C22⋊D5914yescomplemented
237C2×C8—592no—
238C2×C8—1184no—
239C2×C8C22×D5912yes—
240C4⋊C4—592no—
241C4⋊C4—591no—
242C4⋊C4—591no—
243C4⋊C4—1182no—
244C4⋊C4—1182no—
245C4⋊C4—1181no—
246C4⋊C4—1181no—
247C4⋊C4—1181no—
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—22no—
264Q8—21no—
265Q8—22no—
266Q8—21no—
267Q8—42no—
268D4—21no—
269D4—21no—
270D4—42no—
271D4—2362no—
272D4—2362no—
273C2×C4—21no—
274C2×C4—22no—
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×C4D4×D5911yescharacteristic
291C2×C4#1174568712yes—
292C2×C4C2×C22⋊D5912yes—
293C2×C4C23×D5911yescharacteristic
294C8—1182no—
295C8C2×C22⋊D5914yes—
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#1427369812yes—
309C22C2×D4×D5911yescharacteristic
310C4—41no—
311C4—42no—
312C4—1181no—
313C4—1181no—
314C4—2361no—
315C4—2362no—
316C4—2361no—
317C4#1427369812yes—
318C4C22×C22⋊D5911yescharacteristic
319C4C2×#1174568711yescharacteristic
320C2—22no—
321C2—81no—
322C2—1182no—
323C2—2361no—
324C2C2×#1427369811yescharacteristic
325C2#137×D5911yescharacteristic
326C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#137×C59C2
socleC22×C59C22×D4
hypercenterC2×#137D59
hypocenterC59#3056
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×M16×D59C2semidirect
3. C2×#14273703C2semidirect
4. #16837657C2semidirect
5. #16837645C2semidirect
6. #16837640C2semidirect
7. #16837628C2semidirect
8. #16837444C2semidirect
9. #16837411C2semidirect
10. #16837403C2semidirect
11. C2×#137×C59C2semidirect
33. #14273661C22semidirect
34. #14273659C22semidirect
35. #14273651C22semidirect
36. #14273651C22semidirect
37. #14273651C22semidirect
38. #14273648C22semidirect
42. C2×Q16×C59C22semidirect
43. C2×SD16×C59C22semidirect
70. M16×C59D4semidirect
145. C2×D59#137semidirect
164. C2×#137D59semidirect
175. C59#3056semidirect
180. C2×Q16C2×D59semidirect
181. C2×SD16C2×D59semidirect
236. M16C22⋊D59semidirect