Finite Group Databasebeta

← #21435878

Subgroups — #21435878

Order 7552.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#16838216C211yesmaximal, characteristic, complemented
2#16838213C212yesmaximal, complemented
3#16837785C211yesmaximal, characteristic, complemented
4#16837677C211yesmaximal, characteristic, complemented
5#16837669C211yesmaximal, characteristic, complemented
6#16837663C212yesmaximal, complemented
7#16837580C212yesmaximal, complemented
8#16837573C212yesmaximal, complemented
9#16837519C211yesmaximal, characteristic, complemented
10#16837517C211yesmaximal, characteristic, complemented
11C59×#576C211yesmaximal, characteristic, complemented
12#14273774C2212yescomplemented
13#14273757—22no—
14#14273757C2212yes—
15#14273757C2212yescomplemented
16#14273756—22no—
17#14273753—22no—
18#14273753C2212yescomplemented
19#14273747—22no—
20#14273747C2211yescharacteristic
21#14273746—21no—
22C2×Dic236C2211yescharacteristic, complemented
23Q16×D59—21no—
24C2×#11745670—22no—
25C2×#11745670C2212yescomplemented
26#14273734C2212yescomplemented
27#14273733C2211yescharacteristic, complemented
28#14273714C2212yescomplemented
29#14273663C2211yescharacteristic, complemented
30#14273662C2211yescharacteristic, complemented
31#14273654C2211yescharacteristic
32#14273654C2212yescomplemented
33#14273653C2211yescharacteristic, complemented
34#14273645C2212yescomplemented
35#14273644C2212yescomplemented
36C8×Dic59C2211yescharacteristic, complemented
37H(5,𝔽2)×C59C2212yes—
38AGL(1,ℤ/8)×C59—22no—
39AGL(1,ℤ/8)×C59C2212yes—
40#135×C59—21no—
41#135×C59C2211yescharacteristic
42C2×D8×C59—21no—
43C2×D8×C59C2211yescharacteristic
44#131×C59C2211yescharacteristic
45#41×C59—22no—
46#41×C59—22no—
47#41×C59C2311yescharacteristic
48#41×C59C2312yes—
49C2×D4×C59—22no—
50C2×D4×C59—22no—
51C2×D4×C59—42no—
52C2×D4×C59C2312yes—
53Q8×D59—22no—
54#11745687—22no—
55#11745687—42no—
56#11745685—22no—
57#11745685C2311yescharacteristic
58C2×Dic118—22no—
59C2×Dic118C2312yes—
60Q16×C59D411yescharacteristic
61SD16×C59—22no—
62SD16×C59D412yes—
63D8×C59—22no—
64D8×C59—21no—
65D8×C59—21no—
66D8×C59D411yescharacteristic
67M16×C59—21no—
68M16×C59C2311yescharacteristic
69C2×C8×C59—21no—
70C2×C8×C59C2311yescharacteristic
71C22⋊Dic59—42no—
72#11745672—22no—
73#11745672—22no—
74#11745672D411yescharacteristic
75#11745671D411yescharacteristic
76#11745670—22no—
77#11745670—22no—
78#11745670—22no—
79#11745670—22no—
80#11745670—22no—
81#11745670D411yescharacteristic
82#11745669—22no—
83#11745669D411yescharacteristic
84C4×Dic59C2311yescharacteristic
85#11745664—22no—
86#11745664C2311yescharacteristic
87#11745664C2312yes—
88C2×C59⋊C8—22no—
89C2×C59⋊C8C2311yescharacteristic
90Dic236—21no—
91Dic236—21no—
92#11745659—21no—
93C8×D59—21no—
94C23×C59—22no—
95C23×C59—42no—
96Q8×C59C2×D411yescharacteristic
97Q8×C59C2×D412yes—
98D4×C59—22no—
99D4×C59—21no—
100D4×C59—22no—
101D4×C59—22no—
102D4×C59—42no—
103D4×C59—42no—
104D4×C59C2×D411yescharacteristic
105D4×C59C2×D412yes—
106C2×C4×C59—22no—
107C2×C4×C59—21no—
108C2×C4×C59—42no—
109C2×C4×C59C2411yescharacteristic
110C22⋊D59—21no—
111C22⋊D59—42no—
112C2×Dic59—21no—
113C2×Dic59—22no—
114C2×Dic59—42no—
115D236C2×D411yescharacteristic
116C4×D59—21no—
117C4×D59—42no—
118Dic118—22no—
119Dic118—22no—
120Dic118—42no—
121Dic118C2×D411yescharacteristic
122C8×C59—21no—
123C8×C59C2×D411yescharacteristic
124C8×C59C2×D411yescharacteristic
125C59⋊C8—21no—
126C59⋊C8—22no—
127C59⋊C8C2×D411yescharacteristic
128C59⋊C8C2×D411yescharacteristic
129C22×C59—22no—
130C22×C59—21no—
131C22×C59—42no—
132C22×C59—82no—
133C22×C59—162no—
134C22×C59H(5,𝔽2)11yescharacteristic
135C2×D59—21no—
136C4×C59—22no—
137C4×C59—21no—
138C4×C59C22×D411yescharacteristic
139C4×C59C22×D411yescharacteristic
140Dic59—21no—
141Dic59—41no—
142Dic59—42no—
143#3290—591nomaximal, Sylow
144C2×C59—21no—
145C2×C59—42no—
146C2×C59—41no—
147C2×C59—82no—
148C2×C59D4211yescharacteristic
149D59—41no—
150#578—591no—
151#577—592no—
152#576D5911yescharacteristic, complemented
153#495—591no—
154#473—591no—
155#472—591no—
156#471—592no—
157#455—592no—
158#454—592no—
159#443—591no—
160#443—591no—
161C59#329011yescharacteristic, complemented, Sylow
1622−1+4—592no—
163H(5,𝔽2)C2×D5912yes—
164#137—592no—
165#137—592no—
166#137—1182no—
167#137—1182no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—592no—
170AGL(1,ℤ/8)—1182no—
171AGL(1,ℤ/8)C2×D5912yes—
172#135—21no—
173#135—591no—
174#135—1182no—
175#135—1181no—
176#135C2×D5911yescharacteristic
177C2×Q16—591no—
178C2×Q16—1181no—
179C2×SD16—592no—
180C2×SD16—1182no—
181C2×D8—21no—
182C2×D8C2×D5911yescharacteristic
183#131—592no—
184#131—591no—
185#131C2×D5911yescharacteristic
186#124—592no—
187#108—591no—
188#108—591no—
189#104—591no—
190#104—592no—
191#104—591no—
192#101—592no—
193#100—592no—
194C4×C8—591no—
195#41—22no—
196#41—22no—
197#41—591no—
198#41—1182no—
199#41—1182no—
200#41—2362no—
201#41C22×D5911yescharacteristic
202#41C22×D5912yes—
203C2×Q8—592no—
204C2×Q8—1182no—
205C2×Q8—1182no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D5912yes—
210Q16—591no—
211Q16—1182no—
212Q16—1182no—
213Q16—1181no—
214Q16—1181no—
215Q16C22⋊D5911yescharacteristic
216SD16—22no—
217SD16—591no—
218SD16—591no—
219SD16—1182no—
220SD16—1182no—
221SD16—1182no—
222SD16—1182no—
223SD16—1182no—
224SD16C22⋊D5912yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—591no—
229D8—1182no—
230D8C22⋊D5911yescharacteristic
231M16—21no—
232M16—591no—
233M16—592no—
234M16—1182no—
235M16—1181no—
236M16C22×D5911yescharacteristic
237C2×C8—21no—
238C2×C8—591no—
239C2×C8—1182no—
240C2×C8—1181no—
241C2×C8C22×D5911yescharacteristic
242C22⋊C4—2362no—
243C42—591no—
244C23—22no—
245C23—42no—
246Q8—591no—
247Q8—1182no—
248Q8—1182no—
249Q8—2362no—
250Q8D4×D5911yescharacteristic
251Q8C2×C22⋊D5912yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—591no—
259D4—1181no—
260D4—2362no—
261D4D4×D5911yescharacteristic
262D4C2×C22⋊D5912yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—1181no—
267C2×C4—1181no—
268C2×C4—1182no—
269C2×C4—2362no—
270C2×C4—2362no—
271C2×C4C23×D5911yescharacteristic
272C8—21no—
273C8—591no—
274C8—591no—
275C8—1182no—
276C8—1181no—
277C8C2×C22⋊D5911yescharacteristic
278C8C2×C22⋊D5911yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—1181no—
285C22#1427377211yescharacteristic
286C4—21no—
287C4—22no—
288C4—1181no—
289C4—2361no—
290C4—2362no—
291C4C2×D4×D5911yescharacteristic
292C4C22×C22⋊D5911yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—2361no—
298C2D4×C22⋊D5911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#576C2
socleC2×C59D42
hypercenter#576D59
hypocenterC59#3290
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #16838216C2semidirect
2. #16838213C2semidirect
3. #16837785C2semidirect
4. #16837677C2semidirect
5. #16837669C2semidirect
6. #16837663C2semidirect
7. #16837580C2semidirect
8. #16837573C2semidirect
9. #16837519C2semidirect
10. #16837517C2semidirect
11. C59×#576C2semidirect
12. #14273774C22semidirect
15. #14273757C22semidirect
18. #14273753C22semidirect
22. C2×Dic236C22semidirect
25. C2×#11745670C22semidirect
26. #14273734C22semidirect
27. #14273733C22semidirect
28. #14273714C22semidirect
29. #14273663C22semidirect
30. #14273662C22semidirect
32. #14273654C22semidirect
33. #14273653C22semidirect
34. #14273645C22semidirect
35. #14273644C22semidirect
36. C8×Dic59C22semidirect
152. #576D59semidirect
161. C59#3290semidirect