Finite Group Databasebeta

← #21434563

Subgroups — #21434563

Order 7552.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273758C211yesmaximal, characteristic, complemented
2C2×#14273755C211yesmaximal, characteristic, complemented
3C2×#14273752C211yesmaximal, characteristic, complemented
4#16837948C211yesmaximal, characteristic, complemented
5C2×#14273716C211yesmaximal, characteristic, complemented
6#16837795C212yesmaximal, complemented
7#16837788C212yesmaximal, complemented
8#16837787C212yesmaximal, complemented
9#16837783C212yesmaximal, complemented
10M16×Dic59C211yesmaximal, characteristic, complemented
11C2×#137×C59C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×D236C2211yescharacteristic
14#14273758—24no—
15#14273755—24no—
16#14273752—24no—
17C2×#11745672C2212yescomplemented
18C2×#11745660C2212yes—
19C2×#11745671C2212yes—
20C2×#11745671C2212yescomplemented
21C2×D472C2212yes—
22C2×#11745669C2212yes—
23C2×#11745664C2211yescharacteristic
24#14273725C2211yescharacteristic, complemented
25#14273723C2211yescharacteristic, complemented
26#14273716—22no—
27#14273716C2212yes—
28#14273716C2212yes—
29#14273716C2211yescharacteristic, complemented
30#14273714C2211yescharacteristic, complemented
31#14273699—22no—
32C4×C22⋊D59—22no—
33C2×(C2×D59)⋊C4—22no—
34C2×C4×Dic59C2211yescharacteristic
35#14273637C2212yescomplemented
36C8×Dic59C2212yescomplemented
37C2×#41×C59C2211yescharacteristic
38C22×Q8×C59C2211yescharacteristic
39#137×C59—24no—
40C2×Q16×C59C2212yescomplemented
41C2×SD16×C59C2212yescomplemented
42C2×M16×C59C2211yescharacteristic
43C23×D59—21no—
44#41×C59—22no—
45#41×C59—22no—
46C2×Q8×C59—21no—
47C2×Q8×C59—22no—
48C2×Q8×C59—22no—
49C2×Q8×C59C2312yes—
50C2×Q8×C59C2311yescharacteristic
51C2×D4×C59—21no—
52C2×D4×C59C2311yescharacteristic
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59C2311yescharacteristic
56C2×C22⋊D59—21no—
57C2×C22⋊D59—22no—
58C22×Dic59D412yes—
59#11745685—22no—
60#11745685—22no—
61C2×D236—22no—
62C2×D236—22no—
63C2×D236—21no—
64C2×D236C2312yes—
65C2×D236C2311yescharacteristic
66C2×C4×D59—21no—
67C2×Dic118C2311yescharacteristic
68Q16×C59—24no—
69SD16×C59—24no—
70M16×C59D414yescomplemented
71C2×C8×C59C2312yes—
72C22⋊Dic59—22no—
73#11745672—24no—
74#11745671—24no—
75#11745671—24no—
76#11745669—24no—
77(C2×D59)⋊C4—24no—
78(C2×D59)⋊C4—24no—
79(C2×D59)⋊C4—22no—
80Dic59⋊C4—22no—
81C4×Dic59D412yes—
82C4×Dic59C2311yescharacteristic
83C4×Dic59C2311yescharacteristic
84#11745664D414yescomplemented
85C2×C59⋊C8C2312yes—
86D472—24no—
87#11745660—24no—
88C23×C59—21no—
89C23×C59C2×D411yescharacteristic
90C22×D59—22no—
91C22×D59—21no—
92C22×D59—44no—
93C22×D59—42no—
94Q8×C59—21no—
95Q8×C59—22no—
96Q8×C59—22no—
97Q8×C59—21no—
98Q8×C59—42no—
99D4×C59—21no—
100D4×C59—21no—
101D4×C59—42no—
102C2×C4×C59—21no—
103C2×C4×C59—22no—
104C2×C4×C59—42no—
105C2×C4×C59—42no—
106C2×C4×C59C2×D411yescharacteristic
107C2×C4×C59C2×D412yes—
108C2×C4×C59C2×D412yes—
109C2×C4×C59C2411yescharacteristic
110C22⋊D59—44no—
111C22⋊D59—42no—
112C2×Dic59—21no—
113C2×Dic59—42no—
114C2×Dic59C2×D412yes—
115C2×Dic59C2×D412yes—
116D236—22no—
117D236—21no—
118D236—22no—
119D236—21no—
120D236—42no—
121C4×D59—42no—
122Dic118—21no—
123Dic118—21no—
124C8×C59C2×D414yes—
125C59⋊C8C2×D414yes—
126C22×C59—22no—
127C22×C59—41no—
128C22×C59—42no—
129C22×C59#12712yes—
130C22×C59C22×D411yescharacteristic
131C2×D59—41no—
132C2×D59—42no—
133C2×D59—42no—
134C2×D59—44no—
135C2×D59—84no—
136C4×C59—41no—
137C4×C59—42no—
138C4×C59#12712yes—
139C4×C59C22×D411yescharacteristic
140C4×C59C22×D411yescharacteristic
141Dic59—22no—
142Dic59—22no—
143Dic59—41no—
144#3153—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—81no—
147C2×C59C2×#12711yescharacteristic
148C2×C59#57512yes—
149D59—81no—
150D59—82no—
151C2×#137—591no—
152C2×#137D5911yescharacteristic, complemented
153C2×AGL(1,ℤ/8)—591no—
154C2×AGL(1,ℤ/8)—591no—
155#532—591no—
156C2×#124—591no—
157#497—592no—
158#496—592no—
159#495—592no—
160#495—592no—
161C4×M16—591no—
162C59#315311yescharacteristic, complemented, Sylow
163C2×#41—591no—
164C2×#41C2×D5911yescharacteristic
165C22×Q8C2×D5911yescharacteristic
166C22×D4—591no—
167#137—24no—
168#137—1184no—
169AGL(1,ℤ/8)—1184no—
170AGL(1,ℤ/8)—1184no—
171C2×Q16—592no—
172C2×Q16C2×D5912yescomplemented
173C2×SD16—592no—
174C2×SD16—592no—
175C2×SD16—592no—
176C2×SD16C2×D5912yescomplemented
177C2×D8—592no—
178C2×D8—592no—
179C2×M16—591no—
180C2×M16C2×D5911yescharacteristic
181C4⋊Q8—591no—
182#127—591no—
183#124—592no—
184#124—592no—
185#124—591no—
186#124—591no—
187#124—1182no—
188#121—1182no—
189C4×D4—1182no—
190C2×C22⋊C4—1182no—
191C2×C42—591no—
192#97—592no—
193C4×C8—592no—
194C24—1181no—
195#41—22no—
196#41—22no—
197#41—1182no—
198#41—1182no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—591no—
203C2×Q8C22×D5912yes—
204C2×Q8C22×D5911yescharacteristic
205C2×D4—21no—
206C2×D4—592no—
207C2×D4—591no—
208C2×D4—1182no—
209C2×D4—1181no—
210C2×D4—1182no—
211C2×D4—1181no—
212C2×D4—1182no—
213C2×D4C22×D5911yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—592no—
217C22×C4—1181no—
218C22×C4C22×D5911yescharacteristic
219Q16—24no—
220Q16—1184no—
221SD16—24no—
222SD16—1184no—
223SD16—1184no—
224SD16—1184no—
225D8—1184no—
226D8—1184no—
227M16—594no—
228M16C22⋊D5914yescomplemented
229C2×C8—592no—
230C2×C8C22×D5912yes—
231C4⋊C4—1182no—
232C22⋊C4—1184no—
233C22⋊C4—1184no—
234C22⋊C4—1182no—
235C22⋊C4—1182no—
236C42—592no—
237C42—591no—
238C42—591no—
239C23—21no—
240C23—1182no—
241C23—1181no—
242C23—2364no—
243C23—2362no—
244C23D4×D5911yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—1181no—
251Q8—1181no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—1182no—
256D4—1181no—
257D4—1181no—
258D4—1182no—
259D4—2364no—
260D4—2362no—
261D4—2362no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—592no—
267C2×C4—592no—
268C2×C4—1181no—
269C2×C4—2362no—
270C2×C4—2362no—
271C2×C4D4×D5911yescharacteristic
272C2×C4D4×D5912yes—
273C2×C4C2×C22⋊D5912yes—
274C2×C4C23×D5911yescharacteristic
275C8—594no—
276C8C2×C22⋊D5914yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—4724no—
281C22—2361no—
282C22—2362no—
283C22—2362no—
284C22—2364no—
285C22#1427372312yes—
286C22C2×D4×D5911yescharacteristic
287C4—41no—
288C4—42no—
289C4—1182no—
290C4—1182no—
291C4—2361no—
292C4#1427372312yes—
293C4C2×D4×D5911yescharacteristic
294C4C22×C22⋊D5911yescharacteristic
295C2—22no—
296C2—81no—
297C2—4722no—
298C2—4721no—
299C2C2×#1427372311yescharacteristic
300C2#1683820112yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#137×C59C2
socleC22×C59C22×D4
hypercenterC2×#137D59
hypocenterC59#3153
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×#14273758C2semidirect
2. C2×#14273755C2semidirect
3. C2×#14273752C2semidirect
4. #16837948C2semidirect
5. C2×#14273716C2semidirect
6. #16837795C2semidirect
7. #16837788C2semidirect
8. #16837787C2semidirect
9. #16837783C2semidirect
10. M16×Dic59C2semidirect
11. C2×#137×C59C2semidirect
17. C2×#11745672C22semidirect
20. C2×#11745671C22semidirect
24. #14273725C22semidirect
25. #14273723C22semidirect
29. #14273716C22semidirect
30. #14273714C22semidirect
35. #14273637C22semidirect
36. C8×Dic59C22semidirect
40. C2×Q16×C59C22semidirect
41. C2×SD16×C59C22semidirect
70. M16×C59D4semidirect
84. #11745664D4semidirect
152. C2×#137D59semidirect
162. C59#3153semidirect
172. C2×Q16C2×D59semidirect
176. C2×SD16C2×D59semidirect
228. M16C22⋊D59semidirect