Finite Group Databasebeta

← #21434574

Subgroups — #21434574

Order 7552.

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

normal subgroups only

This group has 564 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×#14273752C211yesmaximal, characteristic, complemented
3C2×#14273747C211yesmaximal, characteristic, complemented
4C22×#11745671C211yesmaximal, characteristic, complemented
5#16837971C211yesmaximal, characteristic, complemented
6#16837794C212yesmaximal, complemented
7#16837792C212yesmaximal, complemented
8#16837784C212yesmaximal, complemented
9#16837776C212yesmaximal, complemented
10#16837358C211yesmaximal, characteristic, complemented
11C59×#536C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×D236C2211yescharacteristic
14#14273758—24no—
15#14273752—24no—
16#14273747—24no—
17C2×#11745672C2211yescharacteristic, complemented
18C2×#11745672C2212yescomplemented
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745671—24no—
21C2×#11745671C2212yes—
22C2×#11745671C2212yes—
23C2×#11745671C2212yes—
24C2×#11745671C2211yescharacteristic, complemented
25C2×#11745671C2212yescomplemented
26C2×#11745669C2212yes—
27C2×#11745669C2211yescharacteristic, complemented
28C2×#11745664C2211yescharacteristic
29C22×C59⋊C8C2211yescharacteristic
30#14273724C2212yes—
31#14273715C2212yes—
32#14273702—22no—
33#14273697—22no—
34#14273638C2212yescomplemented
35C4×C59⋊C8C2212yescomplemented
36C2×#41×C59C2211yescharacteristic
37C22×Q8×C59C2211yescharacteristic
38C4⋊Q8×C59C2212yescomplemented
39#124×C59C2212yescomplemented
40#123×C59—22no—
41C22⋊Q8×C59—22no—
42#117×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—
57#11745685—22no—
58#11745685—22no—
59C2×D236—22no—
60C2×D236—22no—
61C2×D236—21no—
62C2×D236—24no—
63C2×D236C2312yes—
64C2×D236C2311yescharacteristic
65C2×C4×D59—21no—
66C2×Dic118C2311yescharacteristic
67C4⋊C4×C59—24no—
68C4⋊C4×C59D412yes—
69C22⋊C4×C59—24no—
70C22⋊C4×C59D412yes—
71C42×C59C2312yes—
72#11745672—22no—
73#11745672—24no—
74#11745671—24no—
75#11745671—24no—
76#11745671—24no—
77#11745671—22no—
78#11745671—24no—
79#11745670—22no—
80#11745669—24no—
81#11745669—22no—
82(C2×D59)⋊C4—24no—
83#11745664D414yescomplemented
84C2×C59⋊C8D414yescomplemented
85C2×C59⋊C8C2311yescharacteristic
86C2×C59⋊C8C2312yes—
87C2×C59⋊C8C2311yescharacteristic
88C23×C59—21no—
89C23×C59C2×D411yescharacteristic
90C22×D59—22no—
91C22×D59—21no—
92C22×D59—42no—
93C22×D59—82no—
94Q8×C59—22no—
95Q8×C59—21no—
96Q8×C59—22no—
97Q8×C59—21no—
98Q8×C59—42no—
99D4×C59—21no—
100D4×C59—21no—
101D4×C59—42no—
102C2×C4×C59—22no—
103C2×C4×C59—21no—
104C2×C4×C59—42no—
105C2×C4×C59—42no—
106C2×C4×C59C2×D412yes—
107C2×C4×C59C2×D412yes—
108C2×C4×C59C2×D414yes—
109C2×C4×C59C2×D411yescharacteristic
110C2×C4×C59C2411yescharacteristic
111C22⋊D59—42no—
112C2×Dic59—21no—
113D236—22no—
114D236—21no—
115D236—22no—
116D236—21no—
117D236—42no—
118D236—84no—
119C4×D59—42no—
120Dic118—21no—
121Dic118—21no—
122C59⋊C8C2×D412yes—
123C59⋊C8C2×D412yes—
124C59⋊C8C2×D414yes—
125C22×C59—22no—
126C22×C59—41no—
127C22×C59—42no—
128C22×C59#12712yes—
129C22×C59C22×D411yescharacteristic
130C2×D59—41no—
131C2×D59—42no—
132C2×D59—42no—
133C2×D59—44no—
134C2×D59—84no—
135C4×C59—24no—
136C4×C59—41no—
137C4×C59—42no—
138C4×C59#12712yes—
139C4×C59C22×D411yescharacteristic
140C4×C59C22×D411yescharacteristic
141Dic59—41no—
142#3154—591nomaximal, Sylow
143C2×C59—22no—
144C2×C59—81no—
145C2×C59C2×#12711yescharacteristic
146C2×C59#57712yes—
147D59—81no—
148D59—82no—
149C2×#137—591no—
150C2×AGL(1,ℤ/8)—591no—
151C2×#135—591no—
152C22×SD16—591no—
153#536D5911yescharacteristic, complemented
154#535—591no—
155#497—592no—
156#496—592no—
157#495—592no—
158#492—592no—
159#405—591no—
160C59#315411yescharacteristic, complemented, Sylow
161C2×#41—591no—
162C2×#41C2×D5911yescharacteristic
163C22×Q8C2×D5911yescharacteristic
164C22×D4—591no—
165#137—1184no—
166AGL(1,ℤ/8)—1184no—
167#135—1184no—
168C2×Q16—591no—
169C2×Q16—592no—
170C2×SD16—592no—
171C2×SD16—592no—
172C2×SD16—591no—
173C2×SD16—592no—
174C2×SD16—592no—
175C2×SD16—591no—
176C2×SD16—1184no—
177C2×D8—591no—
178C2×D8—592no—
179C2×M16—591no—
180C22×C8—591no—
181C4⋊Q8C2×D5912yescomplemented
182#127—592no—
183#124—592no—
184#124C2×D5912yescomplemented
185#123—22no—
186C22⋊Q8—22no—
187#121—1182no—
188#120—1182no—
189#117C2×D5911yescharacteristic
190#97—592no—
191C4×C8—592no—
192C24—1181no—
193#41—22no—
194#41—22no—
195#41—1182no—
196#41—1182no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—591no—
201C2×Q8C22×D5912yes—
202C2×Q8C22×D5911yescharacteristic
203C2×D4—21no—
204C2×D4—592no—
205C2×D4—591no—
206C2×D4—1181no—
207C2×D4—1182no—
208C2×D4—1182no—
209C2×D4—1184no—
210C2×D4—1181no—
211C2×D4C22×D5911yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—1181no—
215C22×C4C22×D5911yescharacteristic
216Q16—1182no—
217Q16—1184no—
218SD16—1182no—
219SD16—1184no—
220SD16—1184no—
221SD16—1182no—
222SD16—1184no—
223SD16—1184no—
224D8—1182no—
225D8—1184no—
226M16—594no—
227C2×C8—594no—
228C2×C8—591no—
229C2×C8—592no—
230C2×C8—591no—
231C4⋊C4—24no—
232C4⋊C4C22⋊D5912yes—
233C22⋊C4—24no—
234C22⋊C4—1184no—
235C22⋊C4C22⋊D5912yes—
236C42C22×D5912yes—
237C23—21no—
238C23—1182no—
239C23—1181no—
240C23—4722no—
241C23—2362no—
242C23C2×C22⋊D5911yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—1181no—
249Q8—1181no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—1182no—
254D4—1181no—
255D4—1182no—
256D4—1181no—
257D4—4724no—
258D4—2362no—
259D4—2362no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—1181no—
265C2×C4—2362no—
266C2×C4D4×D5912yes—
267C2×C4D4×D5912yes—
268C2×C4C2×C22⋊D5914yes—
269C2×C4C2×C22⋊D5911yescharacteristic
270C2×C4C23×D5911yescharacteristic
271C8—592no—
272C8—592no—
273C8—594no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—4724no—
278C22—2361no—
279C22—2362no—
280C22—2362no—
281C22—2364no—
282C22#1427372312yes—
283C22C22×C22⋊D5911yescharacteristic
284C4—24no—
285C4—41no—
286C4—42no—
287C4—2361no—
288C4#1427372312yes—
289C4C2×D4×D5911yescharacteristic
290C4C2×D4×D5911yescharacteristic
291C2—22no—
292C2—81no—
293C2—4722no—
294C2—4721no—
295C2C2×#1427372311yescharacteristic
296C2#1683821012yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#536C2
socleC22×C59C22×D4
hypercenter#536D59
hypocenterC59#3154
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#14273758C2semidirect
2. C2×#14273752C2semidirect
3. C2×#14273747C2semidirect
4. C22×#11745671C2semidirect
5. #16837971C2semidirect
6. #16837794C2semidirect
7. #16837792C2semidirect
8. #16837784C2semidirect
9. #16837776C2semidirect
10. #16837358C2semidirect
11. C59×#536C2semidirect
17. C2×#11745672C22semidirect
18. C2×#11745672C22semidirect
19. C2×#11745670C22semidirect
24. C2×#11745671C22semidirect
25. C2×#11745671C22semidirect
27. C2×#11745669C22semidirect
34. #14273638C22semidirect
35. C4×C59⋊C8C22semidirect
38. C4⋊Q8×C59C22semidirect
39. #124×C59C22semidirect
83. #11745664D4semidirect
84. C2×C59⋊C8D4semidirect
153. #536D59semidirect
160. C59#3154semidirect
181. C4⋊Q8C2×D59semidirect
184. #124C2×D59semidirect