Finite Group Databasebeta

← #21433772

Subgroups — #21433772

Order 7552.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273753C211yesmaximal, characteristic, complemented
2C2×#14273734C211yesmaximal, characteristic, complemented
3#16837980C211yesmaximal, characteristic, complemented
4#16837653C212yesmaximal, complemented
5#16837646C212yesmaximal, complemented
6#16837636C212yesmaximal, complemented
7#16837629C212yesmaximal, complemented
8#16837445C211yesmaximal, characteristic, complemented
9#16837396C211yesmaximal, characteristic, complemented
10C2×#14273648C211yesmaximal, characteristic, complemented
11C59×#535C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13#14273753—24no—
14C2×#11745670C2212yes—
15C2×#11745669C2212yes—
16#14273734—24no—
17C2×#11745664C2211yescharacteristic
18C2×#11745664C2212yescomplemented
19C22×C59⋊C8C2211yescharacteristic
20C22×C59⋊C8C2212yescomplemented
21#14273706C2212yescomplemented
22#14273703—21no—
23#14273701C2212yescomplemented
24#14273699—22no—
25#14273698—21no—
26C2×C4⋊Dic59C2211yescharacteristic
27#14273660C2212yescomplemented
28#14273658C2212yescomplemented
29#14273650C2211yescharacteristic, complemented
30#14273650C2211yescharacteristic, complemented
31#14273648C2212yes—
32#14273648C2212yes—
33#14273647C2211yescharacteristic, complemented
34#14273647C2211yescharacteristic, complemented
35C2×#41×C59C2211yescharacteristic
36C22×D4×C59C2211yescharacteristic
37#127×C59—21no—
38#124×C59—21no—
39#121×C59C2212yes—
40#121×C59C2212yes—
41#120×C59—22no—
42#117×C59C2211yescharacteristic
43C24×C59—21no—
44#41×C59—22no—
45#41×C59—22no—
46C2×Q8×C59D411yescharacteristic
47C2×D4×C59—22no—
48C2×D4×C59—22no—
49C2×D4×C59—22no—
50C2×D4×C59—21no—
51C2×D4×C59—22no—
52C2×D4×C59D412yes—
53C2×D4×C59D411yescharacteristic
54C2×D4×C59C2312yes—
55C22×C4×C59C2312yes—
56C22×C4×C59C2311yescharacteristic
57C2×C22⋊D59—21no—
58C2×C22⋊D59—22no—
59C22×Dic59—21no—
60#11745685—22no—
61#11745685—22no—
62C2×D236C2311yescharacteristic
63C2×C4×D59—21no—
64C2×Dic118C2311yescharacteristic
65C4⋊C4×C59C2311yescharacteristic
66C4⋊C4×C59C2311yescharacteristic
67C22⋊C4×C59—21no—
68C22⋊C4×C59—22no—
69C22⋊C4×C59—22no—
70C42×C59—21no—
71C22⋊Dic59—22no—
72#11745670—24no—
73#11745669—24no—
74(C2×D59)⋊C4—22no—
75C4⋊Dic59—21no—
76C4⋊Dic59C2312yes—
77Dic59⋊C4—22no—
78#11745664—24no—
79#11745664D414yescomplemented
80C2×C59⋊C8—22no—
81C2×C59⋊C8—24no—
82C2×C59⋊C8C2311yescharacteristic
83C2×C59⋊C8C2311yescharacteristic
84C2×C59⋊C8C2312yes—
85C23×C59—22no—
86C23×C59—42no—
87C23×C59—81no—
88C23×C59—81no—
89C23×C59C2×D412yes—
90C23×C59C2×D411yescharacteristic
91C22×D59—21no—
92Q8×C59—22no—
93D4×C59—24no—
94D4×C59—22no—
95D4×C59—22no—
96D4×C59—22no—
97D4×C59—42no—
98D4×C59—82no—
99D4×C59—82no—
100C2×C4×C59—22no—
101C2×C4×C59—22no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59C2×D412yes—
105C2×C4×C59C2×D412yes—
106C2×C4×C59C2×D411yescharacteristic
107C2×C4×C59#4112yes—
108C2×C4×C59C2411yescharacteristic
109C22⋊D59—42no—
110C22⋊D59—82no—
111C2×Dic59—21no—
112C2×Dic59—22no—
113C2×Dic59—81no—
114D236—21no—
115D236—21no—
116C4×D59—42no—
117Dic118—21no—
118Dic118—21no—
119C59⋊C8—21no—
120C59⋊C8—21no—
121C59⋊C8C2×D414yes—
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—42no—
128C22×C59—42no—
129C22×C59—42no—
130C22×C59—84no—
131C22×C59#12112yes—
132C22×C59C22×D411yescharacteristic
133C2×D59—41no—
134C2×D59—41no—
135C2×D59—41no—
136C4×C59—22no—
137C4×C59—41no—
138C4×C59—41no—
139C4×C59#12112yes—
140C4×C59C22×D411yescharacteristic
141C4×C59C2×#4111yescharacteristic
142Dic59—41no—
143Dic59—42no—
144#3062—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—42no—
147C2×C59—82no—
148C2×C59C2×#12111yescharacteristic
149C2×C59#57611yescharacteristic
150C2×C59#57711yescharacteristic
151D59—81no—
152C2×AGL(1,ℤ/8)—591no—
153C2×#131—591no—
154#537—591no—
155#535D5911yescharacteristic, complemented
156#469—592no—
157#468—592no—
158#466—592no—
159#465—592no—
160#428—591no—
161#416—591no—
162C2×#102—591no—
163C59#306211yescharacteristic, complemented, Sylow
164C2×#41—591no—
165C2×#41C2×D5911yescharacteristic
166C22×D4C2×D5911yescharacteristic
167AGL(1,ℤ/8)—1184no—
168C2×SD16—592no—
169C2×D8—592no—
170#131—1184no—
171C2×M16—591no—
172C2×M16—592no—
173C22×C8—591no—
174C22×C8—592no—
175#127—21no—
176#124—21no—
177C22⋊Q8—592no—
178C22⋊Q8—1181no—
179#121—592no—
180#121—1181no—
181#121—1182no—
182#121C2×D5912yes—
183#121C2×D5912yes—
184#120—22no—
185#117C2×D5911yescharacteristic
186C2×C4⋊C4—591no—
187#107—592no—
188#106—592no—
189#103—591no—
190#103—591no—
191#102—592no—
192#102—592no—
193#102—591no—
194#102—591no—
195C24—21no—
196#41—22no—
197#41—22no—
198#41—1182no—
199#41—1182no—
200C2×Q8—591no—
201C2×Q8C22⋊D5911yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—591no—
208C2×D4—1182no—
209C2×D4—1181no—
210C2×D4C22⋊D5912yes—
211C2×D4C22⋊D5911yescharacteristic
212C2×D4C22×D5912yes—
213C22×C4—1181no—
214C22×C4—1181no—
215C22×C4C22×D5912yes—
216C22×C4C22×D5911yescharacteristic
217SD16—1184no—
218D8—1184no—
219M16—594no—
220M16—1184no—
221C2×C8—592no—
222C2×C8—591no—
223C2×C8—591no—
224C2×C8—1184no—
225C2×C8—1182no—
226C4⋊C4—592no—
227C4⋊C4—1181no—
228C4⋊C4—1182no—
229C4⋊C4C22×D5911yescharacteristic
230C4⋊C4C22×D5911yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—1182no—
235C22⋊C4—1182no—
236C42—21no—
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—1181no—
242C23C2×C22⋊D5912yes—
243C23C2×C22⋊D5911yescharacteristic
244Q8—22no—
245Q8—1181no—
246Q8—1181no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—22no—
251D4—42no—
252D4—82no—
253D4—82no—
254D4—1181no—
255D4—1181no—
256D4—4722no—
257D4—2362no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—1182no—
263C2×C4—1181no—
264C2×C4—4721no—
265C2×C4—2362no—
266C2×C4D4×D5912yes—
267C2×C4#1174568712yes—
268C2×C4C2×C22⋊D5912yes—
269C2×C4C2×C22⋊D5911yescharacteristic
270C2×C4C23×D5911yescharacteristic
271C8—594no—
272C8—1181no—
273C8—1181no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—84no—
283C22—2361no—
284C22—2361no—
285C22—2361no—
286C22#1427369912yes—
287C22C22×C22⋊D5911yescharacteristic
288C4—22no—
289C4—41no—
290C4—41no—
291C4—2361no—
292C4—2362no—
293C4#1427369912yes—
294C4C2×D4×D5911yescharacteristic
295C4C2×#1174568711yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—4721no—
300C2C2×#1427369911yescharacteristic
301C2#1683820511yescharacteristic
302C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#535C2
socleC22×C59C22×D4
hypercenter#535D59
hypocenterC59#3062
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. C2×#14273734C2semidirect
3. #16837980C2semidirect
4. #16837653C2semidirect
5. #16837646C2semidirect
6. #16837636C2semidirect
7. #16837629C2semidirect
8. #16837445C2semidirect
9. #16837396C2semidirect
10. C2×#14273648C2semidirect
11. C59×#535C2semidirect
18. C2×#11745664C22semidirect
20. C22×C59⋊C8C22semidirect
21. #14273706C22semidirect
23. #14273701C22semidirect
27. #14273660C22semidirect
28. #14273658C22semidirect
29. #14273650C22semidirect
30. #14273650C22semidirect
33. #14273647C22semidirect
34. #14273647C22semidirect
79. #11745664D4semidirect
155. #535D59semidirect
163. C59#3062semidirect