Finite Group Databasebeta

← #21434791

Subgroups — #21434791

Order 7552.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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#16837950C211yesmaximal, characteristic, complemented
2#16837931C211yesmaximal, characteristic, complemented
3#16837811C211yesmaximal, characteristic, complemented
4#16837766C211yesmaximal, characteristic, complemented
5#16837761C211yesmaximal, characteristic, complemented
6#16837635C212yesmaximal, complemented
7#16837628C212yesmaximal, complemented
8#16837514C212yesmaximal, complemented
9#16837503C212yesmaximal, complemented
10#97×D59C211yesmaximal, characteristic, complemented
11C59×#496C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×C8×D59C2212yes—
14#14273727C2211yescharacteristic
15#14273720—21no—
16#14273719C2211yescharacteristic
17#14273714—21no—
18#14273709—21no—
19#14273703C2211yescharacteristic
20#14273698—21no—
21#14273698C2211yescharacteristic
22#14273698C2212yes—
23Q8×Dic59C2211yescharacteristic
24D4×Dic59—21no—
25D4×Dic59C2211yescharacteristic
26D4×Dic59C2212yes—
27(C22⋊D59)⋊C4—21no—
28#14273683—21no—
29C42×D59C2211yescharacteristic
30#14273661C2212yes—
31#14273659C2212yes—
32#14273651C2212yes—
33#14273648C2212yes—
34#14273648C2212yes—
35#14273648C2212yes—
36#14273638C2211yescharacteristic
37#14273637C2212yes—
38C2×SD16×C59C2212yes—
39C2×D8×C59C2212yes—
40#127×C59C2211yescharacteristic
41#124×C59C2211yescharacteristic
42#97×C59C2211yescharacteristic
43C2×Q8×C59C2311yescharacteristic
44C2×D4×C59—21no—
45C2×D4×C59—21no—
46C2×D4×C59C2311yescharacteristic
47C2×D4×C59C2312yes—
48C2×C22⋊D59—21no—
49C2×C22⋊D59—22no—
50C22×Dic59—21no—
51C22×Dic59—22no—
52#11745687—44no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118—21no—
57SD16×C59—24no—
58D8×C59—24no—
59C2×C8×C59C2312yes—
60C22⋊C4×C59—21no—
61C22⋊C4×C59—21no—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—21no—
64C22⋊Dic59—22no—
65C22⋊Dic59—22no—
66C22⋊Dic59—21no—
67(C2×D59)⋊C4—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59—21no—
70C4⋊Dic59C2311yescharacteristic
71C4⋊Dic59C2311yescharacteristic
72C4⋊Dic59C2312yes—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75Dic59⋊C4—21no—
76C4×Dic59—21no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81C8×D59—24no—
82C23×C59—21no—
83C23×C59—22no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—22no—
86D4×C59—22no—
87D4×C59—22no—
88D4×C59—22no—
89D4×C59—42no—
90D4×C59—42no—
91C2×C4×C59—21no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—44no—
96C22⋊D59—42no—
97C2×Dic59—21no—
98C2×Dic59—21no—
99C2×Dic59—22no—
100C2×Dic59—44no—
101C2×Dic59—42no—
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D411yescharacteristic
104C2×Dic59C2×D411yescharacteristic
105C4×D59—22no—
106C4×D59—22no—
107C4×D59—41no—
108Dic118—42no—
109C8×C59#4114yescomplemented
110C59⋊C8—22no—
111C22×C59—41no—
112C22×C59—42no—
113C22×C59—42no—
114C22×C59—41no—
115C22×C59—41no—
116C22×C59—42no—
117C22×C59C22×D411yescharacteristic
118C2×D59—21no—
119C2×D59—21no—
120C2×D59AGL(1,ℤ/8)12yes—
121C4×C59—21no—
122C4×C59—21no—
123C4×C59—41no—
124C4×C59C2×#4112yes—
125Dic59—21no—
126Dic59—21no—
127Dic59—21no—
128Dic59—42no—
129Dic59—41no—
130Dic59—41no—
131#3180—591nomaximal, Sylow
132C2×C59—82no—
133C2×C59—81no—
134C2×C59#53211yescharacteristic
135C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C59#57511yescharacteristic
137D59—22no—
138#532—591no—
139#529—591no—
140#501—591no—
141#496D5911yescharacteristic, complemented
142#490—591no—
143#489—591no—
144#466—592no—
145#465—592no—
146#442—592no—
147#440—592no—
148C2×#97—591no—
149C59#318011yescharacteristic, complemented, Sylow
150C2×#41—1181no—
151C2×SD16C2×D5912yes—
152C2×D8C2×D5912yes—
153C22×C8—592no—
154C4⋊Q8—591no—
155#127C2×D5911yescharacteristic
156#126—1181no—
157#125—591no—
158#124—1181no—
159#124C2×D5911yescharacteristic
160#123—1181no—
161C22⋊Q8—591no—
162#121—591no—
163#121—592no—
164#121—1181no—
165C4×Q8—591no—
166C4×D4—591no—
167C4×D4—592no—
168C4×D4—1181no—
169C4×D4—1181no—
170#117—1181no—
171C2×C42—591no—
172#107—592no—
173#106—592no—
174#103—592no—
175#102—592no—
176#102—592no—
177#102—592no—
178#97—592no—
179#97—591no—
180#97C2×D5911yescharacteristic
181#41—2364no—
182C2×Q8—1181no—
183C2×Q8C22×D5911yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—1181no—
187C2×D4—1182no—
188C2×D4C22×D5911yescharacteristic
189C2×D4C22×D5912yes—
190C22×C4—591no—
191C22×C4—591no—
192C22×C4—591no—
193C22×C4—1181no—
194C22×C4—1182no—
195SD16—24no—
196D8—24no—
197C2×C8—592no—
198C2×C8—1184no—
199C2×C8C22×D5912yes—
200C4⋊C4—591no—
201C4⋊C4—591no—
202C4⋊C4—592no—
203C4⋊C4—1181no—
204C4⋊C4—1181no—
205C4⋊C4—1181no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—1181no—
211C22⋊C4—1181no—
212C22⋊C4—1182no—
213C22⋊C4—1181no—
214C22⋊C4—1182no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—21no—
221C23—22no—
222C23—591no—
223Q8—22no—
224Q8—2362no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—2362no—
231D4—2364no—
232C2×C4—21no—
233C2×C4—591no—
234C2×C4—591no—
235C2×C4—591no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1181no—
239C2×C4—1181no—
240C2×C4—1182no—
241C2×C4—2361no—
242C2×C4—2362no—
243C2×C4—2364no—
244C2×C4D4×D5911yescharacteristic
245C2×C4D4×D5911yescharacteristic
246C2×C4C23×D5911yescharacteristic
247C8—1182no—
248C8#1174568714yescomplemented
249C22—42no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—42no—
255C22—592no—
256C22—1181no—
257C22—1181no—
258C22C2×D4×D5911yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—1181no—
263C4—1181no—
264C4—1181no—
265C4—2362no—
266C4—2361no—
267C4—2361no—
268C4C2×#1174568712yes—
269C2—82no—
270C2—81no—
271C2—1182no—
272C2#1683795011yescharacteristic
273C2AGL(1,ℤ/8)×D5911yescharacteristic
274C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3180
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16837950C2semidirect
2. #16837931C2semidirect
3. #16837811C2semidirect
4. #16837766C2semidirect
5. #16837761C2semidirect
6. #16837635C2semidirect
7. #16837628C2semidirect
8. #16837514C2semidirect
9. #16837503C2semidirect
10. #97×D59C2semidirect
11. C59×#496C2semidirect
109. C8×C59#41semidirect
141. #496D59semidirect
149. C59#3180semidirect
248. C8#11745687semidirect