Finite Group Databasebeta

← #21435114

Subgroups — #21435114

Order 7552.

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

normal subgroups only

This group has 490 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#16837936C211yesmaximal, characteristic, complemented
2#16837789C212yesmaximal, complemented
3#16837766C212yesmaximal, complemented
4#16837599C212yesmaximal, complemented
5#16837594C212yesmaximal, complemented
6#16837553C212yesmaximal, complemented
7#16837536C212yesmaximal, complemented
8#16837459C211yesmaximal, characteristic, complemented
9C2×#127×C59C211yesmaximal, characteristic, complemented
10C2×#11745670C2214yescomplemented
11C2×#11745669C2214yescomplemented
12#14273721—21no—
13#14273719C2211yescharacteristic, complemented
14#14273715C2211yescharacteristic, complemented
15#14273710—21no—
16#14273706C2211yescharacteristic
17#14273701C2211yescharacteristic
18C4×Dic118C2211yescharacteristic, complemented
19C4×D236C2211yescharacteristic, complemented
20C4×C22⋊D59—21no—
21#14273684—21no—
22C4⋊(C59⋊C8)C2212yescomplemented
23#14273648C2214yescomplemented
24#14273648C2214yescomplemented
25C22⋊(C59⋊C8)C2212yes—
26#14273638C2212yescomplemented
27C22×D4×C59—21no—
28C22×D4×C59—21no—
29C22×D4×C59C2212yes—
30#127×C59—21no—
31#127×C59—21no—
32#127×C59C2212yes—
33#127×C59C2212yes—
34C2×C42×C59C2211yescharacteristic
35C24×C59—22no—
36C2×D4×C59—22no—
37C2×D4×C59—22no—
38C2×D4×C59—22no—
39C2×D4×C59—22no—
40C2×D4×C59—22no—
41C2×D4×C59—44no—
42C2×D4×C59—44no—
43C2×D4×C59—44no—
44C2×D4×C59C2314yes—
45C22×C4×C59D411yescharacteristic
46C22×C4×C59D411yescharacteristic
47C22×C4×C59C2311yescharacteristic
48C2×C22⋊D59—21no—
49C2×D236C2311yescharacteristic
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic
52C42×C59D411yescharacteristic
53C42×C59D411yescharacteristic
54C42×C59C2311yescharacteristic
55C42×C59C2311yescharacteristic
56C22⋊Dic59—21no—
57#11745670—44no—
58#11745669—44no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2311yescharacteristic
65Dic59⋊C4—21no—
66Dic59⋊C4—21no—
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69C4×Dic59—21no—
70C2×C59⋊C8C2314yes—
71C23×C59—24no—
72C23×C59—44no—
73C23×C59—44no—
74C23×C59—44no—
75C23×C59C2×D411yescharacteristic
76C22×D59—21no—
77D4×C59—24no—
78D4×C59—24no—
79D4×C59—44no—
80D4×C59—44no—
81D4×C59—44no—
82D4×C59—44no—
83D4×C59—44no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C22⋊D59—42no—
94C2×Dic59—21no—
95C2×Dic59—21no—
96C2×Dic59—21no—
97D236—22no—
98C4×D59—42no—
99Dic118—22no—
100C59⋊C8—24no—
101C22×C59—21no—
102C22×C59—21no—
103C22×C59—44no—
104C22×C59—44no—
105C22×C59—44no—
106C22×C59—88no—
107C22×C59AGL(1,ℤ/8)12yes—
108C22×C59C22×D411yescharacteristic
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—21no—
116C4×C59AGL(1,ℤ/8)12yes—
117C4×C59H(5,𝔽2)12yes—
118Dic59—41no—
119Dic59—41no—
120Dic59—41no—
121#3217—591nomaximal, Sylow
122C2×C59—22no—
123C2×C59—84no—
124C2×C59#53511yescharacteristic
125C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
127D59—81no—
128C2×#127D5911yescharacteristic, complemented
129#529—591no—
130#496—592no—
131#490—592no—
132#460—592no—
133#459—592no—
134#450—592no—
135#447—592no—
136#432—591no—
137C59#321711yescharacteristic, complemented, Sylow
138C22×D4—21no—
139C22×D4—21no—
140C22×D4C2×D5912yes—
141C2×SD16—594no—
142C2×D8—594no—
143#127—21no—
144#127—21no—
145#127C2×D5912yes—
146#127C2×D5912yes—
147#126—1181no—
148#125—591no—
149#124—591no—
150#123—1181no—
151C22⋊Q8—591no—
152#121—591no—
153C4×Q8—591no—
154C4×D4—591no—
155C4×D4—1181no—
156#117—1181no—
157C2×C42C2×D5911yescharacteristic
158C4⋊C8—592no—
159#102—594no—
160#102—594no—
161C22⋊C8—592no—
162#97—592no—
163C24—22no—
164C2×Q8—591no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—44no—
171C2×D4—44no—
172C2×D4—44no—
173C2×D4—591no—
174C2×D4—1181no—
175C2×D4C22×D5914yes—
176C22×C4—1181no—
177C22×C4C22⋊D5911yescharacteristic
178C22×C4C22⋊D5911yescharacteristic
179C22×C4C22×D5911yescharacteristic
180SD16—2364no—
181D8—2364no—
182C2×C8—594no—
183C4⋊C4—591no—
184C4⋊C4—591no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C22⋊C4—1181no—
190C22⋊C4—1181no—
191C22⋊C4—1181no—
192C22⋊C4—1181no—
193C22⋊C4—1181no—
194C42—1181no—
195C42C22⋊D5911yescharacteristic
196C42C22⋊D5911yescharacteristic
197C42C22×D5911yescharacteristic
198C42C22×D5911yescharacteristic
199C23—24no—
200C23—44no—
201C23—44no—
202C23—44no—
203C23—1181no—
204C23C2×C22⋊D5911yescharacteristic
205Q8—1182no—
206D4—24no—
207D4—24no—
208D4—44no—
209D4—44no—
210D4—44no—
211D4—44no—
212D4—44no—
213D4—1182no—
214D4—2362no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1181no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—2362no—
222C2×C4C2×C22⋊D5911yescharacteristic
223C2×C4C2×C22⋊D5911yescharacteristic
224C2×C4C2×C22⋊D5911yescharacteristic
225C2×C4C2×C22⋊D5911yescharacteristic
226C2×C4C2×C22⋊D5911yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—1184no—
229C22—21no—
230C22—21no—
231C22—44no—
232C22—44no—
233C22—44no—
234C22—88no—
235C22—2361no—
236C22—2361no—
237C22—2361no—
238C22#1427375312yes—
239C22C22×C22⋊D5911yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—2361no—
245C4—2361no—
246C4—2361no—
247C4#1427375312yes—
248C4#1427377212yes—
249C2—22no—
250C2—84no—
251C2—4721no—
252C2#1683796911yescharacteristic
253C2C2×#1427375311yescharacteristic
254C2C2×#1427375311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#127×C59C2
socleC22×C59C22×D4
hypercenterC2×#127D59
hypocenterC59#3217
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #16837936C2semidirect
2. #16837789C2semidirect
3. #16837766C2semidirect
4. #16837599C2semidirect
5. #16837594C2semidirect
6. #16837553C2semidirect
7. #16837536C2semidirect
8. #16837459C2semidirect
9. C2×#127×C59C2semidirect
10. C2×#11745670C22semidirect
11. C2×#11745669C22semidirect
13. #14273719C22semidirect
14. #14273715C22semidirect
18. C4×Dic118C22semidirect
19. C4×D236C22semidirect
22. C4⋊(C59⋊C8)C22semidirect
23. #14273648C22semidirect
24. #14273648C22semidirect
26. #14273638C22semidirect
128. C2×#127D59semidirect
137. C59#3217semidirect