Finite Group Databasebeta

← #21435033

Subgroups — #21435033

Order 7552.

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

normal subgroups only

This group has 488 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#16837957C211yesmaximal, characteristic, complemented
2#127×D59C211yesmaximal, characteristic
3#16837776C211yesmaximal, characteristic, complemented
4#16837749C211yesmaximal, characteristic, complemented
5#16837748C211yesmaximal, characteristic, complemented
6#16837600C214yesmaximal, complemented
7#16837551C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#492C211yesmaximal, characteristic, complemented
10C2×D4×D59—21no—
11C2×D4×D59—21no—
12C2×D4×D59C2212yes—
13C2×#11745671C2214yescomplemented
14#14273727C2211yescharacteristic, complemented
15#14273724C2211yescharacteristic
16#14273723—21no—
17#14273723—21no—
18#14273723C2212yes—
19#14273718—21no—
20#14273707—21no—
21#14273703C2212yes—
22Q8×Dic59C2212yescomplemented
23#14273692—21no—
24#14273685—21no—
25C42×D59C2211yescharacteristic
26Dic59⋊C8C2212yescomplemented
27#14273649C2214yescomplemented
28#14273648C2214yescomplemented
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic, complemented
31C2×SD16×C59C2214yescomplemented
32C4⋊Q8×C59C2211yescharacteristic, complemented
33#127×C59C2211yescharacteristic
34C4×C8×C59C2211yescharacteristic, complemented
35C23×D59—22no—
36C2×Q8×C59C2312yes—
37C2×D4×C59—21no—
38C2×D4×C59—21no—
39C2×D4×C59C2312yes—
40C2×C22⋊D59—22no—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43D4×D59—44no—
44D4×D59—44no—
45D4×D59—44no—
46C2×D236—21no—
47C2×D236—21no—
48C2×D236C2312yes—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53SD16×C59—44no—
54C2×C8×C59C2312yes—
55C4⋊C4×C59—21no—
56C4⋊C4×C59—21no—
57C42×C59C2311yescharacteristic
58#11745671—44no—
59(C2×D59)⋊C4—22no—
60C4⋊Dic59—21no—
61C4⋊Dic59—22no—
62C4⋊Dic59C2312yes—
63Dic59⋊C4—22no—
64C4×Dic59—22no—
65C4×Dic59D411yescharacteristic
66C4×Dic59D411yescharacteristic
67C4×Dic59C2311yescharacteristic
68C2×C59⋊C8C2312yes—
69C23×C59—22no—
70C22×D59—22no—
71C22×D59—44no—
72C22×D59—44no—
73C22×D59—44no—
74C22×D59C2×D411yescharacteristic
75Q8×C59—24no—
76D4×C59—24no—
77D4×C59—42no—
78D4×C59—42no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C22⋊D59—44no—
84C22⋊D59—44no—
85C22⋊D59—44no—
86C2×Dic59—22no—
87C2×Dic59C2×D411yescharacteristic
88C2×Dic59C2×D411yescharacteristic
89C2×Dic59C2×D411yescharacteristic
90D236—24no—
91D236—42no—
92D236—42no—
93C4×D59—22no—
94C4×D59—22no—
95C4×D59SD1614yescomplemented
96Dic118—42no—
97C8×C59—22no—
98C59⋊C8—22no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C2×D59—21no—
104C2×D59—21no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—88no—
109C2×D59C2×SD1612yes—
110C4×C59—42no—
111C4×C59C2×SD1612yes—
112C4×C59AGL(1,ℤ/8)12yes—
113C4×C59H(5,𝔽2)12yes—
114Dic59—21no—
115Dic59—21no—
116Dic59—42no—
117Dic59C2×SD1612yes—
118#3208—591nomaximal, Sylow
119C2×C59—82no—
120C2×C59#53511yescharacteristic
121C2×C59C22×SD1611yescharacteristic
122C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
123D59—22no—
124D59—82no—
125#533—591no—
126C2×#127—591no—
127#492—591no—
128#492D5911yescharacteristic, complemented
129#486—591no—
130#486—591no—
131#460—594no—
132#450—594no—
133#431—591no—
134C59#320811yescharacteristic, complemented, Sylow
135C22×D4—592no—
136C22×D4—1181no—
137C22×D4—1181no—
138C2×SD16—594no—
139C2×SD16C2×D5914yescomplemented
140C4⋊Q8—591no—
141C4⋊Q8C2×D5911yescharacteristic, complemented
142#127—592no—
143#127—591no—
144#127—1181no—
145#127—1181no—
146#127C2×D5911yescharacteristic
147#125—1181no—
148C22⋊Q8—592no—
149C22⋊Q8—1181no—
150C4×Q8—592no—
151C4×Q8—1181no—
152#117—1181no—
153C2×C42—591no—
154C4⋊C8—592no—
155#102—594no—
156#102—594no—
157C22⋊C8—592no—
158C4×C8—591no—
159C4×C8C2×D5911yescharacteristic, complemented
160C24—1182no—
161C2×Q8—1181no—
162C2×Q8C22×D5912yes—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—592no—
166C2×D4—1182no—
167C2×D4—1182no—
168C2×D4—1182no—
169C2×D4—1181no—
170C2×D4—1181no—
171C2×D4—2364no—
172C2×D4—2364no—
173C2×D4—2364no—
174C2×D4C22×D5912yes—
175C22×C4—591no—
176C22×C4—591no—
177C22×C4—591no—
178SD16—44no—
179SD16—2364no—
180C2×C8—592no—
181C2×C8C22×D5912yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—592no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4—1181no—
188C22⋊C4—1182no—
189C42—591no—
190C42—591no—
191C42—591no—
192C42—1182no—
193C42C22×D5911yescharacteristic
194C23—22no—
195C23—591no—
196C23—1182no—
197C23—2364no—
198C23—2364no—
199C23—2364no—
200Q8—24no—
201Q8—2362no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—1184no—
206D4—2364no—
207D4—2364no—
208D4—2364no—
209D4—2362no—
210D4—2362no—
211C2×C4—22no—
212C2×C4—591no—
213C2×C4—594no—
214C2×C4—591no—
215C2×C4—591no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4D4×D5911yescharacteristic
220C2×C4D4×D5911yescharacteristic
221C2×C4C23×D5911yescharacteristic
222C8—22no—
223C8—1182no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—592no—
228C22—1181no—
229C22—1181no—
230C22—4728no—
231C22—2362no—
232C22—2362no—
233C22—2362no—
234C22C2×D4×D5911yescharacteristic
235C4—42no—
236C4—592no—
237C4—1181no—
238C4—1181no—
239C4—2362no—
240C4SD16×D5912yes—
241C4#1427375412yes—
242C4#1427377212yes—
243C2—82no—
244C2—1182no—
245C2—4722no—
246C2#1683796511yescharacteristic
247C2C2×SD16×D5911yescharacteristic
248C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#492C2
socleC22×C59C22×D4
hypercenter#492D59
hypocenterC59#3208
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837776C2semidirect
4. #16837749C2semidirect
5. #16837748C2semidirect
6. #16837600C2semidirect
7. #16837551C2semidirect
8. #16837453C2semidirect
9. C59×#492C2semidirect
13. C2×#11745671C22semidirect
14. #14273727C22semidirect
22. Q8×Dic59C22semidirect
26. Dic59⋊C8C22semidirect
27. #14273649C22semidirect
28. #14273648C22semidirect
30. C4×C59⋊C8C22semidirect
31. C2×SD16×C59C22semidirect
32. C4⋊Q8×C59C22semidirect
34. C4×C8×C59C22semidirect
95. C4×D59SD16semidirect
128. #492D59semidirect
134. C59#3208semidirect
139. C2×SD16C2×D59semidirect
141. C4⋊Q8C2×D59semidirect
159. C4×C8C2×D59semidirect