Finite Group Databasebeta

← #21435109

Subgroups — #21435109

Order 7552.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837959C211yesmaximal, characteristic, complemented
2#16837952C211yesmaximal, characteristic
3#16837796C212yesmaximal, complemented
4#16837762C212yesmaximal, complemented
5#16837613C212yesmaximal, complemented
6#16837603C212yesmaximal, complemented
7#16837566C214yesmaximal, complemented
8C59×#432C211yesmaximal, characteristic, complemented
9C2×#11745685C2212yes—
10C2×Dic236C2214yes—
11C2×#11745660C2214yes—
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273724C2211yescharacteristic
16#14273719—21no—
17#14273715C2212yes—
18#14273706—21no—
19#14273706C2212yes—
20#14273701—21no—
21#14273701—21no—
22C4×Dic118—21no—
23C4×Dic118C2212yes—
24C4×D236—21no—
25C4×D236—21no—
26#14273686—21no—
27#14273652C2214yes—
28#14273649C2214yes—
29C2×C42×C59C2211yescharacteristic
30C4⋊C8×C59C2212yes—
31C22⋊C8×C59C2212yes—
32#97×C59C2212yes—
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C2×C22⋊D59—22no—
37#11745685—44no—
38C2×D236—21no—
39C2×D236—21no—
40C2×D236C2312yes—
41C2×C4×D59—22no—
42C2×Dic118—21no—
43C2×Dic118C2312yes—
44C2×Dic118C2312yes—
45C2×C8×C59C2314yes—
46C42×C59D411yescharacteristic
47C42×C59D411yescharacteristic
48C42×C59C2311yescharacteristic
49C42×C59C2311yescharacteristic
50C22⋊Dic59—22no—
51(C2×D59)⋊C4—22no—
52(C2×D59)⋊C4—22no—
53C4⋊Dic59—21no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61C4×Dic59—22no—
62Dic236—44no—
63#11745660—44no—
64C23×C59C2×D411yescharacteristic
65C22×D59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—41no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2411yescharacteristic
75C22⋊D59—44no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79D236—24no—
80D236—42no—
81D236—42no—
82C4×D59—44no—
83Dic118—22no—
84Dic118—22no—
85Dic118—24no—
86Dic118—42no—
87C8×C59—24no—
88C22×C59—21no—
89C22×C59—21no—
90C22×C59—21no—
91C22×C59C22×D411yescharacteristic
92C2×D59—42no—
93C2×D59—42no—
94C2×D59—42no—
95C4×C59—21no—
96C4×C59—21no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59#13712yes—
100C4×C59H(5,𝔽2)12yes—
101Dic59—42no—
102Dic59—42no—
103Dic59—42no—
104#3216—591nomaximal, Sylow
105C2×C59—41no—
106C2×C59#53511yescharacteristic
107C2×C59C2×#13711yescharacteristic
108C2×C59#57511yescharacteristic
109D59—82no—
110#533—591no—
111#532—591no—
112#497—592no—
113#489—592no—
114#462—592no—
115#460—592no—
116#452—594no—
117#432D5911yescharacteristic, complemented
118C59#321611yescharacteristic, complemented, Sylow
119C2×#41—592no—
120C2×Q16—594no—
121C2×SD16—594no—
122C4⋊Q8—591no—
123C4⋊Q8—591no—
124C4⋊Q8—591no—
125#127—591no—
126#125—1181no—
127#124—592no—
128C22⋊Q8—592no—
129C22⋊Q8—1181no—
130#121—1181no—
131#121—1181no—
132C4×Q8—592no—
133C4×Q8—1181no—
134C4×D4—1181no—
135C4×D4—1181no—
136#117—1181no—
137C2×C42C2×D5911yescharacteristic
138C4⋊C8C2×D5912yes—
139#103—594no—
140#102—594no—
141C22⋊C8C2×D5912yes—
142#97C2×D5912yes—
143#41—2364no—
144C2×Q8—592no—
145C2×Q8—592no—
146C2×Q8—1181no—
147C2×D4—592no—
148C2×D4—1182no—
149C2×D4—1181no—
150C2×D4—1181no—
151C22×C4—1182no—
152C22×C4D23611yescharacteristic
153C22×C4D23611yescharacteristic
154C22×C4C22×D5911yescharacteristic
155Q16—2364no—
156SD16—2364no—
157C2×C8C22×D5914yes—
158C4⋊C4—592no—
159C4⋊C4—1181no—
160C4⋊C4—1181no—
161C4⋊C4—1181no—
162C4⋊C4—1181no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—1181no—
166C22⋊C4—1182no—
167C22⋊C4—1182no—
168C22⋊C4—1182no—
169C42—1182no—
170C42D23611yescharacteristic
171C42D23611yescharacteristic
172C42C22×D5911yescharacteristic
173C42C22×D5911yescharacteristic
174C23—1182no—
175C23C2×D23611yescharacteristic
176Q8—1182no—
177Q8—1182no—
178Q8—1184no—
179Q8—2362no—
180D4—1184no—
181D4—2362no—
182D4—2364no—
183D4—2362no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—2364no—
191C2×C4C2×D23611yescharacteristic
192C2×C4C2×D23611yescharacteristic
193C2×C4C2×D23611yescharacteristic
194C2×C4C2×D23611yescharacteristic
195C2×C4C2×D23611yescharacteristic
196C2×C4C23×D5911yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—2362no—
202C22—2362no—
203C22—2362no—
204C22C22×D23611yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—2362no—
210C4—2362no—
211C4—2362no—
212C4#1427376012yes—
213C4#1427377312yes—
214C2—41no—
215C2—4722no—
216C2#1683797111yescharacteristic
217C2C2×#1427376011yescharacteristic
218C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3216
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16837959C2semidirect
3. #16837796C2semidirect
4. #16837762C2semidirect
5. #16837613C2semidirect
6. #16837603C2semidirect
7. #16837566C2semidirect
8. C59×#432C2semidirect
117. #432D59semidirect
118. C59#3216semidirect