Finite Group Databasebeta

← #21433333

Subgroups — #21433333

Order 7552.

738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×Dic118C211yesmaximal, characteristic, complemented
2C2×#14273760C212yesmaximal, complemented
3#16837913C211yesmaximal, characteristic
4#16837560C214yesmaximal, complemented
5#16837543C214yesmaximal, complemented
6#16837412C212yesmaximal, complemented
7C59×#407C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×Dic118—22no—
10C22×Dic118—21no—
11C22×Dic118—28no—
12C22×Dic118C2214yes—
13C22×Dic118C2212yes—
14C23×Dic59—21no—
15#14273760—28no—
16C2×Dic236C2214yescomplemented
17C2×#11745660C2214yescomplemented
18#14273710—21no—
19#14273706C2212yes—
20#14273701C2212yes—
21#14273696—21no—
22C4×C22⋊D59—22no—
23#14273686C2211yescharacteristic
24#14273652C2218yescomplemented
25C23×C4×C59C2211yescharacteristic
26C2×M16×C59C2212yes—
27C22⋊C8×C59C2214yes—
28C24×C59D411yescharacteristic
29C22×C4×C59—24no—
30C22×C4×C59D412yes—
31C22×C4×C59D411yescharacteristic
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C2×C22⋊D59—22no—
35C2×C22⋊D59—21no—
36C22×Dic59—28no—
37C22×Dic59—24no—
38C22×Dic59—22no—
39#11745685—24no—
40C2×D236C2311yescharacteristic
41C2×C4×D59—21no—
42C2×Dic118—28no—
43C2×Dic118—216no—
44C2×Dic118—24no—
45C2×Dic118—22no—
46C2×Dic118—24no—
47C2×Dic118—216no—
48C2×Dic118D418yescomplemented
49C2×Dic118C2311yescharacteristic
50C2×Dic118C2314yes—
51M16×C59—24no—
52C2×C8×C59C2314yes—
53C22⋊Dic59—21no—
54C22⋊Dic59—22no—
55(C2×D59)⋊C4—22no—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58C4×Dic59—21no—
59Dic236—28no—
60#11745660—28no—
61C23×C59—22no—
62C23×C59—24no—
63C23×C59C2×D411yescharacteristic
64C23×C59C2×D412yes—
65C22×D59—21no—
66C2×C4×C59—22no—
67C2×C4×C59—24no—
68C2×C4×C59—24no—
69C2×C4×C59C2×D412yes—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D414yes—
72C2×C4×C59C2411yescharacteristic
73C22⋊D59—42no—
74C22⋊D59—44no—
75C2×Dic59—216no—
76C2×Dic59—28no—
77C2×Dic59—24no—
78C2×Dic59—22no—
79C2×Dic59—21no—
80D236—22no—
81C4×D59—42no—
82Dic118—216no—
83Dic118—28no—
84Dic118—24no—
85Dic118—22no—
86Dic118C2×D418yes—
87C8×C59—24no—
88C22×C59—28no—
89C22×C59—22no—
90C22×C59—22no—
91C22×C59—22no—
92C22×C59#12012yes—
93C22×C59#13714yescomplemented
94C22×C59C22×D411yescharacteristic
95C2×D59—41no—
96C2×D59—42no—
97C4×C59—22no—
98C4×C59#12012yes—
99C4×C59C22×D412yes—
100Dic59—28no—
101Dic59—41no—
102Dic59—42no—
103#3004—591nomaximal, Sylow
104C2×C59—22no—
105C2×C59—24no—
106C2×C59C2×#12011yescharacteristic
107C2×C59C2×#13712yes—
108D59—81no—
109C23×Q8—591no—
110C2×#137—592no—
111#525—591no—
112#451—594no—
113#448—594no—
114#419—592no—
115#407D5911yescharacteristic, complemented
116C59#300411yescharacteristic, complemented, Sylow
117C2×#41—591no—
118C22×Q8—592no—
119C22×Q8—594no—
120C22×Q8—1188no—
121C22×Q8—1182no—
122C22×Q8—1181no—
123C23×C4—1181no—
124C23×C4C2×D5911yescharacteristic
125#137—1188no—
126C2×Q16—594no—
127C2×SD16—594no—
128C2×M16C2×D5912yes—
129#123—1181no—
130C22⋊Q8—592no—
131#121—592no—
132#120—1181no—
133C4×D4—1182no—
134#117—591no—
135#103—598no—
136C22⋊C8C2×D5914yes—
137C24D23611yescharacteristic
138#41—1184no—
139C2×Q8—598no—
140C2×Q8—594no—
141C2×Q8—591no—
142C2×Q8—11816no—
143C2×Q8—1188no—
144C2×Q8—11816no—
145C2×Q8—1184no—
146C2×Q8—1182no—
147C2×Q8—1184no—
148C2×D4—591no—
149C2×D4—1182no—
150C2×D4—1181no—
151C22×C4—24no—
152C22×C4—1188no—
153C22×C4—1184no—
154C22×C4—1182no—
155C22×C4—1181no—
156C22×C4D23612yes—
157C22×C4D23611yescharacteristic
158C22×C4C22×D5912yes—
159C22×C4C22×D5911yescharacteristic
160Q16—1188no—
161SD16—1188no—
162M16—24no—
163C2×C8C22×D5914yes—
164C4⋊C4—592no—
165C4⋊C4—1182no—
166C22⋊C4—1181no—
167C22⋊C4—1182no—
168C22⋊C4—1182no—
169C42—1181no—
170C23—22no—
171C23—24no—
172C23—1181no—
173C23C2×D23611yescharacteristic
174C23C2×D23612yes—
175Q8—598no—
176Q8—11816no—
177Q8—1188no—
178Q8—1184no—
179Q8—1182no—
180D4—1182no—
181D4—2362no—
182D4—2364no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—11816no—
187C2×C4—1188no—
188C2×C4—1184no—
189C2×C4—1182no—
190C2×C4—1181no—
191C2×C4—2362no—
192C2×C4C2×D23612yes—
193C2×C4C2×D23611yescharacteristic
194C2×C4D4×D5914yes—
195C2×C4C23×D5911yescharacteristic
196C8—24no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—2361no—
202C22—2362no—
203C22#1427369712yes—
204C22#1427376014yescomplemented
205C22C22×D23611yescharacteristic
206C4—22no—
207C4—1188no—
208C4—2361no—
209C4—2362no—
210C4#1427369712yes—
211C4C2×D4×D5912yes—
212C2—22no—
213C2—24no—
214C2—4721no—
215C2C2×#1427369711yescharacteristic
216C2C2×#1427376012yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3004
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×Dic118C2semidirect
2. C2×#14273760C2semidirect
4. #16837560C2semidirect
5. #16837543C2semidirect
6. #16837412C2semidirect
7. C59×#407C2semidirect
16. C2×Dic236C22semidirect
17. C2×#11745660C22semidirect
24. #14273652C22semidirect
48. C2×Dic118D4semidirect
93. C22×C59#137semidirect
115. #407D59semidirect
116. C59#3004semidirect
204. C22#14273760semidirect