Finite Group Databasebeta

← #21434562

Subgroups — #21434562

Order 7552.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14273760C212yesmaximal, complemented
2C2×#14273755C212yesmaximal, complemented
3#16837952C211yesmaximal, characteristic, complemented
4C2×#14273715C211yesmaximal, characteristic, complemented
5#16837796C212yesmaximal, complemented
6#16837791C212yesmaximal, complemented
7#16837786C214yesmaximal, complemented
8C4×M16×C59C211yesmaximal, characteristic, complemented
9C2×#11745685C2212yes—
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12#14273760—28no—
13#14273755—28no—
14C2×Dic236C2214yescomplemented
15C2×#11745660C2214yes—
16C2×#11745660C2214yescomplemented
17C2×D472C2214yes—
18#14273727C2211yescharacteristic, complemented
19#14273724C2211yescharacteristic, complemented
20#14273715—22no—
21#14273715C2212yes—
22#14273715C2212yes—
23#14273715C2212yescomplemented
24#14273701—22no—
25C4×D236—22no—
26C2×(C2×D59)⋊C4—22no—
27C2×M16×C59C2212yes—
28C2×C42×C59C2211yescharacteristic
29#97×C59C2212yescomplemented
30C4×C8×C59C2212yescomplemented
31C23×D59—21no—
32C22×C4×C59D412yes—
33C22×C4×C59C2311yescharacteristic
34C2×C22⋊D59—22no—
35C22×Dic59—21no—
36#11745685—24no—
37#11745685—24no—
38C2×D236—24no—
39C2×D236—22no—
40C2×D236—21no—
41C2×D236C2312yes—
42C2×D236C2312yes—
43C2×C4×D59—22no—
44C2×Dic118—24no—
45C2×Dic118—21no—
46C2×Dic118C2312yes—
47C2×Dic118C2312yes—
48M16×C59D418yescomplemented
49C2×C8×C59C2314yes—
50C42×C59D412yes—
51C42×C59C2311yescharacteristic
52C42×C59C2311yescharacteristic
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—24no—
56C4⋊Dic59—22no—
57Dic236—28no—
58D472—28no—
59#11745660—28no—
60#11745660—28no—
61C23×C59C2×D411yescharacteristic
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—44no—
65C22×D59—42no—
66C2×C4×C59—42no—
67C2×C4×C59C2×D412yes—
68C2×C4×C59C2×D412yes—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D414yes—
71C2×C4×C59C2411yescharacteristic
72C22⋊D59—44no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—42no—
76D236—22no—
77D236—24no—
78D236—22no—
79D236—44no—
80D236—42no—
81C4×D59—44no—
82Dic118—22no—
83Dic118—24no—
84Dic118—22no—
85Dic118—42no—
86C8×C59C2×D418yes—
87C22×C59—22no—
88C22×C59#12712yes—
89C22×C59C22×D411yescharacteristic
90C2×D59—42no—
91C2×D59—42no—
92C2×D59—44no—
93C2×D59—44no—
94C2×D59—84no—
95C4×C59—22no—
96C4×C59—22no—
97C4×C59#12712yes—
98C4×C59C22×D412yes—
99Dic59—42no—
100Dic59—42no—
101#3153—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59C2×#12711yescharacteristic
104C2×C59#57512yes—
105D59—82no—
106D59—82no—
107C2×#137—592no—
108C2×AGL(1,ℤ/8)—592no—
109#532—591no—
110C2×#124—591no—
111#497—592no—
112#496—592no—
113#495—594no—
114C4×M16D5911yescharacteristic, complemented
115C59#315311yescharacteristic, complemented, Sylow
116C2×#41—592no—
117C22×Q8—591no—
118C22×D4—591no—
119#137—1188no—
120AGL(1,ℤ/8)—1188no—
121C2×Q16—594no—
122C2×SD16—594no—
123C2×SD16—594no—
124C2×D8—594no—
125C2×M16C2×D5912yes—
126C4⋊Q8—591no—
127#127—591no—
128#124—592no—
129#124—592no—
130#124—592no—
131#124—1182no—
132#121—1182no—
133C4×D4—1182no—
134C2×C22⋊C4—1182no—
135C2×C42C2×D5911yescharacteristic
136#97C2×D5912yescomplemented
137C4×C8C2×D5912yescomplemented
138C24—1181no—
139#41—1184no—
140#41—1184no—
141C2×Q8—592no—
142C2×Q8—592no—
143C2×Q8—1181no—
144C2×Q8—1184no—
145C2×D4—592no—
146C2×D4—592no—
147C2×D4—1182no—
148C2×D4—1184no—
149C2×D4—1182no—
150C2×D4—1181no—
151C22×C4—1181no—
152C22×C4—1182no—
153C22×C4D23612yes—
154C22×C4C22×D5911yescharacteristic
155Q16—1188no—
156SD16—1188no—
157SD16—1188no—
158D8—1188no—
159M16D23618yescomplemented
160C2×C8C22×D5914yes—
161C4⋊C4—1182no—
162C22⋊C4—1184no—
163C22⋊C4—1184no—
164C22⋊C4—1184no—
165C42D23612yes—
166C42C22×D5911yescharacteristic
167C42C22×D5911yescharacteristic
168C23—1182no—
169C23—1182no—
170C23—2364no—
171C23—2362no—
172C23C2×D23611yescharacteristic
173Q8—1182no—
174Q8—1184no—
175Q8—1182no—
176Q8—2362no—
177D4—1182no—
178D4—1184no—
179D4—1182no—
180D4—2364no—
181D4—2364no—
182D4—2362no—
183C2×C4—42no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—2362no—
187C2×C4—2364no—
188C2×C4C2×D23612yes—
189C2×C4C2×D23612yes—
190C2×C4C2×D23611yescharacteristic
191C2×C4C2×D23614yes—
192C2×C4C23×D5911yescharacteristic
193C8C2×D23618yes—
194C22—22no—
195C22—4724no—
196C22—2362no—
197C22—2362no—
198C22—2364no—
199C22—2364no—
200C22#1427372412yes—
201C22C22×D23611yescharacteristic
202C4—22no—
203C4—22no—
204C4—2362no—
205C4—2362no—
206C4#1427372412yes—
207C4C22×D23612yes—
208C2—22no—
209C2—4722no—
210C2—4722no—
211C2C2×#1427372411yescharacteristic
212C2#1683820212yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC4×M16×C59C2
socleC22×C59C22×D4
hypercenterC4×M16D59
hypocenterC59#3153
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14273760C2semidirect
2. C2×#14273755C2semidirect
3. #16837952C2semidirect
4. C2×#14273715C2semidirect
5. #16837796C2semidirect
6. #16837791C2semidirect
7. #16837786C2semidirect
8. C4×M16×C59C2semidirect
14. C2×Dic236C22semidirect
16. C2×#11745660C22semidirect
18. #14273727C22semidirect
19. #14273724C22semidirect
23. #14273715C22semidirect
29. #97×C59C22semidirect
30. C4×C8×C59C22semidirect
48. M16×C59D4semidirect
114. C4×M16D59semidirect
115. C59#3153semidirect
136. #97C2×D59semidirect
137. C4×C8C2×D59semidirect
159. M16D236semidirect