Finite Group Databasebeta

← #21434560

Subgroups — #21434560

Order 7552.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273758C212yesmaximal, complemented
2C2×#14273753C212yesmaximal, complemented
3#16837952C211yesmaximal, characteristic, complemented
4#16837797C212yesmaximal, complemented
5#16837792C212yesmaximal, complemented
6#16837784C214yesmaximal, complemented
7C4×#11745664C211yesmaximal, characteristic, complemented
8C2×#124×C59C211yesmaximal, characteristic, complemented
9C2×#11745685C2212yes—
10#14273758—28no—
11#14273753—28no—
12C2×#11745672C2214yescomplemented
13C2×#11745670C2214yes—
14C2×#11745671C2214yescomplemented
15C2×#11745669C2214yes—
16C2×#11745664C2212yes—
17#14273727C2211yescharacteristic, complemented
18#14273724C2211yescharacteristic, complemented
19#14273715C2212yescomplemented
20#14273701—22no—
21C4×D236—22no—
22#14273638C2212yescomplemented
23C4×C59⋊C8C2212yescomplemented
24C22×Q8×C59C2211yescharacteristic
25C22×D4×C59C2211yescharacteristic
26#124×C59—22no—
27#124×C59C2212yes—
28#124×C59C2212yes—
29C2×C22⋊C4×C59—22no—
30C2×C42×C59C2211yescharacteristic
31C24×C59—21no—
32C2×Q8×C59—21no—
33C2×Q8×C59—24no—
34C2×Q8×C59C2312yes—
35C2×D4×C59—24no—
36C2×D4×C59—21no—
37C2×D4×C59C2312yes—
38C22×C4×C59—21no—
39C22×C4×C59D412yes—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—22no—
42#11745685—24no—
43#11745685—24no—
44C2×D236—22no—
45C2×D236C2312yes—
46C2×C4×D59—22no—
47C2×Dic118C2312yes—
48C22⋊C4×C59—24no—
49C22⋊C4×C59—24no—
50C42×C59D412yes—
51C42×C59C2311yescharacteristic
52C42×C59C2311yescharacteristic
53#11745672—28no—
54#11745671—28no—
55#11745670—28no—
56#11745669—28no—
57(C2×D59)⋊C4—24no—
58C4⋊Dic59—22no—
59#11745664D418yescomplemented
60C2×C59⋊C8C2314yes—
61C23×C59—22no—
62C23×C59—44no—
63C23×C59—42no—
64C23×C59C2×D411yescharacteristic
65C22×D59—22no—
66Q8×C59—24no—
67Q8×C59—42no—
68D4×C59—24no—
69D4×C59—42no—
70C2×C4×C59—22no—
71C2×C4×C59—42no—
72C2×C4×C59—42no—
73C2×C4×C59C2×D414yes—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2×D412yes—
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2411yescharacteristic
78C22⋊D59—44no—
79C2×Dic59—22no—
80D236—22no—
81D236—22no—
82D236—44no—
83C4×D59—44no—
84Dic118—22no—
85Dic118—22no—
86C59⋊C8C2×D418yes—
87C22×C59—22no—
88C22×C59—42no—
89C22×C59—44no—
90C22×C59—84no—
91C22×C59#12712yes—
92C22×C59C22×D411yescharacteristic
93C2×D59—42no—
94C2×D59—44no—
95C4×C59—22no—
96C4×C59—22no—
97C4×C59—42no—
98C4×C59#12712yes—
99C4×C59C22×D412yes—
100Dic59—42no—
101#3153—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59—82no—
104C2×C59C2×#12711yescharacteristic
105C2×C59#57512yes—
106D59—82no—
107C2×#137—592no—
108C2×AGL(1,ℤ/8)—592no—
109#532—591no—
110C2×#124D5911yescharacteristic, complemented
111#497—592no—
112#496—592no—
113#495—594no—
114C4×M16—591no—
115C59#315311yescharacteristic, complemented, Sylow
116C2×#41—592no—
117C22×Q8C2×D5911yescharacteristic
118C22×D4C2×D5911yescharacteristic
119#137—1188no—
120AGL(1,ℤ/8)—1188no—
121C2×Q16—594no—
122C2×SD16—594no—
123C2×SD16—594no—
124C2×D8—594no—
125C2×M16—592no—
126C4⋊Q8—591no—
127#127—591no—
128#124—22no—
129#124—592no—
130#124C2×D5912yes—
131#124C2×D5912yes—
132#121—1182no—
133C4×D4—1182no—
134C2×C22⋊C4—22no—
135C2×C42C2×D5911yescharacteristic
136#97—592no—
137C4×C8—592no—
138C24—21no—
139#41—1184no—
140#41—1184no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—592no—
144C2×Q8C22×D5912yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—592no—
148C2×D4—1182no—
149C2×D4—1182no—
150C2×D4C22×D5912yes—
151C22×C4—21no—
152C22×C4—1182no—
153C22×C4C22⋊D5912yes—
154C22×C4C22×D5911yescharacteristic
155Q16—1188no—
156SD16—1188no—
157SD16—1188no—
158D8—1188no—
159M16—598no—
160C2×C8—594no—
161C4⋊C4—1182no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—1184no—
165C42C22⋊D5912yes—
166C42C22×D5911yescharacteristic
167C42C22×D5911yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—1182no—
172C23C2×C22⋊D5911yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—1182no—
176Q8—1182no—
177D4—24no—
178D4—42no—
179D4—1182no—
180D4—1182no—
181D4—2364no—
182D4—2364no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—1182no—
187C2×C4—2364no—
188C2×C4D4×D5914yes—
189C2×C4C2×C22⋊D5912yes—
190C2×C4C2×C22⋊D5912yes—
191C2×C4C2×C22⋊D5911yescharacteristic
192C2×C4C23×D5911yescharacteristic
193C8—598no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—2362no—
199C22—2364no—
200C22#1427372312yes—
201C22C22×C22⋊D5911yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—2362no—
206C4#1427372312yes—
207C4C2×D4×D5912yes—
208C2—22no—
209C2—82no—
210C2—4722no—
211C2C2×#1427372311yescharacteristic
212C2#1683820012yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#124×C59C2
socleC22×C59C22×D4
hypercenterC2×#124D59
hypocenterC59#3153
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14273758C2semidirect
2. C2×#14273753C2semidirect
3. #16837952C2semidirect
4. #16837797C2semidirect
5. #16837792C2semidirect
6. #16837784C2semidirect
7. C4×#11745664C2semidirect
8. C2×#124×C59C2semidirect
12. C2×#11745672C22semidirect
14. C2×#11745671C22semidirect
17. #14273727C22semidirect
18. #14273724C22semidirect
19. #14273715C22semidirect
22. #14273638C22semidirect
23. C4×C59⋊C8C22semidirect
59. #11745664D4semidirect
110. C2×#124D59semidirect
115. C59#3153semidirect