Finite Group Databasebeta

← #21434348

Subgroups — #21434348

Order 7552.

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

normal subgroups only

This group has 394 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#16838014C211yesmaximal, characteristic, complemented
2#16837743C212yesmaximal, complemented
3#16837702C212yesmaximal, complemented
4#16837607C212yesmaximal, complemented
5#16837553C212yesmaximal
6#16837502C212yesmaximal, complemented
7C4×#11745670C212yesmaximal, complemented
8#16837463C211yesmaximal, characteristic, complemented
9C59×#518C211yesmaximal, characteristic
10C2×#11745670C2212yes—
11C2×#11745670C2212yes—
12#14273727C2211yescharacteristic, complemented
13#14273720—22no—
14#14273719C2211yescharacteristic, complemented
15#14273717—22no—
16#14273706C2212yes—
17C4×Dic118C2212yescomplemented
18#14273660C2212yescomplemented
19#14273658C2212yescomplemented
20C4⋊(C59⋊C8)C2212yescomplemented
21#14273650C2212yescomplemented
22#14273650C2212yescomplemented
23#14273648C2212yes—
24#14273648C2212yes—
25C22⋊(C59⋊C8)C2212yes—
26#14273638C2211yescharacteristic, complemented
27C4×C59⋊C8C2211yescharacteristic, complemented
28C22×D4×C59C2211yescharacteristic
29C4×D4×C59—22no—
30C4×D4×C59C2212yes—
31C4×D4×C59C2212yes—
32#117×C59C2211yescharacteristic
33#117×C59C2211yescharacteristic
34C2×C22⋊C4×C59—22no—
35C24×C59—21no—
36C2×D4×C59—24no—
37C2×D4×C59—21no—
38C2×D4×C59C2312yes—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2311yescharacteristic
42C2×Dic118C2312yes—
43C4⋊C4×C59D412yes—
44C4⋊C4×C59C2312yes—
45C22⋊C4×C59—21no—
46C22⋊C4×C59—22no—
47C22⋊C4×C59—22no—
48C22⋊C4×C59D412yes—
49C42×C59—21no—
50C42×C59C2311yescharacteristic
51C42×C59C2311yescharacteristic
52C22⋊Dic59—22no—
53#11745670—24no—
54#11745670—24no—
55C4⋊Dic59—22no—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60C4×Dic59—22no—
61C2×C59⋊C8C2312yes—
62C2×C59⋊C8C2312yes—
63C23×C59—24no—
64C23×C59—22no—
65C23×C59—82no—
66C23×C59C2×D411yescharacteristic
67D4×C59—24no—
68D4×C59—22no—
69D4×C59#4114yes—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—82no—
73C2×C4×C59—82no—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2411yescharacteristic
78C2×Dic59—22no—
79C2×Dic59—22no—
80Dic118—22no—
81Dic118—22no—
82C59⋊C8—22no—
83C59⋊C8—22no—
84C22×C59—21no—
85C22×C59—24no—
86C22×C59—22no—
87C22×C59—42no—
88C22×C59—42no—
89C22×C59—84no—
90C22×C59C22×D411yescharacteristic
91C4×C59—21no—
92C4×C59—22no—
93C4×C59—22no—
94C4×C59—42no—
95C4×C59C2×#4112yes—
96Dic59—42no—
97Dic59—42no—
98#3123—591nomaximal, Sylow
99C2×C59—41no—
100C2×C59—44no—
101C2×C59#52511yescharacteristic
102C2×C59#57712yes—
103#541—591no—
104#518D5911yescharacteristic
105#485—592no—
106#478—592no—
107#461—592no—
108#450—592no—
109#440—592no—
110C4×SD16—592no—
111#433—591no—
112C59#312311yescharacteristic, complemented, Sylow
113C22×D4C2×D5911yescharacteristic
114C2×SD16—592no—
115C2×SD16—592no—
116C4⋊Q8—591no—
117#126—1182no—
118#125—591no—
119#125—1182no—
120C22⋊Q8—592no—
121C4×Q8—592no—
122C4×D4—22no—
123C4×D4C2×D5912yes—
124C4×D4C2×D5912yes—
125#117C2×D5911yescharacteristic
126#117C2×D5911yescharacteristic
127C2×C22⋊C4—22no—
128#107—592no—
129#106—592no—
130C4⋊C8—592no—
131#103—592no—
132#103—592no—
133#102—592no—
134#102—592no—
135C22⋊C8—592no—
136#97—591no—
137C4×C8—591no—
138C24—21no—
139C2×Q8—592no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D5912yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D5911yescharacteristic
146SD16—1184no—
147SD16—1184no—
148C2×C8—592no—
149C2×C8—592no—
150C4⋊C4—592no—
151C4⋊C4—1182no—
152C4⋊C4—1182no—
153C4⋊C4—1182no—
154C4⋊C4—1182no—
155C4⋊C4C22⋊D5912yes—
156C4⋊C4C22×D5912yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—1182no—
161C22⋊C4C22⋊D5912yes—
162C42—21no—
163C42—1182no—
164C42C22×D5911yescharacteristic
165C42C22×D5911yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D5911yescharacteristic
170Q8—1182no—
171Q8—1182no—
172D4—24no—
173D4—22no—
174D4#1174568514yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—1182no—
180C2×C4—1182no—
181C2×C4C2×C22⋊D5911yescharacteristic
182C2×C4C2×C22⋊D5912yes—
183C2×C4C2×C22⋊D5912yes—
184C2×C4C23×D5911yescharacteristic
185C8—1182no—
186C8—1182no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D5911yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—2362no—
199C4—2362no—
200C4C2×#1174568512yes—
201C2—41no—
202C2—44no—
203C2#1683791311yescharacteristic
204C2#1683821312yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#518C2
socleC22×C59C22×D4
hypercenter#518D59
hypocenterC59#3123
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16838014C2semidirect
2. #16837743C2semidirect
3. #16837702C2semidirect
4. #16837607C2semidirect
6. #16837502C2semidirect
7. C4×#11745670C2semidirect
8. #16837463C2semidirect
12. #14273727C22semidirect
14. #14273719C22semidirect
17. C4×Dic118C22semidirect
18. #14273660C22semidirect
19. #14273658C22semidirect
20. C4⋊(C59⋊C8)C22semidirect
21. #14273650C22semidirect
22. #14273650C22semidirect
26. #14273638C22semidirect
27. C4×C59⋊C8C22semidirect
112. C59#3123semidirect