Finite Group Databasebeta

← #21423065

Subgroups — #21423065

Order 7552.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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#16837540C212yesmaximal, complemented
2#16837322C211yesmaximal, characteristic, complemented
3#16837136C212yesmaximal, complemented
4#16837128C211yesmaximal, characteristic, complemented
5C59×#537C211yesmaximal, characteristic
6C22×Dic118C2211yescharacteristic
7C2×#11745670—22no—
8C2×Dic59⋊C4—21no—
9#14273650—22no—
10C22⋊(C59⋊C8)C2212yes—
11C59⋊#95—21no—
12C59⋊#95C2211yescharacteristic
13C2×#41×C59—21no—
14C22⋊Q8×C59—22no—
15#121×C59—22no—
16#121×C59—21no—
17#121×C59C2212yes—
18C2×C4⋊C4×C59C2211yescharacteristic
19#41×C59—42no—
20#41×C59—42no—
21C2×Q8×C59—21no—
22C2×D4×C59—21no—
23C2×D4×C59—22no—
24C2×D4×C59—21no—
25C2×D4×C59D412yes—
26C22×C4×C59—22no—
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59C2311yescharacteristic
30C22×Dic59—21no—
31C22×Dic59—21no—
32C2×Dic118—22no—
33C2×Dic118—42no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59—22no—
36C4⋊C4×C59D412yes—
37C22⋊C4×C59—22no—
38C22⋊C4×C59—22no—
39#11745670—44no—
40Dic59⋊C4—42no—
41C2×C59⋊C8—22no—
42C23×C59—22no—
43C23×C59C2×D411yescharacteristic
44Q8×C59—42no—
45D4×C59—42no—
46D4×C59—42no—
47D4×C59—42no—
48D4×C59—42no—
49D4×C59—81no—
50C2×C4×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—22no—
54C2×C4×C59—41no—
55C2×C4×C59—44no—
56C2×C4×C59—41no—
57C2×C4×C59SD1612yescomplemented
58C2×C4×C59C2×D412yes—
59C2×Dic59—22no—
60C2×Dic59—22no—
61C2×Dic59—41no—
62C2×Dic59—41no—
63C2×Dic59—41no—
64C2×Dic59—41no—
65Dic118—24no—
66Dic118—42no—
67C59⋊C8—42no—
68C22×C59—21no—
69C22×C59—21no—
70C22×C59—42no—
71C22×C59—42no—
72C22×C59—42no—
73C22×C59#12011yescharacteristic
74C22×C59C2×SD1611yescharacteristic
75C22×C59AGL(1,ℤ/8)11yescharacteristic
76C4×C59—22no—
77C4×C59—22no—
78C4×C59—42no—
79C4×C59—41no—
80Dic59—42no—
81Dic59—42no—
82#1604—591nomaximal, Sylow
83C2×C59—21no—
84C2×C59—21no—
85C2×C59—82no—
86C2×C59#45011yescharacteristic
87C2×C59#45611yescharacteristic
88C2×C59B(4,𝔽2)11yescharacteristic
89#537D5911yescharacteristic
90#448—592no—
91#395—591no—
92#327—592no—
93#324—591no—
94C59#160411yescharacteristic, complemented, Sylow
95C2×#41—21no—
96C22×Q8—591no—
97C2×SD16—1182no—
98C22⋊Q8—22no—
99#121—22no—
100#121—21no—
101#121C2×D5912yes—
102C2×C4⋊C4—1181no—
103C2×C4⋊C4C2×D5911yescharacteristic
104#103—1182no—
105C22⋊C8—592no—
106#95—591no—
107#95—1181no—
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—1182no—
112C2×Q8—2362no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D5912yes—
117C22×C4—22no—
118C22×C4—1181no—
119C22×C4—1181no—
120C22×C4C22⋊D5911yescharacteristic
121C22×C4C22⋊D5911yescharacteristic
122C22×C4C22×D5911yescharacteristic
123SD16—2364no—
124C2×C8—1182no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—2362no—
128C4⋊C4C22⋊D5912yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D5911yescharacteristic
133Q8—42no—
134Q8—1184no—
135Q8—2362no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—1182no—
149C2×C4—1182no—
150C2×C4—2361no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4—2361no—
154C2×C4#1174567012yescomplemented
155C2×C4C2×C22⋊D5912yes—
156C8—2362no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1427369611yescharacteristic
163C22C2×#1174567011yescharacteristic
164C22#1427375311yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—41no—
169C4—2362no—
170C4—2362no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1683755311yescharacteristic
175C2#1683758511yescharacteristic
176C2#1683758911yescharacteristic
subgroupG/H
centerC22#14273696
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#537C2
socleC22×C59#120
hypercenter#537D59
hypocenterC59#1604
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16837540C2semidirect
2. #16837322C2semidirect
3. #16837136C2semidirect
4. #16837128C2semidirect
57. C2×C4×C59SD16semidirect
94. C59#1604semidirect
154. C2×C4#11745670semidirect