Finite Group Databasebeta

← #21429965

Subgroups — #21429965

Order 7552.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×D236C211yesmaximal, characteristic
2#16837337C212yesmaximal, complemented
3#16837332C212yesmaximal, complemented
4#16837328C212yesmaximal, complemented
5#16837319C212yesmaximal
6#16837273C214yesmaximal, complemented
7#16837270C211yesmaximal, characteristic, complemented
8C2×#125×C59C211yesmaximal, characteristic, complemented
9C22×D236C2211yescharacteristic
10C22×C4×D59C2212yes—
11C4×D236—24no—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×Dic59⋊C4C2214yes—
14C2×(C2×D59)⋊C4C2214yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2214yes—
17C59⋊#95C2212yes—
18C59⋊#95C2212yes—
19C59⋊#95C2212yes—
20C59⋊#95C2214yes—
21#125×C59—24no—
22C2×C4⋊C4×C59C2212yes—
23C2×C4⋊C4×C59C2212yes—
24C2×C4⋊C4×C59C2211yescharacteristic
25C2×C4⋊C4×C59C2211yescharacteristic
26C2×C42×C59C2211yescharacteristic
27C23×D59C2312yes—
28C22×C4×C59C2312yes—
29C22×C4×C59C2312yes—
30C22×C4×C59C2311yescharacteristic
31C22×C4×C59C2311yescharacteristic
32C22×C4×C59C2311yescharacteristic
33C22×Dic59C2314yes—
34C22×Dic59C2312yes—
35C2×D236—24no—
36C2×D236—22no—
37C2×C4×D59—24no—
38C2×C4×D59—44no—
39C4⋊C4×C59—24no—
40C4⋊C4×C59—22no—
41C4⋊C4×C59—22no—
42C4⋊C4×C59—24no—
43C42×C59D414yes—
44(C2×D59)⋊C4—28no—
45(C2×D59)⋊C4—24no—
46(C2×D59)⋊C4—44no—
47C4⋊Dic59—22no—
48Dic59⋊C4—44no—
49C23×C59C2411yescharacteristic
50C22×D59—22no—
51C22×D59—22no—
52C22×D59—24no—
53C22×D59—24no—
54C22×D59#4114yes—
55C2×C4×C59—22no—
56C2×C4×C59—22no—
57C2×C4×C59—22no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—24no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59C2×D412yes—
64C2×C4×C59C2×D412yes—
65C2×C4×C59C2×D412yes—
66C2×Dic59—22no—
67C2×Dic59—24no—
68C2×Dic59—24no—
69C2×Dic59—24no—
70C2×Dic59—24no—
71D236—28no—
72C4×D59—48no—
73C22×C59C22×D411yescharacteristic
74C22×C59C2×#4112yes—
75C22×C59H(5,𝔽2)12yes—
76C22×C592−1+412yes—
77C2×D59—24no—
78C2×D59—28no—
79C2×D59—42no—
80C2×D59—42no—
81C2×D59—44no—
82C4×C59—22no—
83C4×C59—22no—
84C4×C59—22no—
85C4×C59—42no—
86C4×C59—42no—
87Dic59—42no—
88Dic59—44no—
89#2633—591nomaximal, Sylow
90C2×C59#52511yescharacteristic
91C2×C59#53511yescharacteristic
92C2×C59#53611yescharacteristic
93C2×C59#53914yes—
94D59—44no—
95C2×#125D5911yescharacteristic, complemented
96C2×C4×D4—591no—
97#399—592no—
98#398—592no—
99#397—592no—
100#394—592no—
101#385—594no—
102#383—591no—
103C59#263311yescharacteristic, complemented, Sylow
104C22×D4—591no—
105C23×C4—592no—
106#125—24no—
107C4×D4—1184no—
108C2×C4⋊C4—591no—
109C2×C4⋊C4—594no—
110C2×C4⋊C4C2×D5912yes—
111C2×C4⋊C4C2×D5912yes—
112C2×C4⋊C4C2×D5911yescharacteristic
113C2×C4⋊C4C2×D5911yescharacteristic
114C2×C22⋊C4—592no—
115C2×C22⋊C4—594no—
116C2×C22⋊C4—594no—
117C2×C42C2×D5911yescharacteristic
118#95—592no—
119#95—592no—
120#95—592no—
121#95—594no—
122C24—592no—
123C2×D4—1184no—
124C2×D4—1182no—
125C22×C4—594no—
126C22×C4—592no—
127C22×C4—1184no—
128C22×C4—2364no—
129C22×C4C22×D5912yes—
130C22×C4C22×D5912yes—
131C22×C4C22×D5911yescharacteristic
132C22×C4C22×D5911yescharacteristic
133C22×C4C22×D5911yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—24no—
137C4⋊C4—24no—
138C4⋊C4—1182no—
139C4⋊C4—2364no—
140C22⋊C4—1188no—
141C22⋊C4—1184no—
142C22⋊C4—2364no—
143C42C22⋊D5914yes—
144C23—594no—
145C23—1182no—
146C23—1182no—
147C23—1184no—
148C23—1184no—
149C23C23×D5911yescharacteristic
150D4—1188no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—1182no—
160C2×C4—1184no—
161C2×C4—1184no—
162C2×C4—1184no—
163C2×C4—1184no—
164C2×C4—2368no—
165C2×C4C2×C22⋊D5912yes—
166C2×C4C2×C22⋊D5912yes—
167C2×C4C2×C22⋊D5912yes—
168C22—1184no—
169C22—1188no—
170C22—2362no—
171C22—2362no—
172C22—2364no—
173C22C22×C22⋊D5911yescharacteristic
174C22#41×D5912yes—
175C22#1427377312yes—
176C22#1427377512yes—
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—2362no—
183C4—2364no—
184C2—2364no—
185C2#1683790911yescharacteristic
186C2#1683796611yescharacteristic
187C2#1683797611yescharacteristic
188C2#1683800014yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×#125×C59C2
hypercenterC2×#125D59
hypocenterC59#2633
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16837337C2semidirect
3. #16837332C2semidirect
4. #16837328C2semidirect
6. #16837273C2semidirect
7. #16837270C2semidirect
8. C2×#125×C59C2semidirect
95. C2×#125D59semidirect
103. C59#2633semidirect