Finite Group Databasebeta

← #21425080

Subgroups — #21425080

Order 7552.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14273706C211yesmaximal, characteristic
2C4×C22⋊Dic59C211yesmaximal, characteristic
3#16837168C214yesmaximal
4C59×#380C211yesmaximal, characteristic
5C22×Dic118C411yescharacteristic, complemented
6#14273706—21no—
7#14273706—21no—
8#14273706—21no—
9#14273706—21no—
10C2×C4⋊Dic59C411yescharacteristic, complemented
11C2×Dic59⋊C4C412yescomplemented
12C2×C22⋊Dic59C2212yes—
13C2×C22⋊Dic59C2212yes—
14C2×C4×Dic59—21no—
15C59⋊#95—21no—
16C23×C4×C59C2211yescharacteristic
17C2×C4⋊C4×C59—21no—
18C2×C22⋊C4×C59C2212yes—
19#95×C59—21no—
20C24×C59C2311yescharacteristic
21C22×C4×C59—22no—
22C22×C4×C59—42no—
23C22×C4×C59C2×C411yescharacteristic
24C22×C4×C59C2×C411yescharacteristic
25C22×C4×C59D411yescharacteristic
26C22×C4×C59D411yescharacteristic
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×Dic59—22no—
30C22×Dic59C2×C412yes—
31C22×Dic59C2×C412yes—
32C2×Dic118—21no—
33C2×Dic118—21no—
34C2×Dic118—42no—
35C4⋊C4×C59—42no—
36C22⋊C4×C59—24no—
37C22⋊Dic59—22no—
38C22⋊Dic59—22no—
39C22⋊Dic59—22no—
40C22⋊Dic59Q814yescomplemented
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43Dic59⋊C4—22no—
44Dic59⋊C4—22no—
45C4×Dic59—42no—
46C23×C59—41no—
47C23×C59—41no—
48C23×C59C22×C411yescharacteristic
49C23×C59C2×D411yescharacteristic
50C23×C59C2×D411yescharacteristic
51C23×C59C2×Q812yes—
52C23×C59#4112yes—
53C2×C4×C59—22no—
54C2×C4×C59—22no—
55C2×C4×C59—22no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—42no—
60C2×C4×C59—42no—
61C2×C4×C59—42no—
62C2×C4×C59C22⋊C411yescharacteristic
63C2×C4×C59C22⋊C411yescharacteristic
64C2×C4×C59C22⋊C411yescharacteristic
65C2×C4×C59C22⋊C411yescharacteristic
66C2×Dic59—22no—
67C2×Dic59—22no—
68C2×Dic59—24no—
69C2×Dic59—42no—
70C2×Dic59—42no—
71C2×Dic59—42no—
72C2×Dic59—42no—
73Dic118—42no—
74Dic118—42no—
75C22×C59—21no—
76C22×C59—21no—
77C22×C59—21no—
78C22×C59—21no—
79C22×C59—21no—
80C22×C59—21no—
81C22×C59—42no—
82C22×C59—42no—
83C22×C59C2×C22⋊C411yescharacteristic
84C22×C59C4×Q812yes—
85C22×C59C22⋊Q812yes—
86C22×C59#12411yescharacteristic
87C22×C59C4⋊Q811yescharacteristic
88C4×C59—21no—
89C4×C59—21no—
90C4×C59—21no—
91C4×C59—82no—
92C4×C59#9912yes—
93Dic59—44no—
94Dic59—42no—
95Dic59—42no—
96#1996—591nomaximal, Sylow
97C2×C59—22no—
98C2×C59—21no—
99C2×C59—22no—
100C2×C59—21no—
101C2×C59#39111yescharacteristic
102C2×C59C2×#9911yescharacteristic
103C2×C59#41011yescharacteristic
104C2×C22⋊Q8—591no—
105#380D5911yescharacteristic
106C4×C22⋊C4—591no—
107#342—594no—
108C59#199611yescharacteristic, complemented, Sylow
109C22×Q8—591no—
110C23×C4C2×D5911yescharacteristic
111C22⋊Q8—1181no—
112C22⋊Q8—1181no—
113C22⋊Q8—1181no—
114C22⋊Q8—1181no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—592no—
117C2×C4⋊C4—591no—
118C2×C22⋊C4—592no—
119C2×C22⋊C4—592no—
120C2×C22⋊C4C2×D5912yes—
121C2×C42—1181no—
122#95—21no—
123#95—1181no—
124C24C22×D5911yescharacteristic
125C2×Q8—1181no—
126C2×Q8—1181no—
127C2×Q8—2362no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—592no—
131C22×C4—592no—
132C22×C4—1182no—
133C22×C4C4×D5911yescharacteristic
134C22×C4C4×D5911yescharacteristic
135C22×C4D23611yescharacteristic
136C22×C4D23611yescharacteristic
137C22×C4C22⋊D5911yescharacteristic
138C22×C4C22⋊D5911yescharacteristic
139C4⋊C4—42no—
140C4⋊C4—1182no—
141C4⋊C4—1182no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C22⋊C4—24no—
145C22⋊C4—594no—
146C22⋊C4—1182no—
147C22⋊C4—1182no—
148C22⋊C4—1182no—
149C42—2362no—
150C23—41no—
151C23—41no—
152C23C2×C4×D5911yescharacteristic
153C23C2×D23611yescharacteristic
154C23#1174568712yes—
155C23Q8×D5912yes—
156C23C2×C22⋊D5911yescharacteristic
157Q8—2362no—
158Q8—2362no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—1182no—
169C2×C4—1182no—
170C2×C4—1184no—
171C2×C4—2362no—
172C2×C4—2362no—
173C2×C4—2362no—
174C2×C4—2362no—
175C2×C4(C2×D59)⋊C411yescharacteristic
176C2×C4(C2×D59)⋊C411yescharacteristic
177C2×C4(C2×D59)⋊C411yescharacteristic
178C2×C4(C2×D59)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×(C2×D59)⋊C411yescharacteristic
188C22#1427369212yes—
189C22#1427370712yes—
190C22#1427371411yescharacteristic
191C22#1427372511yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—82no—
196C4—2364no—
197C4—2362no—
198C4—2362no—
199C4#1427364112yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#1683730711yescharacteristic
205C2C2×#1427364111yescharacteristic
206C2#1683737511yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC59×#380C2
socleC22×C59C2×C22⋊C4
hypercenter#380D59
hypocenterC59#1996
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
5. C22×Dic118C4semidirect
10. C2×C4⋊Dic59C4semidirect
11. C2×Dic59⋊C4C4semidirect
40. C22⋊Dic59Q8semidirect
108. C59#1996semidirect