Finite Group Databasebeta

← #21422445

Subgroups — #21422445

Order 7552.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14273710C211yesmaximal, characteristic
2C2×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
3#16837127C212yesmaximal, complemented
4#16837125C212yesmaximal, complemented
5C59×#407C211yesmaximal, characteristic, complemented
6C22×C22⋊D59C411yescharacteristic
7C22×C59⋊C8—21no—
8#14273710—21no—
9#14273710—21no—
10#14273710—21no—
11#14273710—21no—
12C2×Dic59⋊C4C411yescharacteristic
13C2×Dic59⋊C4C2211yescharacteristic
14C2×C22⋊Dic59C411yescharacteristic
15C2×(C2×D59)⋊C4C411yescharacteristic
16C2×(C2×D59)⋊C4C2211yescharacteristic
17C22⋊(C59⋊C8)—21no—
18C22⋊(C59⋊C8)C2212yes—
19C23×C4×C59C2211yescharacteristic
20C2×M16×C59—21no—
21C22⋊C8×C59—21no—
22C22⋊C8×C59C2212yes—
23C24×C59C2×C411yescharacteristic
24C23×D59C2×C411yescharacteristic
25C22×C4×C59—42no—
26C22×C4×C59C2×C411yescharacteristic
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D411yescharacteristic
30C22×C4×C59D411yescharacteristic
31C22×C4×C59C2311yescharacteristic
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C2×C22⋊D59—42no—
35C22×Dic59C2×C411yescharacteristic
36C22×Dic59C2×C411yescharacteristic
37C22×Dic59C2×C411yescharacteristic
38M16×C59—42no—
39C2×C8×C59—22no—
40C22⋊Dic59—21no—
41C22⋊Dic59—21no—
42(C2×D59)⋊C4—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45(C2×D59)⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48Dic59⋊C4—21no—
49Dic59⋊C4—21no—
50C2×C59⋊C8—22no—
51C2×C59⋊C8—42no—
52C23×C59—22no—
53C23×C59—22no—
54C23×C59—41no—
55C23×C59C22⋊C411yescharacteristic
56C23×C59C22⋊C411yescharacteristic
57C23×C59C22×C411yescharacteristic
58C22×D59—21no—
59C22×D59—22no—
60C22×D59—41no—
61C22×D59—41no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C22⋊C411yescharacteristic
69C2×C4×C59C22⋊C411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C22⋊D59—42no—
73C22⋊D59—42no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—22no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C8×C59—42no—
81C59⋊C8—42no—
82C22×C59—21no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59—44no—
90C22×C59#9912yes—
91C22×C59C2×C22⋊C411yescharacteristic
92C22×C59#13112yes—
93C2×D59—41no—
94C2×D59—41no—
95C2×D59—41no—
96C2×D59—82no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101Dic59—41no—
102Dic59—41no—
103Dic59—41no—
104#1468—591nomaximal, Sylow
105C2×C59—22no—
106C2×C59—22no—
107C2×C59—41no—
108C2×C59#40811yescharacteristic
109C2×C59C2×#9911yescharacteristic
110C2×C59#41311yescharacteristic
111D59—81no—
112C2×#123—591no—
113#407D5911yescharacteristic, complemented
114C2×C22⋊C8—591no—
115#324—592no—
116#323—592no—
117C59#146811yescharacteristic, complemented, Sylow
118C22×D4—591no—
119C23×C4C2×D5911yescharacteristic
120C2×M16—21no—
121C22×C8—1181no—
122#123—1181no—
123#123—1181no—
124#123—1181no—
125#123—1181no—
126C2×C4⋊C4—591no—
127C2×C4⋊C4—591no—
128C2×C22⋊C4—591no—
129C2×C22⋊C4—591no—
130C2×C22⋊C4—591no—
131C22⋊C8—21no—
132C22⋊C8—592no—
133C22⋊C8—1181no—
134C22⋊C8C2×D5912yes—
135C24—591no—
136C24C4×D5911yescharacteristic
137C2×D4—1181no—
138C2×D4—1181no—
139C2×D4—2362no—
140C22×C4—42no—
141C22×C4—591no—
142C22×C4—591no—
143C22×C4—591no—
144C22×C4C4×D5911yescharacteristic
145C22×C4D23611yescharacteristic
146C22×C4D23611yescharacteristic
147C22×C4C22⋊D5911yescharacteristic
148C22×C4C22⋊D5911yescharacteristic
149C22×C4C22×D5911yescharacteristic
150M16—42no—
151C2×C8—22no—
152C2×C8—1182no—
153C2×C8—2362no—
154C4⋊C4—1181no—
155C4⋊C4—1181no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C22⋊C4—1181no—
159C22⋊C4—1181no—
160C22⋊C4—1181no—
161C22⋊C4—1181no—
162C22⋊C4—1181no—
163C22⋊C4—1181no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—1182no—
168C23—1181no—
169C23—2361no—
170C23—2361no—
171C23(C2×D59)⋊C411yescharacteristic
172C23(C2×D59)⋊C411yescharacteristic
173C23C2×C4×D5911yescharacteristic
174D4—2362no—
175D4—2362no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1181no—
183C2×C4—1181no—
184C2×C4—1181no—
185C2×C4—1182no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4(C2×D59)⋊C411yescharacteristic
189C2×C4(C2×D59)⋊C411yescharacteristic
190C2×C4C2×D23611yescharacteristic
191C2×C4C2×C22⋊D5911yescharacteristic
192C8—42no—
193C8—2362no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—4722no—
203C22—2361no—
204C22—2361no—
205C22—2361no—
206C22#1427364112yes—
207C22C2×(C2×D59)⋊C411yescharacteristic
208C22#1427373512yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—2361no—
214C4—2361no—
215C4—2361no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—4721no—
220C2#1683737011yescharacteristic
221C2C2×#1427364111yescharacteristic
222C2#1683738411yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#407C2
socleC22×C59C2×C22⋊C4
hypercenter#407D59
hypocenterC59#1468
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C59⋊C8)C2semidirect
3. #16837127C2semidirect
4. #16837125C2semidirect
5. C59×#407C2semidirect
113. #407D59semidirect
117. C59#1468semidirect