Finite Group Databasebeta

← #21434195

Subgroups — #21434195

Order 7552.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#16837959C211yesmaximal, characteristic, complemented
2#16837737C212yesmaximal, complemented
3#16837682C212yesmaximal, complemented
4#16837607C212yesmaximal, complemented
5#16837553C212yesmaximal
6#16837502C214yesmaximal, complemented
7#16837459C211yesmaximal, characteristic, complemented
8C2×C4×D4×C59C211yesmaximal, characteristic
9C2×#11745670C2214yes—
10#14273727C2211yescharacteristic, complemented
11#14273727C2211yescharacteristic, complemented
12#14273719—21no—
13#14273706—21no—
14#14273706C2212yes—
15C4×Dic118—21no—
16C4×Dic118C2212yescomplemented
17#14273686—21no—
18#14273660C2214yescomplemented
19C4⋊(C59⋊C8)C2212yescomplemented
20#14273650C2214yescomplemented
21#14273648C2214yes—
22C22⋊(C59⋊C8)C2212yes—
23#14273638C2212yescomplemented
24C22×D4×C59C2211yescharacteristic
25C23×C4×C59—21no—
26C4×D4×C59—21no—
27C4×D4×C59—21no—
28C4×D4×C59C2212yes—
29C4×D4×C59C2212yes—
30C2×C4⋊C4×C59C2211yescharacteristic
31C2×C22⋊C4×C59—21no—
32C2×C42×C59C2211yescharacteristic
33C24×C59—21no—
34C2×D4×C59—24no—
35C2×D4×C59—21no—
36C2×D4×C59C2312yes—
37C22×C4×C59—21no—
38C22×C4×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—44no—
41C22×C4×C59D411yescharacteristic
42C22×C4×C59D411yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C2×Dic118—21no—
45C2×Dic118C2312yes—
46C4⋊C4×C59—21no—
47C4⋊C4×C59C2312yes—
48C22⋊C4×C59—22no—
49C22⋊C4×C59—22no—
50C42×C59D411yescharacteristic
51C42×C59D411yescharacteristic
52C42×C59C2311yescharacteristic
53C42×C59C2311yescharacteristic
54C22⋊Dic59—22no—
55#11745670—28no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63C2×C59⋊C8C2314yes—
64C23×C59—24no—
65C23×C59—22no—
66C23×C59—42no—
67C23×C59—42no—
68C23×C59C2×D411yescharacteristic
69D4×C59—24no—
70D4×C59—22no—
71D4×C59#4114yes—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—44no—
77C2×C4×C59—42no—
78C2×C4×C59—44no—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—22no—
86C2×Dic59—22no—
87Dic118—24no—
88Dic118—42no—
89C59⋊C8—24no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59—24no—
93C22×C59—48no—
94C22×C59—42no—
95C22×C59—42no—
96C22×C59#13712yes—
97C22×C59C22×D411yescharacteristic
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—42no—
103C4×C59AGL(1,ℤ/8)12yes—
104C4×C59C2×#4112yes—
105Dic59—42no—
106Dic59—42no—
107#3110—591nomaximal, Sylow
108C2×C59—22no—
109C2×C59—44no—
110C2×C59#52511yescharacteristic
111C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C59C2×#13711yescharacteristic
113#533—591no—
114C2×C4×D4D5911yescharacteristic
115#484—592no—
116#474—592no—
117#461—592no—
118#450—592no—
119#440—594no—
120#432—591no—
121C59#311011yescharacteristic, complemented, Sylow
122C22×D4C2×D5911yescharacteristic
123C23×C4—21no—
124C2×SD16—594no—
125C4⋊Q8—591no—
126C4⋊Q8—591no—
127#125—1181no—
128C22⋊Q8—592no—
129C22⋊Q8—1181no—
130C4×Q8—592no—
131C4×Q8—1181no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D5912yes—
135C4×D4C2×D5912yes—
136#117—1181no—
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D5911yescharacteristic
140#107—594no—
141C4⋊C8—592no—
142#103—594no—
143#102—594no—
144C22⋊C8—592no—
145#97—592no—
146C24—21no—
147C2×Q8—592no—
148C2×Q8—1181no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D5912yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D5911yescharacteristic
157C22×C4C22⋊D5911yescharacteristic
158C22×C4C22×D5911yescharacteristic
159SD16—1188no—
160C2×C8—594no—
161C4⋊C4—21no—
162C4⋊C4—592no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4—1181no—
168C4⋊C4C22×D5912yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—1182no—
172C42—1182no—
173C42C22⋊D5911yescharacteristic
174C42C22⋊D5911yescharacteristic
175C42C22×D5911yescharacteristic
176C42C22×D5911yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D5911yescharacteristic
182Q8—1184no—
183Q8—2362no—
184D4—24no—
185D4—22no—
186D4#1174568514yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4C2×C22⋊D5911yescharacteristic
197C2×C4C2×C22⋊D5911yescharacteristic
198C2×C4C2×C22⋊D5911yescharacteristic
199C2×C4C2×C22⋊D5911yescharacteristic
200C2×C4C2×C22⋊D5911yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—1184no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1427375712yes—
210C22C22×C22⋊D5911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—2362no—
217C4—2362no—
218C4#1427375312yes—
219C4C2×#1174568512yes—
220C2—22no—
221C2—44no—
222C2#1683791311yescharacteristic
223C2C2×#1427375311yescharacteristic
224C2C2×#1427375711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×C4×D4×C59C2
socleC22×C59C22×D4
hypercenterC2×C4×D4D59
hypocenterC59#3110
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #16837959C2semidirect
2. #16837737C2semidirect
3. #16837682C2semidirect
4. #16837607C2semidirect
6. #16837502C2semidirect
7. #16837459C2semidirect
10. #14273727C22semidirect
11. #14273727C22semidirect
16. C4×Dic118C22semidirect
18. #14273660C22semidirect
19. C4⋊(C59⋊C8)C22semidirect
20. #14273650C22semidirect
23. #14273638C22semidirect
121. C59#3110semidirect