Finite Group Databasebeta

← #323×D59 #21422401

Subgroups — #323×D59 #21422401

Order 7552.

456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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×C22⋊C4×D59C211yesmaximal, characteristic
2C22⋊C8×D59C212yesmaximal, complemented
3#16837126C211yesmaximal, characteristic, complemented
4#16837125C212yesmaximal, complemented
5C59×#323C211yesmaximal, characteristic, complemented
6C24×D59C411yescharacteristic
7C22×C4×D59C411yescharacteristic
8C22×C4×D59C2211yescharacteristic
9C2×C8×D59—22no—
10C2×C22⋊Dic59C411yescharacteristic
11C2×(C2×D59)⋊C4C411yescharacteristic
12C2×(C2×D59)⋊C4C2211yescharacteristic
13C22⋊C4×D59—22no—
14C22⋊C4×D59—22no—
15C22⋊(C59⋊C8)C2212yescomplemented
16(C2×D59)⋊C8—22no—
17C2×C22⋊C4×C59C2211yescharacteristic
18C22⋊C8×C59C2212yescomplemented
19C24×C59C2×C411yescharacteristic
20C23×D59—21no—
21C23×D59—21no—
22C23×D59—22no—
23C23×D59—42no—
24C23×D59—42no—
25C23×D59C814yescomplemented
26C23×D59C2×C411yescharacteristic
27C23×D59C2×C411yescharacteristic
28C22×C4×C59C2×C411yescharacteristic
29C22×C4×C59C2311yescharacteristic
30C22×Dic59C2×C411yescharacteristic
31C22×Dic59C2×C411yescharacteristic
32C2×C4×D59—21no—
33C2×C4×D59—21no—
34C2×C4×D59—42no—
35C2×C4×D59—42no—
36C2×C4×D59D412yes—
37C2×C4×D59D412yes—
38C2×C8×C59—22no—
39C22⋊C4×C59—22no—
40C22⋊Dic59—22no—
41(C2×D59)⋊C4—22no—
42(C2×D59)⋊C4—22no—
43C2×C59⋊C8—22no—
44C8×D59—44no—
45C23×C59—21no—
46C23×C59—21no—
47C23×C59—41no—
48C23×C59—41no—
49C23×C59C2×C812yescomplemented
50C23×C59C22×C411yescharacteristic
51C22×D59—22no—
52C22×D59—22no—
53C22×D59—21no—
54C22×D59—21no—
55C22×D59—24no—
56C22×D59—24no—
57C22×D59—42no—
58C22×D59—42no—
59C22×D59—48no—
60C22×D59—48no—
61C22×D59—42no—
62C22×D59—42no—
63C22×D59—41no—
64C22×D59—41no—
65C22×D59C22⋊C411yescharacteristic
66C22×D59C22⋊C411yescharacteristic
67C22×D59C2×C812yes—
68C22×D59C2×C812yescomplemented
69C22×D59M1612yes—
70C2×C4×C59—21no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59C2×D412yes—
74C2×Dic59—21no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59C22⋊C412yes—
78C4×D59—24no—
79C4×D59—42no—
80C4×D59—42no—
81C4×D59—42no—
82C8×C59—42no—
83C59⋊C8—42no—
84C22×C59—21no—
85C22×C59—21no—
86C22×C59—22no—
87C22×C59—42no—
88C22×C59—42no—
89C22×C59—41no—
90C22×C59—41no—
91C22×C59C2×C22⋊C411yescharacteristic
92C22×C59C22×C811yescharacteristic
93C22×C59C2×M1611yescharacteristic
94C2×D59—21no—
95C2×D59—21no—
96C2×D59—24no—
97C2×D59—24no—
98C2×D59—22no—
99C2×D59—48no—
100C2×D59—42no—
101C2×D59—41no—
102C2×D59—41no—
103C2×D59—48no—
104C2×D59—42no—
105C2×D59C22⋊C812yes—
106C2×D59C22⋊C812yes—
107C2×D59#9912yes—
108C2×D59#10012yes—
109C4×C59—22no—
110C4×C59—41no—
111Dic59—22no—
112Dic59—41no—
113C2×#323—591nomaximal, Sylow
114C2×C59—21no—
115C2×C59—21no—
116C2×C59—42no—
117C2×C59C2×C22⋊C811yescharacteristic
118C2×C59C2×#9911yescharacteristic
119C2×C59C2×#10011yescharacteristic
120D59—22no—
121D59—42no—
122D59#32314yesdirect product factor
123C22×C22⋊C4—591no—
124C2×C22⋊C8—592no—
125#323—591no—
126#323—592no—
127#323D5911yescharacteristic, direct product factor
128C59C2×#32311yescharacteristic, complemented, Sylow
129C25—591no—
130C23×C4—591no—
131C23×C4—591no—
132C22×C8—1182no—
133C2×C22⋊C4—591no—
134C2×C22⋊C4—591no—
135C2×C22⋊C4—591no—
136C2×C22⋊C4—1182no—
137C2×C22⋊C4—1182no—
138C2×C22⋊C4C2×D5911yescharacteristic
139C22⋊C8—592no—
140C22⋊C8—1182no—
141C22⋊C8C2×D5912yescomplemented
142C24—591no—
143C24—594no—
144C24—591no—
145C24—1181no—
146C24—1181no—
147C24—1182no—
148C24—2362no—
149C24—2362no—
150C24C4×D5911yescharacteristic
151C22×C4—591no—
152C22×C4—592no—
153C22×C4—592no—
154C22×C4—591no—
155C22×C4—1181no—
156C22×C4—1181no—
157C22×C4—2362no—
158C22×C4—2362no—
159C22×C4C4×D5911yescharacteristic
160C22×C4C22×D5911yescharacteristic
161C2×C8—22no—
162C2×C8—1182no—
163C2×C8—2364no—
164C22⋊C4—22no—
165C22⋊C4—1182no—
166C22⋊C4—1182no—
167C22⋊C4—1182no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—591no—
173C23—591no—
174C23—592no—
175C23—592no—
176C23—592no—
177C23—1182no—
178C23—1182no—
179C23—1184no—
180C23—1184no—
181C23—1181no—
182C23—1181no—
183C23—2361no—
184C23—2361no—
185C23—2362no—
186C23—2362no—
187C23—2368no—
188C23—2368no—
189C23—2362no—
190C23—2362no—
191C23C8×D5912yescomplemented
192C23C2×C4×D5911yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—592no—
197C2×C4—1184no—
198C2×C4—1181no—
199C2×C4—2362no—
200C2×C4—2362no—
201C2×C4—2362no—
202C2×C4—2361no—
203C2×C4—2361no—
204C2×C4D4×D5912yes—
205C8—42no—
206C8—2362no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—592no—
215C22—592no—
216C22—592no—
217C22—592no—
218C22—1184no—
219C22—1184no—
220C22—1181no—
221C22—1181no—
222C22—1182no—
223C22—2362no—
224C22—2362no—
225C22—2368no—
226C22—2368no—
227C22—2361no—
228C22—2361no—
229C22C22⋊C4×D5911yescharacteristic
230C22C2×C8×D5911yescharacteristic
231C22M16×D5911yescharacteristic
232C4—22no—
233C4—41no—
234C4—1182no—
235C4—2361no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—594no—
240C2—1182no—
241C2—2362no—
242C2C22⋊C8×D5911yescharacteristic
243C2#99×D5911yescharacteristic
244C2#100×D5911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC22×C59C22×C8
FrattiniC22×C4C22×D59
FittingC59×#323C2
socleC22×C59C2×C22⋊C4
hypercenter#323D59
hypocenterC59C2×#323
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D59C2semidirect
3. #16837126C2semidirect
4. #16837125C2semidirect
5. C59×#323C2semidirect
15. C22⋊(C59⋊C8)C22semidirect
18. C22⋊C8×C59C22semidirect
25. C23×D59C8semidirect
49. C23×C59C2×C8semidirect
68. C22×D59C2×C8semidirect
122. D59#323direct (N × H)
127. #323D59direct (N × H)
128. C59C2×#323semidirect
141. C22⋊C8C2×D59semidirect
191. C23C8×D59semidirect