Finite Group Databasebeta

← #21434045

Subgroups — #21434045

Order 7552.

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

normal subgroups only

This group has 410 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×#14273706C211yesmaximal, characteristic
2C2×#14273686C211yesmaximal, characteristic
3#16837744C214yesmaximal, complemented
4#16837738C212yesmaximal, complemented
5#16837733C212yesmaximal, complemented
6#16837444C212yesmaximal, complemented
7#16837412C212yesmaximal, complemented
8C59×#407C211yesmaximal, characteristic
9C22×Dic118C2211yescharacteristic
10#14273706—21no—
11#14273706—21no—
12#14273706C2212yes—
13#14273706C2212yes—
14#14273686—21no—
15#14273686—21no—
16#14273686C2212yes—
17#14273686C2212yes—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊Dic59C2211yescharacteristic
21C2×Dic59⋊C4—21no—
22C2×C22⋊Dic59—21no—
23C2×C22⋊Dic59—21no—
24C2×C4×Dic59—21no—
25#14273661C2214yescomplemented
26#14273659C2214yescomplemented
27#14273652C2214yescomplemented
28#14273652C2214yescomplemented
29C23×C4×C59C2211yescharacteristic
30C2×M16×C59C2212yes—
31C22⋊C8×C59C2212yes—
32C22⋊C8×C59C2212yes—
33C24×C59D411yescharacteristic
34C22×C4×C59—24no—
35C22×C4×C59D411yescharacteristic
36C22×C4×C59D411yescharacteristic
37C22×C4×C59D411yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×Dic59—21no—
42C22×Dic59—21no—
43C22×Dic59—21no—
44C22×Dic59—21no—
45C2×Dic118—24no—
46C2×Dic118—21no—
47C2×Dic118C2312yes—
48M16×C59—24no—
49C2×C8×C59C2314yes—
50C22⋊Dic59—22no—
51C22⋊Dic59—22no—
52C22⋊Dic59—22no—
53C22⋊Dic59—22no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59C2312yes—
58C4⋊Dic59C2312yes—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63C4×Dic59—22no—
64C23×C59—22no—
65C23×C59—22no—
66C23×C59—41no—
67C23×C59C2×D411yescharacteristic
68C23×C59C2×D411yescharacteristic
69C23×C59C2×D411yescharacteristic
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59#4114yes—
79C2×C4×C59C2411yescharacteristic
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—42no—
87C2×Dic59—42no—
88Dic118—24no—
89Dic118—42no—
90C8×C59—24no—
91C22×C59—21no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59—21no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59—21no—
98C22×C59—44no—
99C22×C59#12312yes—
100C22×C59#13712yes—
101C22×C59C22×D411yescharacteristic
102C4×C59—21no—
103C4×C59—21no—
104C4×C59#12312yes—
105C4×C59C2×#4112yes—
106Dic59—42no—
107Dic59—42no—
108Dic59—42no—
109Dic59—42no—
110#3095—591nomaximal, Sylow
111C2×C59—22no—
112C2×C59—22no—
113C2×C59—41no—
114C2×C59C2×#12311yescharacteristic
115C2×C59C2×#13711yescharacteristic
116C2×C59#57511yescharacteristic
117C2×C22⋊Q8—591no—
118C2×#117—591no—
119#485—594no—
120#484—592no—
121#483—592no—
122#428—592no—
123#419—592no—
124#407D5911yescharacteristic
125C59#309511yescharacteristic, complemented, Sylow
126C22×Q8—591no—
127C23×C4C2×D5911yescharacteristic
128C2×M16C2×D5912yes—
129C22⋊Q8—592no—
130C22⋊Q8—592no—
131C22⋊Q8—1181no—
132C22⋊Q8—1181no—
133#117—592no—
134#117—592no—
135#117—1181no—
136#117—1181no—
137C2×C4⋊C4—591no—
138C2×C4⋊C4—591no—
139C2×C4⋊C4—591no—
140C2×C4⋊C4—1181no—
141C2×C22⋊C4—1181no—
142C2×C22⋊C4—1181no—
143C2×C42—1181no—
144#107—594no—
145#106—594no—
146#103—594no—
147#103—594no—
148C22⋊C8C2×D5912yes—
149C22⋊C8C2×D5912yes—
150C24D23611yescharacteristic
151C2×Q8—592no—
152C2×Q8—1181no—
153C2×Q8—1184no—
154C22×C4—24no—
155C22×C4—1181no—
156C22×C4—1181no—
157C22×C4—1181no—
158C22×C4—1181no—
159C22×C4D23611yescharacteristic
160C22×C4D23611yescharacteristic
161C22×C4D23611yescharacteristic
162C22×C4C22×D5911yescharacteristic
163C22×C4C22×D5911yescharacteristic
164C22×C4C22×D5911yescharacteristic
165M16—24no—
166C2×C8C22×D5914yes—
167C4⋊C4—592no—
168C4⋊C4—592no—
169C4⋊C4—592no—
170C4⋊C4—1181no—
171C4⋊C4—1181no—
172C4⋊C4—1181no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C22⋊C4—1182no—
176C22⋊C4—1182no—
177C22⋊C4—1182no—
178C22⋊C4—1182no—
179C42—1182no—
180C42—1182no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×D23611yescharacteristic
185C23C2×D23611yescharacteristic
186C23C2×D23611yescharacteristic
187Q8—1184no—
188Q8—2362no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—2362no—
199C2×C4—2362no—
200C2×C4—2362no—
201C2×C4—2362no—
202C2×C4C2×D23611yescharacteristic
203C2×C4C2×D23611yescharacteristic
204C2×C4C2×D23611yescharacteristic
205C2×C4#1174568714yes—
206C2×C4C23×D5911yescharacteristic
207C8—24no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1427371112yes—
217C22#1427376012yes—
218C22C22×D23611yescharacteristic
219C4—21no—
220C4—21no—
221C4—2362no—
222C4—2362no—
223C4—2362no—
224C4—2362no—
225C4#1427371112yes—
226C4C2×#1174568712yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1427371111yescharacteristic
231C2C2×#1427376011yescharacteristic
232C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3095
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #16837744C2semidirect
4. #16837738C2semidirect
5. #16837733C2semidirect
6. #16837444C2semidirect
7. #16837412C2semidirect
25. #14273661C22semidirect
26. #14273659C22semidirect
27. #14273652C22semidirect
28. #14273652C22semidirect
125. C59#3095semidirect