Finite Group Databasebeta

← #21428384

Subgroups — #21428384

Order 7552.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14273685C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic
3#16837340C211yesmaximal, characteristic, complemented
4#16837334C211yesmaximal, characteristic, complemented
5#16837332C211yesmaximal, characteristic, complemented
6#16837289C212yesmaximal, complemented
7#16837285C212yesmaximal, complemented
8#16837276C212yesmaximal
9#16837264C212yesmaximal
10#16837264C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic, complemented
12C22×C4×D59C2211yescharacteristic
13C22×C4×D59C2211yescharacteristic
14C22×C4×D59C2211yescharacteristic
15#14273685—24no—
16C2×C4⋊Dic59C2212yes—
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C4⋊C4×D59—24no—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×C4×Dic59C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—22no—
49C2×C4×D59—24no—
50C2×C4×D59—22no—
51C2×C4×D59—22no—
52C2×C4×D59—22no—
53C2×C4×D59—24no—
54C2×C4×D59D414yes—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—22no—
57(C2×D59)⋊C4—24no—
58(C2×D59)⋊C4—24no—
59C4⋊Dic59—22no—
60C4⋊Dic59—22no—
61C4⋊Dic59—24no—
62Dic59⋊C4—22no—
63Dic59⋊C4—24no—
64Dic59⋊C4—22no—
65C4×Dic59—24no—
66C23×C59C2411yescharacteristic
67C22×D59—21no—
68C22×D59—21no—
69C22×D59—22no—
70C22×D59C2×D412yes—
71C22×D59#4114yes—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—24no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D412yes—
83C2×C4×C59#4112yes—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59C2×D412yes—
96C2×Dic59#4112yes—
97C4×D59—28no—
98C4×D59—28no—
99C4×D59—44no—
100C22×C59C22×D411yescharacteristic
101C22×C59C2×#4112yes—
102C22×C59C2×#4111yescharacteristic
103C22×C59C2×#4111yescharacteristic
104C22×C592−1+412yes—
105C2×D59—22no—
106C2×D59—22no—
107C2×D59—24no—
108C2×D59—24no—
109C2×D59#12314yes—
110C4×C59—22no—
111C4×C59—22no—
112C4×C59—41no—
113C4×C59—42no—
114C4×C59—42no—
115Dic59—22no—
116Dic59—22no—
117Dic59—41no—
118Dic59—42no—
119Dic59—42no—
120#2484—591nomaximal, Sylow
121C2×C59C2×#12311yescharacteristic
122C2×C59#52511yescharacteristic
123C2×C59#53611yescharacteristic
124C2×C59#55212yes—
125C2×C59#55212yes—
126D59—24no—
127C2×#117—591no—
128C22×C4⋊C4—591no—
129#400—591no—
130#400D5911yescharacteristic, complemented
131#398—591no—
132#398—591no—
133#387—592no—
134#387—592no—
135#385—592no—
136#381—591no—
137#381—592no—
138C59#248411yescharacteristic, complemented, Sylow
139C23×C4—591no—
140C23×C4—591no—
141C23×C4—591no—
142#117—1184no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—591no—
145C2×C4⋊C4—591no—
146C2×C4⋊C4—591no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—592no—
149C2×C4⋊C4—1184no—
150C2×C4⋊C4C2×D5911yescharacteristic
151C2×C4⋊C4C2×D5911yescharacteristic
152C2×C22⋊C4—592no—
153C2×C22⋊C4—592no—
154C2×C42—592no—
155#95—592no—
156#95—592no—
157#95—592no—
158#95—592no—
159#95—591no—
160#95—592no—
161#95C2×D5912yes—
162#95C2×D5911yescharacteristic
163#95C2×D5912yes—
164C24—591no—
165C22×C4—591no—
166C22×C4—591no—
167C22×C4—594no—
168C22×C4—592no—
169C22×C4—591no—
170C22×C4—592no—
171C22×C4—1182no—
172C22×C4—1182no—
173C22×C4—1184no—
174C22×C4—1182no—
175C22×C4—1184no—
176C22×C4—1182no—
177C22×C4C22×D5912yes—
178C22×C4C22×D5912yes—
179C22×C4C22×D5911yescharacteristic
180C22×C4C22×D5911yescharacteristic
181C22×C4C22×D5911yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C4⋊C4—1184no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1184no—
190C22⋊C4—1184no—
191C22⋊C4—1184no—
192C42—1184no—
193C23—592no—
194C23—594no—
195C23—1181no—
196C23—1181no—
197C23—1182no—
198C23C23×D5911yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—592no—
210C2×C4—592no—
211C2×C4—1188no—
212C2×C4—1188no—
213C2×C4—1181no—
214C2×C4—1182no—
215C2×C4—1181no—
216C2×C4—1182no—
217C2×C4—1181no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4—2364no—
225C2×C4D4×D5912yes—
226C2×C4#1174568912yes—
227C22—594no—
228C22—1182no—
229C22—1182no—
230C22—1184no—
231C22—1184no—
232C22C2×D4×D5911yescharacteristic
233C22#41×D5912yes—
234C22#41×D5911yescharacteristic
235C22C2×#1174568911yescharacteristic
236C22#1427377412yes—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—42no—
241C4—42no—
242C4—1182no—
243C4—1182no—
244C4—2361no—
245C4—2362no—
246C4—2362no—
247C2—1184no—
248C2#123×D5911yescharacteristic
249C2#1683791511yescharacteristic
250C2#1683797211yescharacteristic
251C2#1683808812yes—
252C2#1683809012yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2484
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #16837340C2semidirect
4. #16837334C2semidirect
5. #16837332C2semidirect
6. #16837289C2semidirect
7. #16837285C2semidirect
11. C59×#400C2semidirect
130. #400D59semidirect
138. C59#2484semidirect