Finite Group Databasebeta

← #21429734

Subgroups — #21429734

Order 7552.

470 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273721C211yesmaximal, characteristic
2C2×C4×Dic118C211yesmaximal, characteristic, complemented
3#16837342C211yesmaximal, characteristic, complemented
4#16837339C211yesmaximal, characteristic
5#16837323C211yesmaximal, characteristic, complemented
6#16837315C211yesmaximal, characteristic
7#16837300C212yesmaximal, complemented
8#16837294C212yesmaximal
9#16837293C212yesmaximal
10#16837287C212yesmaximal, complemented
11C59×#376C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13#14273721—24no—
14C4×Dic118—24no—
15C2×C4⋊Dic59C2212yes—
16C2×C4⋊Dic59C2212yes—
17C2×C4⋊Dic59C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C42×C59C2212yes—
33C2×C42×C59C2211yescharacteristic
34#95×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2211yescharacteristic
37C23×D59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2312yes—
48C2×Dic118—22no—
49C2×Dic118—24no—
50C42×C59—24no—
51C42×C59D414yes—
52(C2×D59)⋊C4—22no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—24no—
56(C2×D59)⋊C4—24no—
57C4⋊Dic59—22no—
58C4⋊Dic59—24no—
59C4⋊Dic59—24no—
60Dic59⋊C4—24no—
61Dic59⋊C4—22no—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64C4×Dic59—24no—
65C23×C59C2411yescharacteristic
66C22×D59—21no—
67C22×D59—22no—
68C22×D59—22no—
69C22×D59—21no—
70C22×D59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D412yes—
83C2×C4×C59#4114yes—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—21no—
96C2×Dic59#4114yes—
97Dic118—28no—
98C22×C59C22×D411yescharacteristic
99C22×C59C2×#4112yes—
100C22×C59C2×#4112yes—
101C22×C592−1+411yescharacteristic
102C22×C592−1+411yescharacteristic
103C2×D59—41no—
104C2×D59—41no—
105C2×D59—41no—
106C2×D59—42no—
107C2×D59—42no—
108C4×C59—22no—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—24no—
112C4×C59—42no—
113Dic59—24no—
114Dic59—41no—
115Dic59—42no—
116Dic59—41no—
117Dic59—41no—
118#2604—591nomaximal, Sylow
119C2×C59#52511yescharacteristic
120C2×C59#53211yescharacteristic
121C2×C59#53611yescharacteristic
122C2×C59#55212yes—
123C2×C59#55612yes—
124D59—81no—
125C2×#126—591no—
126C2×C4×Q8—591no—
127#400—591no—
128#399—591no—
129#395—591no—
130#393—591no—
131#389—592no—
132#388—592no—
133#388—592no—
134#387—592no—
135#376D5911yescharacteristic, complemented
136C59#260411yescharacteristic, complemented, Sylow
137C22×Q8—591no—
138#126—1184no—
139C4×Q8—1184no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—591no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C22⋊C4—591no—
148C2×C22⋊C4—591no—
149C2×C22⋊C4—591no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4—592no—
152C2×C42—592no—
153C2×C42C2×D5912yes—
154C2×C42C2×D5911yescharacteristic
155#95—592no—
156#95—592no—
157#95—592no—
158#95—592no—
159#95C2×D5912yes—
160#95C2×D5911yescharacteristic
161#95C2×D5911yescharacteristic
162C24—591no—
163C2×Q8—1184no—
164C2×Q8—1182no—
165C22×C4—592no—
166C22×C4—591no—
167C22×C4—592no—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4C22×D5912yes—
171C22×C4C22×D5911yescharacteristic
172C22×C4C22×D5911yescharacteristic
173C22×C4C22×D5911yescharacteristic
174C22×C4C22×D5912yes—
175C4⋊C4—1184no—
176C4⋊C4—1184no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1184no—
182C22⋊C4—1184no—
183C22⋊C4—1182no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—1184no—
187C42—24no—
188C42—1184no—
189C42D23614yes—
190C23—1181no—
191C23—1182no—
192C23—1182no—
193C23—1181no—
194C23—1181no—
195C23C23×D5911yescharacteristic
196Q8—1188no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—594no—
207C2×C4—1182no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1181no—
211C2×C4—1181no—
212C2×C4—1181no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1181no—
218C2×C4—1181no—
219C2×C4C2×D23612yes—
220C2×C4C2×D23612yes—
221C2×C4C2×D23612yes—
222C2×C4#1174568514yes—
223C22—2361no—
224C22—2361no—
225C22—2361no—
226C22—2362no—
227C22—2362no—
228C22C22×D23611yescharacteristic
229C22#41×D5912yes—
230C22C2×#1174568512yes—
231C22#1427377411yescharacteristic
232C22#1427377411yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—24no—
237C4—42no—
238C4—1184no—
239C4—2361no—
240C4—2362no—
241C4—2361no—
242C4—2361no—
243C2—4721no—
244C2#1683791411yescharacteristic
245C2#1683795211yescharacteristic
246C2#1683797811yescharacteristic
247C2#1683808512yes—
248C2#1683812012yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#376C2
hypercenter#376D59
hypocenterC59#2604
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic118C2semidirect
3. #16837342C2semidirect
5. #16837323C2semidirect
7. #16837300C2semidirect
10. #16837287C2semidirect
11. C59×#376C2semidirect
135. #376D59semidirect
136. C59#2604semidirect