Finite Group Databasebeta

← #21429788

Subgroups — #21429788

Order 7552.

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

normal subgroups only

This group has 476 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×#14273719C211yesmaximal, characteristic, complemented
2C2×#14273684C211yesmaximal, characteristic
3#16837342C211yesmaximal, characteristic, complemented
4#16837339C211yesmaximal, characteristic
5#16837334C211yesmaximal, characteristic, complemented
6#16837329C211yesmaximal, characteristic
7#16837300C212yesmaximal, complemented
8#16837293C212yesmaximal
9#16837287C212yesmaximal, complemented
10#16837276C212yesmaximal
11C59×#376C211yesmaximal, characteristic, complemented
12C22×C4×D59C2211yescharacteristic
13#14273719—24no—
14#14273684—24no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×C4⋊Dic59C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
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×Dic59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—22no—
49C2×C4×D59—22no—
50C2×C4×D59—22no—
51C42×C59—24no—
52C42×C59D414yes—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—24no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—24no—
60C4⋊Dic59—24no—
61Dic59⋊C4—22no—
62Dic59⋊C4—22no—
63Dic59⋊C4—24no—
64Dic59⋊C4—24no—
65C4×Dic59—22no—
66C23×C59C2411yescharacteristic
67C22×D59—21no—
68C22×D59—22no—
69C22×D59—21no—
70C22×D59—22no—
71C22×D59#4112yes—
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×C59—22no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D412yes—
83C2×C4×C59C2×D412yes—
84C2×C4×C59#4114yes—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59#4112yes—
98C4×D59—28no—
99C22×C59C22×D411yescharacteristic
100C22×C59C2×#4111yescharacteristic
101C22×C59C2×#4111yescharacteristic
102C22×C59C2×#4112yes—
103C22×C592−1+412yes—
104C2×D59—22no—
105C2×D59—24no—
106C2×D59—41no—
107C2×D59—41no—
108C2×D59—42no—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—22no—
112C4×C59—24no—
113C4×C59—42no—
114Dic59—22no—
115Dic59—42no—
116Dic59—41no—
117Dic59—42no—
118Dic59—41no—
119#2611—591nomaximal, Sylow
120C2×C59#52511yescharacteristic
121C2×C59#53211yescharacteristic
122C2×C59#53611yescharacteristic
123C2×C59#55212yes—
124C2×C59#55212yes—
125D59—42no—
126C2×#125—591no—
127C2×#117—591no—
128#400—591no—
129#399—591no—
130#398—591no—
131#397—591no—
132#389—592no—
133#388—592no—
134#387—592no—
135#385—592no—
136#376D5911yescharacteristic, complemented
137C59#261111yescharacteristic, complemented, Sylow
138C23×C4—591no—
139#125—1184no—
140#117—1184no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—591no—
146C2×C4⋊C4—591no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—592no—
149C2×C22⋊C4—591no—
150C2×C22⋊C4—591no—
151C2×C22⋊C4—592no—
152C2×C22⋊C4—592no—
153C2×C42—591no—
154C2×C42C2×D5912yes—
155C2×C42C2×D5911yescharacteristic
156#95—592no—
157#95—592no—
158#95—592no—
159#95—592no—
160#95C2×D5912yes—
161#95C2×D5911yescharacteristic
162#95C2×D5911yescharacteristic
163C24—591no—
164C22×C4—591no—
165C22×C4—591no—
166C22×C4—591no—
167C22×C4—592no—
168C22×C4—592no—
169C22×C4—1182no—
170C22×C4—1182no—
171C22×C4—1182no—
172C22×C4C22×D5912yes—
173C22×C4C22×D5911yescharacteristic
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5912yes—
177C4⋊C4—1184no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1184no—
181C4⋊C4—1184no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C4⋊C4—1184no—
185C22⋊C4—1184no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—1184no—
189C42—24no—
190C42—1182no—
191C42D23614yes—
192C23—592no—
193C23—1181no—
194C23—1181no—
195C23—1182no—
196C23—1182no—
197C23C23×D5911yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—592no—
208C2×C4—1188no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—1181no—
212C2×C4—1181no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4C2×D23612yes—
222C2×C4C2×D23612yes—
223C2×C4C2×D23612yes—
224C2×C4#1174568514yes—
225C22—1182no—
226C22—1184no—
227C22—2361no—
228C22—2361no—
229C22—2362no—
230C22C22×D23611yescharacteristic
231C22#41×D5911yescharacteristic
232C22#41×D5911yescharacteristic
233C22C2×#1174568512yes—
234C22#1427377412yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—1182no—
241C4—2362no—
242C4—2361no—
243C4—2362no—
244C4—2361no—
245C2—2362no—
246C2#1683791411yescharacteristic
247C2#1683795211yescharacteristic
248C2#1683797811yescharacteristic
249C2#1683808512yes—
250C2#1683809112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#376C2
hypercenter#376D59
hypocenterC59#2611
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
1. C2×#14273719C2semidirect
3. #16837342C2semidirect
5. #16837334C2semidirect
7. #16837300C2semidirect
9. #16837287C2semidirect
11. C59×#376C2semidirect
136. #376D59semidirect
137. C59#2611semidirect