Finite Group Databasebeta

← #21432160

Subgroups — #21432160

Order 7552.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273725C211yesmaximal, characteristic, complemented
2C2×#14273722C211yesmaximal, characteristic
3#16837343C212yesmaximal, complemented
4#16837337C212yesmaximal
5#16837335C212yesmaximal, complemented
6#16837331C212yesmaximal
7#16837322C211yesmaximal, characteristic, complemented
8#16837315C211yesmaximal, characteristic
9#16837313C211yesmaximal, characteristic
10#16837269C211yesmaximal, characteristic, complemented
11C59×#395C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13#14273725—24no—
14#14273722—24no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C2211yescharacteristic
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2211yescharacteristic
21C2×(C2×D59)⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×C4×Dic59C2211yescharacteristic
26C59⋊#95C2211yescharacteristic
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C22×Q8×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C2×Q8×C59—22no—
39C2×Q8×C59—42no—
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2312yes—
48C22×Dic59C2311yescharacteristic
49C22×Dic59C2311yescharacteristic
50C2×Dic118—22no—
51C2×Dic118—42no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—42no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—42no—
58(C2×D59)⋊C4—42no—
59C4⋊Dic59—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—24no—
62Dic59⋊C4—24no—
63Dic59⋊C4—42no—
64C4×Dic59D414yes—
65C23×C59C2411yescharacteristic
66C22×D59—21no—
67C22×D59—22no—
68C22×D59—21no—
69C22×D59—21no—
70C22×D59—22no—
71Q8×C59—44no—
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—21no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59C2×D412yes—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59C2×D412yes—
97C2×Dic59C2×D412yes—
98Dic118—44no—
99C22×C59C22×D411yescharacteristic
100C22×C59H(5,𝔽2)12yes—
101C22×C592−1+411yescharacteristic
102C22×C592−1+411yescharacteristic
103C22×C592−1+412yes—
104C2×D59—41no—
105C2×D59—41no—
106C2×D59—41no—
107C2×D59—42no—
108C2×D59—42no—
109C4×C59—22no—
110C4×C59—41no—
111C4×C59—42no—
112C4×C59—41no—
113C4×C59—42no—
114Dic59—22no—
115Dic59—22no—
116Dic59—42no—
117Dic59—41no—
118Dic59—42no—
119#2821—591nomaximal, Sylow
120C2×C59#53511yescharacteristic
121C2×C59#53611yescharacteristic
122C2×C59#53611yescharacteristic
123C2×C59#56312yes—
124C2×C59#56312yes—
125D59—81no—
126C2×C4⋊Q8—591no—
127C2×#126—591no—
128#400—592no—
129#399—592no—
130#398—592no—
131#397—592no—
132#395—591no—
133#395D5911yescharacteristic, complemented
134#393—591no—
135#393—591no—
136#383—591no—
137C59#282111yescharacteristic, complemented, Sylow
138C22×Q8—591no—
139C22×Q8C2×D5911yescharacteristic
140C4⋊Q8—1184no—
141#126—1184no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4C2×D5911yescharacteristic
148C2×C4⋊C4C2×D5912yes—
149C2×C22⋊C4—591no—
150C2×C22⋊C4—591no—
151C2×C22⋊C4—591no—
152C2×C22⋊C4—592no—
153C2×C22⋊C4—592no—
154C2×C42—591no—
155#95—591no—
156#95—592no—
157#95—592no—
158#95—592no—
159#95—592no—
160#95—592no—
161#95C2×D5911yescharacteristic
162#95C2×D5912yes—
163C24—591no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—1182no—
167C2×Q8—2362no—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4—592no—
171C22×C4—591no—
172C22×C4—592no—
173C22×C4C22×D5912yes—
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5912yes—
176C22×C4C22×D5911yescharacteristic
177C22×C4C22×D5911yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4—1184no—
183C4⋊C4—1184no—
184C4⋊C4—2362no—
185C22⋊C4—1182no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—2362no—
189C22⋊C4—2362no—
190C42—594no—
191C23—1181no—
192C23—1182no—
193C23—1181no—
194C23—1181no—
195C23—1182no—
196C23C23×D5911yescharacteristic
197Q8—44no—
198Q8—2364no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—592no—
212C2×C4—592no—
213C2×C4—1181no—
214C2×C4—1181no—
215C2×C4—1182no—
216C2×C4—1181no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4D4×D5912yes—
225C22—2362no—
226C22—2362no—
227C22—2361no—
228C22—2361no—
229C22—2361no—
230C22C2×D4×D5911yescharacteristic
231C22#1427377212yes—
232C22#1427377411yescharacteristic
233C22#1427377511yescharacteristic
234C22#1427377512yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4—1182no—
241C4—1182no—
242C4—2362no—
243C4—2362no—
244C4—2361no—
245C2—4721no—
246C2#1683796711yescharacteristic
247C2#1683797511yescharacteristic
248C2#1683797711yescharacteristic
249C2#1683815112yes—
250C2#1683815312yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2821
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14273725C2semidirect
3. #16837343C2semidirect
5. #16837335C2semidirect
7. #16837322C2semidirect
10. #16837269C2semidirect
11. C59×#395C2semidirect
133. #395D59semidirect
137. C59#2821semidirect