Finite Group Databasebeta

← #21431925

Subgroups — #21431925

Order 7552.

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

normal subgroups only

This group has 420 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
1#16837341C211yesmaximal, characteristic, complemented
2#16837324C212yesmaximal, complemented
3#16837319C212yesmaximal
4#16837319C211yesmaximal, characteristic
5#16837293C212yesmaximal, complemented
6#16837292C212yesmaximal, complemented
7#16837292C212yesmaximal, complemented
8#16837283C212yesmaximal, complemented
9C59×#384C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4C2212yes—
13C2×(C2×D59)⋊C4C2212yes—
14C2×(C2×D59)⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×C4×Dic59C2212yes—
20C59⋊#95C2211yescharacteristic
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C2×C4⋊C4×C59C2212yes—
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2212yes—
29C2×C4⋊C4×C59C2211yescharacteristic
30C2×C42×C59C2211yescharacteristic
31C23×D59C2312yes—
32C22×C4×C59C2311yescharacteristic
33C22×C4×C59C2312yes—
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2312yes—
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C2×D236—41no—
41C2×D236—42no—
42C4⋊C4×C59—42no—
43C4⋊C4×C59—41no—
44C4⋊C4×C59—41no—
45C4⋊C4×C59—42no—
46C42×C59—22no—
47(C2×D59)⋊C4—24no—
48(C2×D59)⋊C4—24no—
49(C2×D59)⋊C4—24no—
50(C2×D59)⋊C4—42no—
51(C2×D59)⋊C4—42no—
52(C2×D59)⋊C4—42no—
53C4⋊Dic59—41no—
54Dic59⋊C4—24no—
55C4×Dic59—42no—
56C23×C59C2411yescharacteristic
57C22×D59—22no—
58C22×D59—22no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59#4112yes—
76C2×C4×C59#4114yes—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86D236—44no—
87C22×C59C2×#4111yescharacteristic
88C22×C59C2×#4112yes—
89C22×C59H(5,𝔽2)11yescharacteristic
90C22×C59H(5,𝔽2)12yes—
91C22×C592−1+411yescharacteristic
92C2×D59—42no—
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C2×D59—42no—
99C4×C59—22no—
100C4×C59—24no—
101C4×C59—41no—
102C4×C59—42no—
103C4×C59—41no—
104Dic59—42no—
105Dic59—42no—
106Dic59—42no—
107#2795—591nomaximal, Sylow
108C2×C59#53911yescharacteristic
109C2×C59#54212yes—
110C2×C59#55312yes—
111C2×C59#55511yescharacteristic
112C2×C59#56011yescharacteristic
113D59—82no—
114#400—591no—
115#396—592no—
116#394—591no—
117#394—592no—
118#388—592no—
119#388—592no—
120#388—592no—
121#387—592no—
122#384D5911yescharacteristic, complemented
123C59#279511yescharacteristic, complemented, Sylow
124C22×D4—591no—
125C2×C4⋊C4—592no—
126C2×C4⋊C4—591no—
127C2×C4⋊C4C2×D5912yes—
128C2×C4⋊C4C2×D5911yescharacteristic
129C2×C4⋊C4C2×D5912yes—
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C22⋊C4—592no—
132C2×C22⋊C4—592no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C42—592no—
138C2×C42C2×D5911yescharacteristic
139#95—591no—
140#95—592no—
141#95—592no—
142#95—592no—
143#95—591no—
144#95—592no—
145C24—592no—
146C2×D4—2361no—
147C2×D4—2362no—
148C22×C4—592no—
149C22×C4—592no—
150C22×C4—592no—
151C22×C4C22×D5911yescharacteristic
152C22×C4C22×D5912yes—
153C22×C4C22×D5911yescharacteristic
154C22×C4C22×D5911yescharacteristic
155C22×C4C22×D5912yes—
156C4⋊C4—42no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—1184no—
161C4⋊C4—2361no—
162C22⋊C4—1184no—
163C22⋊C4—1184no—
164C22⋊C4—1184no—
165C22⋊C4—2362no—
166C22⋊C4—2362no—
167C22⋊C4—2362no—
168C42—22no—
169C42—2362no—
170C23—1182no—
171C23—1182no—
172C23—1182no—
173C23—1182no—
174C23—1182no—
175C23—1182no—
176C23—1182no—
177C23C23×D5911yescharacteristic
178D4—2364no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4#1174568512yes—
200C2×C4#1174568914yes—
201C22—2362no—
202C22—2362no—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22—2362no—
207C22—2362no—
208C22C2×#1174568511yescharacteristic
209C22C2×#1174568912yes—
210C22#1427377211yescharacteristic
211C22#1427377212yes—
212C22#1427377511yescharacteristic
213C4—22no—
214C4—24no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—2362no—
219C4—2362no—
220C4—2362no—
221C2—4722no—
222C2#1683799911yescharacteristic
223C2#1683802612yes—
224C2#1683810012yes—
225C2#1683811811yescharacteristic
226C2#1683813911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#384C2
hypercenter#384D59
hypocenterC59#2795
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
2. #16837324C2semidirect
5. #16837293C2semidirect
6. #16837292C2semidirect
7. #16837292C2semidirect
8. #16837283C2semidirect
9. C59×#384C2semidirect
122. #384D59semidirect
123. C59#2795semidirect