Finite Group Databasebeta

← #21431775

Subgroups — #21431775

Order 7552.

448 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837344C212yesmaximal, complemented
2#16837329C212yesmaximal, complemented
3#16837319C211yesmaximal, characteristic
4#16837294C212yesmaximal, complemented
5#16837280C212yesmaximal
6#16837276C212yesmaximal, complemented
7#16837273C212yesmaximal, complemented
8#16837267C211yesmaximal, characteristic, complemented
9C59×#400C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×(C2×D59)⋊C4C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×C4×Dic59C2211yescharacteristic
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C2×C4⋊C4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28#95×C59C2212yes—
29#95×C59C2212yes—
30#95×C59C2211yescharacteristic
31C23×D59C2312yes—
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C2×D236—24no—
41C2×D236—41no—
42C2×C4×D59—42no—
43C2×C4×D59—42no—
44C2×C4×D59—42no—
45C4⋊C4×C59—41no—
46C4⋊C4×C59—41no—
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—
52C4⋊Dic59—42no—
53C4⋊Dic59—41no—
54Dic59⋊C4—42no—
55C4×Dic59—22no—
56C23×C59C2411yescharacteristic
57C22×D59—22no—
58C22×D59—22no—
59C22×D59—22no—
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59#4114yes—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59#4112yes—
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—
87C4×D59—48no—
88C22×C59C2×#4112yes—
89C22×C59C2×#4111yescharacteristic
90C22×C59H(5,𝔽2)11yescharacteristic
91C22×C59H(5,𝔽2)12yes—
92C22×C592−1+411yescharacteristic
93C2×D59—24no—
94C2×D59—24no—
95C2×D59—24no—
96C2×D59—42no—
97C2×D59—42no—
98C2×D59—42no—
99C2×D59—42no—
100C4×C59—22no—
101C4×C59—42no—
102C4×C59—41no—
103C4×C59—41no—
104C4×C59—42no—
105Dic59—42no—
106Dic59—42no—
107Dic59—42no—
108#2782—591nomaximal, Sylow
109C2×C59#53912yes—
110C2×C59#53911yescharacteristic
111C2×C59#55111yescharacteristic
112C2×C59#55312yes—
113C2×C59H(3,𝔽4)11yescharacteristic
114D59—44no—
115#400—592no—
116#400D5911yescharacteristic, complemented
117#397—592no—
118#394—591no—
119#388—592no—
120#386—592no—
121#385—592no—
122#385—592no—
123#382—591no—
124C59#278211yescharacteristic, complemented, Sylow
125C22×D4—591no—
126C23×C4—592no—
127C2×C4⋊C4—591no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C4⋊C4C2×D5911yescharacteristic
132C2×C22⋊C4—592no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4—592no—
136C2×C22⋊C4—592no—
137C2×C42—591no—
138#95—592no—
139#95—592no—
140#95—592no—
141#95—592no—
142#95—591no—
143#95C2×D5912yes—
144#95C2×D5912yes—
145#95C2×D5911yescharacteristic
146C24—592no—
147C2×D4—1184no—
148C2×D4—2361no—
149C22×C4—592no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4—2362no—
153C22×C4—2362no—
154C22×C4—2362no—
155C22×C4C22×D5911yescharacteristic
156C22×C4C22×D5911yescharacteristic
157C22×C4C22×D5912yes—
158C22×C4C22×D5912yes—
159C22×C4C22×D5911yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—2362no—
163C4⋊C4—2361no—
164C4⋊C4—2362no—
165C22⋊C4—1184no—
166C22⋊C4—1184no—
167C22⋊C4—1184no—
168C22⋊C4—2362no—
169C22⋊C4—2362no—
170C42—1182no—
171C23—594no—
172C23—1182no—
173C23—1182no—
174C23—1182no—
175C23—1182no—
176C23—1182no—
177C23—1182no—
178C23C23×D5911yescharacteristic
179D4—2364no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—2368no—
202C2×C4#1174568912yes—
203C22—1184no—
204C22—1184no—
205C22—1184no—
206C22—2362no—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22#41×D5912yes—
211C22C2×#1174568911yescharacteristic
212C22#1427377211yescharacteristic
213C22#1427377312yes—
214C22#1427377411yescharacteristic
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—2362no—
221C4—2362no—
222C4—2362no—
223C2—2364no—
224C2#1683799312yes—
225C2#1683800111yescharacteristic
226C2#1683808011yescharacteristic
227C2#1683810512yes—
228C2#1683814411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2782
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #16837344C2semidirect
2. #16837329C2semidirect
4. #16837294C2semidirect
6. #16837276C2semidirect
7. #16837273C2semidirect
8. #16837267C2semidirect
9. C59×#400C2semidirect
116. #400D59semidirect
124. C59#2782semidirect