Finite Group Databasebeta

← #21431929

Subgroups — #21431929

Order 7552.

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

normal subgroups only

This group has 420 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#16837341C211yesmaximal, characteristic, complemented
2#16837325C212yesmaximal, complemented
3#16837316C212yesmaximal
4#16837295C212yesmaximal, complemented
5#16837290C212yesmaximal, complemented
6#16837290C212yesmaximal, complemented
7#16837284C212yesmaximal, complemented
8#16837271C211yesmaximal, characteristic, complemented
9C59×#394C211yesmaximal, characteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4C2212yes—
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×C22⋊Dic59C2212yes—
19C2×C4×Dic59C2211yescharacteristic
20C2×C4×Dic59C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C22×D4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C22⋊C4×C59C2212yes—
29C2×C22⋊C4×C59C2212yes—
30#95×C59C2211yescharacteristic
31C24×C59C2312yes—
32C2×D4×C59—42no—
33C2×D4×C59—41no—
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C4⋊C4×C59—41no—
43C22⋊C4×C59—24no—
44C22⋊C4×C59—42no—
45C22⋊Dic59—24no—
46C22⋊Dic59—24no—
47C22⋊Dic59—42no—
48C22⋊Dic59—42no—
49C4⋊Dic59—41no—
50C4⋊Dic59—41no—
51Dic59⋊C4—24no—
52Dic59⋊C4—42no—
53Dic59⋊C4—42no—
54C4×Dic59—22no—
55C4×Dic59—42no—
56C23×C59—22no—
57C23×C59—22no—
58C23×C59—22no—
59C23×C59—22no—
60C23×C59—22no—
61C23×C59—22no—
62C23×C59—22no—
63C23×C59C2411yescharacteristic
64D4×C59—44no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
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—21no—
74C2×C4×C59#4112yes—
75C2×Dic59—22no—
76C2×Dic59—22no—
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—
86C2×Dic59#4114yes—
87C22×C59—42no—
88C22×C59—42no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59—42no—
94C22×C59C2×#4112yes—
95C22×C59C2×#4111yescharacteristic
96C22×C59H(5,𝔽2)11yescharacteristic
97C22×C59H(5,𝔽2)12yes—
98C22×C592−1+411yescharacteristic
99C4×C59—22no—
100C4×C59—42no—
101C4×C59—41no—
102C4×C59—41no—
103Dic59—24no—
104Dic59—42no—
105Dic59—42no—
106Dic59—42no—
107#2795—591nomaximal, Sylow
108C2×C59—82no—
109C2×C59#53911yescharacteristic
110C2×C59#54212yes—
111C2×C59#55312yes—
112C2×C59#55511yescharacteristic
113C2×C59#56011yescharacteristic
114#400—591no—
115#396—592no—
116#394—592no—
117#394D5911yescharacteristic
118#388—592no—
119#388—592no—
120#388—592no—
121#387—592no—
122#384—591no—
123C59#279511yescharacteristic, complemented, Sylow
124C22×D4C2×D5911yescharacteristic
125C2×C4⋊C4—592no—
126C2×C4⋊C4—592no—
127C2×C4⋊C4—591no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—591no—
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C22⋊C4—592no—
132C2×C22⋊C4—592no—
133C2×C22⋊C4—592no—
134C2×C22⋊C4—592no—
135C2×C22⋊C4C2×D5912yes—
136C2×C22⋊C4C2×D5912yes—
137C2×C42—591no—
138C2×C42—592no—
139#95—592no—
140#95—592no—
141#95—592no—
142#95—591no—
143#95—592no—
144#95C2×D5911yescharacteristic
145C24C22×D5912yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—592no—
149C22×C4—592no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4C22×D5912yes—
153C22×C4C22×D5911yescharacteristic
154C22×C4C22×D5911yescharacteristic
155C22×C4C22×D5911yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—1184no—
158C4⋊C4—2362no—
159C4⋊C4—2362no—
160C4⋊C4—2361no—
161C4⋊C4—2361no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—1184no—
165C22⋊C4—1184no—
166C22⋊C4—2362no—
167C22⋊C4—2362no—
168C42—1182no—
169C42—2362no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D5911yescharacteristic
178D4—44no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—594no—
189C2×C4—1182no—
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—1182no—
200C2×C4#1174568712yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D5912yes—
209C22C2×#1174568711yescharacteristic
210C22#1427377211yescharacteristic
211C22#1427377212yes—
212C22#1427377411yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—1184no—
218C4—2362no—
219C4—2362no—
220C4—2362no—
221C2—82no—
222C2#1683799711yescharacteristic
223C2#1683802012yes—
224C2#1683809912yes—
225C2#1683811411yescharacteristic
226C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2795
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #16837341C2semidirect
2. #16837325C2semidirect
4. #16837295C2semidirect
5. #16837290C2semidirect
6. #16837290C2semidirect
7. #16837284C2semidirect
8. #16837271C2semidirect
123. C59#2795semidirect