Finite Group Databasebeta

← #21432166

Subgroups — #21432166

Order 7552.

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

normal subgroups only

This group has 380 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×#14273718C211yesmaximal, characteristic
2C2×#14273717C211yesmaximal, characteristic
3#16837344C212yesmaximal
4#16837342C211yesmaximal, characteristic
5#16837341C211yesmaximal, characteristic
6#16837336C212yesmaximal
7#16837335C212yesmaximal
8#16837333C211yesmaximal, characteristic
9#16837333C212yesmaximal
10#16837266C211yesmaximal, characteristic
11C59×#398C211yesmaximal, characteristic
12#14273718—24no—
13#14273717—24no—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×C4⋊Dic59C2212yes—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×Dic59⋊C4C2212yes—
23C2×Dic59⋊C4C2212yes—
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C4⋊C4×C59—22no—
49C4⋊C4×C59—22no—
50C4⋊C4×C59—42no—
51C4⋊Dic59—22no—
52C4⋊Dic59—22no—
53C4⋊Dic59—24no—
54Dic59⋊C4—22no—
55Dic59⋊C4—22no—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58Dic59⋊C4—24no—
59Dic59⋊C4—42no—
60Dic59⋊C4—42no—
61C4×Dic59D414yes—
62C23×C59C2411yescharacteristic
63C2×C4×C59—22no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D412yes—
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—22no—
79C2×Dic59—21no—
80C2×Dic59—21no—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—21no—
86C2×Dic59—22no—
87C2×Dic59—24no—
88C2×Dic59—22no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91C22×C59C22×D411yescharacteristic
92C22×C59H(5,𝔽2)11yescharacteristic
93C22×C592−1+412yes—
94C22×C592−1+411yescharacteristic
95C22×C592−1+412yes—
96C4×C59—22no—
97C4×C59—41no—
98C4×C59—41no—
99C4×C59—42no—
100C4×C59—42no—
101Dic59—22no—
102Dic59—22no—
103Dic59—41no—
104Dic59—42no—
105Dic59—41no—
106Dic59—42no—
107#2822—591nomaximal, Sylow
108C2×C59#53611yescharacteristic
109C2×C59#53611yescharacteristic
110C2×C59#53711yescharacteristic
111C2×C59#56312yes—
112C2×C59#56412yes—
113C2×#125—591no—
114C2×#125—591no—
115#400—591no—
116#400—591no—
117#400—592no—
118#398—591no—
119#398—592no—
120#398—592no—
121#398—592no—
122#398D5911yescharacteristic
123#382—591no—
124C59#282211yescharacteristic, complemented, Sylow
125#125—1184no—
126#125—1184no—
127C2×C4⋊C4—591no—
128C2×C4⋊C4—591no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4—591no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—592no—
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C4⋊C4C2×D5911yescharacteristic
139C2×C4⋊C4C2×D5912yes—
140C2×C42—591no—
141#95—592no—
142#95—591no—
143#95—592no—
144#95—592no—
145#95—592no—
146#95—592no—
147#95—592no—
148#95C2×D5911yescharacteristic
149#95C2×D5912yes—
150C22×C4—591no—
151C22×C4—591no—
152C22×C4—592no—
153C22×C4—591no—
154C22×C4—592no—
155C22×C4—591no—
156C22×C4C22×D5912yes—
157C22×C4C22×D5911yescharacteristic
158C22×C4C22×D5911yescharacteristic
159C22×C4C22×D5912yes—
160C22×C4C22×D5911yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1184no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4—1184no—
170C4⋊C4—1182no—
171C4⋊C4—1182no—
172C4⋊C4—2362no—
173C4⋊C4—2362no—
174C42—594no—
175C23C23×D5911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—592no—
189C2×C4—592no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1182no—
193C2×C4—1181no—
194C2×C4—1182no—
195C2×C4—1181no—
196C2×C4—1182no—
197C2×C4—1181no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1181no—
201C2×C4—1182no—
202C2×C4—1184no—
203C2×C4D4×D5912yes—
204C22C2×D4×D5911yescharacteristic
205C22#1427377211yescharacteristic
206C22#1427377412yes—
207C22#1427377411yescharacteristic
208C22#1427377512yes—
209C4—22no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—42no—
214C4—1182no—
215C4—1182no—
216C4—2362no—
217C4—2361no—
218C4—2362no—
219C4—2361no—
220C2#1683797411yescharacteristic
221C2#1683797711yescharacteristic
222C2#1683798111yescharacteristic
223C2#1683815312yes—
224C2C59⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2822
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
124. C59#2822semidirect