Finite Group Databasebeta

← #21429977

Subgroups — #21429977

Order 7552.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14273692C211yesmaximal, characteristic
3#16837343C212yesmaximal
4#16837342C211yesmaximal, characteristic
5#16837341C211yesmaximal, characteristic
6#16837333C211yesmaximal, characteristic
7#16837322C212yesmaximal
8#16837289C212yesmaximal
9#16837288C212yesmaximal
10#16837269C211yesmaximal, characteristic
11C59×#398C211yesmaximal, characteristic
12C22×Dic118C2211yescharacteristic
13#14273718—24no—
14#14273692—24no—
15C2×C4⋊Dic59C2212yes—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×C4×Dic59C2211yescharacteristic
22C2×C4×Dic59C2211yescharacteristic
23C2×C4×Dic59C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2211yescharacteristic
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2212yes—
34C2×C4⋊C4×C59C2211yescharacteristic
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
48C2×Dic118—22no—
49C2×Dic118—22no—
50C2×Dic118—22no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—24no—
54C4⋊Dic59—22no—
55C4⋊Dic59—24no—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58Dic59⋊C4—24no—
59Dic59⋊C4—24no—
60C4×Dic59—22no—
61C4×Dic59—22no—
62C4×Dic59D414yes—
63C23×C59C2411yescharacteristic
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D412yes—
76C2×C4×C59#4112yes—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—21no—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—24no—
88C2×Dic59—22no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91C2×Dic59#4112yes—
92Dic118—28no—
93C22×C59C22×D411yescharacteristic
94C22×C59C2×#4111yescharacteristic
95C22×C59C2×#4111yescharacteristic
96C22×C592−1+412yes—
97C22×C592−1+412yes—
98C4×C59—22no—
99C4×C59—22no—
100C4×C59—42no—
101C4×C59—41no—
102C4×C59—42no—
103Dic59—22no—
104Dic59—22no—
105Dic59—22no—
106Dic59—41no—
107Dic59—42no—
108Dic59—42no—
109#2634—591nomaximal, Sylow
110C2×C59#52511yescharacteristic
111C2×C59#53611yescharacteristic
112C2×C59#53611yescharacteristic
113C2×C59#54112yes—
114C2×C59#54112yes—
115C2×#125—591no—
116C2×C4×Q8—591no—
117#400—591no—
118#400—591no—
119#400—592no—
120#398—591no—
121#398D5911yescharacteristic
122#395—592no—
123#387—592no—
124#387—592no—
125#383—591no—
126C59#263411yescharacteristic, complemented, Sylow
127C22×Q8—591no—
128#125—1184no—
129C4×Q8—1184no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4—591no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4C2×D5911yescharacteristic
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C4⋊C4C2×D5912yes—
139C2×C42—591no—
140C2×C42—591no—
141C2×C42—591no—
142#95—592no—
143#95—592no—
144#95—591no—
145#95—592no—
146#95—592no—
147#95—592no—
148#95—592no—
149#95—592no—
150#95C2×D5911yescharacteristic
151#95C2×D5912yes—
152C2×Q8—1182no—
153C2×Q8—1182no—
154C2×Q8—1182no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—592no—
159C22×C4—591no—
160C22×C4—592no—
161C22×C4C22×D5912yes—
162C22×C4C22×D5911yescharacteristic
163C22×C4C22×D5912yes—
164C22×C4C22×D5911yescharacteristic
165C22×C4C22×D5911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—24no—
169C4⋊C4—1182no—
170C4⋊C4—1184no—
171C4⋊C4—1184no—
172C4⋊C4—1184no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C42—594no—
176C42—1182no—
177C42—1182no—
178C23C23×D5911yescharacteristic
179Q8—1188no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—592no—
192C2×C4—592no—
193C2×C4—592no—
194C2×C4—1181no—
195C2×C4—1181no—
196C2×C4—1181no—
197C2×C4—1181no—
198C2×C4—1182no—
199C2×C4—1181no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1184no—
205C2×C4—1182no—
206C2×C4D4×D5912yes—
207C2×C4#1174568712yes—
208C22C2×D4×D5911yescharacteristic
209C22#41×D5911yescharacteristic
210C22C2×#1174568711yescharacteristic
211C22#1427377412yes—
212C22#1427377512yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—41no—
217C4—42no—
218C4—1182no—
219C4—1182no—
220C4—1182no—
221C4—2361no—
222C4—2362no—
223C4—2362no—
224C2#1683791211yescharacteristic
225C2#1683797411yescharacteristic
226C2#1683797711yescharacteristic
227C2#1683801112yes—
228C2#1683801212yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2634
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
126. C59#2634semidirect