Finite Group Databasebeta

← #21429459

Subgroups — #21429459

Order 7552.

468 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14273692C211yesmaximal, characteristic
2C2×#14273692C211yesmaximal, characteristic
3#16837340C211yesmaximal, characteristic
4#16837323C211yesmaximal, characteristic
5#16837322C211yesmaximal, characteristic
6#16837306C212yesmaximal
7#16837299C212yesmaximal
8#16837285C212yesmaximal
9#16837284C212yesmaximal
10#16837266C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic
12C22×Dic118C2211yescharacteristic
13C22×Dic118C2211yescharacteristic
14#14273692—24no—
15#14273692—24no—
16C2×C4⋊Dic59C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×C4×Dic59C2211yescharacteristic
23C2×C4×Dic59C2211yescharacteristic
24C2×C4×Dic59C2212yes—
25C2×C4×Dic59C2211yescharacteristic
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2211yescharacteristic
35#95×C59C2212yes—
36#95×C59C2212yes—
37C22×C4×C59C2312yes—
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C2×Dic118—22no—
49C2×Dic118—22no—
50C2×Dic118—24no—
51C2×Dic118—22no—
52C2×Dic118Q814yescomplemented
53C4⋊C4×C59—22no—
54C4⋊C4×C59—22no—
55C4⋊Dic59—24no—
56Dic59⋊C4—22no—
57Dic59⋊C4—24no—
58Dic59⋊C4—22no—
59Dic59⋊C4—24no—
60Dic59⋊C4—24no—
61C4×Dic59—22no—
62C4×Dic59—24no—
63C4×Dic59—22no—
64C4×Dic59D414yes—
65C23×C59C2411yescharacteristic
66C2×C4×C59—21no—
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—22no—
74C2×C4×C59—24no—
75C2×C4×C59—22no—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2×Q812yes—
78C2×Dic59—21no—
79C2×Dic59—22no—
80C2×Dic59—21no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—21no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59C2×D412yes—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×Q812yes—
91C2×Dic59C2×Q812yes—
92C2×Dic59#4114yes—
93C2×Dic59#4112yes—
94Dic118—28no—
95Dic118—28no—
96C22×C59C22×D411yescharacteristic
97C22×C59C22×Q811yescharacteristic
98C22×C59C2×#4111yescharacteristic
99C22×C59C2×#4112yes—
100C22×C592−1+412yes—
101C4×C59—22no—
102C4×C59—22no—
103C4×C59—41no—
104C4×C59—42no—
105C4×C59—42no—
106Dic59—22no—
107Dic59—24no—
108Dic59—22no—
109Dic59—41no—
110Dic59—42no—
111Dic59C22⋊Q814yes—
112#2581—591nomaximal, Sylow
113C2×C59C2×C22⋊Q811yescharacteristic
114C2×C59#52511yescharacteristic
115C2×C59#53611yescharacteristic
116C2×C59#55612yes—
117C2×C59#55712yes—
118C2×C4×Q8—591no—
119C2×C4×Q8—591no—
120#400—591no—
121#400D5911yescharacteristic
122#395—591no—
123#395—591no—
124#391—592no—
125#389—592no—
126#387—592no—
127#387—592no—
128#382—591no—
129C59#258111yescharacteristic, complemented, Sylow
130C22×Q8—591no—
131C22×Q8—591no—
132C4×Q8—1184no—
133C4×Q8—1184no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—591no—
136C2×C4⋊C4—591no—
137C2×C4⋊C4—592no—
138C2×C4⋊C4—592no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4C2×D5911yescharacteristic
141C2×C4⋊C4C2×D5911yescharacteristic
142C2×C42—591no—
143C2×C42—591no—
144C2×C42—591no—
145C2×C42—592no—
146#95—592no—
147#95—591no—
148#95—592no—
149#95—592no—
150#95—592no—
151#95—592no—
152#95C2×D5911yescharacteristic
153#95C2×D5912yes—
154#95C2×D5912yes—
155C2×Q8—594no—
156C2×Q8—1182no—
157C2×Q8—1182no—
158C2×Q8—1184no—
159C2×Q8—1182no—
160C22×C4—591no—
161C22×C4—591no—
162C22×C4—591no—
163C22×C4—592no—
164C22×C4—592no—
165C22×C4—591no—
166C22×C4C22×D5912yes—
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169C22×C4C22×D5911yescharacteristic
170C22×C4C22×D5911yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—1182no—
174C4⋊C4—1184no—
175C4⋊C4—1184no—
176C4⋊C4—1184no—
177C4⋊C4—1184no—
178C4⋊C4—1182no—
179C42—594no—
180C42—1182no—
181C42—1184no—
182C42—1182no—
183C23C23×D5911yescharacteristic
184Q8—1188no—
185Q8—1188no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—592no—
197C2×C4—592no—
198C2×C4—592no—
199C2×C4—592no—
200C2×C4—592no—
201C2×C4—594no—
202C2×C4—1181no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1181no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4D4×D5912yes—
213C2×C4Q8×D5912yes—
214C22C2×D4×D5911yescharacteristic
215C22C2×Q8×D5911yescharacteristic
216C22#41×D5911yescharacteristic
217C22#41×D5912yes—
218C22#1427377412yes—
219C4—22no—
220C4—22no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—594no—
225C4—1182no—
226C4—1184no—
227C4—1182no—
228C4—2361no—
229C4—2362no—
230C2C22⋊Q8×D5911yescharacteristic
231C2#1683791011yescharacteristic
232C2#1683797211yescharacteristic
233C2#1683811912yes—
234C2#1683812912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2581
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic118Q8semidirect
129. C59#2581semidirect