Finite Group Databasebeta

← #21429478

Subgroups — #21429478

Order 7552.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14273717C211yesmaximal, characteristic
2C2×Q8×Dic59C211yesmaximal, characteristic
3#16837334C211yesmaximal, characteristic
4#16837332C211yesmaximal, characteristic
5#16837321C211yesmaximal, characteristic
6#16837301C212yesmaximal
7#16837299C212yesmaximal
8#16837299C212yesmaximal
9#16837297C212yesmaximal
10#16837253C211yesmaximal, characteristic
11C59×#395C211yesmaximal, characteristic
12#14273717—24no—
13Q8×Dic59—24no—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×C4⋊Dic59C2212yes—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2212yes—
23C2×Dic59⋊C4C2212yes—
24C2×Dic59⋊C4C2212yes—
25C2×C4×Dic59C2212yes—
26C2×C4×Dic59C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C22×Q8×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C2×Q8×C59—22no—
38C2×Q8×C59—24no—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×C4×C59C2312yes—
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2312yes—
49C22×Dic59C2311yescharacteristic
50C4⋊C4×C59—22no—
51C4⋊C4×C59—24no—
52C4⋊Dic59—22no—
53C4⋊Dic59—24no—
54C4⋊Dic59—22no—
55C4⋊Dic59—42no—
56Dic59⋊C4—22no—
57Dic59⋊C4—24no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—42no—
62Dic59⋊C4Q818yescomplemented
63C4×Dic59—24no—
64C4×Dic59—42no—
65C4×Dic59D414yes—
66C23×C59C2411yescharacteristic
67Q8×C59—28no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59C2×D412yes—
79C2×C4×C59C2×Q814yes—
80C2×C4×C59#4114yes—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59—21no—
93C2×Dic59C2×D412yes—
94C2×Dic59C2×D412yes—
95C2×Dic59C2×Q814yes—
96C2×Dic59C2×Q814yes—
97C22×C59C22×D411yescharacteristic
98C22×C59C22×Q812yes—
99C22×C59C2×#4112yes—
100C22×C59H(5,𝔽2)11yescharacteristic
101C22×C592−1+411yescharacteristic
102C4×C59—22no—
103C4×C59—24no—
104C4×C59—24no—
105C4×C59—41no—
106C4×C59—41no—
107Dic59—22no—
108Dic59—24no—
109Dic59—41no—
110Dic59—42no—
111Dic59—41no—
112Dic59C4⋊Q814yes—
113#2584—591nomaximal, Sylow
114C2×C59#52511yescharacteristic
115C2×C59C2×C4⋊Q811yescharacteristic
116C2×C59#53711yescharacteristic
117C2×C59#55412yes—
118C2×C59#55712yes—
119C2×#125—591no—
120C2×C4×Q8—591no—
121#398—591no—
122#398—591no—
123#395—591no—
124#395D5911yescharacteristic
125#389—592no—
126#389—592no—
127#389—592no—
128#389—592no—
129C4×C4⋊C4—591no—
130C59#258411yescharacteristic, complemented, Sylow
131C22×Q8C2×D5911yescharacteristic
132#125—1184no—
133C4×Q8—1184no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—591no—
137C2×C4⋊C4—591no—
138C2×C4⋊C4—591no—
139C2×C4⋊C4—591no—
140C2×C4⋊C4—591no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—592no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4C2×D5911yescharacteristic
146C2×C4⋊C4C2×D5912yes—
147C2×C42—591no—
148C2×C42—592no—
149C2×C42—592no—
150#95—591no—
151#95—592no—
152#95—592no—
153#95—592no—
154#95C2×D5911yescharacteristic
155#95C2×D5912yes—
156C2×Q8—22no—
157C2×Q8—24no—
158C22×C4—591no—
159C22×C4—592no—
160C22×C4—591no—
161C22×C4—592no—
162C22×C4—591no—
163C22×C4—591no—
164C22×C4C22×D5911yescharacteristic
165C22×C4C22×D5911yescharacteristic
166C22×C4C22×D5911yescharacteristic
167C22×C4C22×D5912yes—
168C22×C4C22×D5912yes—
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—598no—
172C4⋊C4—1184no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1184no—
180C4⋊C4—2362no—
181C4⋊C4—2362no—
182C42—594no—
183C42—1184no—
184C42—2362no—
185C23C23×D5911yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—592no—
198C2×C4—594no—
199C2×C4—592no—
200C2×C4—594no—
201C2×C4—1182no—
202C2×C4—1181no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—1182no—
206C2×C4—1181no—
207C2×C4—1181no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1181no—
211C2×C4—1182no—
212C2×C4—1181no—
213C2×C4D4×D5912yes—
214C2×C4#1174568714yes—
215C2×C4Q8×D5914yes—
216C22C2×D4×D5911yescharacteristic
217C22C2×Q8×D5912yes—
218C22C2×#1174568712yes—
219C22#1427377311yescharacteristic
220C22#1427377511yescharacteristic
221C4—22no—
222C4—24no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—594no—
227C4—1182no—
228C4—1184no—
229C4—2361no—
230C4—2362no—
231C4—2361no—
232C2#1683790811yescharacteristic
233C2C4⋊Q8×D5911yescharacteristic
234C2#1683798211yescharacteristic
235C2#1683811012yes—
236C2#1683812712yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2584
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
62. Dic59⋊C4Q8semidirect
130. C59#2584semidirect