Finite Group Databasebeta

← #21430260

Subgroups — #21430260

Order 7552.

434 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273720C211yesmaximal, characteristic
2C2×#14273718C211yesmaximal, characteristic, complemented
3#16837340C211yesmaximal, characteristic, complemented
4#16837334C211yesmaximal, characteristic, complemented
5#16837333C212yesmaximal, complemented
6#16837327C211yesmaximal, characteristic
7#16837325C212yesmaximal
8#16837301C212yesmaximal, complemented
9#16837295C212yesmaximal
10#16837253C211yesmaximal, characteristic, complemented
11C59×#399C211yesmaximal, characteristic
12#14273720—24no—
13#14273718—24no—
14C2×C4⋊Dic59C2212yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×C22⋊Dic59C2211yescharacteristic
23C2×C22⋊Dic59C2211yescharacteristic
24C2×C22⋊Dic59C2212yes—
25C2×C4×Dic59C2212yes—
26C2×C4×Dic59C2211yescharacteristic
27C59⋊#95C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2212yes—
34C2×C22⋊C4×C59C2211yescharacteristic
35C2×C22⋊C4×C59C2212yes—
36#95×C59C2211yescharacteristic
37C24×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C4⋊C4×C59—22no—
49C4⋊C4×C59—24no—
50C22⋊C4×C59—22no—
51C22⋊C4×C59—24no—
52C22⋊Dic59—22no—
53C22⋊Dic59—22no—
54C22⋊Dic59—42no—
55C4⋊Dic59—22no—
56C4⋊Dic59—24no—
57C4⋊Dic59—22no—
58C4⋊Dic59—42no—
59Dic59⋊C4—22no—
60Dic59⋊C4—24no—
61Dic59⋊C4—24no—
62Dic59⋊C4—22no—
63C4×Dic59—42no—
64C4×Dic59D414yes—
65C23×C59—21no—
66C23×C59—22no—
67C23×C59—21no—
68C23×C59—22no—
69C23×C59—21no—
70C23×C59C2411yescharacteristic
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D412yes—
80C2×C4×C59#4114yes—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59C2×D412yes—
96C2×Dic59C2×D412yes—
97C22×C59—41no—
98C22×C59—41no—
99C22×C59—41no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C22×C59C2×#4112yes—
104C22×C59H(5,𝔽2)11yescharacteristic
105C22×C592−1+412yes—
106C22×C592−1+411yescharacteristic
107C4×C59—22no—
108C4×C59—24no—
109C4×C59—41no—
110C4×C59—42no—
111Dic59—22no—
112Dic59—22no—
113Dic59—41no—
114Dic59—42no—
115Dic59—41no—
116Dic59—42no—
117#2664—591nomaximal, Sylow
118C2×C59—81no—
119C2×C59#53211yescharacteristic
120C2×C59#53611yescharacteristic
121C2×C59#53711yescharacteristic
122C2×C59#53912yes—
123C2×C59#54112yes—
124C2×#126—591no—
125C2×#125—591no—
126#400—591no—
127#399D5911yescharacteristic
128#398—592no—
129#398—591no—
130#397—591no—
131#396—592no—
132#389—592no—
133#388—592no—
134C4×C4⋊C4—591no—
135C59#266411yescharacteristic, complemented, Sylow
136#126—1184no—
137#125—1184no—
138C2×C4⋊C4—592no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—591no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4C2×D5911yescharacteristic
147C2×C4⋊C4C2×D5912yes—
148C2×C22⋊C4—591no—
149C2×C22⋊C4—591no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4C2×D5911yescharacteristic
152C2×C22⋊C4C2×D5912yes—
153C2×C42—591no—
154C2×C42—592no—
155#95—591no—
156#95—592no—
157#95—592no—
158#95—592no—
159#95—592no—
160#95C2×D5911yescharacteristic
161C24C22×D5911yescharacteristic
162C22×C4—591no—
163C22×C4—591no—
164C22×C4—592no—
165C22×C4—591no—
166C22×C4—591no—
167C22×C4—592no—
168C22×C4C22×D5911yescharacteristic
169C22×C4C22×D5912yes—
170C22×C4C22×D5911yescharacteristic
171C22×C4C22×D5912yes—
172C4⋊C4—22no—
173C4⋊C4—24no—
174C4⋊C4—1184no—
175C4⋊C4—1184no—
176C4⋊C4—1182no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1184no—
181C4⋊C4—2362no—
182C22⋊C4—22no—
183C22⋊C4—24no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—2362no—
187C42—594no—
188C42—2362no—
189C23—21no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23C23×D5911yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—592no—
204C2×C4—592no—
205C2×C4—1182no—
206C2×C4—1181no—
207C2×C4—1181no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1181no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1181no—
218C2×C4—1182no—
219C2×C4D4×D5912yes—
220C2×C4#1174568714yes—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22C2×D4×D5911yescharacteristic
227C22C2×#1174568712yes—
228C22#1427377311yescharacteristic
229C22#1427377412yes—
230C22#1427377511yescharacteristic
231C4—22no—
232C4—24no—
233C4—41no—
234C4—42no—
235C4—1182no—
236C4—1182no—
237C4—2361no—
238C4—2361no—
239C4—2362no—
240C4—2362no—
241C2—81no—
242C2#1683795011yescharacteristic
243C2#1683797411yescharacteristic
244C2#1683798211yescharacteristic
245C2#1683799612yes—
246C2#1683801212yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#399C2
hypercenter#399D59
hypocenterC59#2664
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#14273718C2semidirect
3. #16837340C2semidirect
4. #16837334C2semidirect
5. #16837333C2semidirect
8. #16837301C2semidirect
10. #16837253C2semidirect
135. C59#2664semidirect