Finite Group Databasebeta

← #21422654

Subgroups — #21422654

Order 7552.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#16837947C211yesmaximal, characteristic
2#16837452C211yesmaximal, characteristic, complemented
3#16837266C211yesmaximal, characteristic, complemented
4#16837137C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837135C211yesmaximal, characteristic, complemented
7C59×#327C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9#14273726C411yescharacteristic, complemented
10#14273723C411yescharacteristic, complemented
11#14273713—21no—
12#14273701C2211yescharacteristic
13#14273699—21no—
14D4×Dic59C411yescharacteristic, complemented
15#14273689C411yescharacteristic, complemented
16(C22⋊D59)⋊C4—21no—
17C2×Dic59⋊C4—21no—
18C2×C4×Dic59C2211yescharacteristic
19Dic59⋊C8—21no—
20C22⋊(C59⋊C8)C2211yescharacteristic
21C8×Dic59—21no—
22C59⋊#95—21no—
23C59⋊#95C2211yescharacteristic
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59C2×C411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37C22×Dic59D411yescharacteristic
38#11745687—42no—
39#11745687—42no—
40C2×D236C2×C411yescharacteristic
41C2×C4×D59—21no—
42C2×Dic118—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59C2×C411yescharacteristic
45C22⋊C4×C59—21no—
46C22⋊Dic59—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49C4⋊Dic59C2×C411yescharacteristic
50Dic59⋊C4—21no—
51Dic59⋊C4—42no—
52C4×Dic59C2×C411yescharacteristic
53C4×Dic59C2×C411yescharacteristic
54C4×Dic59D411yescharacteristic
55C4×Dic59D411yescharacteristic
56C2×C59⋊C8—21no—
57C23×C59—21no—
58C23×C59C2×D411yescharacteristic
59C22×D59—21no—
60D4×C59—41no—
61D4×C59—41no—
62D4×C59—41no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C22×C411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C22⋊D59—42no—
71C22⋊D59—41no—
72C22⋊D59—41no—
73C22⋊D59—42no—
74C2×Dic59—21no—
75C2×Dic59—41no—
76C2×Dic59—42no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59C22⋊C411yescharacteristic
81C2×Dic59C22⋊C411yescharacteristic
82C2×Dic59C22⋊C411yescharacteristic
83C2×Dic59C22⋊C411yescharacteristic
84C2×Dic59D812yes—
85C2×Dic59SD1612yes—
86D236—41no—
87C4×D59—42no—
88Dic118—42no—
89C8×C59—41no—
90C59⋊C8—41no—
91C22×C59—21no—
92C22×C59—21no—
93C22×C59—41no—
94C22×C59—41no—
95C22×C59—41no—
96C22×C59C2×C22⋊C411yescharacteristic
97C22×C59C2×D811yescharacteristic
98C22×C59C2×SD1611yescharacteristic
99C2×D59—41no—
100C2×D59—41no—
101C2×D59—41no—
102C4×C59—21no—
103C4×C59—21no—
104C4×C59—41no—
105C4×C59—81no—
106Dic59—21no—
107Dic59—21no—
108Dic59—41no—
109Dic59—81no—
110Dic59#10212yes—
111Dic59#10212yes—
112#1517—591nomaximal, Sylow
113C2×C59—21no—
114C2×C59—21no—
115C2×C59—81no—
116C2×C59#41011yescharacteristic
117C2×C59C2×#10211yescharacteristic
118C2×C59#42111yescharacteristic
119D59—81no—
120#532—591no—
121#431—591no—
122#382—591no—
123#327—591no—
124#327—591no—
125#327—591no—
126#327D5911yescharacteristic, complemented
127C59#151711yescharacteristic, complemented, Sylow
128C2×#41—1181no—
129C4⋊Q8—591no—
130#127—591no—
131#124—1181no—
132#121—591no—
133#121—1181no—
134#121C2×D5911yescharacteristic
135C4×D4—591no—
136C4×D4—591no—
137C4×D4—1181no—
138C2×C4⋊C4—1181no—
139C2×C42—591no—
140C4⋊C8—1181no—
141C22⋊C8—591no—
142C22⋊C8C2×D5911yescharacteristic
143C4×C8—1181no—
144#95—591no—
145#95—1181no—
146#95C2×D5911yescharacteristic
147#41—2362no—
148#41—2362no—
149C2×Q8—1181no—
150C2×D4—21no—
151C2×D4—591no—
152C2×D4—1181no—
153C2×D4—1181no—
154C2×D4—1181no—
155C2×D4C4×D5911yescharacteristic
156C22×C4—21no—
157C22×C4—591no—
158C22×C4—591no—
159C22×C4—1181no—
160C22×C4—1181no—
161C22×C4—1181no—
162C22×C4C22×D5911yescharacteristic
163C2×C8—21no—
164C2×C8—1181no—
165C4⋊C4—591no—
166C4⋊C4—1181no—
167C4⋊C4—2362no—
168C4⋊C4C4×D5911yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—1181no—
171C22⋊C4—1181no—
172C22⋊C4—1181no—
173C42—591no—
174C42—591no—
175C42—591no—
176C42—591no—
177C23—21no—
178C23—1181no—
179C23D4×D5911yescharacteristic
180Q8—2362no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—2361no—
185D4—2362no—
186D4—2362no—
187D4—2361no—
188D4—2361no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—591no—
195C2×C4—591no—
196C2×C4—592no—
197C2×C4—592no—
198C2×C4—591no—
199C2×C4—591no—
200C2×C4—1181no—
201C2×C4—2362no—
202C2×C4—2362no—
203C2×C4—2361no—
204C2×C4—2361no—
205C2×C4—2361no—
206C2×C4—2361no—
207C2×C4C2×C4×D5911yescharacteristic
208C2×C4D4×D5911yescharacteristic
209C8—41no—
210C8—2361no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2361no—
217C22—2361no—
218C22—2361no—
219C22C22⋊C4×D5911yescharacteristic
220C22D8×D5911yescharacteristic
221C22SD16×D5911yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—592no—
227C4—592no—
228C4—1181no—
229C4—1181no—
230C4—4721no—
231C4—2361no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—4721no—
236C2#1683737411yescharacteristic
237C2#102×D5911yescharacteristic
238C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59C2×C22⋊C4
hypercenter#327D59
hypocenterC59#1517
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837452C2semidirect
3. #16837266C2semidirect
4. #16837137C2semidirect
5. #16837136C2semidirect
6. #16837135C2semidirect
7. C59×#327C2semidirect
9. #14273726C4semidirect
10. #14273723C4semidirect
14. D4×Dic59C4semidirect
15. #14273689C4semidirect
126. #327D59semidirect
127. C59#1517semidirect