Finite Group Databasebeta

← #21422601

Subgroups — #21422601

Order 7552.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#16837913C211yesmaximal, characteristic
2C2×C59⋊#95C211yesmaximal, characteristic, complemented
3#16837140C212yesmaximal, complemented
4#16837137C212yesmaximal, complemented
5C59×#407C211yesmaximal, characteristic, complemented
6C2×#11745685C411yescharacteristic, complemented
7C23×Dic59—21no—
8#14273710—21no—
9#14273706C411yescharacteristic, complemented
10#14273706C2211yescharacteristic
11#14273701C411yescharacteristic, complemented
12#14273701C2211yescharacteristic
13#14273696—21no—
14C4×C22⋊D59—21no—
15C4×C22⋊D59—21no—
16#14273686C411yescharacteristic, complemented
17C59⋊#95—21no—
18C59⋊#95C2212yes—
19C23×C4×C59C2211yescharacteristic
20C2×M16×C59—21no—
21C22⋊C8×C59—21no—
22C22⋊C8×C59C2212yes—
23C24×C59D411yescharacteristic
24C22×C4×C59—42no—
25C22×C4×C59C2×C411yescharacteristic
26C22×C4×C59C2×C411yescharacteristic
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D411yescharacteristic
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—24no—
35C22×Dic59—22no—
36C22×Dic59—42no—
37C22×Dic59—42no—
38#11745685—42no—
39C2×D236C2×C411yescharacteristic, complemented
40C2×C4×D59—21no—
41C2×Dic118C2×C411yescharacteristic, complemented
42M16×C59—42no—
43C2×C8×C59—22no—
44C22⋊Dic59—21no—
45C22⋊Dic59—21no—
46C22⋊Dic59—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49C4⋊Dic59C2×C411yescharacteristic, complemented
50C4⋊Dic59C2×C411yescharacteristic, complemented
51Dic59⋊C4—21no—
52Dic59⋊C4—21no—
53C4×Dic59—21no—
54C23×C59—22no—
55C23×C59—22no—
56C23×C59—21no—
57C23×C59—21no—
58C23×C59C22⋊C411yescharacteristic
59C23×C59C22⋊C411yescharacteristic
60C23×C59C2×D411yescharacteristic
61C22×D59—21no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C22⋊C411yescharacteristic
69C2×C4×C59C22⋊C411yescharacteristic
70C2×C4×C59C22×C411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C22⋊D59—42no—
73C22⋊D59—42no—
74C22⋊D59—41no—
75C22⋊D59—41no—
76C2×Dic59—24no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—48no—
81C2×Dic59—42no—
82C2×Dic59—42no—
83D236—41no—
84C4×D59—42no—
85Dic118—41no—
86C8×C59—42no—
87C22×C59—24no—
88C22×C59—24no—
89C22×C59—21no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59—21no—
95C22×C59#9912yes—
96C22×C59#10412yes—
97C22×C59C2×C22⋊C411yescharacteristic
98C22×C59AGL(1,ℤ/8)11yescharacteristic
99C22×C59#13711yescharacteristic
100C2×D59—41no—
101C2×D59—41no—
102C2×D59—41no—
103C4×C59—21no—
104C4×C59—21no—
105C4×C59—21no—
106C4×C59—21no—
107Dic59—44no—
108Dic59—41no—
109Dic59—41no—
110Dic59—41no—
111#1504—591nomaximal, Sylow
112C2×C59—21no—
113C2×C59—22no—
114C2×C59—22no—
115C2×C59—21no—
116C2×C59C2×#9911yescharacteristic
117C2×C59#41711yescharacteristic
118C2×C59C2×#10411yescharacteristic
119D59—81no—
120#525—591no—
121#407D5911yescharacteristic, complemented
122C2×#95—591no—
123#328—592no—
124#327—592no—
125C59#150411yescharacteristic, complemented, Sylow
126C2×#41—591no—
127C23×C4—1181no—
128C23×C4C2×D5911yescharacteristic
129C2×M16—21no—
130#123—1181no—
131C22⋊Q8—591no—
132C22⋊Q8—591no—
133#121—591no—
134#121—591no—
135#120—1181no—
136C4×D4—1181no—
137C4×D4—1181no—
138#117—591no—
139C22⋊C8—21no—
140C22⋊C8C2×D5912yes—
141#95—592no—
142#95—1181no—
143C24D23611yescharacteristic
144#41—2362no—
145C2×Q8—591no—
146C2×D4—591no—
147C2×D4—1181no—
148C2×D4—1181no—
149C2×D4—1181no—
150C22×C4—42no—
151C22×C4—1184no—
152C22×C4—1182no—
153C22×C4—1181no—
154C22×C4—2362no—
155C22×C4—2362no—
156C22×C4C4×D5911yescharacteristic
157C22×C4C4×D5911yescharacteristic
158C22×C4D23611yescharacteristic
159C22×C4C22⋊D5911yescharacteristic
160C22×C4C22⋊D5911yescharacteristic
161C22×C4C22×D5911yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—591no—
165C4⋊C4—591no—
166C4⋊C4—1181no—
167C4⋊C4—1181no—
168C22⋊C4—1181no—
169C22⋊C4—1181no—
170C22⋊C4—1181no—
171C22⋊C4—1181no—
172C22⋊C4—1181no—
173C42—1181no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—1181no—
179C23(C2×D59)⋊C411yescharacteristic
180C23(C2×D59)⋊C411yescharacteristic
181C23C2×D23611yescharacteristic
182Q8—2361no—
183D4—2361no—
184D4—2362no—
185D4—2362no—
186D4—2361no—
187D4—2361no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1184no—
195C2×C4—1181no—
196C2×C4—1181no—
197C2×C4—1181no—
198C2×C4—2362no—
199C2×C4—2368no—
200C2×C4—2362no—
201C2×C4—2362no—
202C2×C4(C2×D59)⋊C411yescharacteristic
203C2×C4(C2×D59)⋊C411yescharacteristic
204C2×C4C2×C4×D5911yescharacteristic
205C2×C4C2×C22⋊D5911yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—2361no—
216C22—2361no—
217C22—2361no—
218C22#1427364112yes—
219C22#1427365312yes—
220C22C2×(C2×D59)⋊C411yescharacteristic
221C22#1427375511yescharacteristic
222C22#1427376011yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—2364no—
228C4—2361no—
229C4—2361no—
230C4—2361no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—4721no—
236C2C2×#1427364111yescharacteristic
237C2#1683740411yescharacteristic
238C2C2×#1427365311yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#407C2
socleC22×C59C2×C22⋊C4
hypercenter#407D59
hypocenterC59#1504
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C59⋊#95C2semidirect
3. #16837140C2semidirect
4. #16837137C2semidirect
5. C59×#407C2semidirect
6. C2×#11745685C4semidirect
9. #14273706C4semidirect
11. #14273701C4semidirect
16. #14273686C4semidirect
39. C2×D236C2×C4semidirect
41. C2×Dic118C2×C4semidirect
49. C4⋊Dic59C2×C4semidirect
50. C4⋊Dic59C2×C4semidirect
121. #407D59semidirect
125. C59#1504semidirect