Finite Group Databasebeta

← #21435266

Subgroups — #21435266

Order 7552.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837936C211yesmaximal, characteristic
2C2×#14273719C211yesmaximal, characteristic, complemented
3#16837804C212yesmaximal, complemented
4#16837757C212yesmaximal, complemented
5#16837738C211yesmaximal, characteristic, complemented
6#16837733C211yesmaximal, characteristic, complemented
7#16837721C211yesmaximal, characteristic
8#16837716C211yesmaximal, characteristic
9#16837710C212yesmaximal, complemented
10#16837703C212yesmaximal, complemented
11C59×#431C211yesmaximal, characteristic, complemented
12#14273721—21no—
13#14273719—21no—
14#14273719—21no—
15#14273719C2212yes—
16#14273719C2212yes—
17#14273719C2211yescharacteristic
18#14273715C2211yescharacteristic
19#14273710—21no—
20#14273706C2211yescharacteristic
21#14273701C2211yescharacteristic
22C4×Dic118C2211yescharacteristic
23C4×D236C2211yescharacteristic
24C4×C22⋊D59—21no—
25#14273684—21no—
26C2×C4⋊Dic59C2211yescharacteristic
27C2×C4⋊Dic59C2211yescharacteristic
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30#14273661C2212yes—
31#14273661C2212yes—
32#14273659C2212yes—
33#14273659C2212yes—
34#14273652C2212yes—
35#14273652C2212yes—
36#14273649C2212yes—
37#14273649C2212yes—
38C2×C42×C59C2211yescharacteristic
39C4⋊C8×C59C2212yes—
40C22⋊C8×C59C2211yescharacteristic
41C22⋊C8×C59C2211yescharacteristic
42C4×C8×C59C2212yes—
43C22×C4×C59D411yescharacteristic
44C22×C4×C59D411yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C22×Dic59—21no—
48C22×Dic59—21no—
49C2×D236C2311yescharacteristic
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2312yes—
53C2×C8×C59C2312yes—
54C42×C59D411yescharacteristic
55C42×C59D411yescharacteristic
56C42×C59C2311yescharacteristic
57C42×C59C2311yescharacteristic
58C22⋊Dic59—21no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63C4⋊Dic59—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59C2312yes—
66C4⋊Dic59C2312yes—
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—22no—
70Dic59⋊C4—22no—
71Dic59⋊C4—22no—
72Dic59⋊C4—22no—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77C4×Dic59—21no—
78C23×C59C2×D411yescharacteristic
79C22×D59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—41no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2411yescharacteristic
89C22⋊D59—42no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—42no—
96C2×Dic59—42no—
97D236—22no—
98C4×D59—42no—
99Dic118—22no—
100C8×C59—22no—
101C8×C59—22no—
102C22×C59—21no—
103C22×C59—21no—
104C22×C59#13512yes—
105C22×C59C22×D411yescharacteristic
106C2×D59—41no—
107C2×D59—41no—
108C2×D59—41no—
109C4×C59—21no—
110C4×C59—21no—
111C4×C59—21no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C592−1+412yes—
115Dic59—41no—
116Dic59—42no—
117Dic59—41no—
118Dic59—41no—
119Dic59—42no—
120#3232—591nomaximal, Sylow
121C2×C59—22no—
122C2×C59#53611yescharacteristic
123C2×C59C2×#13511yescharacteristic
124C2×C59#57511yescharacteristic
125D59—81no—
126#529—591no—
127C2×#125—591no—
128#499—592no—
129#488—592no—
130#484—591no—
131#483—591no—
132#481—591no—
133#480—591no—
134#479—592no—
135#478—592no—
136#431D5911yescharacteristic, complemented
137C59#323211yescharacteristic, complemented, Sylow
138#126—1181no—
139#125—592no—
140#125—592no—
141#125—591no—
142#125—1181no—
143#125—1181no—
144#124—591no—
145#123—1181no—
146C22⋊Q8—591no—
147#121—591no—
148C4×Q8—591no—
149C4×D4—591no—
150C4×D4—1181no—
151#117—1181no—
152C2×C4⋊C4—591no—
153C2×C4⋊C4—591no—
154C2×C4⋊C4—1181no—
155C2×C4⋊C4—1181no—
156C2×C42C2×D5911yescharacteristic
157#107—592no—
158#107—592no—
159#106—592no—
160#106—592no—
161C4⋊C8C2×D5912yes—
162#103—592no—
163#103—592no—
164#102—592no—
165#102—592no—
166C22⋊C8C2×D5911yescharacteristic
167C22⋊C8C2×D5911yescharacteristic
168C4×C8C2×D5912yes—
169C2×Q8—591no—
170C2×D4—591no—
171C2×D4—1181no—
172C22×C4—1181no—
173C22×C4—1181no—
174C22×C4—1181no—
175C22×C4D23611yescharacteristic
176C22×C4D23611yescharacteristic
177C22×C4C22×D5911yescharacteristic
178C2×C8C22×D5912yes—
179C2×C8C22×D5912yes—
180C4⋊C4—592no—
181C4⋊C4—592no—
182C4⋊C4—591no—
183C4⋊C4—591no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1182no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C22⋊C4—1181no—
195C22⋊C4—1181no—
196C22⋊C4—1181no—
197C22⋊C4—1181no—
198C22⋊C4—1181no—
199C42—1181no—
200C42D23611yescharacteristic
201C42D23611yescharacteristic
202C42C22×D5911yescharacteristic
203C42C22×D5911yescharacteristic
204C23—1181no—
205C23C2×D23611yescharacteristic
206Q8—1182no—
207D4—1182no—
208D4—2362no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—1181no—
213C2×C4—1181no—
214C2×C4—1181no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—2362no—
218C2×C4—2362no—
219C2×C4—2362no—
220C2×C4C2×D23611yescharacteristic
221C2×C4C2×D23611yescharacteristic
222C2×C4C2×D23611yescharacteristic
223C2×C4C2×D23611yescharacteristic
224C2×C4C2×D23611yescharacteristic
225C2×C4C23×D5911yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—2361no—
231C22—2361no—
232C22—2361no—
233C22#1427374912yes—
234C22C22×D23611yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—2362no—
241C4—2361no—
242C4—2361no—
243C4—2362no—
244C4—2361no—
245C4#1427377412yes—
246C2—22no—
247C2—4721no—
248C2#1683797811yescharacteristic
249C2C2×#1427374911yescharacteristic
250C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#431C2
socleC22×C59C22×D4
hypercenter#431D59
hypocenterC59#3232
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×#14273719C2semidirect
3. #16837804C2semidirect
4. #16837757C2semidirect
5. #16837738C2semidirect
6. #16837733C2semidirect
9. #16837710C2semidirect
10. #16837703C2semidirect
11. C59×#431C2semidirect
136. #431D59semidirect
137. C59#3232semidirect