Finite Group Databasebeta

← #21435277

Subgroups — #21435277

Order 7552.

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

normal subgroups only

This group has 332 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#16837959C211yesmaximal, characteristic, complemented
2#16837936C211yesmaximal, characteristic
3#16837804C212yesmaximal, complemented
4#16837757C212yesmaximal, complemented
5#16837744C212yesmaximal, complemented
6#16837727C212yesmaximal
7#16837698C211yesmaximal, characteristic, complemented
8#16837693C211yesmaximal, characteristic, complemented
9#16837688C211yesmaximal, characteristic, complemented
10#16837683C211yesmaximal, characteristic, complemented
11C59×#431C211yesmaximal, characteristic, complemented
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273721—21no—
15#14273719C2211yescharacteristic
16#14273719C2212yes—
17#14273715C2211yescharacteristic
18#14273710—21no—
19#14273706—21no—
20#14273706—21no—
21#14273706C2211yescharacteristic
22#14273701C2211yescharacteristic
23C4×Dic118—21no—
24C4×Dic118—21no—
25C4×Dic118C2211yescharacteristic
26C4×D236C2211yescharacteristic
27C4×C22⋊D59—21no—
28#14273686C2212yes—
29#14273684—21no—
30#14273661C2212yes—
31#14273661C2212yes—
32#14273659C2212yes—
33#14273659C2212yes—
34#14273652C2212yes—
35#14273652C2212yes—
36#14273649C2212yes—
37#14273649C2212yes—
38C2×C42×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic
40C4⋊C8×C59C2211yescharacteristic
41C22⋊C8×C59C2212yes—
42C4×C8×C59C2212yes—
43C22×C4×C59D411yescharacteristic
44C22×C4×C59D411yescharacteristic
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C2×D236C2311yescharacteristic
48C2×C4×D59—21no—
49C2×Dic118—21no—
50C2×Dic118—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2312yes—
53C2×C8×C59C2312yes—
54C42×C59D411yescharacteristic
55C42×C59D411yescharacteristic
56C42×C59C2311yescharacteristic
57C42×C59C2311yescharacteristic
58C22⋊Dic59—22no—
59C22⋊Dic59—21no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59C2312yes—
67C4⋊Dic59C2312yes—
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74Dic59⋊C4—22no—
75Dic59⋊C4—21no—
76C4×Dic59—21no—
77C4×Dic59—22no—
78C23×C59C2×D411yescharacteristic
79C22×D59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—41no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2411yescharacteristic
90C22⋊D59—42no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—21no—
96D236—21no—
97D236—21no—
98C4×D59—42no—
99Dic118—21no—
100Dic118—21no—
101Dic118—42no—
102Dic118—42no—
103C8×C59—22no—
104C8×C59—22no—
105C22×C59—21no—
106C22×C59—21no—
107C22×C59—21no—
108C22×C59C22×D411yescharacteristic
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—21no—
116C4×C59#13512yes—
117C4×C592−1+411yescharacteristic
118C4×C592−1+411yescharacteristic
119Dic59—41no—
120Dic59—42no—
121Dic59—41no—
122Dic59—42no—
123Dic59—41no—
124#3233—591nomaximal, Sylow
125C2×C59—41no—
126C2×C59#53611yescharacteristic
127C2×C59C2×#13511yescharacteristic
128C2×C59#57511yescharacteristic
129D59—81no—
130#533—591no—
131#529—591no—
132#499—592no—
133#488—592no—
134#485—592no—
135#482—592no—
136#477—591no—
137#476—591no—
138#475—591no—
139#474—591no—
140#431D5911yescharacteristic, complemented
141C59#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—591no—
143C4⋊Q8—591no—
144#126—1181no—
145#125—591no—
146#125—592no—
147#124—591no—
148#123—1181no—
149C22⋊Q8—591no—
150C22⋊Q8—1181no—
151C22⋊Q8—1181no—
152#121—591no—
153C4×Q8—591no—
154C4×Q8—1181no—
155C4×Q8—1181no—
156C4×D4—591no—
157C4×D4—1181no—
158#117—592no—
159#117—1181no—
160C2×C42C2×D5911yescharacteristic
161#107—592no—
162#107—592no—
163#106—592no—
164#106—592no—
165C4⋊C8C2×D5911yescharacteristic
166C4⋊C8C2×D5911yescharacteristic
167#103—592no—
168#103—592no—
169#102—592no—
170#102—592no—
171C22⋊C8C2×D5912yes—
172C4×C8C2×D5912yes—
173C2×Q8—591no—
174C2×Q8—1181no—
175C2×Q8—1181no—
176C2×D4—591no—
177C2×D4—1181no—
178C22×C4—1181no—
179C22×C4D23611yescharacteristic
180C22×C4D23611yescharacteristic
181C22×C4C22×D5911yescharacteristic
182C2×C8C22×D5912yes—
183C2×C8C22×D5912yes—
184C4⋊C4—592no—
185C4⋊C4—592no—
186C4⋊C4—591no—
187C4⋊C4—591no—
188C4⋊C4—1181no—
189C4⋊C4—1181no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4—1182no—
193C4⋊C4—1182no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C22⋊C4—1182no—
197C22⋊C4—1181no—
198C22⋊C4—1181no—
199C22⋊C4—1181no—
200C22⋊C4—1181no—
201C22⋊C4—1181no—
202C42—1182no—
203C42—1181no—
204C42D23611yescharacteristic
205C42D23611yescharacteristic
206C42C22×D5911yescharacteristic
207C42C22×D5911yescharacteristic
208C23—1181no—
209C23C2×D23611yescharacteristic
210Q8—1181no—
211Q8—1181no—
212Q8—2362no—
213Q8—2362no—
214D4—1181no—
215D4—1181no—
216D4—2362no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—1181no—
222C2×C4—1181no—
223C2×C4—1182no—
224C2×C4—1182no—
225C2×C4—1181no—
226C2×C4—2362no—
227C2×C4C2×D23611yescharacteristic
228C2×C4C2×D23611yescharacteristic
229C2×C4C2×D23611yescharacteristic
230C2×C4C2×D23611yescharacteristic
231C2×C4C2×D23611yescharacteristic
232C2×C4C23×D5911yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—2361no—
239C22—2361no—
240C22—2361no—
241C22C22×D23611yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—2361no—
247C4—2362no—
248C4—2361no—
249C4—2362no—
250C4—2361no—
251C4#1427374912yes—
252C4#1427377411yescharacteristic
253C4#1427377411yescharacteristic
254C2—41no—
255C2—4721no—
256C2#1683797811yescharacteristic
257C2C2×#1427374911yescharacteristic
258C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#431C2
socleC22×C59C22×D4
hypercenter#431D59
hypocenterC59#3233
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
1. #16837959C2semidirect
3. #16837804C2semidirect
4. #16837757C2semidirect
5. #16837744C2semidirect
7. #16837698C2semidirect
8. #16837693C2semidirect
9. #16837688C2semidirect
10. #16837683C2semidirect
11. C59×#431C2semidirect
140. #431D59semidirect
141. C59#3233semidirect