Finite Group Databasebeta

← #21435280

Subgroups — #21435280

Order 7552.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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#16837957C211yesmaximal, characteristic, complemented
2#16837939C211yesmaximal, characteristic
3#16837803C212yesmaximal, complemented
4#16837758C212yesmaximal, complemented
5#16837742C212yesmaximal, complemented
6#16837729C212yesmaximal
7#16837689C211yesmaximal, characteristic, complemented
8#16837687C211yesmaximal, characteristic, complemented
9#16837683C211yesmaximal, characteristic, complemented
10#16837454C211yesmaximal, characteristic, complemented
11C59×#477C211yesmaximal, characteristic, complemented
12#14273727C2211yescharacteristic
13#14273722—21no—
14#14273718C2211yescharacteristic
15#14273718C2212yes—
16#14273716C2211yescharacteristic
17#14273712—21no—
18#14273707—21no—
19#14273703—21no—
20#14273703C2211yescharacteristic
21#14273702C2211yescharacteristic
22Q8×Dic59—21no—
23#14273692—21no—
24C4×D236—21no—
25C4×D236C2211yescharacteristic
26#14273685C2212yes—
27#14273684—21no—
28C42×D59C2211yescharacteristic
29#14273661C2212yes—
30#14273658C2212yes—
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273651C2212yes—
34#14273649C2212yes—
35#14273647C2212yes—
36(C2×D59)⋊C8C2212yes—
37C8×Dic59C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45C2×D236—21no—
46C2×D236C2311yescharacteristic
47C2×C4×D59—21no—
48C2×C4×D59D411yescharacteristic
49C2×C4×D59D411yescharacteristic
50C2×C4×D59C2311yescharacteristic
51C2×Dic118—21no—
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C42×C59—21no—
58C42×C59C2311yescharacteristic
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—22no—
68C4⋊Dic59C2312yes—
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78C22×D59—21no—
79C22×D59C2×D411yescharacteristic
80Q8×C59—21no—
81Q8×C59—21no—
82Q8×C59—42no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2411yescharacteristic
89C2×Dic59—22no—
90C2×Dic59—21no—
91C2×Dic59C2×D411yescharacteristic
92C2×Dic59C2×D411yescharacteristic
93C2×Dic59C2×D411yescharacteristic
94D236—21no—
95D236—21no—
96D236—42no—
97C4×D59—22no—
98C4×D59—21no—
99C4×D59—21no—
100C4×D59—41no—
101C4×D59—42no—
102Dic118—42no—
103C8×C59—22no—
104C59⋊C8—22no—
105C22×C59C22×D411yescharacteristic
106C2×D59—21no—
107C2×D59—21no—
108C2×D59—21no—
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—21no—
113C4×C59—41no—
114C4×C59—41no—
115C4×C59—42no—
116C4×C59#13512yes—
117C4×C592−1+411yescharacteristic
118C4×C592−1+411yescharacteristic
119Dic59—21no—
120Dic59—21no—
121Dic59—21no—
122Dic59—42no—
123Dic59—41no—
124#3233—591nomaximal, Sylow
125C2×C59#53611yescharacteristic
126C2×C59C2×#13511yescharacteristic
127C2×C59#57511yescharacteristic
128D59—41no—
129D59—81no—
130#533—591no—
131#529—591no—
132#499—592no—
133#488—592no—
134#485—592no—
135#482—592no—
136#477D5911yescharacteristic, complemented
137#476—591no—
138#475—591no—
139#474—591no—
140#431—591no—
141C59#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—591no—
143C4⋊Q8C2×D5911yescharacteristic
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—1181no—
154C4×Q8—1181no—
155C4×Q8C2×D5911yescharacteristic
156C4×D4—591no—
157C4×D4—1181no—
158#117—592no—
159#117—1181no—
160C2×C42—591no—
161#107—592no—
162#107C2×D5912yes—
163#106—592no—
164#106—592no—
165C4⋊C8—591no—
166C4⋊C8C2×D5911yescharacteristic
167#103—592no—
168#103C2×D5912yes—
169#102—592no—
170#102—592no—
171C22⋊C8—592no—
172C4×C8—592no—
173C2×Q8—21no—
174C2×Q8—1181no—
175C2×Q8C22×D5911yescharacteristic
176C2×D4—591no—
177C2×D4—1181no—
178C22×C4—591no—
179C22×C4—591no—
180C22×C4—591no—
181C22×C4—1181no—
182C2×C8—592no—
183C2×C8C22×D5912yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—592no—
187C4⋊C4—591no—
188C4⋊C4—1181no—
189C4⋊C4—1181no—
190C4⋊C4—1181no—
191C4⋊C4—1182no—
192C4⋊C4—1182no—
193C4⋊C4—1181no—
194C4⋊C4C22×D5912yes—
195C4⋊C4C22×D5911yescharacteristic
196C22⋊C4—1181no—
197C22⋊C4—1181no—
198C22⋊C4—1181no—
199C22⋊C4—1182no—
200C22⋊C4—1181no—
201C22⋊C4—1181no—
202C42—21no—
203C42—591no—
204C42—591no—
205C42—591no—
206C42—1182no—
207C42C22×D5911yescharacteristic
208C23—591no—
209C23—1181no—
210Q8—21no—
211Q8—21no—
212Q8—42no—
213Q8—2362no—
214D4—1181no—
215D4—1181no—
216D4—2362no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—591no—
221C2×C4—591no—
222C2×C4—591no—
223C2×C4—1182no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—1182no—
227C2×C4—1181no—
228C2×C4—2361no—
229C2×C4—2362no—
230C2×C4D4×D5911yescharacteristic
231C2×C4D4×D5911yescharacteristic
232C2×C4C23×D5911yescharacteristic
233C8—22no—
234C8—1182no—
235C22—1181no—
236C22—1181no—
237C22—1181no—
238C22—2361no—
239C22—2361no—
240C22—2361no—
241C22C2×D4×D5911yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—41no—
246C4—1181no—
247C4—1181no—
248C4—1181no—
249C4—2361no—
250C4—2362no—
251C4#1427375012yes—
252C4#1427377411yescharacteristic
253C4#1427377511yescharacteristic
254C2—4721no—
255C2—2361no—
256C2#1683797511yescharacteristic
257C2C2×#1427375011yescharacteristic
258C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3233
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837803C2semidirect
4. #16837758C2semidirect
5. #16837742C2semidirect
7. #16837689C2semidirect
8. #16837687C2semidirect
9. #16837683C2semidirect
10. #16837454C2semidirect
11. C59×#477C2semidirect
136. #477D59semidirect
141. C59#3233semidirect