Finite Group Databasebeta

← #21435411

Subgroups — #21435411

Order 7552.

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

normal subgroups only

This group has 392 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#16837956C211yesmaximal, characteristic, complemented
2#16837953C211yesmaximal, characteristic
3#16837691C212yesmaximal, complemented
4#16837684C211yesmaximal, characteristic, complemented
5#16837634C212yesmaximal, complemented
6#16837632C212yesmaximal, complemented
7#16837606C212yesmaximal, complemented
8#16837603C211yesmaximal, characteristic, complemented
9#16837602C211yesmaximal, characteristic, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#475C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×#11745660C2212yes—
14C2×#11745671C2212yes—
15C2×C8×D59C2212yes—
16#14273726C2211yescharacteristic
17#14273725C2211yescharacteristic
18#14273724C2211yescharacteristic
19#14273717—21no—
20#14273716—21no—
21#14273707C2211yescharacteristic
22#14273705—21no—
23#14273703C2211yescharacteristic
24#14273702—21no—
25#14273702C2212yes—
26C4×Dic118—21no—
27C4×Dic118C2211yescharacteristic
28#14273689—21no—
29#14273689C2212yes—
30#14273684—21no—
31C42×D59C2211yescharacteristic
32#14273658C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273650C2212yes—
36#14273649C2212yes—
37#14273647C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#106×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45#11745689—44no—
46C2×D236—22no—
47C2×D236—21no—
48C2×D236—21no—
49C2×D236C2312yes—
50C2×C4×D59—22no—
51C2×C4×D59D411yescharacteristic
52C2×C4×D59D411yescharacteristic
53C2×C4×D59C2311yescharacteristic
54C2×Dic118—21no—
55C2×Dic118C2311yescharacteristic
56C2×C8×C59C2312yes—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59C2312yes—
60C4⋊C4×C59C2311yescharacteristic
61C42×C59—21no—
62C42×C59C2311yescharacteristic
63#11745671—42no—
64(C2×D59)⋊C4—21no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—22no—
67(C2×D59)⋊C4—22no—
68C4⋊Dic59—21no—
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75C4×Dic59—21no—
76C4×Dic59D411yescharacteristic
77C4×Dic59D411yescharacteristic
78C4×Dic59C2311yescharacteristic
79C2×C59⋊C8C2312yes—
80#11745660—42no—
81C8×D59—42no—
82C22×D59—22no—
83C22×D59C2×D411yescharacteristic
84Q8×C59—21no—
85Q8×C59—21no—
86Q8×C59—42no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C2×Dic59—21no—
94C2×Dic59—21no—
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98D236—22no—
99D236—22no—
100D236—42no—
101D236—44no—
102D236—42no—
103C4×D59—21no—
104C4×D59—21no—
105C4×D59—41no—
106C4×D59—44no—
107C4×D59SD1614yescomplemented
108Dic118—21no—
109Dic118—21no—
110Dic118—42no—
111C8×C59—22no—
112C59⋊C8—22no—
113C22×C59C22×D411yescharacteristic
114C2×D59—21no—
115C2×D59—21no—
116C2×D59—42no—
117C2×D59—42no—
118C2×D59—42no—
119C2×D59C2×SD1612yes—
120C4×C59—21no—
121C4×C59—41no—
122C4×C59—42no—
123C4×C59—41no—
124C4×C59C2×SD1612yes—
125C4×C59H(5,𝔽2)11yescharacteristic
126C4×C592−1+411yescharacteristic
127Dic59—21no—
128Dic59—21no—
129Dic59—41no—
130Dic59—41no—
131Dic59C2×SD1612yes—
132#3246—591nomaximal, Sylow
133C2×C59#53711yescharacteristic
134C2×C59C22×SD1611yescharacteristic
135C2×C59#57511yescharacteristic
136D59—22no—
137D59—82no—
138#533—591no—
139#532—591no—
140#476—592no—
141#475—591no—
142#475D5911yescharacteristic, complemented
143#465—592no—
144#465—592no—
145#461—592no—
146#460—591no—
147#460—591no—
148C2×C4⋊C8—591no—
149C59#324611yescharacteristic, complemented, Sylow
150C2×#41—1181no—
151C2×SD16—592no—
152C2×SD16—592no—
153C22×C8—592no—
154C4⋊Q8—591no—
155C4⋊Q8—591no—
156C4⋊Q8C2×D5911yescharacteristic
157#127—591no—
158#125—1181no—
159#124—1181no—
160C22⋊Q8—591no—
161C22⋊Q8—591no—
162C22⋊Q8—1181no—
163#121—592no—
164#121—1181no—
165C4×Q8—591no—
166C4×Q8—1181no—
167C4×Q8C2×D5911yescharacteristic
168C4×D4—592no—
169C4×D4—1181no—
170#117—1181no—
171C2×C42—591no—
172#106—592no—
173#106C2×D5912yes—
174C4⋊C8—592no—
175C4⋊C8—591no—
176C4⋊C8C2×D5911yescharacteristic
177#103—592no—
178#103C2×D5912yes—
179#102—592no—
180#102—592no—
181#41—2364no—
182C2×Q8—21no—
183C2×Q8—591no—
184C2×Q8—1181no—
185C2×Q8C22×D5911yescharacteristic
186C2×D4—592no—
187C2×D4—1182no—
188C2×D4—1181no—
189C2×D4—1181no—
190C22×C4—591no—
191C22×C4—591no—
192C22×C4—591no—
193C22×C4—1182no—
194SD16—2362no—
195SD16—2362no—
196C2×C8—592no—
197C2×C8—2362no—
198C2×C8C22×D5912yes—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—591no—
202C4⋊C4—1181no—
203C4⋊C4—1181no—
204C4⋊C4—1181no—
205C4⋊C4—1181no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C4⋊C4C22×D5911yescharacteristic
209C4⋊C4C22×D5912yes—
210C22⋊C4—1182no—
211C22⋊C4—1182no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C42—21no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—591no—
221C23—1182no—
222Q8—21no—
223Q8—21no—
224Q8—42no—
225Q8—1181no—
226Q8—1181no—
227Q8—2362no—
228D4—1182no—
229D4—1182no—
230D4—2362no—
231D4—2364no—
232D4—2362no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—591no—
237C2×C4—594no—
238C2×C4—591no—
239C2×C4—591no—
240C2×C4—1181no—
241C2×C4—1181no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—2361no—
245C2×C4—2364no—
246C2×C4D4×D5911yescharacteristic
247C2×C4D4×D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—22no—
250C8—1182no—
251C22—592no—
252C22—1181no—
253C22—1181no—
254C22—2362no—
255C22—2362no—
256C22—2362no—
257C22C2×D4×D5911yescharacteristic
258C4—21no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—592no—
263C4—1181no—
264C4—1181no—
265C4—2361no—
266C4—2361no—
267C4SD16×D5912yes—
268C4#1427377311yescharacteristic
269C4#1427377511yescharacteristic
270C2—1182no—
271C2—4722no—
272C2#1683798211yescharacteristic
273C2C2×SD16×D5911yescharacteristic
274C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#475C2
socleC22×C59C22×D4
hypercenter#475D59
hypocenterC59#3246
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16837956C2semidirect
3. #16837691C2semidirect
4. #16837684C2semidirect
5. #16837634C2semidirect
6. #16837632C2semidirect
7. #16837606C2semidirect
8. #16837603C2semidirect
9. #16837602C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#475C2semidirect
107. C4×D59SD16semidirect
142. #475D59semidirect
149. C59#3246semidirect