Finite Group Databasebeta

← #21435124

Subgroups — #21435124

Order 7552.

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

normal subgroups only

This group has 386 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
1C4⋊Q8×D59C211yesmaximal, characteristic, complemented
2#16837937C211yesmaximal, characteristic
3#16837796C211yesmaximal, characteristic, complemented
4#16837794C211yesmaximal, characteristic, complemented
5#16837772C211yesmaximal, characteristic, complemented
6#16837611C212yesmaximal, complemented
7#16837606C212yesmaximal, complemented
8#16837559C212yesmaximal, complemented
9#16837542C212yesmaximal
10#16837457C211yesmaximal, characteristic, complemented
11C59×#491C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2212yes—
13C2×Dic236C2212yes—
14C2×#11745672C2212yes—
15C2×#11745660C2212yes—
16C2×#11745671C2212yes—
17#14273727C2211yescharacteristic
18#14273726—21no—
19#14273726—21no—
20#14273725C2212yes—
21#14273722—21no—
22#14273715C2211yescharacteristic
23#14273712—21no—
24#14273707C2211yescharacteristic
25#14273702C2211yescharacteristic
26#14273692C2211yescharacteristic
27#14273689—21no—
28#14273689C2211yescharacteristic
29#14273685—21no—
30C4⋊C4×D59—21no—
31C4⋊C4×D59—21no—
32C42×D59C2211yescharacteristic
33Dic59⋊C8C2212yes—
34#14273650C2212yes—
35#14273650C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#103×C59C2212yes—
41#103×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59C2312yes—
44Q8×D59—42no—
45Q8×D59—42no—
46C2×D236—21no—
47C2×D236C2311yescharacteristic
48C2×C4×D59—22no—
49C2×C4×D59—21no—
50C2×C4×D59D411yescharacteristic
51C2×C4×D59D411yescharacteristic
52C2×C4×D59C2311yescharacteristic
53C2×Dic118—22no—
54C2×Dic118C2312yes—
55C2×Dic118C2311yescharacteristic
56C2×C8×C59C2312yes—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59—21no—
61C4⋊C4×C59C2311yescharacteristic
62C4⋊C4×C59C2311yescharacteristic
63C42×C59C2311yescharacteristic
64#11745672—42no—
65#11745671—42no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71C4⋊Dic59—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59—21no—
74Dic59⋊C4—22no—
75Dic59⋊C4—22no—
76Dic59⋊C4—21no—
77C4×Dic59—21no—
78C4×Dic59D411yescharacteristic
79C4×Dic59D411yescharacteristic
80C4×Dic59C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82Dic236—42no—
83#11745660—42no—
84C22×D59—21no—
85C22×D59C2×D411yescharacteristic
86Q8×C59—22no—
87Q8×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59—21no—
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2411yescharacteristic
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98C2×Dic59C2×D411yescharacteristic
99D236—22no—
100D236—42no—
101C4×D59—22no—
102C4×D59—22no—
103C4×D59—22no—
104C4×D59—44no—
105C4×D59—42no—
106Dic118—22no—
107Dic118—22no—
108Dic118—22no—
109Dic118—44no—
110C8×C59—22no—
111C59⋊C8—22no—
112C22×C59C22×D411yescharacteristic
113C2×D59—21no—
114C2×D59—21no—
115C2×D59—41no—
116C2×D59—41no—
117C2×D59—41no—
118C2×D59#13712yes—
119C4×C59—21no—
120C4×C59—21no—
121C4×C59—42no—
122C4×C59—41no—
123C4×C59—41no—
124C4×C59H(5,𝔽2)12yes—
125Dic59—21no—
126Dic59—21no—
127Dic59—42no—
128Dic59—41no—
129Dic59#13712yes—
130#3218—591nomaximal, Sylow
131C2×C59#53511yescharacteristic
132C2×C59C2×#13711yescharacteristic
133C2×C59C2×#13711yescharacteristic
134D59—22no—
135D59—81no—
136C2×C4⋊Q8—591no—
137#529—591no—
138#497—591no—
139#497—591no—
140#491—591no—
141#491D5911yescharacteristic, complemented
142#462—592no—
143#461—592no—
144#451—592no—
145#448—592no—
146#432—591no—
147C59#321811yescharacteristic, complemented, Sylow
148C22×Q8—592no—
149C2×Q16—592no—
150C2×Q16—592no—
151C2×SD16—592no—
152C2×SD16—592no—
153C4⋊Q8—592no—
154C4⋊Q8—591no—
155C4⋊Q8—1181no—
156C4⋊Q8—1181no—
157C4⋊Q8C2×D5911yescharacteristic
158#126—1181no—
159#125C2×D5911yescharacteristic
160#124—591no—
161#123—1181no—
162C22⋊Q8—591no—
163#121—591no—
164C4×Q8—591no—
165C4×D4—591no—
166C4×D4—1181no—
167#117—1181no—
168C2×C4⋊C4—1181no—
169C2×C4⋊C4—1181no—
170C2×C42—591no—
171C4⋊C8—592no—
172#103—592no—
173#103—592no—
174#103C2×D5912yes—
175#103C2×D5912yes—
176C22⋊C8—592no—
177#97—591no—
178#97C2×D5911yescharacteristic
179C2×Q8—592no—
180C2×Q8—591no—
181C2×Q8—1182no—
182C2×Q8—2362no—
183C2×Q8—2362no—
184C2×Q8C22×D5912yes—
185C2×D4—591no—
186C2×D4—1181no—
187C22×C4—591no—
188C22×C4—591no—
189C22×C4—591no—
190C22×C4—1181no—
191C22×C4—1182no—
192Q16—2362no—
193Q16—2362no—
194SD16—2362no—
195SD16—2362no—
196C2×C8—592no—
197C2×C8C22×D5912yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—1182no—
203C4⋊C4—1182no—
204C4⋊C4—1181no—
205C4⋊C4—1181no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C4⋊C4C22×D5911yescharacteristic
209C4⋊C4C22×D5911yescharacteristic
210C22⋊C4—1181no—
211C22⋊C4—1181no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—591no—
221C23—1181no—
222Q8—22no—
223Q8—22no—
224Q8—1182no—
225Q8—1182no—
226Q8—1182no—
227Q8—2364no—
228D4—1182no—
229D4—2362no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—591no—
234C2×C4—591no—
235C2×C4—591no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4—1181no—
240C2×C4—1182no—
241C2×C4—2362no—
242C2×C4—2364no—
243C2×C4D4×D5911yescharacteristic
244C2×C4D4×D5911yescharacteristic
245C2×C4C23×D5911yescharacteristic
246C8—22no—
247C8—1182no—
248C22—592no—
249C22—1181no—
250C22—1181no—
251C22—2361no—
252C22—2361no—
253C22—2361no—
254C22C2×D4×D5911yescharacteristic
255C4—21no—
256C4—21no—
257C4—41no—
258C4—41no—
259C4—42no—
260C4—592no—
261C4—1181no—
262C4—1181no—
263C4—2362no—
264C4—2361no—
265C4#1427377312yes—
266C2—1182no—
267C2—4721no—
268C2#1683797011yescharacteristic
269C2#137×D5911yescharacteristic
270C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#491C2
socleC22×C59C22×D4
hypercenter#491D59
hypocenterC59#3218
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D59C2semidirect
3. #16837796C2semidirect
4. #16837794C2semidirect
5. #16837772C2semidirect
6. #16837611C2semidirect
7. #16837606C2semidirect
8. #16837559C2semidirect
10. #16837457C2semidirect
11. C59×#491C2semidirect
141. #491D59semidirect
147. C59#3218semidirect