Finite Group Databasebeta

← #21434481

Subgroups — #21434481

Order 7552.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#124×D59C211yesmaximal, characteristic
3#16837764C211yesmaximal, characteristic, complemented
4#16837762C211yesmaximal, characteristic, complemented
5#16837761C211yesmaximal, characteristic, complemented
6#16837758C212yesmaximal, complemented
7#16837755C212yesmaximal, complemented
8#16837409C212yesmaximal, complemented
9#16837405C212yesmaximal
10#16837354C211yesmaximal, characteristic, complemented
11C59×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C2×D4×D59C2211yescharacteristic
14C2×#11745659C2212yes—
15#14273727C2211yescharacteristic, complemented
16#14273718C2212yescomplemented
17#14273716C2211yescharacteristic
18#14273715C2211yescharacteristic
19#14273714C2211yescharacteristic
20#14273713—21no—
21#14273713—21no—
22#14273707—21no—
23#14273703—21no—
24Q8×Dic59—21no—
25#14273692—21no—
26#14273685C2212yes—
27C22⋊C4×D59—21no—
28C22⋊C4×D59—21no—
29C42×D59C2211yescharacteristic
30#14273652C2212yescomplemented
31#14273651C2212yescomplemented
32#14273650C2212yescomplemented
33#14273649C2212yes—
34#14273648C2212yes—
35#14273647C2212yes—
36#14273638C2211yescharacteristic, complemented
37C8×Dic59C2212yescomplemented
38C4⋊Q8×C59C2211yescharacteristic, complemented
39#124×C59C2211yescharacteristic
40#103×C59C2212yescomplemented
41#102×C59C2212yes—
42#97×C59C2211yescharacteristic, complemented
43C23×D59—21no—
44C2×Q8×C59—21no—
45C2×Q8×C59C2311yescharacteristic
46C2×D4×C59C2311yescharacteristic
47C2×C22⋊D59—21no—
48Q8×D59—24no—
49D4×D59—24no—
50C2×D236C2311yescharacteristic
51C2×C4×D59—21no—
52C2×C4×D59D411yescharacteristic
53C2×C4×D59D411yescharacteristic
54C2×C4×D59C2311yescharacteristic
55C2×Dic118—21no—
56C2×Dic118—21no—
57C2×Dic118C2311yescharacteristic
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C22⋊C4×C59—21no—
62C22⋊C4×C59—21no—
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65C22⋊Dic59—21no—
66(C2×D59)⋊C4—22no—
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—22no—
73C4⋊Dic59C2312yes—
74Dic59⋊C4—22no—
75C4×Dic59—22no—
76C4×Dic59D411yescharacteristic
77C4×Dic59D411yescharacteristic
78C4×Dic59C2311yescharacteristic
79C2×C59⋊C8C2312yes—
80#11745659—24no—
81C23×C59—21no—
82C22×D59—21no—
83C22×D59—42no—
84C22×D59—42no—
85C22×D59—42no—
86C22×D59C2×D411yescharacteristic
87Q8×C59—22no—
88Q8×C59—42no—
89D4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—42no—
96C2×Dic59—22no—
97C2×Dic59—21no—
98C2×Dic59C2×D411yescharacteristic
99C2×Dic59C2×D411yescharacteristic
100C2×Dic59C2×D411yescharacteristic
101D236—22no—
102C4×D59—41no—
103C4×D59—41no—
104C4×D59—42no—
105C4×D59#4114yes—
106Dic118—22no—
107Dic118—42no—
108Dic118—42no—
109C8×C59—22no—
110C59⋊C8—22no—
111C22×C59—41no—
112C22×C59—41no—
113C22×C59—41no—
114C22×C59C22×D411yescharacteristic
115C2×D59—21no—
116C2×D59—21no—
117C2×D59—41no—
118C2×D59—41no—
119C2×D59—41no—
120C2×D59—84no—
121C2×D59#12412yes—
122C4×C59—21no—
123C4×C59—21no—
124C4×C59—41no—
125C4×C59—42no—
126C4×C59C2×#4112yes—
127Dic59—21no—
128Dic59—21no—
129Dic59—41no—
130Dic59—42no—
131Dic59#12412yes—
132#3140—591nomaximal, Sylow
133C2×C59—81no—
134C2×C59C2×#12411yescharacteristic
135C2×C59#57511yescharacteristic
136C2×C59#57511yescharacteristic
137D59—22no—
138D59—81no—
139#533—591no—
140C2×#124—591no—
141#489—591no—
142#489—591no—
143#489—591no—
144#489D5911yescharacteristic, complemented
145#488—592no—
146#488—592no—
147#419—592no—
148#418—592no—
149C4×M16—591no—
150C59#314011yescharacteristic, complemented, Sylow
151C22×Q8—591no—
152C22×D4—591no—
153C2×M16—592no—
154C4⋊Q8—591no—
155C4⋊Q8C2×D5911yescharacteristic, complemented
156#125—592no—
157#124—591no—
158#124—591no—
159#124—591no—
160#124—1181no—
161#124—1181no—
162#124C2×D5911yescharacteristic
163C22⋊Q8—1181no—
164C22⋊Q8—1181no—
165C4×Q8—1181no—
166C4×Q8—1181no—
167#117—592no—
168C2×C22⋊C4—1181no—
169C2×C22⋊C4—1181no—
170C2×C42—591no—
171#103—592no—
172#103—592no—
173#103—592no—
174#103C2×D5912yescomplemented
175#102—592no—
176#102—592no—
177#102—592no—
178#102C2×D5912yes—
179#97—591no—
180#97C2×D5911yescharacteristic, complemented
181C4×C8—592no—
182C24—1181no—
183C2×Q8—21no—
184C2×Q8—591no—
185C2×Q8—1181no—
186C2×Q8—1184no—
187C2×Q8—1181no—
188C2×Q8C22×D5911yescharacteristic
189C2×D4—591no—
190C2×D4—1184no—
191C2×D4—1181no—
192C2×D4C22×D5911yescharacteristic
193C22×C4—591no—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4—1181no—
197M16—1184no—
198C2×C8—592no—
199C2×C8C22×D5912yes—
200C4⋊C4—21no—
201C4⋊C4—592no—
202C4⋊C4—1182no—
203C4⋊C4—1182no—
204C4⋊C4—1181no—
205C4⋊C4C22×D5912yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—1181no—
209C22⋊C4—1181no—
210C22⋊C4—1182no—
211C22⋊C4—1181no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1182no—
219C42C22×D5911yescharacteristic
220C23—21no—
221C23—591no—
222C23—1181no—
223C23—2362no—
224C23—2362no—
225C23—2362no—
226Q8—22no—
227Q8—42no—
228Q8—1182no—
229Q8—2362no—
230Q8—2362no—
231D4—22no—
232D4—1182no—
233D4—2362no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—591no—
237C2×C4—594no—
238C2×C4—591no—
239C2×C4—591no—
240C2×C4—1182no—
241C2×C4—1181no—
242C2×C4—2361no—
243C2×C4—2361no—
244C2×C4—2362no—
245C2×C4D4×D5911yescharacteristic
246C2×C4D4×D5911yescharacteristic
247C2×C4C23×D5911yescharacteristic
248C8—22no—
249C8—1182no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—592no—
254C22—1181no—
255C22—1181no—
256C22—4724no—
257C22—2361no—
258C22—2361no—
259C22—2361no—
260C22C2×D4×D5911yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—42no—
265C4—592no—
266C4—1181no—
267C4—1181no—
268C4—2361no—
269C4—2362no—
270C4#41×D5912yes—
271C2—81no—
272C2—1182no—
273C2—4721no—
274C2#124×D5911yescharacteristic
275C2#1683819811yescharacteristic
276C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#489C2
socleC22×C59C22×D4
hypercenter#489D59
hypocenterC59#3140
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837764C2semidirect
4. #16837762C2semidirect
5. #16837761C2semidirect
6. #16837758C2semidirect
7. #16837755C2semidirect
8. #16837409C2semidirect
10. #16837354C2semidirect
11. C59×#489C2semidirect
15. #14273727C22semidirect
16. #14273718C22semidirect
30. #14273652C22semidirect
31. #14273651C22semidirect
32. #14273650C22semidirect
36. #14273638C22semidirect
37. C8×Dic59C22semidirect
38. C4⋊Q8×C59C22semidirect
40. #103×C59C22semidirect
42. #97×C59C22semidirect
144. #489D59semidirect
150. C59#3140semidirect
155. C4⋊Q8C2×D59semidirect
174. #103C2×D59semidirect
180. #97C2×D59semidirect