Finite Group Databasebeta

← #21435293

Subgroups — #21435293

Order 7552.

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

normal subgroups only

This group has 366 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#16837949C211yesmaximal, characteristic
3#16837810C212yesmaximal, complemented
4#16837765C212yesmaximal, complemented
5#16837729C212yesmaximal, complemented
6#16837725C212yesmaximal, complemented
7#16837693C211yesmaximal, characteristic, complemented
8#16837692C211yesmaximal, characteristic, complemented
9#16837679C211yesmaximal, characteristic, complemented
10#16837458C211yesmaximal, characteristic, complemented
11C59×#474C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13#14273727C2211yescharacteristic
14#14273726C2211yescharacteristic
15#14273723C2211yescharacteristic
16#14273718C2212yes—
17#14273713—21no—
18#14273707—21no—
19#14273703—21no—
20#14273702C2211yescharacteristic
21#14273700—21no—
22#14273698C2211yescharacteristic
23Q8×Dic59—21no—
24#14273692—21no—
25C4×D236C2211yescharacteristic
26C4×C22⋊D59—21no—
27#14273685C2212yes—
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273659C2212yes—
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273649C2212yes—
34#14273648C2212yes—
35#14273647C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273637C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×D4×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#102×C59C2212yes—
43C2×Q8×C59—21no—
44C2×D4×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C2×C22⋊D59—21no—
47C2×C22⋊D59—21no—
48C2×C22⋊D59—21no—
49#11745685—44no—
50C2×D236—21no—
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118—21no—
57C2×Dic118—21no—
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C4⋊C4×C59C2311yescharacteristic
62C22⋊C4×C59—21no—
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65(C2×D59)⋊C4—22no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59—22no—
70C4⋊Dic59C2312yes—
71C4⋊Dic59C2311yescharacteristic
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74C4×Dic59—22no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79C23×C59—21no—
80C22×D59—21no—
81C22×D59C2×D411yescharacteristic
82Q8×C59—42no—
83D4×C59—21no—
84D4×C59—21no—
85C2×C4×C59—22no—
86C2×C4×C59—21no—
87C2×C4×C59—42no—
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2411yescharacteristic
91C22⋊D59—42no—
92C22⋊D59—42no—
93C22⋊D59—42no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98C2×Dic59C2×D411yescharacteristic
99D236—21no—
100D236—21no—
101D236—42no—
102C4×D59—22no—
103C4×D59—21no—
104C4×D59—21no—
105C4×D59—41no—
106C4×D59—42no—
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—21no—
118C2×D59—41no—
119C2×D59—41no—
120C2×D59—41no—
121C4×C59—21no—
122C4×C59—41no—
123C4×C59—42no—
124C4×C59AGL(1,ℤ/8)12yes—
125C4×C592−1+411yescharacteristic
126C4×C592−1+411yescharacteristic
127Dic59—21no—
128Dic59—21no—
129Dic59—21no—
130Dic59—41no—
131Dic59—42no—
132#3235—591nomaximal, Sylow
133C2×C59—81no—
134C2×C59#53611yescharacteristic
135C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C59#57511yescharacteristic
137D59—41no—
138D59—81no—
139#533—591no—
140#532—591no—
141#501—592no—
142#490—592no—
143#482—592no—
144#482—592no—
145#476—591no—
146#476—591no—
147#474—591no—
148#474D5911yescharacteristic, complemented
149#432—591no—
150C59#323511yescharacteristic, complemented, Sylow
151C2×#41—1181no—
152C4⋊Q8—591no—
153C4⋊Q8—591no—
154C4⋊Q8C2×D5911yescharacteristic
155#127—591no—
156#125—592no—
157#124—1181no—
158C22⋊Q8—1181no—
159C22⋊Q8—1181no—
160#121—591no—
161#121—591no—
162#121—1181no—
163C4×Q8—1181no—
164C4×Q8—1181no—
165C4×D4—591no—
166C4×D4—1181no—
167C4×D4C2×D5911yescharacteristic
168#117—592no—
169C2×C42—591no—
170#107—592no—
171#107C2×D5912yes—
172#106—592no—
173#106—592no—
174C4⋊C8—591no—
175C4⋊C8C2×D5911yescharacteristic
176#102—592no—
177#102—592no—
178#102—592no—
179#102C2×D5912yes—
180C22⋊C8—592no—
181#97—592no—
182#41—2364no—
183C2×Q8—21no—
184C2×Q8—1181no—
185C2×Q8—1181no—
186C2×D4—591no—
187C2×D4—1181no—
188C2×D4—1181no—
189C2×D4—1181no—
190C2×D4—1181no—
191C2×D4C22×D5911yescharacteristic
192C22×C4—21no—
193C22×C4—591no—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4—1181no—
197C2×C8—592no—
198C2×C8C22×D5912yes—
199C4⋊C4—21no—
200C4⋊C4—592no—
201C4⋊C4—591no—
202C4⋊C4—1181no—
203C4⋊C4—1182no—
204C4⋊C4—1182no—
205C4⋊C4—1181no—
206C4⋊C4C22×D5912yes—
207C4⋊C4C22×D5911yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—1181no—
210C22⋊C4—1182no—
211C22⋊C4—1181no—
212C22⋊C4—1181no—
213C42—591no—
214C42—591no—
215C42—591no—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—21no—
219C23—591no—
220C23—1181no—
221Q8—42no—
222Q8—2362no—
223Q8—2362no—
224D4—21no—
225D4—21no—
226D4—1181no—
227D4—1181no—
228D4—2362no—
229D4—2362no—
230D4—2362no—
231D4—2362no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—591no—
236C2×C4—591no—
237C2×C4—591no—
238C2×C4—1182no—
239C2×C4—1181no—
240C2×C4—1181no—
241C2×C4—1182no—
242C2×C4—1181no—
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—1181no—
254C22—1181no—
255C22—1181no—
256C22—2361no—
257C22—2361no—
258C22—2361no—
259C22C2×D4×D5911yescharacteristic
260C4—21no—
261C4—41no—
262C4—42no—
263C4—1181no—
264C4—1181no—
265C4—1181no—
266C4—2361no—
267C4—2362no—
268C4#1427375112yes—
269C4#1427377411yescharacteristic
270C4#1427377511yescharacteristic
271C2—81no—
272C2—4721no—
273C2—2361no—
274C2#1683797511yescharacteristic
275C2C2×#1427375111yescharacteristic
276C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3235
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837810C2semidirect
4. #16837765C2semidirect
5. #16837729C2semidirect
6. #16837725C2semidirect
7. #16837693C2semidirect
8. #16837692C2semidirect
9. #16837679C2semidirect
10. #16837458C2semidirect
11. C59×#474C2semidirect
148. #474D59semidirect
150. C59#3235semidirect