Finite Group Databasebeta

← #21435481

Subgroups — #21435481

Order 7552.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#16837950C211yesmaximal, characteristic
3#16837698C211yesmaximal, characteristic, complemented
4#16837697C211yesmaximal, characteristic, complemented
5#16837680C212yesmaximal, complemented
6#16837647C212yesmaximal, complemented
7#16837645C212yesmaximal, complemented
8#16837605C212yesmaximal, complemented
9#16837599C211yesmaximal, characteristic, complemented
10#16837424C211yesmaximal, characteristic, complemented
11C59×#460C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×#11745670C2212yes—
14C2×#11745659C2212yes—
15#14273727C2211yescharacteristic
16#14273726C2211yescharacteristic
17#14273725C2211yescharacteristic
18#14273717—21no—
19#14273714—21no—
20#14273707C2211yescharacteristic
21#14273705—21no—
22#14273703C2211yescharacteristic
23#14273698—21no—
24#14273698C2212yes—
25C4×Dic118—21no—
26C4×Dic118C2211yescharacteristic
27D4×Dic59—21no—
28D4×Dic59C2212yes—
29#14273684—21no—
30C42×D59C2211yescharacteristic
31#14273661C2212yes—
32#14273660C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273652C2212yes—
36#14273651C2212yes—
37#14273648C2212yes—
38C2×SD16×C59C2212yes—
39#127×C59C2211yescharacteristic
40C4×Q8×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#102×C59C2212yes—
43C2×Q8×C59C2311yescharacteristic
44C2×D4×C59—21no—
45C2×D4×C59—21no—
46C2×D4×C59C2312yes—
47C2×C22⋊D59—22no—
48C22×Dic59—22no—
49#11745687—44no—
50C2×C4×D59D411yescharacteristic
51C2×C4×D59D411yescharacteristic
52C2×C4×D59C2311yescharacteristic
53C2×Dic118—21no—
54C2×Dic118—21no—
55C2×Dic118C2311yescharacteristic
56SD16×C59—42no—
57C2×C8×C59C2312yes—
58C4⋊C4×C59—21no—
59C4⋊C4×C59C2311yescharacteristic
60C42×C59—21no—
61C42×C59C2311yescharacteristic
62C22⋊Dic59—22no—
63C22⋊Dic59—22no—
64#11745670—42no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59C2311yescharacteristic
70C4⋊Dic59C2312yes—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75Dic59⋊C4—21no—
76C4×Dic59—21no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81#11745659—42no—
82C23×C59—22no—
83C22×D59C2×D411yescharacteristic
84Q8×C59—21no—
85Q8×C59—21no—
86D4×C59—22no—
87D4×C59—22no—
88D4×C59—42no—
89D4×C59—42no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—44no—
96C2×Dic59—21no—
97C2×Dic59—21no—
98C2×Dic59—22no—
99C2×Dic59—44no—
100C2×Dic59C2×D411yescharacteristic
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103C4×D59—22no—
104C4×D59—21no—
105C4×D59—21no—
106C4×D59—22no—
107Dic118—21no—
108Dic118—21no—
109Dic118—42no—
110Dic118—42no—
111C8×C59—22no—
112C59⋊C8—22no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59C22×D411yescharacteristic
117C2×D59—21no—
118C2×D59—21no—
119C2×D59—21no—
120C4×C59—21no—
121C4×C59—41no—
122C4×C59—41no—
123C4×C59#13712yes—
124C4×C59H(5,𝔽2)11yescharacteristic
125C4×C592−1+411yescharacteristic
126Dic59—21no—
127Dic59—21no—
128Dic59—41no—
129Dic59—41no—
130Dic59—42no—
131Dic59AGL(1,ℤ/8)12yes—
132#3254—591nomaximal, Sylow
133C2×C59—82no—
134C2×C59#53711yescharacteristic
135C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C59C2×#13711yescharacteristic
137D59—41no—
138#533—591no—
139#532—591no—
140#477—591no—
141#477—591no—
142#474—592no—
143#468—592no—
144#468—592no—
145#461—592no—
146#460—591no—
147#460D5911yescharacteristic, complemented
148#423—591no—
149C59#325411yescharacteristic, complemented, Sylow
150C2×#41—1181no—
151C2×SD16—592no—
152C2×SD16C2×D5912yes—
153C2×M16—592no—
154C4⋊Q8—591no—
155C4⋊Q8—591no—
156C4⋊Q8—591no—
157#127C2×D5911yescharacteristic
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#107—592no—
173#107—592no—
174C4⋊C8—592no—
175C4⋊C8—591no—
176C4⋊C8C2×D5911yescharacteristic
177#103—592no—
178#103—592no—
179#102—592no—
180#102C2×D5912yes—
181#41—2364no—
182C2×Q8—591no—
183C2×Q8—1181no—
184C2×Q8—1181no—
185C2×Q8C22×D5911yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—1182no—
189C2×D4C22×D5912yes—
190C22×C4—591no—
191C22×C4—591no—
192C22×C4—591no—
193C22×C4—1182no—
194SD16—42no—
195SD16—2362no—
196M16—2362no—
197C2×C8—592no—
198C2×C8C22×D5912yes—
199C4⋊C4—21no—
200C4⋊C4—591no—
201C4⋊C4—592no—
202C4⋊C4—1181no—
203C4⋊C4—1181no—
204C4⋊C4—1181no—
205C4⋊C4—1181no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4C22×D5911yescharacteristic
210C22⋊C4—1181no—
211C22⋊C4—1181no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C42—21no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—22no—
221C23—591no—
222Q8—21no—
223Q8—21no—
224Q8—1181no—
225Q8—1181no—
226Q8—2362no—
227Q8—2362no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—42no—
232D4—2364no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—591no—
236C2×C4—591no—
237C2×C4—591no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1181no—
241C2×C4—1181no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—1182no—
245C2×C4—2364no—
246C2×C4D4×D5911yescharacteristic
247C2×C4D4×D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—22no—
250C8—1182no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—1181no—
255C22—1181no—
256C22—1181no—
257C22C2×D4×D5911yescharacteristic
258C4—21no—
259C4—41no—
260C4—41no—
261C4—592no—
262C4—1181no—
263C4—1181no—
264C4—2362no—
265C4—2361no—
266C4—2361no—
267C4#1427375612yes—
268C4#1427377211yescharacteristic
269C4#1427377411yescharacteristic
270C2—82no—
271C2—2361no—
272C2#1683798111yescharacteristic
273C2AGL(1,ℤ/8)×D5911yescharacteristic
274C2C2×#1427375611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#460C2
socleC22×C59C22×D4
hypercenter#460D59
hypocenterC59#3254
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16837956C2semidirect
3. #16837698C2semidirect
4. #16837697C2semidirect
5. #16837680C2semidirect
6. #16837647C2semidirect
7. #16837645C2semidirect
8. #16837605C2semidirect
9. #16837599C2semidirect
10. #16837424C2semidirect
11. C59×#460C2semidirect
147. #460D59semidirect
149. C59#3254semidirect