Finite Group Databasebeta

← #21435420

Subgroups — #21435420

Order 7552.

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

normal subgroups only

This group has 398 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#16837950C211yesmaximal, characteristic, complemented
2#16837939C211yesmaximal, characteristic, complemented
3#16837704C212yesmaximal, complemented
4#16837697C211yesmaximal, characteristic, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837637C212yesmaximal, complemented
7#16837628C212yesmaximal, complemented
8#16837619C212yesmaximal, complemented
9#16837594C211yesmaximal, characteristic, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#460C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×#11745669C2212yes—
14C2×C8×D59C2212yes—
15#14273727C2211yescharacteristic
16#14273722—21no—
17#14273718C2211yescharacteristic
18#14273716C2211yescharacteristic
19#14273714—21no—
20#14273712—21no—
21#14273703C2211yescharacteristic
22#14273702C2211yescharacteristic
23#14273698—21no—
24#14273698C2212yes—
25C4×D236—21no—
26C4×D236C2211yescharacteristic
27D4×Dic59—21no—
28D4×Dic59C2212yes—
29#14273684—21no—
30C42×D59C2211yescharacteristic
31#14273660C2212yes—
32#14273659C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273651C2212yes—
36#14273649C2212yes—
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×D236—21no—
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118—21no—
57SD16×C59—42no—
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2311yescharacteristic
61C42×C59—21no—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—22no—
64C22⋊Dic59—22no—
65#11745669—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⋊Dic59C2311yescharacteristic
74C4⋊Dic59C2312yes—
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81C8×D59—42no—
82C23×C59—22no—
83C22×D59—21no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—21no—
86Q8×C59—21no—
87D4×C59—22no—
88D4×C59—22no—
89D4×C59—42no—
90D4×C59—42no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2411yescharacteristic
96C22⋊D59—44no—
97C2×Dic59—21no—
98C2×Dic59—22no—
99C2×Dic59—44no—
100C2×Dic59C2×D411yescharacteristic
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103D236—21no—
104D236—21no—
105D236—42no—
106C4×D59—22no—
107C4×D59—22no—
108C4×D59—21no—
109C4×D59—21no—
110C4×D59—42no—
111Dic118—42no—
112C8×C59—22no—
113C59⋊C8—22no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59—42no—
117C22×C59C22×D411yescharacteristic
118C2×D59—21no—
119C2×D59—21no—
120C2×D59—41no—
121C2×D59—41no—
122C2×D59—41no—
123C2×D59AGL(1,ℤ/8)12yes—
124C4×C59—21no—
125C4×C59—41no—
126C4×C59—41no—
127C4×C59#13512yes—
128C4×C59H(5,𝔽2)11yescharacteristic
129C4×C592−1+411yescharacteristic
130Dic59—21no—
131Dic59—21no—
132Dic59—21no—
133Dic59—41no—
134Dic59—42no—
135#3247—591nomaximal, Sylow
136C2×C59—82no—
137C2×C59#53711yescharacteristic
138C2×C59C2×#13511yescharacteristic
139C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
140D59—22no—
141D59—81no—
142#532—591no—
143#529—591no—
144#478—592no—
145#477—591no—
146#476—591no—
147#466—592no—
148#465—592no—
149#463—592no—
150#460D5911yescharacteristic, complemented
151#459—591no—
152C2×C4⋊C8—591no—
153C59#324711yescharacteristic, complemented, Sylow
154C2×#41—1181no—
155C2×SD16C2×D5912yes—
156C2×D8—592no—
157C22×C8—592no—
158C4⋊Q8—591no—
159#127C2×D5911yescharacteristic
160#126—1181no—
161#125—591no—
162#124—591no—
163#124—1181no—
164#123—1181no—
165C22⋊Q8—591no—
166#121—592no—
167#121—591no—
168#121—1181no—
169C4×Q8C2×D5911yescharacteristic
170C4×D4—592no—
171C4×D4—591no—
172C4×D4—1181no—
173C4×D4—1181no—
174#117—1181no—
175C2×C42—591no—
176#107—592no—
177#106—592no—
178C4⋊C8—592no—
179C4⋊C8—591no—
180C4⋊C8C2×D5911yescharacteristic
181#103—592no—
182#102—592no—
183#102—592no—
184#102C2×D5912yes—
185#41—2364no—
186C2×Q8—1181no—
187C2×Q8C22×D5911yescharacteristic
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—591no—
191C2×D4—1181no—
192C2×D4—1182no—
193C2×D4C22×D5912yes—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4—591no—
197C22×C4—1182no—
198C22×C4—1181no—
199SD16—42no—
200D8—2362no—
201C2×C8—592no—
202C2×C8—2362no—
203C2×C8C22×D5912yes—
204C4⋊C4—21no—
205C4⋊C4—591no—
206C4⋊C4—592no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4—1181no—
210C4⋊C4—1181no—
211C4⋊C4C22×D5911yescharacteristic
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C22⋊C4—1181no—
216C22⋊C4—1182no—
217C22⋊C4—1182no—
218C22⋊C4—1181no—
219C42—21no—
220C42—591no—
221C42—591no—
222C42—591no—
223C42C22×D5911yescharacteristic
224C23—22no—
225C23—591no—
226C23—1181no—
227Q8—21no—
228Q8—21no—
229Q8—2362no—
230D4—22no—
231D4—22no—
232D4—42no—
233D4—42no—
234D4—1181no—
235D4—1181no—
236D4—2362no—
237D4—2364no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—591no—
241C2×C4—591no—
242C2×C4—591no—
243C2×C4—1182no—
244C2×C4—1182no—
245C2×C4—1181no—
246C2×C4—1181no—
247C2×C4—1181no—
248C2×C4—1182no—
249C2×C4—2364no—
250C2×C4—2362no—
251C2×C4D4×D5911yescharacteristic
252C2×C4D4×D5911yescharacteristic
253C2×C4C23×D5911yescharacteristic
254C8—22no—
255C8—1182no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—592no—
260C22—1181no—
261C22—1181no—
262C22—2361no—
263C22—2361no—
264C22—2361no—
265C22C2×D4×D5911yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—1181no—
270C4—1181no—
271C4—1181no—
272C4—2361no—
273C4—2362no—
274C4#1427374812yes—
275C4#1427377211yescharacteristic
276C4#1427377411yescharacteristic
277C2—82no—
278C2—1182no—
279C2—4721no—
280C2#1683798111yescharacteristic
281C2C2×#1427374811yescharacteristic
282C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#460C2
socleC22×C59C22×D4
hypercenter#460D59
hypocenterC59#3247
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. #16837950C2semidirect
2. #16837939C2semidirect
3. #16837704C2semidirect
4. #16837697C2semidirect
5. #16837693C2semidirect
6. #16837637C2semidirect
7. #16837628C2semidirect
8. #16837619C2semidirect
9. #16837594C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#460C2semidirect
150. #460D59semidirect
153. C59#3247semidirect