Finite Group Databasebeta

← #21436335

Subgroups — #21436335

Order 7552.

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

normal subgroups only

This group has 460 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#16838118C211yesmaximal, characteristic, complemented
2D4×D236C211yesmaximal, characteristic, complemented
3#16837750C211yesmaximal, characteristic, complemented
4#16837728C212yesmaximal, complemented
5#16837656C212yesmaximal, complemented
6#16837598C211yesmaximal, characteristic, complemented
7#16837537C212yesmaximal, complemented
8C4×#11745669C211yesmaximal, characteristic, complemented
9#16837479C211yesmaximal, characteristic, complemented
10#16837405C212yesmaximal, complemented
11C59×#476C211yesmaximal, characteristic, complemented
12C22×D236—21no—
13C2×D4×D59C2212yes—
14C2×D472C2212yescomplemented
15C2×#11745669C2211yescharacteristic
16C2×#11745659C2212yescomplemented
17#14273724C2211yescharacteristic
18#14273716—22no—
19#14273702—21no—
20#14273702C2212yes—
21#14273702C2212yescomplemented
22#14273701—21no—
23#14273697—22no—
24C4×D236C2211yescharacteristic
25C4×D236C2211yescharacteristic, complemented
26#14273685—21no—
27#14273685C2212yescomplemented
28#14273660C2211yescharacteristic, complemented
29#14273649C2212yescomplemented
30#14273648C2211yescharacteristic
31#14273647C2211yescharacteristic, complemented
32#14273647C2212yescomplemented
33#14273647C2212yescomplemented
34(C2×D59)⋊C8C2212yescomplemented
35C4×C59⋊C8C2211yescharacteristic, complemented
36C4⋊Q8×C59C2211yescharacteristic, complemented
37C4×D4×C59C2211yescharacteristic
38#106×C59C2212yescomplemented
39C4⋊C8×C59C2211yescharacteristic, complemented
40#102×C59C2212yes—
41C23×D59—22no—
42C2×Q8×C59—21no—
43C2×D4×C59C2311yescharacteristic
44C22×C4×C59—21no—
45C2×C22⋊D59—22no—
46D4×D59—24no—
47D4×D59—42no—
48C2×D236—22no—
49C2×D236—21no—
50C2×D236—22no—
51C2×D236—21no—
52C2×D236—44no—
53C2×D236D411yescharacteristic
54C2×D236C2312yes—
55C2×D236C2311yescharacteristic
56C2×C4×D59—21no—
57C2×C4×D59C2312yes—
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C4⋊C4×C59C2311yescharacteristic
62C22⋊C4×C59—21no—
63C42×C59C2311yescharacteristic
64#11745669—22no—
65(C2×D59)⋊C4—22no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—22no—
69(C2×D59)⋊C4D412yes—
70C4⋊Dic59D411yescharacteristic
71C4⋊Dic59C2311yescharacteristic
72C4×Dic59—22no—
73C2×C59⋊C8C2311yescharacteristic
74C2×C59⋊C8C2311yescharacteristic
75D472—42no—
76#11745659—42no—
77C23×C59—21no—
78C22×D59—21no—
79C22×D59—22no—
80C22×D59—44no—
81C22×D59—44no—
82C22×D59—82no—
83C22×D59C2×D412yes—
84Q8×C59—81no—
85D4×C59—21no—
86D4×C59#4112yes—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—42no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C22⋊D59—44no—
94C2×Dic59—21no—
95C2×Dic59C2×D412yes—
96D236—22no—
97D236—21no—
98D236—22no—
99D236—21no—
100D236—22no—
101D236—44no—
102D236—42no—
103D236—81no—
104D236—82no—
105C4×D59—22no—
106C4×D59—22no—
107C4×D59—42no—
108C8×C59—22no—
109C59⋊C8—21no—
110C59⋊C8—21no—
111C22×C59—22no—
112C22×C59—41no—
113C22×C59—41no—
114C22×C59C22×D411yescharacteristic
115C2×D59—22no—
116C2×D59—22no—
117C2×D59—22no—
118C2×D59—42no—
119C2×D59—41no—
120C2×D59—41no—
121C2×D59—42no—
122C2×D59—41no—
123C2×D59—42no—
124C2×D59—88no—
125C4×C59—21no—
126C4×C59—41no—
127C4×C59—42no—
128C4×C59AGL(1,ℤ/8)12yes—
129C4×C59C2×#4111yescharacteristic
130C4×C59H(5,𝔽2)11yescharacteristic
131Dic59—22no—
132Dic59—41no—
133#3325—591nomaximal, Sylow
134C2×C59—42no—
135C2×C59#54611yescharacteristic
136C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C59#57611yescharacteristic
138D59—42no—
139D59—81no—
140D59—82no—
141#555—591no—
142D42—591no—
143#486—591no—
144#482—592no—
145#476D5911yescharacteristic, complemented
146#469—592no—
147#459—591no—
148#447—592no—
149C4×D8—591no—
150#436—591no—
151#418—592no—
152C59#332511yescharacteristic, complemented, Sylow
153C22×D4—592no—
154C22×D4—1181no—
155C2×D8—591no—
156C2×D8—592no—
157C2×M16—592no—
158C4⋊Q8C2×D5911yescharacteristic, complemented
159#127—591no—
160#124—1182no—
161#121—592no—
162#121—592no—
163#121—1181no—
164#121—1181no—
165#120—1182no—
166C4×D4—591no—
167C4×D4—591no—
168C4×D4C2×D5911yescharacteristic
169#117—592no—
170#117—1181no—
171#107—591no—
172#106C2×D5912yescomplemented
173C4⋊C8C2×D5911yescharacteristic, complemented
174#102—591no—
175#102—592no—
176#102—592no—
177#102—591no—
178#102—592no—
179#102C2×D5912yes—
180C22⋊C8—592no—
181C4×C8—591no—
182C24—1182no—
183C2×Q8—21no—
184C2×D4—591no—
185C2×D4—592no—
186C2×D4—591no—
187C2×D4—1182no—
188C2×D4—1182no—
189C2×D4—1182no—
190C2×D4—1184no—
191C2×D4—1181no—
192C2×D4—1181no—
193C2×D4—2364no—
194C2×D4—2362no—
195C2×D4C22×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—592no—
198C22×C4—1181no—
199D8—1182no—
200D8—2362no—
201M16—2362no—
202C2×C8—591no—
203C2×C8—591no—
204C2×C8C22×D5912yes—
205C4⋊C4—21no—
206C4⋊C4—591no—
207C4⋊C4—591no—
208C4⋊C4C22×D5912yes—
209C4⋊C4C22×D5911yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—592no—
212C22⋊C4—1182no—
213C22⋊C4—1182no—
214C22⋊C4—1182no—
215C22⋊C4—1181no—
216C42—1182no—
217C42C22×D5911yescharacteristic
218C23—21no—
219C23—592no—
220C23—1181no—
221C23—1182no—
222C23—4722no—
223C23—2364no—
224C23—2364no—
225Q8—81no—
226D4—21no—
227D4—1182no—
228D4—1181no—
229D4—1182no—
230D4—1181no—
231D4—1182no—
232D4—4721no—
233D4—4722no—
234D4—2364no—
235D4—2364no—
236D4—2362no—
237D4#1174568912yes—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—592no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—1181no—
245C2×C4—2362no—
246C2×C4D4×D5911yescharacteristic
247C2×C4D4×D5911yescharacteristic
248C2×C4C23×D5911yescharacteristic
249C8—22no—
250C8—1181no—
251C8—1181no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—1182no—
256C22—1182no—
257C22—1182no—
258C22—4728no—
259C22—2361no—
260C22—2362no—
261C22—2361no—
262C22—2362no—
263C22—2362no—
264C22—2361no—
265C22C2×D4×D5911yescharacteristic
266C4—21no—
267C4—41no—
268C4—42no—
269C4—1182no—
270C4—2361no—
271C4#1427375412yes—
272C4C2×#1174568911yescharacteristic
273C4#1427377311yescharacteristic
274C2—42no—
275C2—4722no—
276C2—4721no—
277C2—2362no—
278C2#1683804311yescharacteristic
279C2C2×#1427375411yescharacteristic
280C2#1683820611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#476C2
socleC22×C59C22×D4
hypercenter#476D59
hypocenterC59#3325
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16838118C2semidirect
2. D4×D236C2semidirect
3. #16837750C2semidirect
4. #16837728C2semidirect
5. #16837656C2semidirect
6. #16837598C2semidirect
7. #16837537C2semidirect
8. C4×#11745669C2semidirect
9. #16837479C2semidirect
10. #16837405C2semidirect
11. C59×#476C2semidirect
14. C2×D472C22semidirect
16. C2×#11745659C22semidirect
21. #14273702C22semidirect
25. C4×D236C22semidirect
27. #14273685C22semidirect
28. #14273660C22semidirect
29. #14273649C22semidirect
31. #14273647C22semidirect
32. #14273647C22semidirect
33. #14273647C22semidirect
34. (C2×D59)⋊C8C22semidirect
35. C4×C59⋊C8C22semidirect
36. C4⋊Q8×C59C22semidirect
38. #106×C59C22semidirect
39. C4⋊C8×C59C22semidirect
145. #476D59semidirect
152. C59#3325semidirect
158. C4⋊Q8C2×D59semidirect
172. #106C2×D59semidirect
173. C4⋊C8C2×D59semidirect