Finite Group Databasebeta

← #21435070

Subgroups — #21435070

Order 7552.

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

normal subgroups only

This group has 400 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#16837950C211yesmaximal, characteristic, complemented
2#16837934C211yesmaximal, characteristic, complemented
3#16837785C212yesmaximal, complemented
4#16837755C212yesmaximal, complemented
5#16837613C211yesmaximal, characteristic, complemented
6#16837607C211yesmaximal, characteristic, complemented
7#16837599C211yesmaximal, characteristic, complemented
8#16837565C212yesmaximal, complemented
9#16837544C212yesmaximal, complemented
10#16837454C211yesmaximal, characteristic, complemented
11C59×#459C211yesmaximal, characteristic, complemented
12C2×#11745687C2212yes—
13C2×Dic236C2212yes—
14C2×#11745670C2212yes—
15C2×#11745670C2212yes—
16#14273727C2211yescharacteristic
17#14273720—21no—
18#14273718C2211yescharacteristic
19#14273714C2211yescharacteristic
20#14273714C2212yes—
21#14273709—21no—
22#14273707C2211yescharacteristic
23#14273698—21no—
24#14273698—21no—
25#14273698C2211yescharacteristic
26C4×Dic118C2211yescharacteristic
27D4×Dic59—21no—
28D4×Dic59—21no—
29C4×C22⋊D59—21no—
30#14273686—21no—
31C42×D59C2211yescharacteristic
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273650C2212yes—
35#14273648C2212yes—
36(C2×D59)⋊C8C2212yes—
37C8×Dic59C2212yes—
38C2×D8×C59C2212yes—
39#127×C59C2211yescharacteristic
40C4×D4×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#102×C59C2212yes—
43C2×D4×C59—21no—
44C2×D4×C59—21no—
45C2×D4×C59C2312yes—
46C2×D4×C59C2311yescharacteristic
47C22×C4×C59—21no—
48C2×C22⋊D59—21no—
49C2×C22⋊D59—22no—
50C22×Dic59—22no—
51#11745687—42no—
52#11745687—42no—
53C2×C4×D59D411yescharacteristic
54C2×C4×D59D411yescharacteristic
55C2×C4×D59C2311yescharacteristic
56C2×Dic118C2312yes—
57C2×Dic118C2311yescharacteristic
58D8×C59—42no—
59C2×C8×C59C2312yes—
60C4⋊C4×C59C2311yescharacteristic
61C22⋊C4×C59—21no—
62C42×C59C2311yescharacteristic
63C22⋊Dic59—21no—
64C22⋊Dic59—21no—
65C22⋊Dic59—21no—
66C22⋊Dic59—22no—
67C22⋊Dic59—22no—
68#11745670—42no—
69#11745670—42no—
70(C2×D59)⋊C4—21no—
71C4⋊Dic59—21no—
72C4⋊Dic59—21no—
73C4⋊Dic59—21no—
74C4⋊Dic59—21no—
75C4⋊Dic59C2311yescharacteristic
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78C4×Dic59—21no—
79C4×Dic59D411yescharacteristic
80C4×Dic59D411yescharacteristic
81C4×Dic59C2311yescharacteristic
82C2×C59⋊C8C2312yes—
83Dic236—42no—
84C23×C59—21no—
85C23×C59—22no—
86C22×D59C2×D411yescharacteristic
87D4×C59—21no—
88D4×C59—22no—
89D4×C59—21no—
90D4×C59—22no—
91D4×C59—42no—
92D4×C59—42no—
93C2×C4×C59—21no—
94C2×C4×C59—42no—
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2411yescharacteristic
98C22⋊D59—44no—
99C22⋊D59—42no—
100C2×Dic59—21no—
101C2×Dic59—21no—
102C2×Dic59—22no—
103C2×Dic59—44no—
104C2×Dic59C2×D411yescharacteristic
105C2×Dic59C2×D411yescharacteristic
106C2×Dic59C2×D411yescharacteristic
107C4×D59—22no—
108C4×D59—21no—
109C4×D59—21no—
110C4×D59—41no—
111Dic118—21no—
112Dic118—22no—
113Dic118—21no—
114Dic118—22no—
115C8×C59—22no—
116C59⋊C8—22no—
117C22×C59—42no—
118C22×C59—41no—
119C22×C59—41no—
120C22×C59—42no—
121C22×C59—41no—
122C22×C59—42no—
123C22×C59C22×D411yescharacteristic
124C2×D59—21no—
125C2×D59—21no—
126C2×D59—21no—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59#13512yes—
130C4×C59H(5,𝔽2)11yescharacteristic
131C4×C59H(5,𝔽2)11yescharacteristic
132Dic59—21no—
133Dic59—21no—
134Dic59—21no—
135Dic59—41no—
136Dic59—42no—
137Dic59—41no—
138#3212—591nomaximal, Sylow
139C2×C59—82no—
140C2×C59—81no—
141C2×C59#53511yescharacteristic
142C2×C59C2×#13511yescharacteristic
143C2×C59#57511yescharacteristic
144D59—41no—
145#532—591no—
146#529—591no—
147#495—592no—
148#488—592no—
149#462—591no—
150#461—591no—
151#460—591no—
152#459D5911yescharacteristic, complemented
153#452—592no—
154#449—592no—
155#431—591no—
156C59#321211yescharacteristic, complemented, Sylow
157C2×#41—592no—
158C2×Q16—592no—
159C2×SD16—592no—
160C2×SD16—592no—
161C2×D8C2×D5912yes—
162C4⋊Q8—591no—
163#127C2×D5911yescharacteristic
164#126—1181no—
165#125—591no—
166#124—591no—
167#124—592no—
168#123—1181no—
169C22⋊Q8—591no—
170#121—591no—
171#121—1181no—
172#121—1181no—
173C4×Q8—591no—
174C4×D4—1181no—
175C4×D4—1181no—
176C4×D4—1181no—
177C4×D4C2×D5911yescharacteristic
178#117—1181no—
179C2×C42—591no—
180C4⋊C8—591no—
181C4⋊C8C2×D5911yescharacteristic
182#103—592no—
183#103—592no—
184#102—592no—
185#102C2×D5912yes—
186C22⋊C8—592no—
187C4×C8—592no—
188#41—2362no—
189#41—2362no—
190C2×Q8—592no—
191C2×Q8—591no—
192C2×D4—21no—
193C2×D4—21no—
194C2×D4—1181no—
195C2×D4—1182no—
196C2×D4C22×D5912yes—
197C2×D4C22×D5911yescharacteristic
198C22×C4—21no—
199C22×C4—591no—
200C22×C4—591no—
201C22×C4—591no—
202C22×C4—1182no—
203Q16—2362no—
204SD16—2362no—
205SD16—2362no—
206D8—42no—
207C2×C8—592no—
208C2×C8C22×D5912yes—
209C4⋊C4—591no—
210C4⋊C4—1181no—
211C4⋊C4—1181no—
212C4⋊C4—1181no—
213C4⋊C4—1181no—
214C4⋊C4—1181no—
215C4⋊C4—1181no—
216C4⋊C4C22×D5911yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—1181no—
219C22⋊C4—1181no—
220C22⋊C4—1181no—
221C22⋊C4—1182no—
222C22⋊C4—1182no—
223C22⋊C4—1181no—
224C42—591no—
225C42—591no—
226C42—591no—
227C42—1181no—
228C42C22×D5911yescharacteristic
229C23—21no—
230C23—22no—
231C23—591no—
232Q8—1181no—
233Q8—1182no—
234Q8—1181no—
235Q8—1182no—
236D4—21no—
237D4—22no—
238D4—21no—
239D4—22no—
240D4—42no—
241D4—42no—
242D4—2362no—
243D4—2364no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—591no—
247C2×C4—591no—
248C2×C4—591no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—1181no—
252C2×C4—1181no—
253C2×C4—1181no—
254C2×C4—1182no—
255C2×C4—2361no—
256C2×C4—2364no—
257C2×C4D4×D5911yescharacteristic
258C2×C4D4×D5911yescharacteristic
259C2×C4C23×D5911yescharacteristic
260C8—22no—
261C8—1182no—
262C22—41no—
263C22—42no—
264C22—42no—
265C22—41no—
266C22—42no—
267C22—41no—
268C22—1181no—
269C22—1181no—
270C22—1181no—
271C22C2×D4×D5911yescharacteristic
272C4—21no—
273C4—41no—
274C4—1181no—
275C4—1181no—
276C4—1181no—
277C4—2361no—
278C4—2362no—
279C4—2361no—
280C4#1427374612yes—
281C4#1427377211yescharacteristic
282C4#1427377311yescharacteristic
283C2—81no—
284C2—82no—
285C2—2361no—
286C2#1683796811yescharacteristic
287C2C2×#1427374611yescharacteristic
288C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3212
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16837950C2semidirect
2. #16837934C2semidirect
3. #16837785C2semidirect
4. #16837755C2semidirect
5. #16837613C2semidirect
6. #16837607C2semidirect
7. #16837599C2semidirect
8. #16837565C2semidirect
9. #16837544C2semidirect
10. #16837454C2semidirect
11. C59×#459C2semidirect
152. #459D59semidirect
156. C59#3212semidirect