Finite Group Databasebeta

← #21435404

Subgroups — #21435404

Order 7552.

436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837949C211yesmaximal, characteristic, complemented
3#16837683C211yesmaximal, characteristic, complemented
4#16837682C211yesmaximal, characteristic, complemented
5#16837680C212yesmaximal, complemented
6#16837637C212yesmaximal, complemented
7#16837635C212yesmaximal, complemented
8#16837595C212yesmaximal, complemented
9#16837594C211yesmaximal, characteristic, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#459C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×#11745687—21no—
14C2×#11745669C2212yes—
15C2×C8×D59C2212yes—
16#14273727C2211yescharacteristic
17#14273726C2211yescharacteristic
18#14273723C2211yescharacteristic
19#14273714—21no—
20#14273713—21no—
21#14273702C2211yescharacteristic
22#14273700—21no—
23#14273698—21no—
24#14273698C2211yescharacteristic
25#14273698C2212yes—
26C4×D236C2211yescharacteristic
27D4×Dic59—21no—
28D4×Dic59C2212yes—
29C4×C22⋊D59—21no—
30C42×D59C2211yescharacteristic
31#14273661C2212yes—
32#14273660C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273649C2212yes—
36#14273648C2212yes—
37#14273648C2212yes—
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—22no—
49C2×C22⋊D59—21no—
50C2×C22⋊D59—21no—
51C2×C22⋊D59—21no—
52C22×Dic59—22no—
53#11745687—44no—
54#11745685—44no—
55C2×D236—21no—
56C2×D236C2311yescharacteristic
57C2×C4×D59—21no—
58C2×C4×D59D411yescharacteristic
59C2×C4×D59D411yescharacteristic
60C2×C4×D59C2311yescharacteristic
61C2×Dic118—21no—
62C2×Dic118—21no—
63D8×C59—42no—
64C2×C8×C59C2312yes—
65C4⋊C4×C59C2311yescharacteristic
66C22⋊C4×C59—21no—
67C42×C59C2311yescharacteristic
68C22⋊Dic59—21no—
69C22⋊Dic59—22no—
70C22⋊Dic59—22no—
71#11745669—42no—
72(C2×D59)⋊C4—21no—
73(C2×D59)⋊C4—21no—
74C4⋊Dic59—21no—
75C4⋊Dic59C2311yescharacteristic
76C4⋊Dic59C2312yes—
77Dic59⋊C4—21no—
78C4×Dic59D411yescharacteristic
79C4×Dic59D411yescharacteristic
80C4×Dic59C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82C8×D59—42no—
83C23×C59—22no—
84C23×C59—21no—
85C22×D59—21no—
86C22×D59C2×D411yescharacteristic
87D4×C59—22no—
88D4×C59—21no—
89D4×C59—22no—
90D4×C59—21no—
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—42no—
99C22⋊D59—42no—
100C22⋊D59—44no—
101C22⋊D59—42no—
102C2×Dic59—21no—
103C2×Dic59—22no—
104C2×Dic59—44no—
105C2×Dic59C2×D411yescharacteristic
106C2×Dic59C2×D411yescharacteristic
107C2×Dic59C2×D411yescharacteristic
108D236—21no—
109D236—21no—
110D236—42no—
111C4×D59—21no—
112C4×D59—21no—
113C4×D59—41no—
114C4×D59—42no—
115C4×D59D814yescomplemented
116Dic118—42no—
117Dic118—42no—
118C8×C59—22no—
119C59⋊C8—22no—
120C22×C59—42no—
121C22×C59—41no—
122C22×C59—42no—
123C22×C59—41no—
124C22×C59—41no—
125C22×C59—42no—
126C22×C59C22×D411yescharacteristic
127C2×D59—21no—
128C2×D59—21no—
129C2×D59—41no—
130C2×D59—41no—
131C2×D59—41no—
132C2×D59C2×D812yes—
133C4×C59—21no—
134C4×C59—41no—
135C4×C59C2×D812yes—
136C4×C59H(5,𝔽2)11yescharacteristic
137C4×C592−1+411yescharacteristic
138Dic59—21no—
139Dic59—21no—
140Dic59—41no—
141Dic59—42no—
142Dic59C2×D812yes—
143#3245—591nomaximal, Sylow
144C2×C59—82no—
145C2×C59—81no—
146C2×C59#53711yescharacteristic
147C2×C59C22×D811yescharacteristic
148C2×C59#57511yescharacteristic
149D59—22no—
150D59—81no—
151#532—591no—
152#532—591no—
153#474—591no—
154#474—591no—
155#474—592no—
156#466—592no—
157#466—592no—
158#459—592no—
159#459—591no—
160#459D5911yescharacteristic, complemented
161C2×C4⋊C8—591no—
162C59#324511yescharacteristic, complemented, Sylow
163C2×#41—1181no—
164C2×#41—1181no—
165C2×D8—592no—
166C2×D8C2×D5912yes—
167C22×C8—592no—
168C4⋊Q8—591no—
169C4⋊Q8—591no—
170#127—591no—
171#127C2×D5911yescharacteristic
172#124—1181no—
173#124—1181no—
174#121—591no—
175#121—592no—
176#121—591no—
177#121—1181no—
178#121—1181no—
179C4×D4—592no—
180C4×D4—591no—
181C4×D4—1181no—
182C4×D4—1181no—
183C4×D4C2×D5911yescharacteristic
184C2×C42—591no—
185#107—592no—
186#107—592no—
187C4⋊C8—592no—
188C4⋊C8—591no—
189C4⋊C8C2×D5911yescharacteristic
190#102—592no—
191#102—592no—
192#102—592no—
193#102C2×D5912yes—
194#41—2364no—
195#41—2364no—
196C2×Q8—1181no—
197C2×Q8—1181no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—591no—
201C2×D4—1181no—
202C2×D4—1181no—
203C2×D4—1181no—
204C2×D4—1181no—
205C2×D4—1182no—
206C2×D4C22×D5911yescharacteristic
207C2×D4C22×D5912yes—
208C22×C4—21no—
209C22×C4—591no—
210C22×C4—591no—
211C22×C4—591no—
212C22×C4—1182no—
213C22×C4—1181no—
214D8—42no—
215D8—2362no—
216C2×C8—592no—
217C2×C8—2362no—
218C2×C8C22×D5912yes—
219C4⋊C4—591no—
220C4⋊C4—592no—
221C4⋊C4—1181no—
222C4⋊C4—1181no—
223C4⋊C4C22×D5911yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1181no—
226C22⋊C4—1182no—
227C22⋊C4—1181no—
228C22⋊C4—1182no—
229C22⋊C4—1181no—
230C42—591no—
231C42—591no—
232C42—591no—
233C42C22×D5911yescharacteristic
234C23—21no—
235C23—22no—
236C23—591no—
237C23—1181no—
238Q8—2362no—
239Q8—2362no—
240D4—21no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—42no—
246D4—1181no—
247D4—1181no—
248D4—2362no—
249D4—2362no—
250D4—2362no—
251D4—2362no—
252D4—2364no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—591no—
256C2×C4—594no—
257C2×C4—591no—
258C2×C4—591no—
259C2×C4—1181no—
260C2×C4—1181no—
261C2×C4—1181no—
262C2×C4—1182no—
263C2×C4—2361no—
264C2×C4—2364no—
265C2×C4—2362no—
266C2×C4D4×D5911yescharacteristic
267C2×C4D4×D5911yescharacteristic
268C2×C4C23×D5911yescharacteristic
269C8—22no—
270C8—1182no—
271C22—41no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—592no—
278C22—1181no—
279C22—1181no—
280C22—2361no—
281C22—2361no—
282C22—2361no—
283C22C2×D4×D5911yescharacteristic
284C4—21no—
285C4—41no—
286C4—592no—
287C4—1181no—
288C4—1181no—
289C4—2362no—
290C4—2361no—
291C4D8×D5912yes—
292C4#1427377211yescharacteristic
293C4#1427377411yescharacteristic
294C2—81no—
295C2—82no—
296C2—1182no—
297C2—4721no—
298C2#1683798111yescharacteristic
299C2C2×D8×D5911yescharacteristic
300C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3245
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. #16837949C2semidirect
3. #16837683C2semidirect
4. #16837682C2semidirect
5. #16837680C2semidirect
6. #16837637C2semidirect
7. #16837635C2semidirect
8. #16837595C2semidirect
9. #16837594C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#459C2semidirect
115. C4×D59D8semidirect
160. #459D59semidirect
162. C59#3245semidirect