Finite Group Databasebeta

← #21435170

Subgroups — #21435170

Order 7552.

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

normal subgroups only

This group has 396 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#16838014C211yesmaximal, characteristic, complemented
2#16837971C211yesmaximal, characteristic
3#16837796C211yesmaximal, characteristic, complemented
4#16837775C211yesmaximal, characteristic, complemented
5#16837767C211yesmaximal, characteristic, complemented
6#16837757C211yesmaximal, characteristic, complemented
7#16837625C212yesmaximal, complemented
8#16837603C212yesmaximal, complemented
9#16837566C212yesmaximal, complemented
10#16837555C212yesmaximal, complemented
11C59×#433C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×D236C2211yescharacteristic
14C2×Dic236C2212yescomplemented
15C2×#11745660C2212yes—
16C2×#11745660C2212yes—
17C2×#11745660C2212yescomplemented
18#14273727C2211yescharacteristic, complemented
19#14273724C2211yescharacteristic
20#14273724C2211yescharacteristic
21#14273720—22no—
22#14273719C2211yescharacteristic, complemented
23#14273717—22no—
24#14273715C2211yescharacteristic
25#14273715C2211yescharacteristic
26#14273706C2212yes—
27#14273702—22no—
28#14273697—22no—
29C4×Dic118C2212yescomplemented
30#14273652C2212yescomplemented
31#14273649C2212yes—
32#14273649C2212yes—
33#14273649C2212yescomplemented
34#117×C59C2211yescharacteristic
35C4⋊C8×C59C2212yescomplemented
36C22⋊C8×C59C2212yes—
37#97×C59C2211yescharacteristic, complemented
38C4×C8×C59C2211yescharacteristic, complemented
39C23×D59—21no—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—21no—
42#11745685—42no—
43C2×D236—21no—
44C2×D236—22no—
45C2×D236—22no—
46C2×D236—42no—
47C2×D236C2311yescharacteristic
48C2×D236C2311yescharacteristic
49C2×D236C2311yescharacteristic
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic
52C2×Dic118C2312yes—
53C2×C8×C59C2312yes—
54C2×C8×C59C2312yes—
55C4⋊C4×C59D412yes—
56C22⋊C4×C59D412yes—
57C42×C59C2311yescharacteristic
58C42×C59C2311yescharacteristic
59C22⋊Dic59—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59—22no—
63C4⋊Dic59C2312yes—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67C4×Dic59—22no—
68Dic236—42no—
69#11745660—42no—
70#11745660—42no—
71#11745660—42no—
72C23×C59C2×D411yescharacteristic
73C22×D59—21no—
74C22×D59—21no—
75C22×D59—21no—
76C22×D59—42no—
77C22×D59—82no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D412yes—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2411yescharacteristic
83C22⋊D59—42no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87D236—22no—
88D236—22no—
89D236—22no—
90D236—42no—
91D236—82no—
92D236—82no—
93C4×D59—42no—
94Dic118—22no—
95Dic118—22no—
96Dic118—22no—
97C8×C59—22no—
98C8×C59—22no—
99C22×C59—21no—
100C22×C59—22no—
101C22×C59C22×D411yescharacteristic
102C2×D59—41no—
103C2×D59—41no—
104C2×D59—41no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—84no—
109C4×C59—21no—
110C4×C59—22no—
111C4×C59—22no—
112C4×C59H(5,𝔽2)12yes—
113Dic59—41no—
114Dic59—42no—
115Dic59—42no—
116#3222—591nomaximal, Sylow
117C2×C59—41no—
118C2×C59#53511yescharacteristic
119C2×C59#57712yes—
120D59—81no—
121D59—81no—
122D59—81no—
123#541—591no—
124#535—591no—
125#497—591no—
126#492—591no—
127#490—591no—
128#488—591no—
129#464—592no—
130#460—592no—
131#452—592no—
132#450—592no—
133#433D5911yescharacteristic, complemented
134C59#322211yescharacteristic, complemented, Sylow
135C2×#41—591no—
136C22×D4—591no—
137C2×Q16—592no—
138C2×SD16—592no—
139C2×SD16—592no—
140C2×SD16—592no—
141C4⋊Q8—591no—
142#127—591no—
143#127—591no—
144#126—1182no—
145#125—591no—
146#125—1182no—
147#124—591no—
148#124—591no—
149C22⋊Q8—592no—
150#121—1182no—
151#120—1182no—
152C4×Q8—592no—
153#117C2×D5911yescharacteristic
154C4⋊C8C2×D5912yescomplemented
155#103—592no—
156#102—592no—
157#102—592no—
158#102—592no—
159C22⋊C8C2×D5912yes—
160#97C2×D5911yescharacteristic, complemented
161C4×C8C2×D5911yescharacteristic, complemented
162C24—1181no—
163#41—2362no—
164C2×Q8—591no—
165C2×Q8—592no—
166C2×D4—591no—
167C2×D4—591no—
168C2×D4—591no—
169C2×D4—1181no—
170C2×D4—1182no—
171C2×D4—1182no—
172C2×D4—1181no—
173C2×D4—2362no—
174C22×C4—1181no—
175C22×C4C22×D5911yescharacteristic
176Q16—2362no—
177SD16—2362no—
178SD16—2362no—
179SD16—2362no—
180C2×C8C22×D5912yes—
181C2×C8C22×D5912yes—
182C4⋊C4—592no—
183C4⋊C4—1182no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4D23612yes—
188C22⋊C4—1182no—
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C22⋊C4D23612yes—
192C42—1182no—
193C42C22×D5911yescharacteristic
194C42C22×D5911yescharacteristic
195C23—1181no—
196C23—1181no—
197C23—1181no—
198C23—4722no—
199C23—2362no—
200C23C2×D23611yescharacteristic
201Q8—1182no—
202Q8—1182no—
203Q8—1182no—
204D4—1182no—
205D4—1182no—
206D4—1182no—
207D4—4722no—
208D4—4722no—
209D4—2362no—
210D4—2362no—
211C2×C4—22no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1181no—
215C2×C4—2362no—
216C2×C4C2×D23612yes—
217C2×C4C2×D23612yes—
218C2×C4C2×D23611yescharacteristic
219C2×C4C23×D5911yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—4724no—
225C22—2362no—
226C22—2362no—
227C22—2362no—
228C22—2361no—
229C22—2361no—
230C22—2361no—
231C22C22×D23611yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—2362no—
236C4—2361no—
237C4—2362no—
238C4#1427377312yes—
239C2—41no—
240C2—4721no—
241C2—4721no—
242C2—4721no—
243C2#1683797111yescharacteristic
244C2#1683821412yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3222
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838014C2semidirect
3. #16837796C2semidirect
4. #16837775C2semidirect
5. #16837767C2semidirect
6. #16837757C2semidirect
7. #16837625C2semidirect
8. #16837603C2semidirect
9. #16837566C2semidirect
10. #16837555C2semidirect
11. C59×#433C2semidirect
14. C2×Dic236C22semidirect
17. C2×#11745660C22semidirect
18. #14273727C22semidirect
22. #14273719C22semidirect
29. C4×Dic118C22semidirect
30. #14273652C22semidirect
33. #14273649C22semidirect
35. C4⋊C8×C59C22semidirect
37. #97×C59C22semidirect
38. C4×C8×C59C22semidirect
133. #433D59semidirect
134. C59#3222semidirect
154. C4⋊C8C2×D59semidirect
160. #97C2×D59semidirect
161. C4×C8C2×D59semidirect