Finite Group Databasebeta

← #21434938

Subgroups — #21434938

Order 7552.

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

normal subgroups only

This group has 418 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#16837913C212yesmaximal, complemented
2#16837744C212yesmaximal, complemented
3#16837727C212yesmaximal, complemented
4#16837660C211yesmaximal, characteristic, complemented
5#16837655C211yesmaximal, characteristic, complemented
6#16837648C212yesmaximal, complemented
7#16837566C212yesmaximal, complemented
8#16837549C212yesmaximal, complemented
9C59×#407C211yesmaximal, characteristic, complemented
10C2×#11745685C2212yes—
11C2×Dic236C2211yescharacteristic, complemented
12C2×#11745660C2212yescomplemented
13C2×D472C2211yescharacteristic, complemented
14#14273710—22no—
15#14273706C2212yes—
16#14273706C2212yes—
17#14273701C2212yes—
18#14273701C2212yes—
19#14273696—22no—
20C4×C22⋊D59—22no—
21C4×C22⋊D59—22no—
22#14273686C2212yes—
23#14273661C2212yescomplemented
24#14273659C2211yescharacteristic, complemented
25#14273659C2211yescharacteristic, complemented
26#14273652C2212yescomplemented
27#14273652C2212yescomplemented
28#14273649C2212yescomplemented
29#14273649C2212yescomplemented
30C23×C4×C59C2211yescharacteristic
31C2×M16×C59C2211yescharacteristic
32C2×M16×C59C2211yescharacteristic
33C22⋊C8×C59C2212yes—
34C22⋊C8×C59C2212yes—
35C24×C59D411yescharacteristic
36C22×C4×C59—41no—
37C22×C4×C59—41no—
38C22×C4×C59D411yescharacteristic
39C22×C4×C59D412yes—
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C2×C22⋊D59—22no—
43C2×C22⋊D59—22no—
44C2×C22⋊D59—22no—
45#11745685—42no—
46#11745685—42no—
47C2×D236C2312yes—
48C2×C4×D59—22no—
49C2×Dic118C2312yes—
50M16×C59—41no—
51M16×C59—41no—
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2312yes—
54C2×C8×C59C2311yescharacteristic
55C22⋊Dic59—22no—
56C22⋊Dic59—22no—
57C22⋊Dic59—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60C4⋊Dic59C2312yes—
61C4⋊Dic59C2312yes—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64C4×Dic59—22no—
65Dic236—41no—
66D472—41no—
67#11745660—42no—
68C23×C59—41no—
69C23×C59—42no—
70C23×C59C2×D412yes—
71C23×C59C2×D411yescharacteristic
72C22×D59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—41no—
78C2×C4×C59—42no—
79C2×C4×C59C2×D412yes—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C22⋊D59—44no—
83C22⋊D59—44no—
84C22⋊D59—44no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88D236—22no—
89D236—22no—
90C4×D59—44no—
91Dic118—22no—
92Dic118—22no—
93C8×C59—22no—
94C8×C59—21no—
95C8×C59—21no—
96C22×C59—22no—
97C22×C59—21no—
98C22×C59—22no—
99C22×C59—22no—
100C22×C59—22no—
101C22×C59—44no—
102C22×C59C22×D411yescharacteristic
103C2×D59—42no—
104C2×D59—42no—
105C2×D59—42no—
106C4×C59—22no—
107C4×C59—21no—
108C4×C59H(5,𝔽2)11yescharacteristic
109C4×C59H(5,𝔽2)11yescharacteristic
110Dic59—42no—
111Dic59—42no—
112Dic59—42no—
113#3197—591nomaximal, Sylow
114C2×C59—42no—
115C2×C59—41no—
116C2×C59#53411yescharacteristic
117C2×C59#57512yes—
118D59—82no—
119#525—592no—
120#485—592no—
121#482—592no—
122#470—591no—
123#469—591no—
124#468—592no—
125#452—592no—
126#449—592no—
127#407D5911yescharacteristic, complemented
128C59#319711yescharacteristic, complemented, Sylow
129C2×#41—592no—
130C23×C4C2×D5911yescharacteristic
131C2×Q16—591no—
132C2×SD16—592no—
133C2×D8—591no—
134C2×M16C2×D5911yescharacteristic
135C2×M16C2×D5911yescharacteristic
136#123—1182no—
137C22⋊Q8—592no—
138C22⋊Q8—592no—
139#121—592no—
140#121—592no—
141#120—1182no—
142C4×D4—1182no—
143C4×D4—1182no—
144#117—592no—
145#107—592no—
146#106—591no—
147#106—591no—
148#103—592no—
149#103—592no—
150#102—592no—
151#102—592no—
152C22⋊C8C2×D5912yes—
153C22⋊C8C2×D5912yes—
154C24D23611yescharacteristic
155#41—2362no—
156#41—2362no—
157C2×Q8—592no—
158C2×D4—592no—
159C2×D4—1182no—
160C2×D4—1182no—
161C2×D4—1182no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—1182no—
165C22×C4D23611yescharacteristic
166C22×C4D23612yes—
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169Q16—2361no—
170SD16—2362no—
171D8—2361no—
172M16—41no—
173M16—41no—
174C2×C8C22×D5911yescharacteristic
175C2×C8C22×D5912yes—
176C2×C8C22×D5911yescharacteristic
177C4⋊C4—592no—
178C4⋊C4—592no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C42—1182no—
187C23—41no—
188C23—42no—
189C23—1182no—
190C23C2×D23611yescharacteristic
191C23C2×D23612yes—
192Q8—1182no—
193Q8—1182no—
194D4—1182no—
195D4—1182no—
196D4—2364no—
197D4—2364no—
198D4—2364no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4—2364no—
209C2×C4C2×D23612yes—
210C2×C4C2×D23611yescharacteristic
211C2×C4C23×D5911yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—2362no—
222C22—2362no—
223C22—2362no—
224C22C22×D23611yescharacteristic
225C4—22no—
226C4—21no—
227C4—2362no—
228C4—2362no—
229C4—2362no—
230C4#1427377211yescharacteristic
231C4#1427377211yescharacteristic
232C2—41no—
233C2—42no—
234C2—4722no—
235C2#1683796411yescharacteristic
236C2#1683820212yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#407C2
socleC22×C59C22×D4
hypercenter#407D59
hypocenterC59#3197
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #16837913C2semidirect
2. #16837744C2semidirect
3. #16837727C2semidirect
4. #16837660C2semidirect
5. #16837655C2semidirect
6. #16837648C2semidirect
7. #16837566C2semidirect
8. #16837549C2semidirect
9. C59×#407C2semidirect
11. C2×Dic236C22semidirect
12. C2×#11745660C22semidirect
13. C2×D472C22semidirect
23. #14273661C22semidirect
24. #14273659C22semidirect
25. #14273659C22semidirect
26. #14273652C22semidirect
27. #14273652C22semidirect
28. #14273649C22semidirect
29. #14273649C22semidirect
127. #407D59semidirect
128. C59#3197semidirect