Finite Group Databasebeta

← #21435093

Subgroups — #21435093

Order 7552.

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

normal subgroups only

This group has 434 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#16837952C211yesmaximal, characteristic, complemented
2#16837952C211yesmaximal, characteristic, complemented
3#16837791C212yesmaximal, complemented
4#16837762C212yesmaximal, complemented
5#16837608C212yesmaximal, complemented
6#16837598C212yesmaximal, complemented
7#16837549C214yesmaximal, complemented
8C59×#432C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10C2×#11745685C2212yes—
11C2×#11745660C2214yes—
12C2×D472C2214yes—
13#14273727C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273724C2211yescharacteristic
16#14273724C2211yescharacteristic
17#14273715—21no—
18#14273715C2212yes—
19#14273701—21no—
20#14273701—21no—
21#14273701—21no—
22#14273701C2212yes—
23C4×D236—21no—
24C4×D236—21no—
25C4×D236—21no—
26C4×D236C2212yes—
27#14273652C2214yes—
28#14273649C2214yes—
29C2×C42×C59C2211yescharacteristic
30C4⋊C8×C59C2212yes—
31C22⋊C8×C59C2212yes—
32#97×C59C2212yes—
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C2×C22⋊D59—22no—
37C2×C22⋊D59—22no—
38#11745685—44no—
39#11745685—44no—
40C2×D236—21no—
41C2×D236—21no—
42C2×D236—21no—
43C2×D236—21no—
44C2×D236C2312yes—
45C2×D236C2312yes—
46C2×C4×D59—22no—
47C2×C4×D59—22no—
48C2×Dic118—21no—
49C2×Dic118C2312yes—
50C2×C8×C59C2314yes—
51C42×C59D411yescharacteristic
52C42×C59D411yescharacteristic
53C42×C59C2311yescharacteristic
54C42×C59C2311yescharacteristic
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59C4⋊Dic59—21no—
60C4⋊Dic59—21no—
61C4⋊Dic59—21no—
62C4⋊Dic59C2312yes—
63D472—44no—
64#11745660—44no—
65C23×C59C2×D411yescharacteristic
66C22×D59—22no—
67C22×D59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—41no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2411yescharacteristic
77C22⋊D59—44no—
78C22⋊D59—44no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81D236—22no—
82D236—22no—
83D236—24no—
84D236—42no—
85D236—42no—
86D236—42no—
87D236—42no—
88C4×D59—44no—
89C4×D59—44no—
90Dic118—24no—
91Dic118—42no—
92C8×C59—24no—
93C22×C59—21no—
94C22×C59—21no—
95C22×C59—21no—
96C22×C59C22×D411yescharacteristic
97C2×D59—42no—
98C2×D59—42no—
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C4×C59—21no—
104C4×C59—21no—
105C4×C59—21no—
106C4×C59—21no—
107C4×C59AGL(1,ℤ/8)12yes—
108C4×C59H(5,𝔽2)12yes—
109Dic59—42no—
110Dic59—42no—
111#3214—591nomaximal, Sylow
112C2×C59—41no—
113C2×C59#53511yescharacteristic
114C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C59#57511yescharacteristic
116D59—82no—
117D59—82no—
118#532—591no—
119#532—591no—
120#496—592no—
121#489—592no—
122#461—592no—
123#459—592no—
124#449—594no—
125#432D5911yescharacteristic, complemented
126C59#321411yescharacteristic, complemented, Sylow
127C2×#41—592no—
128C2×#41—1181no—
129C2×SD16—594no—
130C2×D8—594no—
131C4⋊Q8—591no—
132C4⋊Q8—591no—
133#127—591no—
134#127—591no—
135#124—592no—
136#124—1181no—
137#121—592no—
138#121—1181no—
139#121—1181no—
140#121—1181no—
141C4×D4—592no—
142C4×D4—1181no—
143C4×D4—1181no—
144C4×D4—1181no—
145C2×C42C2×D5911yescharacteristic
146C4⋊C8C2×D5912yes—
147#103—594no—
148#102—594no—
149C22⋊C8C2×D5912yes—
150#97C2×D5912yes—
151#41—2364no—
152#41—2364no—
153C2×Q8—592no—
154C2×Q8—1181no—
155C2×D4—592no—
156C2×D4—592no—
157C2×D4—1182no—
158C2×D4—1182no—
159C2×D4—1181no—
160C2×D4—1181no—
161C2×D4—1181no—
162C2×D4—1181no—
163C22×C4—1182no—
164C22×C4—1182no—
165C22×C4D23611yescharacteristic
166C22×C4D23611yescharacteristic
167C22×C4C22×D5911yescharacteristic
168SD16—2364no—
169D8—2364no—
170C2×C8C22×D5914yes—
171C4⋊C4—592no—
172C4⋊C4—1181no—
173C4⋊C4—1181no—
174C4⋊C4—1181no—
175C22⋊C4—1182no—
176C22⋊C4—1182no—
177C22⋊C4—1182no—
178C22⋊C4—1182no—
179C42D23611yescharacteristic
180C42D23611yescharacteristic
181C42C22×D5911yescharacteristic
182C42C22×D5911yescharacteristic
183C23—1182no—
184C23—1182no—
185C23C2×D23611yescharacteristic
186Q8—1184no—
187Q8—2362no—
188D4—1182no—
189D4—1184no—
190D4—1182no—
191D4—2362no—
192D4—2362no—
193D4—2362no—
194D4—2364no—
195D4—2364no—
196D4—2362no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—2364no—
203C2×C4—2364no—
204C2×C4C2×D23611yescharacteristic
205C2×C4C2×D23611yescharacteristic
206C2×C4C2×D23611yescharacteristic
207C2×C4C2×D23611yescharacteristic
208C2×C4C2×D23611yescharacteristic
209C2×C4C23×D5911yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—2362no—
215C22—2362no—
216C22—2362no—
217C22—2362no—
218C22—2362no—
219C22—2362no—
220C22C22×D23611yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—2362no—
226C4—2362no—
227C4#1427375512yes—
228C4#1427377312yes—
229C2—41no—
230C2—4722no—
231C2—4722no—
232C2#1683797111yescharacteristic
233C2C2×#1427375511yescharacteristic
234C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3214
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16837952C2semidirect
2. #16837952C2semidirect
3. #16837791C2semidirect
4. #16837762C2semidirect
5. #16837608C2semidirect
6. #16837598C2semidirect
7. #16837549C2semidirect
8. C59×#432C2semidirect
125. #432D59semidirect
126. C59#3214semidirect