Finite Group Databasebeta

← #21434813

Subgroups — #21434813

Order 7552.

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

normal subgroups only

This group has 402 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#16837957C211yesmaximal, characteristic, complemented
2#16837950C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837774C211yesmaximal, characteristic, complemented
5#16837753C211yesmaximal, characteristic, complemented
6#16837647C214yesmaximal, complemented
7#16837499C214yesmaximal, complemented
8C4×#11745659C211yesmaximal, characteristic, complemented
9C59×#486C211yesmaximal, characteristic, complemented
10C2×#11745687—21no—
11C2×#11745670C2214yes—
12C2×#11745659C2212yes—
13#14273727C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273718—21no—
16#14273714—21no—
17#14273707C2212yes—
18#14273703—21no—
19#14273698—21no—
20#14273698C2212yes—
21Q8×Dic59—21no—
22#14273692C2212yes—
23D4×Dic59—21no—
24D4×Dic59C2212yes—
25#14273685—21no—
26C42×D59C2211yescharacteristic
27#14273660C2214yes—
28#14273652C2214yes—
29#14273637C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32#127×C59C2211yescharacteristic
33#102×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×D4×C59—21no—
37C2×D4×C59—21no—
38C2×D4×C59C2312yes—
39C2×C22⋊D59—22no—
40C22×Dic59—22no—
41#11745687—44no—
42C2×C4×D59D411yescharacteristic
43C2×C4×D59D411yescharacteristic
44C2×C4×D59C2311yescharacteristic
45C2×Dic118—21no—
46C2×Dic118C2312yes—
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C42×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52C22⋊Dic59—22no—
53#11745670—28no—
54(C2×D59)⋊C4—22no—
55C4⋊Dic59—21no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59—22no—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61C4×Dic59—22no—
62C4×Dic59D411yescharacteristic
63C4×Dic59D411yescharacteristic
64C4×Dic59C2311yescharacteristic
65C2×C59⋊C8C2312yes—
66#11745659—24no—
67C23×C59—22no—
68C22×D59C2×D411yescharacteristic
69Q8×C59—42no—
70D4×C59—24no—
71D4×C59—42no—
72D4×C59—42no—
73C2×C4×C59—22no—
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2411yescharacteristic
77C22⋊D59—44no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—44no—
81C2×Dic59C2×D411yescharacteristic
82C2×Dic59C2×D411yescharacteristic
83C2×Dic59C2×D411yescharacteristic
84C4×D59—22no—
85C4×D59—22no—
86C4×D59—22no—
87Dic118—24no—
88Dic118—42no—
89C8×C59—22no—
90C59⋊C8#4114yescomplemented
91C22×C59—42no—
92C22×C59—42no—
93C22×C59—42no—
94C22×C59C22×D411yescharacteristic
95C2×D59—21no—
96C2×D59—21no—
97C2×D59—21no—
98C4×C59—42no—
99C4×C59AGL(1,ℤ/8)12yes—
100C4×C59#13712yes—
101C4×C59C2×#4112yes—
102Dic59—21no—
103Dic59—21no—
104Dic59—21no—
105Dic59—42no—
106Dic59—42no—
107#3182—591nomaximal, Sylow
108C2×C59—82no—
109C2×C59#53211yescharacteristic
110C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C59C2×#13711yescharacteristic
112D59—41no—
113#533—591no—
114#532—591no—
115#500—591no—
116#492—591no—
117#487—591no—
118#486D5911yescharacteristic, complemented
119#468—594no—
120#440—594no—
121C4×M16—591no—
122C59#318211yescharacteristic, complemented, Sylow
123C2×#41—1181no—
124C2×SD16—594no—
125C2×M16—592no—
126C4⋊Q8—591no—
127C4⋊Q8—591no—
128C4⋊Q8C2×D5911yescharacteristic
129#127C2×D5911yescharacteristic
130#125—1181no—
131#124—1181no—
132C22⋊Q8—592no—
133C22⋊Q8—1181no—
134#121—592no—
135#121—1181no—
136C4×Q8—592no—
137C4×Q8—1181no—
138C4×D4—592no—
139C4×D4—1181no—
140#117—1181no—
141C2×C42—591no—
142#107—594no—
143#103—594no—
144#102C2×D5914yes—
145#97—592no—
146C4×C8—591no—
147C4×C8C2×D5911yescharacteristic
148#41—2364no—
149C2×Q8—21no—
150C2×Q8—592no—
151C2×Q8—1181no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—1182no—
155C2×D4C22×D5912yes—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—591no—
159C22×C4—1182no—
160SD16—1188no—
161M16—1184no—
162C2×C8—592no—
163C2×C8C22×D5912yes—
164C4⋊C4—21no—
165C4⋊C4—592no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1181no—
169C4⋊C4—1181no—
170C4⋊C4—1181no—
171C4⋊C4C22×D5912yes—
172C22⋊C4—1182no—
173C22⋊C4—1182no—
174C22⋊C4—1182no—
175C42—591no—
176C42—591no—
177C42—591no—
178C42—1182no—
179C42C22×D5911yescharacteristic
180C23—22no—
181C23—591no—
182Q8—42no—
183Q8—1184no—
184Q8—2362no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—2364no—
189C2×C4—22no—
190C2×C4—591no—
191C2×C4—591no—
192C2×C4—591no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—2364no—
199C2×C4D4×D5911yescharacteristic
200C2×C4D4×D5911yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—22no—
203C8—594no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—1181no—
208C22—1181no—
209C22—1181no—
210C22C2×D4×D5911yescharacteristic
211C4—42no—
212C4—1181no—
213C4—1181no—
214C4—1181no—
215C4—2362no—
216C4—2362no—
217C4#1427375112yes—
218C4#1427375612yes—
219C4#41×D5912yes—
220C2—82no—
221C2—2361no—
222C2#1683795111yescharacteristic
223C2C2×#1427375111yescharacteristic
224C2C2×#1427375611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3182
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837805C2semidirect
4. #16837774C2semidirect
5. #16837753C2semidirect
6. #16837647C2semidirect
7. #16837499C2semidirect
8. C4×#11745659C2semidirect
9. C59×#486C2semidirect
90. C59⋊C8#41semidirect
118. #486D59semidirect
122. C59#3182semidirect