Finite Group Databasebeta

← #21434468

Subgroups — #21434468

Order 7552.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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#16837955C211yesmaximal, characteristic, complemented
2C2×#14273723C211yesmaximal, characteristic
3#16837765C214yesmaximal, complemented
4#16837747C214yesmaximal, complemented
5#16837408C211yesmaximal, characteristic, complemented
6#16837407C211yesmaximal, characteristic, complemented
7#16837406C211yesmaximal, characteristic, complemented
8M16×Dic59C211yesmaximal, characteristic, complemented
9C59×#418C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C22⋊D59—22no—
12C2×#11745664C2211yescharacteristic
13#14273726C2212yescomplemented
14#14273723—22no—
15#14273723C2212yes—
16#14273723C2212yes—
17#14273718C2212yescomplemented
18#14273704—22no—
19C4×Dic118—22no—
20#14273686C2211yescharacteristic
21C2×C4×Dic59C2211yescharacteristic
22#14273649C2214yescomplemented
23#14273648C2214yescomplemented
24#14273647C2214yescomplemented
25#14273637C2212yescomplemented
26C8×Dic59C2212yescomplemented
27C22×D4×C59C2211yescharacteristic
28C2×M16×C59C2211yescharacteristic
29#117×C59C2211yescharacteristic
30#102×C59C2214yescomplemented
31C24×C59—21no—
32C23×D59—21no—
33C2×D4×C59—21no—
34C2×D4×C59—22no—
35C2×D4×C59—22no—
36C2×D4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—24no—
39C2×C22⋊D59—24no—
40C2×C22⋊D59—48no—
41C22×Dic59D412yes—
42C2×D236—22no—
43C2×D236—22no—
44C2×D236—21no—
45C2×D236C2312yes—
46C2×Dic118—22no—
47M16×C59—22no—
48C2×C8×C59C2312yes—
49C4⋊C4×C59C2312yes—
50C22⋊C4×C59—21no—
51C42×C59—21no—
52C22⋊Dic59—21no—
53C4⋊Dic59—22no—
54C4⋊Dic59C2312yes—
55Dic59⋊C4—22no—
56Dic59⋊C4—22no—
57C4×Dic59—21no—
58C4×Dic59D412yes—
59C4×Dic59C2311yescharacteristic
60C4×Dic59C2311yescharacteristic
61#11745664—22no—
62C2×C59⋊C8C2312yes—
63C23×C59—22no—
64C23×C59—44no—
65C23×C59—42no—
66C23×C59C2×D411yescharacteristic
67C22×D59—22no—
68C22×D59—44no—
69C22×D59—42no—
70D4×C59—22no—
71D4×C59—22no—
72D4×C59—42no—
73C2×C4×C59—22no—
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59#4112yes—
76C2×C4×C59#4112yes—
77C2×C4×C59C2411yescharacteristic
78C22⋊D59—48no—
79C22⋊D59—48no—
80C2×Dic59—24no—
81C2×Dic59—22no—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D412yes—
84D236—22no—
85D236—22no—
86D236—42no—
87Dic118—44no—
88C8×C59—22no—
89C59⋊C8—22no—
90C22×C59—22no—
91C22×C59—42no—
92C22×C59—44no—
93C22×C59—84no—
94C22×C59#12412yes—
95C22×C59C22×D411yescharacteristic
96C2×D59—42no—
97C2×D59—44no—
98C2×D59—84no—
99C4×C59—42no—
100C4×C59#12412yes—
101C4×C59C2×#4111yescharacteristic
102C4×C59C2×#4111yescharacteristic
103Dic59—22no—
104Dic59—42no—
105Dic59AGL(1,ℤ/8)14yes—
106#3138—591nomaximal, Sylow
107C2×C59—22no—
108C2×C59—82no—
109C2×C59C2×#12411yescharacteristic
110C2×C59C2×AGL(1,ℤ/8)12yes—
111D59—82no—
112#533—591no—
113C2×#127—591no—
114#490—594no—
115#486—594no—
116#418—591no—
117#418—591no—
118#418—591no—
119#418D5911yescharacteristic, complemented
120C4×M16—591no—
121C59#313811yescharacteristic, complemented, Sylow
122C22×D4—591no—
123C22×D4—1182no—
124C22×D4C2×D5911yescharacteristic
125C2×M16—591no—
126C2×M16C2×D5911yescharacteristic
127C4⋊Q8—592no—
128#127—592no—
129#127—592no—
130#127—1182no—
131#125—592no—
132C22⋊Q8—1182no—
133C4×Q8—1182no—
134#117—591no—
135#117C2×D5911yescharacteristic
136C2×C42—591no—
137#102—594no—
138#102—594no—
139#102—594no—
140#102C2×D5914yescomplemented
141#97—592no—
142C4×C8—592no—
143C24—21no—
144C24—1181no—
145C2×Q8—1182no—
146C2×D4—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—592no—
150C2×D4—1184no—
151C2×D4—1184no—
152C2×D4—1182no—
153C2×D4—1181no—
154C2×D4—1182no—
155C2×D4—2368no—
156C2×D4C22×D5912yes—
157C22×C4—592no—
158C22×C4C22×D5911yescharacteristic
159M16—22no—
160M16—1182no—
161C2×C8—592no—
162C2×C8C22×D5912yes—
163C4⋊C4—592no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4C22×D5912yes—
168C22⋊C4—21no—
169C22⋊C4—1181no—
170C42—21no—
171C42—592no—
172C42—591no—
173C42—591no—
174C42—1181no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—1182no—
179C23—2364no—
180C23—2362no—
181C23D4×D5911yescharacteristic
182Q8—2364no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—1182no—
187D4—1182no—
188D4—2368no—
189D4—2368no—
190D4—2362no—
191C2×C4—22no—
192C2×C4—592no—
193C2×C4—592no—
194C2×C4—1184no—
195C2×C4—1182no—
196C2×C4#1174568512yes—
197C2×C4D4×D5911yescharacteristic
198C2×C4#1174568712yes—
199C2×C4C23×D5911yescharacteristic
200C8—22no—
201C8—1182no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—4724no—
207C22—2362no—
208C22—2364no—
209C22#1427371312yes—
210C22C2×D4×D5911yescharacteristic
211C4—42no—
212C4—594no—
213C4—1182no—
214C4—2362no—
215C4#1427371312yes—
216C4C2×#1174568711yescharacteristic
217C4C2×#1174568511yescharacteristic
218C2—22no—
219C2—82no—
220C2—4722no—
221C2C2×#1427371311yescharacteristic
222C2AGL(1,ℤ/8)×D5912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#418C2
socleC22×C59C22×D4
hypercenter#418D59
hypocenterC59#3138
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16837955C2semidirect
3. #16837765C2semidirect
4. #16837747C2semidirect
5. #16837408C2semidirect
6. #16837407C2semidirect
7. #16837406C2semidirect
8. M16×Dic59C2semidirect
9. C59×#418C2semidirect
13. #14273726C22semidirect
17. #14273718C22semidirect
22. #14273649C22semidirect
23. #14273648C22semidirect
24. #14273647C22semidirect
25. #14273637C22semidirect
26. C8×Dic59C22semidirect
30. #102×C59C22semidirect
119. #418D59semidirect
121. C59#3138semidirect
140. #102C2×D59semidirect