Finite Group Databasebeta

← #21434025

Subgroups — #21434025

Order 7552.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14273686C211yesmaximal, characteristic, complemented
2#16837740C214yesmaximal, complemented
3#16837723C214yesmaximal, complemented
4#16837445C212yesmaximal, complemented
5#16837403C212yesmaximal, complemented
6#16837366C211yesmaximal, characteristic, complemented
7C59×#525C211yesmaximal, characteristic
8C2×#11745664C2212yes—
9#14273686—22no—
10#14273686C2214yes—
11C2×C4⋊Dic59C2212yes—
12C2×C22⋊Dic59—21no—
13C2×C4×Dic59—21no—
14#14273660C2214yescomplemented
15#14273658C2214yescomplemented
16#14273651C2214yescomplemented
17#14273648C2214yescomplemented
18C22⋊(C59⋊C8)C2214yes—
19C2×#41×C59C2211yescharacteristic
20C23×C4×C59C2211yescharacteristic
21#123×C59—21no—
22C22⋊Q8×C59C2212yes—
23#121×C59C2212yes—
24#120×C59—21no—
25C4×D4×C59—22no—
26#117×C59C2211yescharacteristic
27C24×C59D411yescharacteristic
28#41×C59—24no—
29C2×Q8×C59C2311yescharacteristic
30C2×D4×C59—22no—
31C2×D4×C59—21no—
32C2×D4×C59C2311yescharacteristic
33C22×C4×C59—24no—
34C22×C4×C59—21no—
35C22×C4×C59D412yes—
36C22×C4×C59D411yescharacteristic
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×Dic59—22no—
40C4⋊C4×C59—22no—
41C4⋊C4×C59C2312yes—
42C22⋊C4×C59—21no—
43C22⋊C4×C59—22no—
44C22⋊C4×C59—22no—
45C42×C59—21no—
46C22⋊Dic59—24no—
47C4⋊Dic59—22no—
48C4⋊Dic59C2314yes—
49C4×Dic59—24no—
50#11745664—24no—
51C2×C59⋊C8C2314yes—
52C23×C59—22no—
53C23×C59—21no—
54C23×C59—42no—
55C23×C59C2×D412yes—
56C23×C59C2×D411yescharacteristic
57Q8×C59—22no—
58D4×C59—22no—
59D4×C59—44no—
60D4×C59—42no—
61C2×C4×C59—22no—
62C2×C4×C59—24no—
63C2×C4×C59—24no—
64C2×C4×C59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—42no—
67C2×C4×C59C2×D412yes—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59#4114yes—
70C2×C4×C59C2411yescharacteristic
71C2×Dic59—24no—
72C2×Dic59—44no—
73C59⋊C8—24no—
74C22×C59—22no—
75C22×C59—22no—
76C22×C59—22no—
77C22×C59—22no—
78C22×C59—44no—
79C22×C59—41no—
80C22×C59—42no—
81C22×C59#12312yes—
82C22×C59C22×D411yescharacteristic
83C4×C59—22no—
84C4×C59—41no—
85C4×C59—42no—
86C4×C59#12312yes—
87C4×C59C2×#4112yes—
88Dic59—44no—
89#3093—591nomaximal, Sylow
90C2×C59—22no—
91C2×C59—42no—
92C2×C59—81no—
93C2×C59C2×#12311yescharacteristic
94C2×C59#57512yes—
95#525D5911yescharacteristic
96C2×#117—591no—
97#485—594no—
98#482—594no—
99#428—592no—
100#417—592no—
101#407—591no—
102C59#309311yescharacteristic, complemented, Sylow
103C2×#41C2×D5911yescharacteristic
104C23×C4C2×D5911yescharacteristic
105C2×M16—592no—
106#123—21no—
107C22⋊Q8C2×D5912yes—
108#121C2×D5912yes—
109#120—21no—
110C4×D4—22no—
111#117—594no—
112#117—1182no—
113#117C2×D5911yescharacteristic
114C2×C4⋊C4—592no—
115C2×C22⋊C4—1181no—
116C2×C42—1181no—
117#107—594no—
118#106—594no—
119#103—594no—
120#102—594no—
121C22⋊C8—594no—
122C24C22⋊D5911yescharacteristic
123#41—24no—
124C2×Q8C22×D5911yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D5911yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—1182no—
131C22×C4C22⋊D5911yescharacteristic
132C22×C4C22⋊D5912yes—
133C22×C4C22×D5912yes—
134C22×C4C22×D5911yescharacteristic
135M16—1184no—
136C2×C8—594no—
137C4⋊C4—22no—
138C4⋊C4—594no—
139C4⋊C4—1182no—
140C4⋊C4C22×D5912yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—1184no—
145C42—21no—
146C42—1184no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D5912yes—
151C23C2×C22⋊D5911yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—1184no—
163C2×C4—2364no—
164C2×C4#1174568714yes—
165C2×C4C2×C22⋊D5912yes—
166C2×C4C2×C22⋊D5911yescharacteristic
167C2×C4C23×D5911yescharacteristic
168C8—1184no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#1427370812yes—
177C22C22×C22⋊D5911yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—2364no—
182C4#1427370812yes—
183C4C2×#1174568712yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#1427370811yescharacteristic
188C2#1683820012yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#525C2
socleC22×C59C22×D4
hypercenter#525D59
hypocenterC59#3093
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#14273686C2semidirect
2. #16837740C2semidirect
3. #16837723C2semidirect
4. #16837445C2semidirect
5. #16837403C2semidirect
6. #16837366C2semidirect
14. #14273660C22semidirect
15. #14273658C22semidirect
16. #14273651C22semidirect
17. #14273648C22semidirect
102. C59#3093semidirect