Finite Group Databasebeta

← #21434961

Subgroups — #21434961

Order 7552.

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

normal subgroups only

This group has 442 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#16837966C212yesmaximal, complemented
2#16837727C214yesmaximal, complemented
3#16837655C212yesmaximal, complemented
4#16837638C212yesmaximal, complemented
5#16837538C214yesmaximal, complemented
6C59×#408C211yesmaximal, characteristic, complemented
7C22×D236C2212yescomplemented
8C2×D472C2212yes—
9C2×D472C2212yes—
10#14273723—22no—
11#14273716—22no—
12#14273701C2214yes—
13#14273701C2214yescomplemented
14#14273695—22no—
15#14273695—22no—
16#14273686C2212yescomplemented
17#14273661C2212yescomplemented
18#14273659C2212yescomplemented
19#14273649C2214yescomplemented
20#14273649C2214yescomplemented
21C2×#41×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic, complemented
23C22×C8×C59C2211yescharacteristic, complemented
24C22⋊C8×C59C2214yescomplemented
25C23×D59—22no—
26#41×C59—41no—
27#41×C59—41no—
28C2×Q8×C59D411yescharacteristic
29C2×D4×C59D411yescharacteristic
30C2×D4×C59D412yes—
31C22×C4×C59C2312yes—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—24no—
34C2×C22⋊D59—24no—
35C2×D236—22no—
36C2×D236—42no—
37C2×D236—42no—
38C2×D236C2314yes—
39M16×C59—41no—
40C2×C8×C59—41no—
41C2×C8×C59C2312yes—
42C2×C8×C59C2312yes—
43C22⋊Dic59—22no—
44(C2×D59)⋊C4—24no—
45(C2×D59)⋊C4—24no—
46C4⋊Dic59C2314yes—
47C4×Dic59—22no—
48D472—42no—
49D472—42no—
50C23×C59C2×D412yes—
51C23×C59C2×D411yescharacteristic
52C22×D59—24no—
53C22×D59—44no—
54C22×D59—84no—
55Q8×C59—41no—
56D4×C59—42no—
57D4×C59—41no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—22no—
61C2×C4×C59—22no—
62C2×C4×C59C2×D412yes—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59C2411yescharacteristic
65C22⋊D59—84no—
66C22⋊D59—84no—
67C2×Dic59—24no—
68D236—24no—
69D236—24no—
70D236—44no—
71C8×C59—22no—
72C8×C59—22no—
73C22×C59—22no—
74C22×C59—21no—
75C22×C59—22no—
76C22×C59—24no—
77C22×C59C22×D411yescharacteristic
78C2×D59—44no—
79C2×D59—44no—
80C2×D59—44no—
81C2×D59—88no—
82C4×C59—22no—
83C4×C59—21no—
84C4×C59H(5,𝔽2)11yescharacteristic
85C4×C59H(5,𝔽2)11yescharacteristic
86Dic59—44no—
87#3199—591nomaximal, Sylow
88C2×C59—42no—
89C2×C59—41no—
90C2×C59#53411yescharacteristic
91C2×C59#57612yes—
92D59—84no—
93#535—592no—
94#482—594no—
95#469—592no—
96#466—592no—
97#447—594no—
98#408D5911yescharacteristic, complemented
99C59#319911yescharacteristic, complemented, Sylow
100C2×#41C2×D5911yescharacteristic
101C22×D4—592no—
102C2×D8—592no—
103C2×D8—592no—
104C2×M16C2×D5911yescharacteristic, complemented
105C22×C8C2×D5911yescharacteristic, complemented
106#127—1182no—
107#124—1182no—
108#121—594no—
109#121—594no—
110#120—1182no—
111#120—1182no—
112#117—592no—
113#107—592no—
114#106—592no—
115#102—594no—
116#102—594no—
117C22⋊C8C2×D5914yescomplemented
118C24—1182no—
119#41—41no—
120#41—41no—
121C2×Q8D23611yescharacteristic
122C2×D4—594no—
123C2×D4—1184no—
124C2×D4—1184no—
125C2×D4—1182no—
126C2×D4—2362no—
127C2×D4—2362no—
128C2×D4D23611yescharacteristic
129C2×D4D23612yes—
130C22×C4C22×D5912yes—
131C22×C4C22×D5911yescharacteristic
132D8—2362no—
133D8—2362no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D5912yes—
137C2×C8C22×D5912yes—
138C4⋊C4—594no—
139C22⋊C4—1182no—
140C22⋊C4—1184no—
141C22⋊C4—1184no—
142C42—1182no—
143C23—1184no—
144C23—4724no—
145C23—2364no—
146C23C2×D23612yes—
147C23C2×D23611yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—1184no—
152D4—1184no—
153D4—4724no—
154D4—4724no—
155D4—2364no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—1184no—
161C2×C4C2×D23612yes—
162C2×C4C2×D23611yescharacteristic
163C2×C4C23×D5911yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—4728no—
171C22—2364no—
172C22—2364no—
173C22—2364no—
174C22C22×D23611yescharacteristic
175C4—22no—
176C4—21no—
177C4—2364no—
178C4#1427377211yescharacteristic
179C4#1427377211yescharacteristic
180C2—42no—
181C2—41no—
182C2—4724no—
183C2#1683796411yescharacteristic
184C2#1683820712yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3199
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16837966C2semidirect
2. #16837727C2semidirect
3. #16837655C2semidirect
4. #16837638C2semidirect
5. #16837538C2semidirect
6. C59×#408C2semidirect
7. C22×D236C22semidirect
13. #14273701C22semidirect
16. #14273686C22semidirect
17. #14273661C22semidirect
18. #14273659C22semidirect
19. #14273649C22semidirect
20. #14273649C22semidirect
22. C2×M16×C59C22semidirect
23. C22×C8×C59C22semidirect
24. C22⋊C8×C59C22semidirect
98. #408D59semidirect
99. C59#3199semidirect
104. C2×M16C2×D59semidirect
105. C22×C8C2×D59semidirect
117. C22⋊C8C2×D59semidirect