Finite Group Databasebeta

← #21422673

Subgroups — #21422673

Order 7552.

218 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 77 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#16837455C211yesmaximal, characteristic, complemented
2#16837270C211yesmaximal, characteristic, complemented
3#16837139C212yesmaximal, complemented
4#16837136C212yesmaximal
5C59×#529C211yesmaximal, characteristic
6C4⋊(C59⋊C8)—21no—
7C22⋊(C59⋊C8)C2212yes—
8C4×C59⋊C8—21no—
9C59⋊#95—21no—
10C59⋊#95—21no—
11C59⋊#95C2212yes—
12#126×C59—21no—
13#125×C59C411yescharacteristic, complemented
14#124×C59C411yescharacteristic, complemented
15#123×C59—21no—
16C22⋊Q8×C59C2211yescharacteristic
17#121×C59C2211yescharacteristic
18C4×Q8×C59C411yescharacteristic, complemented
19C4×D4×C59—21no—
20C4×D4×C59C411yescharacteristic, complemented
21#117×C59—21no—
22C2×C42×C59C2211yescharacteristic
23C2×Q8×C59C2×C411yescharacteristic
24C2×D4×C59—21no—
25C2×D4×C59C2×C411yescharacteristic
26C22×C4×C59—21no—
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59C2311yescharacteristic
30C22×Dic59—22no—
31C4⋊C4×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59C2×C411yescharacteristic
36C4⋊C4×C59C2×C411yescharacteristic
37C22⋊C4×C59—21no—
38C22⋊C4×C59—21no—
39C22⋊C4×C59—21no—
40C22⋊C4×C59—21no—
41C22⋊C4×C59—21no—
42C42×C59—21no—
43C42×C59C2×C411yescharacteristic
44C42×C59C2×C411yescharacteristic
45C42×C59D411yescharacteristic
46C42×C59D411yescharacteristic
47C2×C59⋊C8—22no—
48C23×C59—21no—
49C23×C59C2×D411yescharacteristic
50Q8×C59—41no—
51D4×C59—41no—
52D4×C59—42no—
53C2×C4×C59—22no—
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—42no—
60C2×C4×C59C22⋊C411yescharacteristic
61C2×C4×C59C22⋊C411yescharacteristic
62C2×C4×C59C22⋊C411yescharacteristic
63C2×C4×C59C22⋊C411yescharacteristic
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×Dic59—42no—
67C2×Dic59—42no—
68C2×Dic59—42no—
69C59⋊C8—42no—
70C22×C59—21no—
71C22×C59—21no—
72C22×C59—41no—
73C22×C59—41no—
74C22×C59—41no—
75C22×C59C2×C22⋊C411yescharacteristic
76C22×C59#13512yes—
77C4×C59—21no—
78C4×C59—21no—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—21no—
83C4×C59—41no—
84C4×C59—41no—
85C4×C59—41no—
86Dic59—82no—
87#1521—591nomaximal, Sylow
88C2×C59—22no—
89C2×C59—81no—
90C2×C59#41011yescharacteristic
91C2×C59#41611yescharacteristic
92C2×C59#42111yescharacteristic
93#529D5911yescharacteristic
94#431—591no—
95#383—591no—
96#328—592no—
97#327—592no—
98C59#152111yescharacteristic, complemented, Sylow
99#126—21no—
100#125Dic5911yescharacteristic, complemented
101#124Dic5911yescharacteristic, complemented
102#123—21no—
103C22⋊Q8C2×D5911yescharacteristic
104#121C2×D5911yescharacteristic
105C4×Q8Dic5911yescharacteristic, complemented
106C4×D4—21no—
107C4×D4Dic5911yescharacteristic, complemented
108#117—21no—
109C2×C42C2×D5911yescharacteristic
110C4⋊C8—1181no—
111C22⋊C8—592no—
112C4×C8—1181no—
113#95—592no—
114#95—1181no—
115#95—1181no—
116C2×Q8C2×Dic5911yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic5911yescharacteristic
119C22×C4—21no—
120C22×C4—1182no—
121C22×C4C22⋊D5911yescharacteristic
122C22×C4C22⋊D5911yescharacteristic
123C22×C4C22×D5911yescharacteristic
124C2×C8—1182no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×Dic5911yescharacteristic
130C4⋊C4C2×Dic5911yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42C2×Dic5911yescharacteristic
138C42C2×Dic5911yescharacteristic
139C42C22⋊D5911yescharacteristic
140C42C22⋊D5911yescharacteristic
141C23—21no—
142C23C2×C22⋊D5911yescharacteristic
143Q8—41no—
144D4—41no—
145D4—42no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—2362no—
154C2×C4—2362no—
155C2×C4—2362no—
156C2×C4C22⋊Dic5911yescharacteristic
157C2×C4C22⋊Dic5911yescharacteristic
158C2×C4C22⋊Dic5911yescharacteristic
159C2×C4C22⋊Dic5911yescharacteristic
160C2×C4C22×Dic5911yescharacteristic
161C2×C4C2×C22⋊D5911yescharacteristic
162C8—2362no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22C2×C22⋊Dic5911yescharacteristic
169C22#1427374712yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—4722no—
180C2—22no—
181C2—81no—
182C2#1683737611yescharacteristic
183C2#1683739811yescharacteristic
184C2#1683741911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#529C2
socleC22×C59C2×C22⋊C4
hypercenter#529D59
hypocenterC59#1521
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #16837455C2semidirect
2. #16837270C2semidirect
3. #16837139C2semidirect
13. #125×C59C4semidirect
14. #124×C59C4semidirect
18. C4×Q8×C59C4semidirect
20. C4×D4×C59C4semidirect
98. C59#1521semidirect
100. #125Dic59semidirect
101. #124Dic59semidirect
105. C4×Q8Dic59semidirect
107. C4×D4Dic59semidirect