Finite Group Databasebeta

← #21432162

Subgroups — #21432162

Order 7552.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273717C212yesmaximal
2#16837344C212yesmaximal
3#16837343C212yesmaximal
4#16837336C212yesmaximal
5#16837335C212yesmaximal
6#16837335C212yesmaximal
7#16837332C211yesmaximal, characteristic
8#16837267C211yesmaximal, characteristic
9C59×#398C211yesmaximal, characteristic
10#14273717—28no—
11C2×C4⋊Dic59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×C4×Dic59C2211yescharacteristic
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30#95×C59C2212yes—
31#95×C59C2211yescharacteristic
32C22×C4×C59C2311yescharacteristic
33C22×C4×C59C2312yes—
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×Dic59C2312yes—
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C4⋊C4×C59—24no—
42C4⋊C4×C59—41no—
43C4⋊C4×C59—41no—
44C4⋊Dic59—24no—
45C4⋊Dic59—41no—
46C4⋊Dic59—41no—
47Dic59⋊C4—24no—
48Dic59⋊C4—24no—
49Dic59⋊C4—24no—
50Dic59⋊C4—24no—
51Dic59⋊C4—42no—
52C4×Dic59D414yes—
53C23×C59C2411yescharacteristic
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—22no—
57C2×C4×C59—22no—
58C2×C4×C59—22no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59C2×D412yes—
67C2×Dic59—22no—
68C2×Dic59—22no—
69C2×Dic59—22no—
70C2×Dic59—22no—
71C2×Dic59—22no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—24no—
77C2×Dic59C2×D414yes—
78C22×C59C22×D411yescharacteristic
79C22×C59H(5,𝔽2)11yescharacteristic
80C22×C592−1+412yes—
81C22×C592−1+411yescharacteristic
82C22×C592−1+412yes—
83C4×C59—22no—
84C4×C59—42no—
85C4×C59—42no—
86C4×C59—41no—
87C4×C59—41no—
88Dic59—24no—
89Dic59—42no—
90Dic59—42no—
91Dic59—42no—
92#2822—591nomaximal, Sylow
93C2×C59#53612yes—
94C2×C59#53711yescharacteristic
95C2×C59#56311yescharacteristic
96C2×C59#56311yescharacteristic
97C2×C59#56412yes—
98C2×#125—592no—
99#400—592no—
100#400—592no—
101#398—591no—
102#398—592no—
103#398—592no—
104#398—592no—
105#398D5911yescharacteristic
106#382—591no—
107C59#282211yescharacteristic, complemented, Sylow
108#125—1188no—
109C2×C4⋊C4—592no—
110C2×C4⋊C4—592no—
111C2×C4⋊C4—592no—
112C2×C4⋊C4—592no—
113C2×C4⋊C4—592no—
114C2×C4⋊C4—591no—
115C2×C4⋊C4—592no—
116C2×C4⋊C4—591no—
117C2×C4⋊C4C2×D5912yes—
118C2×C4⋊C4C2×D5911yescharacteristic
119C2×C4⋊C4C2×D5911yescharacteristic
120C2×C42—591no—
121#95—592no—
122#95—592no—
123#95—592no—
124#95—592no—
125#95—592no—
126#95—592no—
127#95—591no—
128#95C2×D5912yes—
129#95C2×D5911yescharacteristic
130C22×C4—592no—
131C22×C4—592no—
132C22×C4—592no—
133C22×C4—592no—
134C22×C4C22×D5911yescharacteristic
135C22×C4C22×D5911yescharacteristic
136C22×C4C22×D5912yes—
137C22×C4C22×D5912yes—
138C22×C4C22×D5911yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—1184no—
143C4⋊C4—1184no—
144C4⋊C4—1184no—
145C4⋊C4—1184no—
146C4⋊C4—1184no—
147C4⋊C4—2362no—
148C4⋊C4—2361no—
149C4⋊C4—2361no—
150C42—594no—
151C23C23×D5911yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—594no—
165C2×C4—1182no—
166C2×C4—1182no—
167C2×C4—1182no—
168C2×C4—1182no—
169C2×C4—1182no—
170C2×C4—1182no—
171C2×C4—1182no—
172C2×C4—1182no—
173C2×C4—1184no—
174C2×C4—1182no—
175C2×C4D4×D5912yes—
176C22C2×D4×D5911yescharacteristic
177C22#1427377211yescharacteristic
178C22#1427377412yes—
179C22#1427377411yescharacteristic
180C22#1427377512yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—1184no—
187C4—2362no—
188C4—2362no—
189C4—2362no—
190C2#1683797512yes—
191C2#1683797911yescharacteristic
192C2#1683815111yescharacteristic
193C2#1683815511yescharacteristic
194C2C59⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2822
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
107. C59#2822semidirect