Finite Group Databasebeta

← #20251275

Subgroups — #20251275

Order 6016.

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

normal subgroups only

This group has 376 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
1#15689064C212yesmaximal
2#15689062C211yesmaximal, characteristic
3#15689053C212yesmaximal
4#15689030C212yesmaximal
5#15689028C211yesmaximal, characteristic
6#15689027C212yesmaximal
7#15689009C212yesmaximal
8#15689006C212yesmaximal
9C47×#395C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C4×Dic47C2211yescharacteristic
16C2×C4×Dic47C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×Q8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C2×Q8×C47—24no—
32C2×Q8×C47—41no—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C2×Dic94—41no—
43C2×Dic94—41no—
44C2×Dic94Q814yescomplemented
45C4⋊C4×C47—24no—
46C4⋊C4×C47—41no—
47C4⋊Dic47—24no—
48C4⋊Dic47—41no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51C4×Dic47—42no—
52C4×Dic47—41no—
53C23×C47C2411yescharacteristic
54Q8×C47—44no—
55C2×C4×C47—22no—
56C2×C4×C47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47C2×Q812yes—
67C2×C4×C47#4114yes—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47C2×Q814yes—
79Dic94—44no—
80C22×C47C22×Q811yescharacteristic
81C22×C47C2×#4112yes—
82C22×C47H(5,𝔽2)11yescharacteristic
83C22×C47H(5,𝔽2)11yescharacteristic
84C22×C472−1+412yes—
85C4×C47—22no—
86C4×C47—24no—
87C4×C47—42no—
88C4×C47—41no—
89C4×C47—41no—
90Dic47—24no—
91Dic47—42no—
92Dic47—42no—
93Dic47—42no—
94#2799—471nomaximal, Sylow
95C2×C47#54212yes—
96C2×C47#54311yescharacteristic
97C2×C47#55111yescharacteristic
98C2×C47#55712yes—
99C2×C47#56311yescharacteristic
100#400—471no—
101#400—472no—
102#398—472no—
103#395D4711yescharacteristic
104#391—472no—
105#391—471no—
106#391—472no—
107#387—472no—
108#387—472no—
109C47#279911yescharacteristic, complemented, Sylow
110C22×Q8—471no—
111C22×Q8C2×D4711yescharacteristic
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4C2×D4712yes—
117C2×C4⋊C4C2×D4711yescharacteristic
118C2×C42—471no—
119C2×C42—472no—
120#95—472no—
121#95—472no—
122#95—472no—
123#95—472no—
124#95—472no—
125#95—472no—
126#95—472no—
127#95—472no—
128#95—471no—
129#95C2×D4712yes—
130#95C2×D4711yescharacteristic
131C2×Q8—24no—
132C2×Q8—41no—
133C2×Q8—474no—
134C2×Q8—1881no—
135C2×Q8—1881no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4—472no—
139C22×C4—472no—
140C22×C4C22×D4711yescharacteristic
141C22×C4C22×D4711yescharacteristic
142C22×C4C22×D4712yes—
143C22×C4C22×D4712yes—
144C22×C4C22×D4711yescharacteristic
145C4⋊C4—24no—
146C4⋊C4—41no—
147C4⋊C4—944no—
148C4⋊C4—1882no—
149C4⋊C4—1882no—
150C4⋊C4—1881no—
151C42—1882no—
152C42—1881no—
153C23C23×D4711yescharacteristic
154Q8—44no—
155Q8—1884no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—474no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—944no—
178C2×C4#1062535214yes—
179C2×C4Q8×D4712yes—
180C22C2×Q8×D4711yescharacteristic
181C22C2×#1062535212yes—
182C22#1309406911yescharacteristic
183C22#1309407011yescharacteristic
184C22#1309407212yes—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—944no—
191C4—1882no—
192C4—1882no—
193C4—1882no—
194C2#1568974612yes—
195C2#1568974811yescharacteristic
196C2#1568980411yescharacteristic
197C2#1568984812yes—
198C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2799
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
44. C2×Dic94Q8semidirect
109. C47#2799semidirect