Finite Group Databasebeta

← #20251654

Subgroups — #20251654

Order 6016.

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

normal subgroups only

This group has 348 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
1#15689064C212yesmaximal
2#15689062C211yesmaximal, characteristic
3#15689057C212yesmaximal
4#15689056C212yesmaximal
5#15689054C212yesmaximal
6#15689042C212yesmaximal
7#15688992C211yesmaximal, characteristic
8#15688990C212yesmaximal
9C47×#395C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C4×Dic47C2211yescharacteristic
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C22×Q8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2212yes—
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C2×Q8×C47—42no—
32C2×Q8×C47—41no—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C4⋊C4×C47—41no—
43C4⋊C4×C47—42no—
44C4⋊Dic47—41no—
45C4⋊Dic47—41no—
46Dic47⋊C4—42no—
47Dic47⋊C4—42no—
48Dic47⋊C4—42no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51C4×Dic47Q814yescomplemented
52C23×C47C2411yescharacteristic
53Q8×C47—44no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—21no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47C2×Q812yes—
67C2×Dic47—22no—
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—24no—
77C2×Dic47C2×Q814yes—
78C22×C47C22×Q811yescharacteristic
79C22×C47H(5,𝔽2)12yes—
80C22×C47H(5,𝔽2)11yescharacteristic
81C22×C472−1+411yescharacteristic
82C22×C472−1+412yes—
83C4×C47—22no—
84C4×C47—41no—
85C4×C47—42no—
86C4×C47—41no—
87C4×C47—42no—
88Dic47—24no—
89Dic47—42no—
90Dic47—42no—
91Dic47—42no—
92#2843—471nomaximal, Sylow
93C2×C47#54412yes—
94C2×C47#54411yescharacteristic
95C2×C47#56011yescharacteristic
96C2×C47#56311yescharacteristic
97C2×C47#56312yes—
98#400—471no—
99#400—472no—
100#398—472no—
101#398—472no—
102#398—472no—
103#395—472no—
104#395D4711yescharacteristic
105#384—471no—
106#383—472no—
107C47#284311yescharacteristic, complemented, Sylow
108C22×Q8C2×D4711yescharacteristic
109C2×C4⋊C4—472no—
110C2×C4⋊C4—472no—
111C2×C4⋊C4—472no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4C2×D4711yescharacteristic
117C2×C4⋊C4C2×D4712yes—
118C2×C42—471no—
119#95—472no—
120#95—472no—
121#95—472no—
122#95—472no—
123#95—472no—
124#95—472no—
125#95—471no—
126#95—472no—
127#95C2×D4712yes—
128#95C2×D4711yescharacteristic
129C2×Q8—42no—
130C2×Q8—41no—
131C22×C4—472no—
132C22×C4—472no—
133C22×C4—472no—
134C22×C4—472no—
135C22×C4C22×D4712yes—
136C22×C4C22×D4712yes—
137C22×C4C22×D4711yescharacteristic
138C22×C4C22×D4711yescharacteristic
139C22×C4C22×D4711yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—1882no—
143C4⋊C4—1882no—
144C4⋊C4—1882no—
145C4⋊C4—1882no—
146C4⋊C4—1882no—
147C4⋊C4—1881no—
148C4⋊C4—1881no—
149C42—474no—
150C23C23×D4711yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—474no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—944no—
174C2×C4—942no—
175C2×C4Q8×D4712yes—
176C22C2×Q8×D4711yescharacteristic
177C22#1309406912yes—
178C22#1309406911yescharacteristic
179C22#1309407111yescharacteristic
180C22#1309407212yes—
181C4—22no—
182C4—42no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—944no—
187C4—1882no—
188C4—1882no—
189C4—1882no—
190C2#1568975012yes—
191C2#1568975211yescharacteristic
192C2#1568986211yescharacteristic
193C2#1568987211yescharacteristic
194C2#1568987412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2843
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic47Q8semidirect
107. C47#2843semidirect