Finite Group Databasebeta

← #20250884

Subgroups — #20250884

Order 6016.

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

normal subgroups only

This group has 344 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#15689062C211yesmaximal, characteristic
2#15689062C212yesmaximal
3#15689055C212yesmaximal
4#15689022C212yesmaximal
5#15689008C212yesmaximal
6#15689004C212yesmaximal
7#15688990C212yesmaximal
8#15688988C211yesmaximal, characteristic
9C47×#398C211yesmaximal, characteristic
10C2×C4⋊Dic47C2212yes—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×C4×Dic47C2211yescharacteristic
16C2×C4×Dic47C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2211yescharacteristic
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C4⋊C4×C47—24no—
41C4⋊C4×C47—41no—
42C4⋊C4×C47—41no—
43C4⋊Dic47—24no—
44C4⋊Dic47—41no—
45C4⋊Dic47—42no—
46C4⋊Dic47—41no—
47Dic47⋊C4—24no—
48C4×Dic47—22no—
49C4×Dic47—24no—
50C23×C47C2411yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47#4112yes—
63C2×C4×C47#4114yes—
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—22no—
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—
76C22×C47C2×#4111yescharacteristic
77C22×C47C2×#4112yes—
78C22×C47H(5,𝔽2)11yescharacteristic
79C22×C472−1+411yescharacteristic
80C22×C472−1+412yes—
81C4×C47—22no—
82C4×C47—24no—
83C4×C47—42no—
84C4×C47—41no—
85C4×C47—41no—
86Dic47—42no—
87Dic47—42no—
88Dic47—42no—
89Dic47—42no—
90#2769—471nomaximal, Sylow
91C2×C47#53911yescharacteristic
92C2×C47#54112yes—
93C2×C47#55212yes—
94C2×C47#55511yescharacteristic
95C2×C47#56311yescharacteristic
96#400—472no—
97#400—471no—
98#398—472no—
99#398D4711yescharacteristic
100#389—472no—
101#387—472no—
102#387—472no—
103#383—472no—
104#382—471no—
105C47#276911yescharacteristic, complemented, Sylow
106C2×C4⋊C4—472no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—472no—
110C2×C4⋊C4—471no—
111C2×C4⋊C4C2×D4712yes—
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C4⋊C4C2×D4711yescharacteristic
114C2×C42—471no—
115C2×C42—472no—
116#95—472no—
117#95—472no—
118#95—471no—
119#95—472no—
120#95—472no—
121#95—472no—
122#95—472no—
123#95—472no—
124#95—472no—
125#95C2×D4712yes—
126#95C2×D4711yescharacteristic
127C22×C4—472no—
128C22×C4—472no—
129C22×C4—472no—
130C22×C4—472no—
131C22×C4C22×D4711yescharacteristic
132C22×C4C22×D4711yescharacteristic
133C22×C4C22×D4712yes—
134C22×C4C22×D4711yescharacteristic
135C22×C4C22×D4712yes—
136C4⋊C4—24no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—944no—
140C4⋊C4—944no—
141C4⋊C4—1881no—
142C4⋊C4—1882no—
143C4⋊C4—1881no—
144C42—942no—
145C42—944no—
146C23C23×D4711yescharacteristic
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—942no—
161C2×C4—942no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4#1062535212yes—
171C2×C4#1062535414yes—
172C22C2×#1062535211yescharacteristic
173C22C2×#1062535412yes—
174C22#1309406911yescharacteristic
175C22#1309407111yescharacteristic
176C22#1309407112yes—
177C4—24no—
178C4—22no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4—1882no—
183C4—1882no—
184C4—1882no—
185C4—1882no—
186C2#1568971811yescharacteristic
187C2#1568973612yes—
188C2#1568981512yes—
189C2#1568983911yescharacteristic
190C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2769
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
105. C47#2769semidirect