Finite Group Databasebeta

← #20251371

Subgroups — #20251371

Order 6016.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689057C212yesmaximal
3#15689056C212yesmaximal
4#15689028C211yesmaximal, characteristic
5#15689027C212yesmaximal
6#15689020C212yesmaximal
7#15689008C212yesmaximal
8#15689005C212yesmaximal
9C47×#400C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C4×Dic47C2212yes—
18C2×C4×Dic47C2211yescharacteristic
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#95×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2212yes—
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×Dic94—41no—
41C2×Dic94—41no—
42C2×Dic94Q814yes—
43C4⋊C4×C47—41no—
44C4⋊C4×C47—41no—
45C4⋊Dic47—24no—
46C4⋊Dic47—41no—
47Dic47⋊C4—24no—
48Dic47⋊C4—24no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51C4×Dic47—41no—
52C4×Dic47—42no—
53C23×C47C2411yescharacteristic
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—21no—
63C2×C4×C47—22no—
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—22no—
77C2×Dic47C2×Q814yes—
78C2×Dic47#4114yes—
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—42no—
87C4×C47—42no—
88C4×C47—41no—
89C4×C47—41no—
90Dic47—24no—
91Dic47—24no—
92Dic47—42no—
93Dic47—42no—
94#2809—471nomaximal, Sylow
95C2×C47#53912yes—
96C2×C47#54311yescharacteristic
97C2×C47#55511yescharacteristic
98C2×C47#55712yes—
99C2×C47#56311yescharacteristic
100#400—471no—
101#400D4711yescharacteristic
102#398—472no—
103#398—472no—
104#391—471no—
105#391—472no—
106#389—472no—
107#387—472no—
108#387—472no—
109C47#280911yescharacteristic, complemented, Sylow
110C22×Q8—471no—
111C2×C4⋊C4—472no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—472no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4C2×D4711yescharacteristic
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C42—472no—
120C2×C42—471no—
121#95—471no—
122#95—472no—
123#95—472no—
124#95—472no—
125#95—472no—
126#95—472no—
127#95—472no—
128#95C2×D4711yescharacteristic
129#95C2×D4712yes—
130#95C2×D4712yes—
131C2×Q8—474no—
132C2×Q8—1881no—
133C2×Q8—1881no—
134C22×C4—472no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4C22×D4711yescharacteristic
139C22×C4C22×D4711yescharacteristic
140C22×C4C22×D4712yes—
141C22×C4C22×D4712yes—
142C22×C4C22×D4711yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—944no—
146C4⋊C4—944no—
147C4⋊C4—944no—
148C4⋊C4—1882no—
149C4⋊C4—1882no—
150C4⋊C4—1881no—
151C42—1881no—
152C42—1882no—
153C23C23×D4711yescharacteristic
154Q8—1884no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—474no—
168C2×C4—474no—
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—942no—
178C2×C4—942no—
179C2×C4Q8×D4712yes—
180C22C2×Q8×D4711yescharacteristic
181C22#41×D4712yes—
182C22#1309406911yescharacteristic
183C22#1309407011yescharacteristic
184C22#1309407112yes—
185C4—22no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—42no—
190C4—944no—
191C4—944no—
192C4—1882no—
193C4—1882no—
194C2#1568971412yes—
195C2#1568974811yescharacteristic
196C2#1568983511yescharacteristic
197C2#1568985012yes—
198C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2809
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
109. C47#2809semidirect