Finite Group Databasebeta

← #20244741

Subgroups — #20244741

Order 6016.

314 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689749C211yesmaximal, characteristic
2#15688996C212yesmaximal
3#15688890C211yesmaximal, characteristic
4#15688889C212yesmaximal
5C47×#385C211yesmaximal, characteristic
6#13094003—21no—
7#13094003—21no—
8#13094001—22no—
9#13094001—22no—
10C2×Dic47⋊C4—22no—
11C2×C22⋊Dic47C2212yes—
12C2×C22⋊Dic47C2212yes—
13C47⋊#95—22no—
14C23×C4×C47C2211yescharacteristic
15C2×C4⋊C4×C47—21no—
16C2×C22⋊C4×C47C2211yescharacteristic
17C2×C22⋊C4×C47C2211yescharacteristic
18#95×C47—21no—
19C24×C47C2311yescharacteristic
20C22×C4×C47—21no—
21C22×C4×C47—21no—
22C22×C4×C47—22no—
23C22×C4×C47—42no—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×Dic47—22no—
27C22×Dic47D412yes—
28C22×Dic47D412yes—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C4⋊C4×C47—42no—
32C22⋊C4×C47—22no—
33C22⋊C4×C47—21no—
34C22⋊C4×C47Q812yescomplemented
35C22⋊Dic47—22no—
36C22⋊Dic47—22no—
37C22⋊Dic47—22no—
38C22⋊Dic47Q814yescomplemented
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41Dic47⋊C4—22no—
42Dic47⋊C4—22no—
43Dic47⋊C4—44no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47C2×D412yes—
47C23×C47C2×D411yescharacteristic
48C23×C47C2×Q811yescharacteristic
49C23×C47C2×Q812yes—
50C23×C47#4111yescharacteristic
51C2×C4×C47—24no—
52C2×C4×C47—22no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—22no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—42no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47—24no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70Dic94—81no—
71Dic94—81no—
72C22×C47—22no—
73C22×C47—21no—
74C22×C47—22no—
75C22×C47—21no—
76C22×C47—41no—
77C22×C47—42no—
78C22×C47—41no—
79C22×C47#12011yescharacteristic
80C22×C47C22⋊Q812yes—
81C22×C47C22⋊Q811yescharacteristic
82C22×C47C4⋊Q811yescharacteristic
83C22×C47C4⋊Q812yes—
84C4×C47—42no—
85C4×C47—41no—
86C4×C47—42no—
87C4×C47—41no—
88Dic47—44no—
89Dic47—42no—
90Dic47—42no—
91#2062—471nomaximal, Sylow
92C2×C47—22no—
93C2×C47—21no—
94C2×C47—21no—
95C2×C47—22no—
96C2×C47#39511yescharacteristic
97C2×C47B(4,𝔽2)11yescharacteristic
98C2×C47#45811yescharacteristic
99#543—471no—
100#385—472no—
101#385D4711yescharacteristic
102#342—472no—
103#342—471no—
104C47#206211yescharacteristic, complemented, Sylow
105C23×C4C2×D4711yescharacteristic
106C22⋊Q8—942no—
107C22⋊Q8—942no—
108C22⋊Q8—941no—
109C22⋊Q8—941no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—942no—
112C2×C22⋊C4—472no—
113C2×C22⋊C4—472no—
114C2×C22⋊C4C2×D4711yescharacteristic
115C2×C22⋊C4C2×D4711yescharacteristic
116#95—21no—
117#95—942no—
118C24C22×D4711yescharacteristic
119C2×Q8—941no—
120C2×Q8—941no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—42no—
125C22×C4—472no—
126C22×C4—472no—
127C22×C4—942no—
128C22×C4C22⋊D4711yescharacteristic
129C22×C4C22⋊D4711yescharacteristic
130C4⋊C4—42no—
131C4⋊C4—942no—
132C4⋊C4—942no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4—1884no—
136C22⋊C4—21no—
137C22⋊C4—22no—
138C22⋊C4—474no—
139C22⋊C4—942no—
140C22⋊C4—942no—
141C22⋊C4—942no—
142C22⋊C4Dic9412yescomplemented
143C23—41no—
144C23—41no—
145C23C2×Dic9411yescharacteristic
146C23#1062535011yescharacteristic
147C23D4×D4712yes—
148C23Q8×D4712yes—
149C23C2×C22⋊D4711yescharacteristic
150Q8—3761no—
151Q8—3761no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—944no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4—1882no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22#1309399211yescharacteristic
179C22#1309400212yes—
180C22#1309400311yescharacteristic
181C22#1309402211yescharacteristic
182C22#1309402312yes—
183C4—42no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—1884no—
188C4—1882no—
189C4—1882no—
190C2—21no—
191C2—22no—
192C2—21no—
193C2—22no—
194C2#1568904311yescharacteristic
195C2#1568930911yescharacteristic
196C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC24×C47C23
FrattiniC24C22×D47
FittingC47×#385C2
socleC22×C47#120
hypercenter#385D47
hypocenterC47#2062
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
34. C22⋊C4×C47Q8semidirect
38. C22⋊Dic47Q8semidirect
104. C47#2062semidirect
142. C22⋊C4Dic94semidirect