Finite Group Databasebeta

← #20244230

Subgroups — #20244230

Order 6016.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#13094022C211yesmaximal, characteristic
2#15689146C211yesmaximal, characteristic
3C2×#13093943C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic
6M16×Dic47C211yesmaximal, characteristic
7C2×#101×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094022—21no—
12#13094022—21no—
13#13094022—22no—
14C2×Dic47⋊C4C414yes—
15C2×C4×Dic47C2211yescharacteristic
16Dic47⋊C8—22no—
17#13093943—22no—
18#13093942—22no—
19#13093942—22no—
20#13093934—21no—
21C8×Dic47—21no—
22C22×Q8×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25#101×C47—22no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C22×C4×C47C2×C412yes—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47C2×C412yes—
35C22×Dic47C2×C412yes—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48Dic47⋊C4—24no—
49Dic47⋊C4—24no—
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C4×Dic47D412yes—
53#10625329—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329D412yes—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47C22×C411yescharacteristic
60Q8×C47—41no—
61Q8×C47—41no—
62Q8×C47—41no—
63Q8×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—24no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47C22⋊C412yes—
78C2×Dic47C22⋊C412yes—
79Dic94—41no—
80Dic94—41no—
81Dic94—41no—
82Dic94—41no—
83C8×C47—22no—
84C8×C47—41no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—22no—
88C22×C47C2×C22⋊C411yescharacteristic
89C22×C47C4×D411yescharacteristic
90C22×C47C4×D411yescharacteristic
91C4×C47—42no—
92C4×C47#12111yescharacteristic
93C4×C47#12111yescharacteristic
94C4×C47#12411yescharacteristic
95C4×C47#12711yescharacteristic
96Dic47—22no—
97Dic47—42no—
98Dic47#10114yescomplemented
99#1966—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#39011yescharacteristic
103C2×C47C2×#10112yes—
104C2×C4⋊Q8—471no—
105#423—471no—
106C2×#101—471no—
107C2×#101—471no—
108C2×#101—471no—
109C2×#101D4711yescharacteristic
110C4×M16—471no—
111C47#196611yescharacteristic, complemented, Sylow
112C22×Q8—471no—
113C22×Q8C2×D4711yescharacteristic
114C2×M16—471no—
115C2×M16—471no—
116C2×M16C2×D4711yescharacteristic
117C2×M16C2×D4711yescharacteristic
118C4⋊Q8—941no—
119C4⋊Q8—941no—
120C4⋊Q8—942no—
121C2×C4⋊C4—474no—
122C2×C42—471no—
123C4⋊C8—942no—
124#101—22no—
125#101—942no—
126#101—942no—
127#101—942no—
128#97—941no—
129C4×C8—941no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—941no—
137C2×Q8—941no—
138C2×Q8—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—941no—
142C22×C4—472no—
143C22×C4—472no—
144C22×C4C4×D4712yes—
145C22×C4C22×D4711yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—472no—
150M16—941no—
151M16—941no—
152M16—941no—
153M16C22⋊D4712yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—941no—
157C2×C8—941no—
158C4⋊C4—944no—
159C4⋊C4—944no—
160C42—471no—
161C42—471no—
162C42—472no—
163C23C2×C4×D4711yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—1881no—
169Q8—1881no—
170Q8—1881no—
171Q8—1881no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—472no—
176C2×C4—472no—
177C2×C4—944no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4#1062535011yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4#1062535211yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C8—22no—
188C8—41no—
189C8—942no—
190C8—1881no—
191C22—22no—
192C22C22⋊C4×D4711yescharacteristic
193C22(C22⋊D47)⋊C411yescharacteristic
194C22C4×C22⋊D4711yescharacteristic
195C4—42no—
196C4—474no—
197C4—942no—
198C4—1882no—
199C4#1309399611yescharacteristic
200C4#1309399711yescharacteristic
201C4#1309401011yescharacteristic
202C4#1309402011yescharacteristic
203C2—21no—
204C2—21no—
205C2#1568902311yescharacteristic
206C2#101×D4712yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#101×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#101D47
hypocenterC47#1966
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
98. Dic47#101semidirect
111. C47#1966semidirect