Finite Group Databasebeta

← #20244547

Subgroups — #20244547

Order 6016.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689751C211yesmaximal, characteristic
2#15689132C211yesmaximal, characteristic
3#15689030C211yesmaximal, characteristic
4#15688891C211yesmaximal, characteristic
5#15688884C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#419C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094024—21no—
10#13094023—21no—
11#13094016—21no—
12#13094015—21no—
13#13094001—22no—
14#13093983C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4×Dic47C2211yescharacteristic
17#13093948—21no—
18#13093948—21no—
19C47⋊#95—22no—
20C22×Q8×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#103×C47—21no—
24#103×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47Q812yescomplemented
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47D412yes—
35C2×Dic94—22no—
36M16×C47—21no—
37M16×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C4⋊C4×C47D411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C22⋊Dic47—21no—
44C4⋊Dic47—22no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47D411yescharacteristic
48C4⋊Dic47D411yescharacteristic
49Dic47⋊C4—22no—
50Dic47⋊C4—22no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C4×Dic47—21no—
54#10625329—21no—
55#10625329—21no—
56C2×C47⋊C8—21no—
57C23×C47C2×D411yescharacteristic
58Q8×C47—22no—
59Q8×C47—22no—
60Q8×C47—41no—
61Q8×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×Q811yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—22no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—42no—
80Dic94—82no—
81C8×C47—41no—
82C47⋊C8—41no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47#12011yescharacteristic
86C22×C47C22⋊Q811yescharacteristic
87C22×C47#12411yescharacteristic
88C4×C47—42no—
89C4×C47—41no—
90C4×C47—41no—
91C4×C47C22⋊Q811yescharacteristic
92C4×C47C22⋊Q811yescharacteristic
93C4×C47#12411yescharacteristic
94C4×C47#12411yescharacteristic
95Dic47—42no—
96Dic47—41no—
97Dic47—42no—
98Dic47—41no—
99#2028—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#39311yescharacteristic
103C2×C47#45511yescharacteristic
104C2×C47#45611yescharacteristic
105#544—471no—
106#419—471no—
107#419D4711yescharacteristic
108#391—471no—
109#343—471no—
110#339—471no—
111#339—471no—
112C47#202811yescharacteristic, complemented, Sylow
113C22×Q8C2×D4711yescharacteristic
114C2×M16—471no—
115C2×M16C2×D4711yescharacteristic
116C4⋊Q8—941no—
117C4⋊Q8—941no—
118#125—941no—
119#125—941no—
120C22⋊Q8—942no—
121#117—471no—
122#117C2×D4711yescharacteristic
123C2×C4⋊C4—471no—
124C2×C42—471no—
125#103—21no—
126#103—21no—
127#103—941no—
128#103—941no—
129#95—942no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—942no—
136C2×Q8Dic9412yescomplemented
137C22×C4—21no—
138C22×C4—472no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141M16—21no—
142M16—21no—
143M16—941no—
144M16—941no—
145C2×C8—21no—
146C2×C8—941no—
147C4⋊C4—471no—
148C4⋊C4—471no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C4⋊C4C22⋊D4711yescharacteristic
155C4⋊C4C22⋊D4711yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—941no—
158C42—21no—
159C42—941no—
160C42—941no—
161C42—941no—
162C23D4×D4711yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—3762no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—942no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—942no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1882no—
180C2×C4C2×Dic9411yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4#1062535211yescharacteristic
184C2×C4#1062535211yescharacteristic
185C2×C4C2×C22⋊D4711yescharacteristic
186C8—41no—
187C8—1881no—
188C22—21no—
189C22—21no—
190C22#1309399211yescharacteristic
191C22#1309400111yescharacteristic
192C22#1309401011yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1882no—
197C4—1882no—
198C4—1881no—
199C4—1881no—
200C4#1309400111yescharacteristic
201C4#1309400311yescharacteristic
202C4#1309401011yescharacteristic
203C4#1309401111yescharacteristic
204C2—21no—
205C2—21no—
206C2#1568903511yescharacteristic
207C2#1568929911yescharacteristic
208C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC22×C47#120
hypercenter#419D47
hypocenterC47#2028
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C47Q8semidirect
112. C47#2028semidirect
136. C2×Q8Dic94semidirect