Finite Group Databasebeta

← #20244064

Subgroups — #20244064

Order 6016.

256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13093949C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3#15689029C211yesmaximal, characteristic
4#15689021C211yesmaximal, characteristic
5#15688886C211yesmaximal, characteristic
6#15688886C211yesmaximal, characteristic
7C2×C4×C8×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093949—22no—
14#13093949C414yescomplemented
15C47⋊#95—21no—
16C47⋊#95—21no—
17C47⋊#95—21no—
18C22×C8×C47C2211yescharacteristic
19C22×C8×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21C4×C8×C47—22no—
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94C2×C412yes—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47C2×C412yes—
40C2×C8×C47D412yes—
41C42×C47—21no—
42C42×C47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47C2×C412yes—
49Dic47⋊C4—42no—
50C23×C47C2×D411yescharacteristic
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47SD1612yes—
56C2×C4×C47Q1612yes—
57C2×C4×C47C22×C411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75Dic94—22no—
76Dic94—22no—
77Dic94—41no—
78Dic94—41no—
79C8×C47—22no—
80C8×C47—22no—
81C22×C47C4×D411yescharacteristic
82C22×C47#12111yescharacteristic
83C22×C47#12411yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C22×C47#13511yescharacteristic
87C22×C47#13511yescharacteristic
88C4×C47—22no—
89C4×C47—22no—
90C4×C47#11711yescharacteristic
91C4×C47C4×D411yescharacteristic
92C4×C47#12311yescharacteristic
93C4×C47#12611yescharacteristic
94Dic47—42no—
95Dic47—42no—
96Dic47—81no—
97Dic47—81no—
98#1933—471nomaximal, Sylow
99C2×C47#38811yescharacteristic
100C2×C47C4×SD1611yescharacteristic
101C2×C47C4×Q1611yescharacteristic
102C2×C47#46511yescharacteristic
103C2×C47#46711yescharacteristic
104C2×C47#48711yescharacteristic
105C2×C47#48811yescharacteristic
106C2×#103—471no—
107C2×#103—471no—
108C2×C4×C8D4711yescharacteristic
109#391—471no—
110#389—471no—
111#340—471no—
112#340—471no—
113C47#193311yescharacteristic, complemented, Sylow
114C22×Q8—471no—
115C22×C8C2×D4711yescharacteristic
116C22×C8C2×D4711yescharacteristic
117C2×C4⋊C4—471no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—941no—
121C2×C42C2×D4711yescharacteristic
122#103—474no—
123#103—942no—
124C4×C8—22no—
125#95—941no—
126#95—941no—
127#95—941no—
128C2×Q8—472no—
129C2×Q8—941no—
130C2×Q8—941no—
131C2×Q8—941no—
132C2×Q8—941no—
133C2×Q8—941no—
134C22×C4—941no—
135C22×C4—941no—
136C22×C4—941no—
137C22×C4—941no—
138C22×C4D18811yescharacteristic
139C22×C4D18811yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8C4×D4712yes—
146C2×C8C22⋊D4712yes—
147C4⋊C4—472no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C4⋊C4—1882no—
154C42—21no—
155C42—21no—
156C23C2×D18811yescharacteristic
157Q8—942no—
158Q8—942no—
159Q8—1881no—
160Q8—1881no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4#1062532512yes—
178C2×C4Dic18812yes—
179C2×C4C2×C4×D4711yescharacteristic
180C2×C4#1062535011yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4#1062535011yescharacteristic
184C2×C4C2×C22⋊D4711yescharacteristic
185C8—22no—
186C8—22no—
187C22C4×D18811yescharacteristic
188C22#1309399811yescharacteristic
189C22#1309401211yescharacteristic
190C22C2×#1062532511yescharacteristic
191C22C2×Dic18811yescharacteristic
192C22#1309404611yescharacteristic
193C22#1309404611yescharacteristic
194C4—22no—
195C4—22no—
196C4—3761no—
197C4—3761no—
198C4—1882no—
199C4—1882no—
200C4#1309398111yescharacteristic
201C4C4×C22⋊D4711yescharacteristic
202C4#1309400711yescharacteristic
203C4#1309401811yescharacteristic
204C2#1568901411yescharacteristic
205C2C4×#1062532511yescharacteristic
206C2C4×Dic18811yescharacteristic
207C2#1568935211yescharacteristic
208C2#1568936411yescharacteristic
209C2#1568947411yescharacteristic
210C2#1568947811yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C4×C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×C8D47
hypocenterC47#1933
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
14. #13093949C4semidirect
113. C47#1933semidirect