Finite Group Databasebeta

← #20244824

Subgroups — #20244824

Order 6016.

256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13093955C211yesmaximal, characteristic, complemented
2C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
3#15688983C211yesmaximal, characteristic
4#15688885C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#380C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C22⋊Dic47—21no—
13#13093955—22no—
14C22⋊(C47⋊C8)—22no—
15C47⋊#95—21no—
16C23×C4×C47C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47—21no—
20#95×C47—21no—
21C24×C47D411yescharacteristic
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33C22×Dic47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C22⋊C4×C47—42no—
39C22⋊Dic47—42no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8D412yes—
50C23×C47—21no—
51C23×C47—21no—
52C23×C47—21no—
53C23×C47—21no—
54C23×C47—21no—
55C23×C47—21no—
56C23×C47SD1612yes—
57C23×C47C2×D411yescharacteristic
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C47⋊C8—22no—
84C47⋊C8—41no—
85C22×C47—22no—
86C22×C47—22no—
87C22×C47—22no—
88C22×C47—41no—
89C22×C47—41no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47#12111yescharacteristic
93C22×C47#12311yescharacteristic
94C22×C47#12311yescharacteristic
95C22×C47C2×SD1611yescharacteristic
96C22×C47#13511yescharacteristic
97C22×C47AGL(1,ℤ/8)11yescharacteristic
98C22×C47#13711yescharacteristic
99C4×C47—41no—
100C4×C47—81no—
101C4×C47—81no—
102C4×C47#12311yescharacteristic
103C4×C47#12411yescharacteristic
104C4×C47#12611yescharacteristic
105C4×C47#12611yescharacteristic
106Dic47—81no—
107Dic47—81no—
108#2077—471nomaximal, Sylow
109C2×C47—42no—
110C2×C47#39711yescharacteristic
111C2×C47#46511yescharacteristic
112C2×C47#46811yescharacteristic
113C2×C47#48111yescharacteristic
114C2×C47#48211yescharacteristic
115C2×C47#48311yescharacteristic
116C2×C47#48511yescharacteristic
117C2×#106—471no—
118C2×C22⋊C8—471no—
119#380—471no—
120#380D4711yescharacteristic
121#340—471no—
122#340—471no—
123#340—471no—
124C47#207711yescharacteristic, complemented, Sylow
125C23×C4C2×D4711yescharacteristic
126C22×C8—471no—
127C22×C8—471no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C22⋊C4—21no—
133C2×C22⋊C4—941no—
134#106—942no—
135C22⋊C8—942no—
136#95—21no—
137#95—941no—
138C24C22⋊D4711yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C2×C8—472no—
152C2×C8—941no—
153C2×C8—941no—
154C2×C8—941no—
155C2×C8—941no—
156C2×C8—941no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C22⋊C4—42no—
166C22⋊C4—1882no—
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#1062533512yes—
174C23C2×C22⋊D4711yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4—1881no—
192C2×C4—1881no—
193C2×C4—1881no—
194C2×C4#1062535011yescharacteristic
195C2×C4#1062535011yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4#1062535211yescharacteristic
198C2×C4#1062535211yescharacteristic
199C2×C4#1062535211yescharacteristic
200C8—942no—
201C8—1881no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#1309399611yescharacteristic
210C22#1309400511yescharacteristic
211C22#1309400711yescharacteristic
212C22C2×#1062533511yescharacteristic
213C22#1309404411yescharacteristic
214C22#1309404911yescharacteristic
215C22#1309405511yescharacteristic
216C4—41no—
217C4—81no—
218C4—81no—
219C4—3761no—
220C4—3761no—
221C4#1309400611yescharacteristic
222C4#1309401011yescharacteristic
223C4#1309401711yescharacteristic
224C4#1309401711yescharacteristic
225C2—42no—
226C2#1568905111yescharacteristic
227C2#1568935011yescharacteristic
228C2#1568937111yescharacteristic
229C2#1568943911yescharacteristic
230C2#1568944711yescharacteristic
231C2#1568945311yescharacteristic
232C2#1568946111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#380C2
socleC23×C47C2×D4
hypercenter#380D47
hypocenterC47#2077
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#13093955C2semidirect
4. #15688885C2semidirect
5. #15688885C2semidirect
6. #15688885C2semidirect
124. C47#2077semidirect