Finite Group Databasebeta

← #20243307

Subgroups — #20243307

Order 6016.

820 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×D4×D47C211yesmaximal, characteristic
2C2×#13093941C211yesmaximal, characteristic, complemented
3C2×#13093940C212yesmaximal, complemented
4#15689086C212yesmaximal, complemented
5C2×#100×C47C211yesmaximal, characteristic, complemented
6C24×D47C412yes—
7C22×D188C2211yescharacteristic
8C22×C22⋊D47C412yes—
9C2×D4×D47—22no—
10C2×D4×D47—22no—
11C2×D4×D47—24no—
12C2×D4×D47—24no—
13C22×C4×D47C2211yescharacteristic
14C2×#10625329C2212yescomplemented
15#13093941—22no—
16#13093940—24no—
17(C2×D47)⋊C8—24no—
18C22×D4×C47C2211yescharacteristic
19C2×M16×C47C2212yescomplemented
20#100×C47—22no—
21C24×C47C2×C412yes—
22C23×D47—24no—
23C23×D47—24no—
24C23×D47—24no—
25C23×D47—48no—
26C23×D47C2×C411yescharacteristic
27C23×D47C2×C412yes—
28C2×D4×C47—22no—
29C2×D4×C47—22no—
30C2×D4×C47D412yes—
31C2×D4×C47D412yes—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—24no—
34C2×C22⋊D47—24no—
35C2×C22⋊D47—24no—
36C22×Dic47C2×C411yescharacteristic
37D4×D47—216no—
38D4×D47—216no—
39C2×D188—21no—
40C2×D188—22no—
41C2×D188—21no—
42C2×D188D414yes—
43C2×C4×D47—21no—
44C2×C4×D47—22no—
45C2×C4×D47—21no—
46C2×C4×D47D414yes—
47M16×C47—22no—
48M16×C47—22no—
49C2×C8×C47—22no—
50#10625329—22no—
51#10625329—22no—
52C2×C47⋊C8—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—44no—
56C23×C47C22⋊C414yes—
57C23×C47C22×C411yescharacteristic
58C22×D47—21no—
59C22×D47—21no—
60C22×D47—24no—
61C22×D47—216no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—416no—
65C22×D47—416no—
66C22×D47—48no—
67C22×D47—48no—
68C22×D47—44no—
69C22×D47C22⋊C412yes—
70C22×D47C22⋊C414yes—
71D4×C47—24no—
72D4×C47—24no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C22⋊D47—216no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47C22⋊C412yes—
81D188—24no—
82D188—24no—
83C4×D47—24no—
84C4×D47—24no—
85C8×C47—42no—
86C47⋊C8—42no—
87C22×C47—22no—
88C22×C47—24no—
89C22×C47—44no—
90C22×C47—44no—
91C22×C47—44no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47C2×C22⋊C411yescharacteristic
94C22×C47C2×C22⋊C411yescharacteristic
95C2×D47—24no—
96C2×D47—24no—
97C2×D47—22no—
98C2×D47—22no—
99C2×D47—24no—
100C2×D47—432no—
101C2×D47—44no—
102C2×D47—44no—
103C2×D47—44no—
104C2×D47#10014yescomplemented
105C4×C47#12012yes—
106C4×C47#12012yes—
107Dic47—22no—
108#1783—471nomaximal, Sylow
109C2×C47—21no—
110C2×C47—21no—
111C2×C47—44no—
112C2×C47#37911yescharacteristic
113C2×C47C2×#10012yes—
114D47—24no—
115D47—44no—
116C23×D4—471no—
117C2×#100—471no—
118C2×#100—472no—
119C2×#100D4711yescharacteristic, complemented
120#407—472no—
121C47#178311yescharacteristic, complemented, Sylow
122C25—472no—
123C22×D4—472no—
124C22×D4—471no—
125C22×D4—944no—
126C22×D4—944no—
127C22×D4—942no—
128C22×D4—942no—
129C22×D4C2×D4711yescharacteristic
130C23×C4—471no—
131C2×M16—472no—
132C2×M16C2×D4712yescomplemented
133#100—22no—
134#100—944no—
135#100—942no—
136C22⋊C8—944no—
137C24—471no—
138C24—472no—
139C24—944no—
140C24—944no—
141C24—944no—
142C24—1888no—
143C24C4×D4712yes—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—474no—
147C2×D4—944no—
148C2×D4—9416no—
149C2×D4—9416no—
150C2×D4—944no—
151C2×D4—944no—
152C2×D4—941no—
153C2×D4—942no—
154C2×D4—941no—
155C2×D4D18812yes—
156C2×D4C22⋊D4712yes—
157C22×C4—471no—
158C22×C4—474no—
159C22×C4—941no—
160C22×C4—942no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163M16—22no—
164M16—22no—
165M16—942no—
166M16—942no—
167C2×C8—22no—
168C2×C8—942no—
169C23—22no—
170C23—22no—
171C23—44no—
172C23—472no—
173C23—474no—
174C23—944no—
175C23—9416no—
176C23—941no—
177C23—941no—
178C23—942no—
179C23—942no—
180C23—1884no—
181C23—1888no—
182C23—18816no—
183C23—18816no—
184C23—1888no—
185C23(C2×D47)⋊C414yes—
186C23C2×C4×D4711yescharacteristic
187D4—24no—
188D4—24no—
189D4—9416no—
190D4—944no—
191D4—944no—
192C2×C4—472no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—944no—
196C2×C4—944no—
197C2×C4C2×D18811yescharacteristic
198C2×C4D4×D4712yes—
199C2×C4D4×D4712yes—
200C2×C4C2×C22⋊D4711yescharacteristic
201C8—42no—
202C8—1882no—
203C22—22no—
204C22—24no—
205C22—44no—
206C22—44no—
207C22—44no—
208C22—474no—
209C22—944no—
210C22—944no—
211C22—942no—
212C22—942no—
213C22—944no—
214C22—1884no—
215C22—1884no—
216C22—18832no—
217C22—1884no—
218C22C22⋊C4×D4711yescharacteristic
219C22C22⋊C4×D4711yescharacteristic
220C22C2×(C2×D47)⋊C411yescharacteristic
221C4—942no—
222C4#1309399212yes—
223C4#1309399412yes—
224C2—21no—
225C2—21no—
226C2—44no—
227C2—944no—
228C2—1884no—
229C2#1568897811yescharacteristic
230C2#100×D4712yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#100×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#100D47
hypocenterC47#1783
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#13093941C2semidirect
3. C2×#13093940C2semidirect
4. #15689086C2semidirect
5. C2×#100×C47C2semidirect
14. C2×#10625329C22semidirect
19. C2×M16×C47C22semidirect
104. C2×D47#100semidirect
119. C2×#100D47semidirect
121. C47#1783semidirect
132. C2×M16C2×D47semidirect