Finite Group Databasebeta

← #20243419

Subgroups — #20243419

Order 6016.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10625329C211yesmaximal, characteristic
2C2×#13093957C211yesmaximal, characteristic, complemented
3C2×#13093955C211yesmaximal, characteristic, complemented
4#15688983C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#380C211yesmaximal, characteristic
8C2×#10625329—22no—
9C2×#10625329—22no—
10C2×#10625329C414yescomplemented
11C22×C47⋊C8C2211yescharacteristic
12C22×C47⋊C8C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47—21no—
16#13093957—22no—
17#13093955—22no—
18C47⋊#95—21no—
19C23×C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C22⋊C4×C47—21no—
23#95×C47—21no—
24C24×C47D411yescharacteristic
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47C2×C412yes—
32C22×C4×C47D411yescharacteristic
33C22×C4×C47Q812yes—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—21no—
36C22×Dic47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C22⋊C4×C47—42no—
42C22⋊Dic47—42no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47#10625329—28no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8C2×C412yes—
51C2×C47⋊C8C2×C412yes—
52C2×C47⋊C8D412yes—
53C2×C47⋊C8D412yes—
54C23×C47—21no—
55C23×C47—21no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—21no—
60C23×C47C4⋊C412yes—
61C23×C47C2×D411yescharacteristic
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47C4⋊C412yes—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×Q811yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C47⋊C8—22no—
88C47⋊C8C22⋊C414yescomplemented
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—22no—
92C22×C47—41no—
93C22×C47—41no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47C2×C4⋊C411yescharacteristic
97C22×C47#12111yescharacteristic
98C22×C47#12111yescharacteristic
99C22×C47AGL(1,ℤ/8)11yescharacteristic
100C22×C47AGL(1,ℤ/8)11yescharacteristic
101C22×C47#13711yescharacteristic
102C22×C47#13711yescharacteristic
103C4×C47—22no—
104C4×C47—81no—
105C4×C47—81no—
106C4×C47C2×C22⋊C411yescharacteristic
107C4×C47#11711yescharacteristic
108C4×C47C22⋊Q811yescharacteristic
109C4×C47C22⋊Q811yescharacteristic
110Dic47—81no—
111Dic47—81no—
112#1809—471nomaximal, Sylow
113C2×C47—42no—
114C2×C47#38011yescharacteristic
115C2×C47#42811yescharacteristic
116C2×C47#42811yescharacteristic
117C2×C47#46811yescharacteristic
118C2×C47#46811yescharacteristic
119C2×C47#46911yescharacteristic
120C2×C47#47011yescharacteristic
121C22×M16—471no—
122C2×#107—471no—
123C2×#106—471no—
124#380—471no—
125#380D4711yescharacteristic
126#340—471no—
127#340—471no—
128C47#180911yescharacteristic, complemented, Sylow
129C23×C4C2×D4711yescharacteristic
130C2×M16—474no—
131C2×M16—942no—
132C2×M16—942no—
133C22×C8—471no—
134C22×C8—471no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—471no—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—21no—
140C2×C22⋊C4—941no—
141#107—942no—
142#106—942no—
143#95—21no—
144#95—941no—
145C24C22⋊D4711yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—941no—
153C22×C4—941no—
154C22×C4Dic9412yes—
155C22×C4C4×D4712yes—
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22×D4711yescharacteristic
158M16—948no—
159C2×C8—472no—
160C2×C8—472no—
161C2×C8—472no—
162C2×C8—472no—
163C2×C8—941no—
164C2×C8—941no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C4⋊C4—941no—
173C22⋊C4—42no—
174C22⋊C4—1882no—
175C23—21no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23Dic47⋊C412yes—
182C23C2×C22⋊D4711yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4—1881no—
200C2×C4—1881no—
201C2×C4Dic47⋊C412yes—
202C2×C4C2×Dic9411yescharacteristic
203C2×C4C2×C4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4D4×D4711yescharacteristic
206C2×C4#1062535211yescharacteristic
207C2×C4#1062535211yescharacteristic
208C8—474no—
209C8—942no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×Dic47⋊C411yescharacteristic
218C22#1309399611yescharacteristic
219C22#1309399611yescharacteristic
220C22#1309404911yescharacteristic
221C22#1309405011yescharacteristic
222C22#1309405411yescharacteristic
223C22#1309405511yescharacteristic
224C4—22no—
225C4—81no—
226C4—81no—
227C4—3761no—
228C4—3761no—
229C4C22⋊C4×D4711yescharacteristic
230C4#1309398011yescharacteristic
231C4#1309400111yescharacteristic
232C4#1309400111yescharacteristic
233C2—42no—
234C2#1568898111yescharacteristic
235C2#1568916311yescharacteristic
236C2#1568916611yescharacteristic
237C2#1568936711yescharacteristic
238C2#1568937111yescharacteristic
239C2#1568937411yescharacteristic
240C2#1568937911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#380C2
socleC23×C47C2×D4
hypercenter#380D47
hypocenterC47#1809
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#13093957C2semidirect
3. C2×#13093955C2semidirect
5. #15688885C2semidirect
6. #15688885C2semidirect
10. C2×#10625329C4semidirect
88. C47⋊C8C22⋊C4semidirect
128. C47#1809semidirect