Finite Group Databasebeta

← #20244012

Subgroups — #20244012

Order 6016.

290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13093945C211yesmaximal, characteristic
3C2×#13093945C211yesmaximal, characteristic
4C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C47×#390C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4×Dic47—21no—
13#13093955—22no—
14#13093945—22no—
15#13093945C414yescomplemented
16C47⋊#95—21no—
17C22×D4×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47—21no—
20C2×C22⋊C4×C47—21no—
21C2×C42×C47C2211yescharacteristic
22C24×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47C2×C412yes—
29C22×C4×C47—21no—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C22⋊C4×C47—42no—
38C22⋊C4×C47—42no—
39C42×C47—21no—
40C42×C47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47C2×C412yes—
44C4⋊Dic47D412yes—
45C4×Dic47—42no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8C2×C412yes—
52C23×C47—22no—
53C23×C47—41no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47—41no—
59C23×C47C2×D411yescharacteristic
60D4×C47—22no—
61D4×C47—22no—
62D4×C47—41no—
63D4×C47—41no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47SD1612yes—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47—81no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47—81no—
94C22×C47C4×D411yescharacteristic
95C22×C47#12111yescharacteristic
96C22×C47#12311yescharacteristic
97C22×C47C2×SD1611yescharacteristic
98C22×C47#13511yescharacteristic
99C22×C47AGL(1,ℤ/8)11yescharacteristic
100C22×C47AGL(1,ℤ/8)11yescharacteristic
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—81no—
104C4×C47#11711yescharacteristic
105C4×C47C4×D411yescharacteristic
106C4×C47#12411yescharacteristic
107C4×C47#12611yescharacteristic
108Dic47—42no—
109Dic47—42no—
110#1926—471nomaximal, Sylow
111C2×C47—82no—
112C2×C47#38811yescharacteristic
113C2×C47C4×SD1611yescharacteristic
114C2×C47#44211yescharacteristic
115C2×C47#46011yescharacteristic
116C2×C47#46311yescharacteristic
117C2×C47#48111yescharacteristic
118C2×C47#48211yescharacteristic
119C2×#106—471no—
120C2×#102—471no—
121C2×#102—471no—
122#390D4711yescharacteristic
123C4×C4⋊C4—471no—
124#340—471no—
125#336—471no—
126C47#192611yescharacteristic, complemented, Sylow
127C22×D4C2×D4711yescharacteristic
128C22×C8—471no—
129C22×C8—471no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C42—941no—
136C2×C42C2×D4711yescharacteristic
137#106—942no—
138#102—474no—
139#102—942no—
140#95—941no—
141C24—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C4×D4712yes—
148C22×C4—21no—
149C22×C4—941no—
150C22×C4—941no—
151C22×C4C22⋊D4711yescharacteristic
152C22×C4C22⋊D4711yescharacteristic
153C22×C4C22×D4711yescharacteristic
154C2×C8—472no—
155C2×C8—941no—
156C2×C8—941no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8—941no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—472no—
163C4⋊C4—472no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C42—21no—
169C42—21no—
170C42—1882no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23C2×C22⋊D4711yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—1881no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4#1062533512yes—
198C2×C4C2×C4×D4711yescharacteristic
199C2×C4#1062535011yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4#1062535211yescharacteristic
202C2×C4#1062535211yescharacteristic
203C2×C4#1062535211yescharacteristic
204C8—942no—
205C8—1881no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22C4×C22⋊D4711yescharacteristic
214C22#1309399511yescharacteristic
215C22#1309400511yescharacteristic
216C22C2×#1062533511yescharacteristic
217C22#1309404411yescharacteristic
218C22#1309404911yescharacteristic
219C22#1309405011yescharacteristic
220C4—22no—
221C4—41no—
222C4—81no—
223C4—1882no—
224C4—1882no—
225C4#1309398011yescharacteristic
226C4(C22⋊D47)⋊C411yescharacteristic
227C4#1309401011yescharacteristic
228C4#1309401711yescharacteristic
229C2—82no—
230C2#1568901111yescharacteristic
231C2C4×#1062533511yescharacteristic
232C2#1568923311yescharacteristic
233C2#1568932011yescharacteristic
234C2#1568933511yescharacteristic
235C2#1568943911yescharacteristic
236C2#1568944411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC23×C47C2×D4
hypercenter#390D47
hypocenterC47#1926
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13093955C2semidirect
4. C4×C4⋊Dic47C2semidirect
5. #15688885C2semidirect
6. #15688878C2semidirect
15. #13093945C4semidirect
126. C47#1926semidirect