Finite Group Databasebeta

← #20244244

Subgroups — #20244244

Order 6016.

348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13093956C211yesmaximal, characteristic, complemented
2C2×#13093948C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4C2×C8×Dic47C211yesmaximal, characteristic, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15689026C211yesmaximal, characteristic
7C22×SD16×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C22⋊Dic47—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093956—22no—
14#13093948—22no—
15#13093945—22no—
16C8×Dic47—22no—
17C47⋊#95—22no—
18C22×Q8×C47C2211yescharacteristic
19C22×D4×C47C2211yescharacteristic
20C2×SD16×C47—22no—
21C2×SD16×C47—22no—
22C2×SD16×C47C414yescomplemented
23C22×C8×C47C2211yescharacteristic
24C24×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47C2×C412yes—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47C2×C412yes—
37C22×C4×C47—21no—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C22×Dic47—21no—
41C22×Dic47D412yes—
42SD16×C47—28no—
43C2×C8×C47C2×C412yes—
44C2×C8×C47D412yes—
45C2×C8×C47D412yes—
46C22⋊Dic47—44no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8D412yes—
56C23×C47—22no—
57C23×C47—41no—
58C23×C47—41no—
59C23×C47—42no—
60C23×C47—42no—
61C23×C47C2×D411yescharacteristic
62Q8×C47—22no—
63Q8×C47—22no—
64Q8×C47—41no—
65Q8×C47—41no—
66D4×C47—22no—
67D4×C47—22no—
68D4×C47—41no—
69D4×C47—41no—
70C2×C4×C47—22no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47SD1614yescomplemented
86C8×C47C22⋊C414yescomplemented
87C47⋊C8—22no—
88C22×C47—42no—
89C22×C47—44no—
90C22×C47—82no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47C4×D411yescharacteristic
94C22×C47#12111yescharacteristic
95C22×C47#12711yescharacteristic
96C22×C47C2×SD1612yes—
97C22×C47#13512yes—
98C4×C47—42no—
99C4×C47C2×C22⋊C411yescharacteristic
100C4×C47C4×D411yescharacteristic
101C4×C47#12111yescharacteristic
102C4×C47#12411yescharacteristic
103Dic47—24no—
104Dic47—81no—
105Dic47—81no—
106#1968—471nomaximal, Sylow
107C2×C47—82no—
108C2×C47#39011yescharacteristic
109C2×C47C4×SD1612yes—
110C2×C47#46512yes—
111C2×C47#49211yescharacteristic
112C2×C47#49511yescharacteristic
113C22×SD16D4711yescharacteristic
114C2×#106—471no—
115C2×#103—471no—
116C2×#102—471no—
117C2×C4×C8—471no—
118#391—471no—
119#390—471no—
120C47#196811yescharacteristic, complemented, Sylow
121C22×Q8C2×D4711yescharacteristic
122C22×D4C2×D4711yescharacteristic
123C2×SD16—22no—
124C2×SD16—22no—
125C2×SD16Dic4714yescomplemented
126C22×C8—471no—
127C22×C8C2×D4711yescharacteristic
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C22⋊C4—942no—
131C2×C42—471no—
132#106—942no—
133#103—942no—
134#102—942no—
135C4×C8—942no—
136#95—942no—
137C24—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C2×Dic4712yes—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C2×Dic4712yes—
150C22×C4—21no—
151C22×C4—472no—
152C22×C4—941no—
153C22×C4—941no—
154C22×C4C22×D4711yescharacteristic
155SD16—28no—
156C2×C8—472no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8C2×Dic4712yes—
160C2×C8C22⋊D4712yes—
161C2×C8C22⋊D4712yes—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C22⋊C4—1884no—
167C42—941no—
168C42—941no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D4711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—474no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4—1882no—
192C2×C4—1882no—
193C2×C4D4×D4711yescharacteristic
194C2×C4#1062535211yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C22×Dic4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C8—942no—
200C8C22⋊Dic4714yescomplemented
201C22—42no—
202C22—44no—
203C22—81no—
204C22—81no—
205C22—82no—
206C22D4×Dic4711yescharacteristic
207C22#1309399511yescharacteristic
208C22#1309402011yescharacteristic
209C22SD16×D4712yes—
210C22#1309404512yes—
211C4—42no—
212C4—944no—
213C4—3761no—
214C4—3761no—
215C4C2×C22⋊Dic4711yescharacteristic
216C4D4×Dic4711yescharacteristic
217C4#1309399511yescharacteristic
218C4#1309401111yescharacteristic
219C2—82no—
220C2#1568902611yescharacteristic
221C2SD16×Dic4712yes—
222C2#1568934912yes—
223C2#1568949411yescharacteristic
224C2#1568950411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC23×C47C2×D4
hypercenterC22×SD16D47
hypocenterC47#1968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13093956C2semidirect
2. C2×#13093948C2semidirect
4. C2×C8×Dic47C2semidirect
5. #15689030C2semidirect
22. C2×SD16×C47C4semidirect
85. C2×Dic47SD16semidirect
86. C8×C47C22⋊C4semidirect
120. C47#1968semidirect
125. C2×SD16Dic47semidirect
200. C8C22⋊Dic47semidirect