Finite Group Databasebeta

← #20243207

Subgroups — #20243207

Order 6016.

332 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093989C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3C2×#13093947C211yesmaximal, characteristic
4C2×C8×Dic47C211yesmaximal, characteristic
5C4⋊C4×Dic47C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13093989—22no—
11#13093989C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4—21no—
14C2×C4×Dic47—21no—
15C2×C4×Dic47—21no—
16C2×C4×Dic47C2211yescharacteristic
17#13093949C414yescomplemented
18#13093947C414yescomplemented
19C8×Dic47—22no—
20C47⋊#95—21no—
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47—21no—
29C22×Dic47D411yescharacteristic
30C22×Dic47D411yescharacteristic
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94C2×C412yes—
35C2×Dic94C2×C412yes—
36C2×Dic94C2×C412yes—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47C2×C412yes—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47C2×C412yes—
43C4⋊C4×C47C2×C412yes—
44C4⋊Dic47—21no—
45C4⋊Dic47C2×C412yes—
46Dic47⋊C4—24no—
47C4×Dic47—24no—
48C4×Dic47—42no—
49C4×Dic47C2×C412yes—
50C4×Dic47D412yes—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8C2×C412yes—
54C23×C47C2×D411yescharacteristic
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—22no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47C22⋊C412yes—
76C2×Dic47C22⋊C412yes—
77C2×Dic47SD1612yes—
78C2×Dic47Q1612yes—
79Dic94—22no—
80Dic94—22no—
81Dic94—22no—
82Dic94C4214yescomplemented
83C8×C47—22no—
84C47⋊C8—22no—
85C22×C47C2×C22⋊C411yescharacteristic
86C22×C47C4×D411yescharacteristic
87C22×C47C4×D411yescharacteristic
88C22×C47C2×SD1611yescharacteristic
89C22×C47C2×Q1611yescharacteristic
90C22×C47#13511yescharacteristic
91C22×C47#13511yescharacteristic
92C4×C47—42no—
93C4×C47—42no—
94C4×C47C2×C4211yescharacteristic
95C4×C47#11711yescharacteristic
96C4×C47C4×D411yescharacteristic
97C4×C47C4×D411yescharacteristic
98Dic47—24no—
99Dic47—22no—
100Dic47—42no—
101Dic47#10314yescomplemented
102C4×#103—471nomaximal, Sylow
103C2×C47C4×C22⋊C411yescharacteristic
104C2×C47C2×#10311yescharacteristic
105C2×C47#41611yescharacteristic
106C2×C47C4×SD1611yescharacteristic
107C2×C47C4×SD1611yescharacteristic
108C2×C47C4×Q1611yescharacteristic
109C2×C47C4×Q1611yescharacteristic
110C2×C4×Q8—471no—
111C2×#103—471no—
112C2×#103—471no—
113C2×C4×C8—471no—
114C4×C4⋊C4—471no—
115#340—471no—
116#340D4711yescharacteristic
117C47C4×#10311yescharacteristic, complemented, Sylow
118C22×Q8—471no—
119C22×C8—471no—
120C22×C8C2×D4711yescharacteristic
121C4×Q8—474no—
122C4×Q8—942no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—941no—
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C42—471no—
128C2×C42—941no—
129C2×C42—941no—
130#103—474no—
131#103—474no—
132C4×C8—942no—
133#95—941no—
134C2×Q8—472no—
135C2×Q8—472no—
136C2×Q8—472no—
137C2×Q8—941no—
138C2×Q8—941no—
139C2×Q8—941no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—941no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—472no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8C4×D4712yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—472no—
156C4⋊C4—944no—
157C4⋊C4—941no—
158C4⋊C4C4×D4712yes—
159C4⋊C4C4×D4712yes—
160C42—472no—
161C42—472no—
162C42—944no—
163C42—1882no—
164C23D4×D4711yescharacteristic
165Q8—474no—
166Q8—942no—
167Q8—942no—
168Q8—942no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—472no—
176C2×C4—472no—
177C2×C4—472no—
178C2×C4—472no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—942no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4C2×C4×D4711yescharacteristic
188C2×C4C2×C4×D4711yescharacteristic
189C2×C4C2×C4×D4711yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4#1062535211yescharacteristic
192C2×C4#1062535411yescharacteristic
193C8—22no—
194C8—942no—
195C22C22⋊C4×D4711yescharacteristic
196C22(C22⋊D47)⋊C411yescharacteristic
197C22#1309398611yescharacteristic
198C22SD16×D4711yescharacteristic
199C22Q16×D4711yescharacteristic
200C22#1309404311yescharacteristic
201C22#1309404511yescharacteristic
202C4—42no—
203C4—42no—
204C4—474no—
205C4—944no—
206C4—942no—
207C4—1882no—
208C4C42×D4711yescharacteristic
209C4#1309398211yescharacteristic
210C4(C22⋊D47)⋊C411yescharacteristic
211C4#1309398611yescharacteristic
212C2#1568897011yescharacteristic
213C2#103×D4711yescharacteristic
214C2#1568911611yescharacteristic
215C2#1568921011yescharacteristic
216C2#1568921411yescharacteristic
217C2#1568921511yescharacteristic
218C2#1568921711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47C4×#103
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #13093989C4semidirect
17. #13093949C4semidirect
18. #13093947C4semidirect
82. Dic94C42semidirect
101. Dic47#103semidirect
117. C47C4×#103semidirect