Finite Group Databasebeta

← #20243392

Subgroups — #20243392

Order 6016.

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

normal subgroups only

This group has 308 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
1C2×#13093989C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic
3C2×#13093949C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic
5#15688992C211yesmaximal, 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×Dic47⋊C4—21no—
15C2×Dic47⋊C4—21no—
16C2×C4×Dic47—21no—
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—22no—
19#13093949—22no—
20#13093947—22no—
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×Dic94D412yes—
36C2×Dic94Q812yes—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47C2×C412yes—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46Dic47⋊C4—24no—
47Dic47⋊C4—42no—
48Dic47⋊C4—42no—
49C4×Dic47—24no—
50C4×Dic47C2×C412yes—
51C4×Dic47D412yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C2×C4×C47—22no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×Q811yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47C22⋊C412yes—
77C2×Dic47C22⋊C412yes—
78C2×Dic47SD1612yes—
79C2×Dic47Q1612yes—
80Dic94—22no—
81Dic94—22no—
82Dic94—22no—
83Dic94C4⋊C414yescomplemented
84C8×C47—41no—
85C47⋊C8—41no—
86C22×C47C2×C22⋊C411yescharacteristic
87C22×C47#12111yescharacteristic
88C22×C47C22⋊Q811yescharacteristic
89C22×C47C2×SD1611yescharacteristic
90C22×C47C2×Q1611yescharacteristic
91C22×C47AGL(1,ℤ/8)11yescharacteristic
92C22×C47#13711yescharacteristic
93C4×C47—42no—
94C4×C47—81no—
95C4×C47C2×C4⋊C411yescharacteristic
96C4×C47#11711yescharacteristic
97C4×C47#12111yescharacteristic
98C4×C47C22⋊Q811yescharacteristic
99Dic47—24no—
100Dic47—22no—
101Dic47—81no—
102Dic47#10314yescomplemented
103#1803—471nomaximal, Sylow
104C2×C47#38011yescharacteristic
105C2×C47C2×#10311yescharacteristic
106C2×C47#41711yescharacteristic
107C2×C47#46011yescharacteristic
108C2×C47#46211yescharacteristic
109C2×C47#47511yescharacteristic
110C2×C47#47711yescharacteristic
111C2×C4×Q8—471no—
112C2×C4⋊C8—471no—
113C2×#103—471no—
114C2×#103—471no—
115#384—471no—
116#340—471no—
117#340D4711yescharacteristic
118C47#180311yescharacteristic, complemented, Sylow
119C22×Q8—471no—
120C22×C8—471no—
121C22×C8C2×D4711yescharacteristic
122C4×Q8—474no—
123C4×Q8—942no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—941no—
126C2×C4⋊C4—941no—
127C2×C4⋊C4—941no—
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C4⋊C4C2×D4711yescharacteristic
130C2×C42—471no—
131C2×C42—941no—
132C4⋊C8—942no—
133#103—942no—
134#103—942no—
135C2×Q8—472no—
136C2×Q8—472no—
137C2×Q8—472no—
138C2×Q8—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—471no—
144C22×C4—471no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4C22×D4711yescharacteristic
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—941no—
152C2×C8—941no—
153C2×C8—941no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—944no—
158C4⋊C4—941no—
159C4⋊C4—941no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4C4×D4712yes—
163C42—472no—
164C42—472no—
165C42—944no—
166C23D4×D4711yescharacteristic
167Q8—474no—
168Q8—942no—
169Q8—942no—
170Q8—942no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—472no—
178C2×C4—472no—
179C2×C4—472no—
180C2×C4—472no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—941no—
185C2×C4—941no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4—1881no—
189C2×C4C2×C4×D4711yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4#1062535011yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4Q8×D4711yescharacteristic
195C8—41no—
196C8—1881no—
197C22C22⋊C4×D4711yescharacteristic
198C22#1309399711yescharacteristic
199C22#1309400211yescharacteristic
200C22SD16×D4711yescharacteristic
201C22Q16×D4711yescharacteristic
202C22#1309404811yescharacteristic
203C22#1309405311yescharacteristic
204C4—42no—
205C4—81no—
206C4—474no—
207C4—944no—
208C4—942no—
209C4—3761no—
210C4C4⋊C4×D4711yescharacteristic
211C4#1309398111yescharacteristic
212C4#1309399711yescharacteristic
213C4#1309400211yescharacteristic
214C2#1568898211yescharacteristic
215C2#103×D4711yescharacteristic
216C2#1568912111yescharacteristic
217C2#1568932211yescharacteristic
218C2#1568933211yescharacteristic
219C2#1568940711yescharacteristic
220C2#1568941711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1803
LCSG ▷ C2×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
83. Dic94C4⋊C4semidirect
102. Dic47#103semidirect
118. C47#1803semidirect