Finite Group Databasebeta

← #20243922

Subgroups — #20243922

Order 6016.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#15689694C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689140C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic, complemented
5#15688880C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094022C412yescomplemented
11#13094011C412yescomplemented
12#13094005—22no—
13#13094003—22no—
14C4×Dic94—22no—
15#13093989—22no—
16#13093983C2211yescharacteristic
17#13093983C2211yescharacteristic
18#13093980—22no—
19#13093951—22no—
20#13093942—22no—
21C2×#41×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#104×C47—22no—
25#41×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29C2×Q8×C47C2×C411yescharacteristic
30C2×D4×C47—21no—
31C2×D4×C47C2×C411yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47D412yes—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94C2×C412yes—
40C2×Dic94D412yes—
41M16×C47—21no—
42M16×C47—21no—
43C2×C8×C47—21no—
44C4⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C42×C47D412yes—
47C22⋊Dic47—21no—
48C22⋊Dic47—21no—
49C22⋊Dic47—24no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54C4×Dic47—24no—
55C4×Dic47C2×C412yes—
56C4×Dic47D412yes—
57#10625329—21no—
58#10625329—21no—
59C2×C47⋊C8—21no—
60C23×C47—21no—
61C23×C47C2×D411yescharacteristic
62Q8×C47—21no—
63Q8×C47—21no—
64D4×C47—21no—
65D4×C47—21no—
66D4×C47—41no—
67D4×C47—41no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47C22⋊C414yes—
83Dic94—22no—
84Dic94—22no—
85Dic94—22no—
86Dic94—22no—
87C8×C47—41no—
88C47⋊C8—41no—
89C22×C47—41no—
90C22×C47—42no—
91C22×C47—41no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47#12011yescharacteristic
94C22×C47#12311yescharacteristic
95C4×C47—42no—
96C4×C47—41no—
97C4×C47C4×D411yescharacteristic
98C4×C47C4×D411yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12111yescharacteristic
101Dic47—24no—
102Dic47—42no—
103Dic47—42no—
104#1912—471nomaximal, Sylow
105C2×C47—21no—
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—81no—
109C2×C47#38611yescharacteristic
110#536—471no—
111#519—471no—
112#421—471no—
113#421D4711yescharacteristic
114C2×#101—471no—
115H(3,ℤ/4)—471no—
116H(3,ℤ/4)—471no—
117C47#191211yescharacteristic, complemented, Sylow
118C2×#41C2×D4711yescharacteristic
119C22×Q8—471no—
120C2×M16—471no—
121C2×M16C2×D4711yescharacteristic
122C4⋊Q8—472no—
123#124—472no—
124#123—942no—
125C22⋊Q8—942no—
126C4×Q8—942no—
127C4×Q8—942no—
128#117—471no—
129#117—471no—
130#117—942no—
131#117C2×D4711yescharacteristic
132#104—22no—
133#104—942no—
134#101—942no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—472no—
140C2×Q8—472no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×Q8—941no—
145C2×Q8C4×D4711yescharacteristic
146C2×D4—21no—
147C2×D4C4×D4711yescharacteristic
148C22×C4—21no—
149C22×C4—472no—
150C22×C4C22×D4711yescharacteristic
151M16—21no—
152M16—21no—
153M16—941no—
154M16—941no—
155C2×C8—21no—
156C2×C8—941no—
157C4⋊C4—21no—
158C4⋊C4—944no—
159C4⋊C4—944no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C22⋊C4—21no—
163C22⋊C4—944no—
164C22⋊C4—941no—
165C22⋊C4—941no—
166C42—472no—
167C42—472no—
168C42—944no—
169C42C22⋊D4712yes—
170C23—21no—
171C23D4×D4711yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—942no—
175Q8—942no—
176Q8—942no—
177Q8—942no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—474no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4#1062535011yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4D4×D4711yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—41no—
198C8—1881no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22⋊C4×D4711yescharacteristic
203C22#1309399211yescharacteristic
204C22#1309400611yescharacteristic
205C4—42no—
206C4—41no—
207C4—944no—
208C4—1882no—
209C4—1882no—
210C4(C22⋊D47)⋊C411yescharacteristic
211C4C4×C22⋊D4711yescharacteristic
212C4#1309399511yescharacteristic
213C4#1309399711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#386
hypercenter#421D47
hypocenterC47#1912
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
4. C2×#13093942C2semidirect
5. #15688880C2semidirect
6. #15688879C2semidirect
10. #13094022C4semidirect
11. #13094011C4semidirect
117. C47#1912semidirect