Finite Group Databasebeta

← #20243613

Subgroups — #20243613

Order 6016.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#15689604C211yesmaximal, characteristic
2#15689163C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic
4#15689122C211yesmaximal, characteristic
5#15688892C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C47×#384C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13093989—21no—
12#13093986—21no—
13C4×C22⋊D47—22no—
14#13093983C2211yescharacteristic
15#13093982—21no—
16C4⋊C4×D47—21no—
17#13093957—21no—
18#13093955—21no—
19#13093952C414yescomplemented
20#13093947—21no—
21#13093944—21no—
22C2×C4⋊C4×C47—22no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C42×C47C2211yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47D412yes—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31#10625350—21no—
32#10625350—21no—
33#10625350C2×C412yes—
34#10625350Q812yes—
35C2×D188D411yescharacteristic
36C2×C4×D47—21no—
37C2×C4×D47—22no—
38C2×Dic94D411yescharacteristic
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—44no—
44C42×C47—21no—
45C42×C47C2×C412yescomplemented
46C22⋊Dic47—21no—
47(C2×D47)⋊C4—22no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—22no—
51C4×Dic47—22no—
52C4×Dic47—21no—
53#10625329—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329C2×C412yescomplemented
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47C2×D411yescharacteristic
60C22×D47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47—41no—
68C2×C4×C47C22×C411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×Q811yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C22⋊D47—22no—
75C22⋊D47—22no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79D188—21no—
80D188C4⋊C412yescomplemented
81C4×D47—22no—
82C4×D47—22no—
83C4×D47—82no—
84Dic94—21no—
85Dic94C4⋊C412yescomplemented
86C47⋊C8—22no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47C4×D411yescharacteristic
91C22×C47#12011yescharacteristic
92C22×C47C22⋊Q811yescharacteristic
93C2×D47—22no—
94C2×D47—41no—
95C2×D47—41no—
96C4×C47—24no—
97C4×C47—42no—
98C4×C47—81no—
99C4×C47C2×C4⋊C411yescharacteristic
100C4×C47C4×D411yescharacteristic
101C4×C47C22⋊Q811yescharacteristic
102C4×C47#12311yescharacteristic
103Dic47—22no—
104Dic47—41no—
105Dic47—41no—
106#1859—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47#38511yescharacteristic
110C2×C47#45311yescharacteristic
111C2×C47#45611yescharacteristic
112D47—42no—
113#520—471no—
114#428—471no—
115C2×#104—471no—
116#417—471no—
117#384D4711yescharacteristic, complemented
118#343—471no—
119#339—471no—
120C47#185911yescharacteristic, complemented, Sylow
121C2×#41—471no—
122C2×M16—471no—
123C2×M16—471no—
124C4×Q8—941no—
125C4×D4—941no—
126C4×D4—942no—
127#117—471no—
128#117—941no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—941no—
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C42C2×D4711yescharacteristic
134#107—941no—
135#106—941no—
136#104—474no—
137#103—941no—
138#102—941no—
139#41—472no—
140#41—472no—
141#41—941no—
142#41—941no—
143C2×Q8—471no—
144C2×D4—471no—
145C2×D4—941no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—942no—
149C22×C4—941no—
150C22×C4C22⋊D4712yes—
151C22×C4C22×D4711yescharacteristic
152M16—472no—
153M16—941no—
154M16—941no—
155M16—941no—
156C2×C8—941no—
157C2×C8—941no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—44no—
163C4⋊C4—471no—
164C4⋊C4—471no—
165C4⋊C4—942no—
166C22⋊C4—942no—
167C22⋊C4—941no—
168C42—21no—
169C42—942no—
170C42—941no—
171C42C4×D4712yescomplemented
172C23—941no—
173C23C2×C22⋊D4711yescharacteristic
174Q8—472no—
175Q8—941no—
176D4—472no—
177D4—942no—
178D4—942no—
179D4—941no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—941no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—3762no—
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4#1062535011yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4Q8×D4711yescharacteristic
198C2×C4#1062535411yescharacteristic
199C8—942no—
200C8—1881no—
201C22—21no—
202C22—21no—
203C22—942no—
204C22—1881no—
205C22—1881no—
206C22C4×C22⋊D4711yescharacteristic
207C22#1309399211yescharacteristic
208C22#1309400011yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—942no—
213C4—1881no—
214C4—1881no—
215C4C4⋊C4×D4711yescharacteristic
216C4#1309398611yescharacteristic
217C4#1309400211yescharacteristic
218C4#1309400911yescharacteristic
219C2—21no—
220C2—21no—
221C2—1882no—
222C2#1568899411yescharacteristic
223C2#1568929011yescharacteristic
224C2#1568930511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#384C2
socleC22×C47#120
hypercenter#384D47
hypocenterC47#1859
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #15689163C2semidirect
5. #15688892C2semidirect
6. #15688883C2semidirect
7. C47×#384C2semidirect
19. #13093952C4semidirect
45. C42×C47C2×C4semidirect
56. #10625329C2×C4semidirect
80. D188C4⋊C4semidirect
85. Dic94C4⋊C4semidirect
117. #384D47semidirect
120. C47#1859semidirect
171. C42C4×D47semidirect