Finite Group Databasebeta

← #20243881

Subgroups — #20243881

Order 6016.

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

normal subgroups only

This group has 310 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
1C2×#13094057C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic
4#15689133C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic
6#15688880C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10#13094057—22no—
11#13094057—22no—
12C2×Dic188C412yescomplemented
13C2×#10625325C412yescomplemented
14C4×Dic94—22no—
15#13093989—22no—
16#13093983C2211yescharacteristic
17#13093983C2211yescharacteristic
18#13093980—22no—
19#13093950—22no—
20#13093949—22no—
21#13093938—22no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24#117×C47C2211yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27C22×Dic47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32C2×D188C2×C411yescharacteristic
33C2×C4×D47—21no—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94C2×C411yescharacteristic
38C2×Dic94C2×C412yes—
39C2×Dic94D412yes—
40C2×Dic94D412yes—
41M16×C47—21no—
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47C2×C412yes—
47C4⋊C4×C47—21no—
48C22⋊C4×C47D412yes—
49C42×C47—21no—
50C22⋊Dic47—21no—
51C22⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54Dic47⋊C4—24no—
55C4×Dic47—24no—
56C4×Dic47—21no—
57C4×Dic47D412yes—
58Dic188—24no—
59#10625325—24no—
60C23×C47C2×D411yescharacteristic
61C22×D47—21no—
62C2×C4×C47—22no—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C22⋊D47—41no—
70C22⋊D47—41no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—21no—
75C2×Dic47—22no—
76C2×Dic47—41no—
77D188—21no—
78D188—21no—
79C4×D47—41no—
80C4×D47—41no—
81Dic94—22no—
82Dic94—22no—
83Dic94—22no—
84Dic94—21no—
85Dic94—21no—
86Dic94C22⋊C414yes—
87C8×C47—22no—
88C8×C47—41no—
89C22×C47—41no—
90C22×C47C4×D411yescharacteristic
91C22×C47#12011yescharacteristic
92C22×C47#12111yescharacteristic
93C2×D47—41no—
94C2×D47—81no—
95C4×C47—42no—
96C4×C47C2×C22⋊C411yescharacteristic
97C4×C47C4×D411yescharacteristic
98C4×C47#12111yescharacteristic
99C4×C47#12311yescharacteristic
100Dic47—24no—
101Dic47—42no—
102Dic47—41no—
103Dic47—81no—
104#1905—471nomaximal, Sylow
105C2×C47—21no—
106C2×C47—21no—
107C2×C47—21no—
108C2×C47#38611yescharacteristic
109D47—81no—
110C2×#137—471no—
111#519—471no—
112#421—471no—
113#419—471no—
114#410—471no—
115#344D4711yescharacteristic, complemented
116H(3,ℤ/4)—471no—
117C47#190511yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C22×Q8—471no—
120#137—942no—
121#137—942no—
122C2×Q16—472no—
123C2×SD16—472no—
124C2×M16C2×D4711yescharacteristic
125C2×M16C2×D4711yescharacteristic
126C4×Q8—942no—
127C4×Q8—942no—
128#117—471no—
129#117—471no—
130#117—942no—
131#117C2×D4711yescharacteristic
132#104—942no—
133#103—942no—
134#99—942no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—472no—
140C2×Q8—471no—
141C2×Q8—472no—
142C2×Q8—472no—
143C2×Q8—941no—
144C2×Q8—941no—
145C2×Q8—941no—
146C2×D4—471no—
147C2×D4—941no—
148C22×C4—941no—
149C22×C4—941no—
150C22×C4C22×D4711yescharacteristic
151Q16—944no—
152SD16—944no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157C2×C8—21no—
158C2×C8C4×D4712yes—
159C4⋊C4—21no—
160C4⋊C4—944no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C22⋊C4—941no—
164C22⋊C4—941no—
165C22⋊C4D18812yes—
166C42—21no—
167C42—472no—
168C42—944no—
169C42—941no—
170C23—941no—
171C23C2×D18811yescharacteristic
172Q8—474no—
173Q8—942no—
174Q8—942no—
175Q8—942no—
176Q8—941no—
177Q8—941no—
178D4—941no—
179D4—941no—
180D4—1881no—
181D4—1881no—
182C2×C4—22no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—941no—
187C2×C4—942no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4#1062535011yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4D4×D4711yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4#1062535411yescharacteristic
197C8—22no—
198C8—41no—
199C22—41no—
200C22—3761no—
201C22—1881no—
202C22C4×D18811yescharacteristic
203C22#1309399411yescharacteristic
204C22#1309399911yescharacteristic
205C4—42no—
206C4—944no—
207C4—3761no—
208C4—1882no—
209C4—1881no—
210C4C22⋊C4×D4711yescharacteristic
211C4#1309398611yescharacteristic
212C4#1309399711yescharacteristic
213C4#1309400911yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—3761no—
218C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1905
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
4. #15689133C2semidirect
6. #15688880C2semidirect
7. C47×#344C2semidirect
12. C2×Dic188C4semidirect
13. C2×#10625325C4semidirect
115. #344D47semidirect
117. C47#1905semidirect