Finite Group Databasebeta

← #20243862

Subgroups — #20243862

Order 6016.

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

normal subgroups only

This group has 304 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#15689889C211yesmaximal, characteristic
3#15689139C211yesmaximal, characteristic
4#15689133C211yesmaximal, characteristic, complemented
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15688894C211yesmaximal, characteristic, complemented
7C47×#338C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10#13094057—22no—
11#13094057—22no—
12C2×Dic188C412yescomplemented
13C2×#10625325C412yescomplemented
14#13094032—22no—
15#13094030—22no—
16C2×#10625329C2211yescharacteristic
17M16×D47—22no—
18#13093983C2211yescharacteristic
19#13093950—22no—
20#13093949—22no—
21#13093942—22no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27C22×Dic47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350D412yes—
31#10625350D412yes—
32C2×D188C2×C411yescharacteristic
33C2×C4×D47—21no—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94C2×C412yes—
40C2×Dic94C2×C411yescharacteristic
41M16×C47—21no—
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47—21no—
46M16×C47—21no—
47C2×C8×C47—21no—
48C2×C8×C47C2×C412yes—
49C2×C8×C47D412yes—
50C22⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4×Dic47—21no—
53#10625329—21no—
54#10625329D412yes—
55C2×C47⋊C8—21no—
56Dic188—24no—
57#10625325—24no—
58#10625324—24no—
59C8×D47—24no—
60C23×C47#4111yescharacteristic
61C22×D47—21no—
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C22⋊D47—22no—
69C22⋊D47—22no—
70C2×Dic47—21no—
71C2×Dic47—22no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75D188—21no—
76D188C22⋊C412yes—
77C4×D47—22no—
78C4×D47—22no—
79Dic94—21no—
80Dic94—22no—
81Dic94—22no—
82Dic94—41no—
83Dic94—41no—
84Dic94C22⋊C412yes—
85C8×C47—22no—
86C8×C47—22no—
87C8×C47—41no—
88C47⋊C8—22no—
89C22×C47—41no—
90C22×C47C4×D411yescharacteristic
91C22×C47#12111yescharacteristic
92C22×C47#12311yescharacteristic
93C2×D47—22no—
94C2×D47—81no—
95C4×C47C2×C22⋊C411yescharacteristic
96C4×C47C4×D411yescharacteristic
97C4×C47#12011yescharacteristic
98C4×C47#12111yescharacteristic
99Dic47—22no—
100Dic47—42no—
101Dic47—81no—
102#1902—471nomaximal, Sylow
103C2×C47—21no—
104C2×C47—21no—
105C2×C47—21no—
106C2×C47#38611yescharacteristic
107D47—42no—
108C2×#137—471no—
109#568—471no—
110#421—471no—
111#419—471no—
112C2×#101—471no—
113#344—471no—
114#338D4711yescharacteristic, complemented
115C47#190211yescharacteristic, complemented, Sylow
116C2×#41—471no—
117C22×Q8—471no—
118#137—942no—
119#137—942no—
120C2×Q16—472no—
121C2×SD16—472no—
122#131—942no—
123#131—942no—
124C2×M16—471no—
125C2×M16—942no—
126C2×M16C2×D4711yescharacteristic
127C2×M16C2×D4711yescharacteristic
128C2×M16C2×D4711yescharacteristic
129#117—471no—
130#104—942no—
131#103—942no—
132#101—942no—
133#41—472no—
134#41—472no—
135#41—941no—
136#41—941no—
137C2×Q8—471no—
138C2×Q8—472no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×D4—471no—
145C2×D4—941no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4C22×D4711yescharacteristic
149Q16—944no—
150SD16—944no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—472no—
158M16—944no—
159M16—941no—
160C2×C8—21no—
161C2×C8—944no—
162C2×C8—941no—
163C2×C8C4×D4712yes—
164C2×C8D18812yes—
165C4⋊C4—941no—
166C22⋊C4—941no—
167C42—941no—
168C23—941no—
169C23#1062535411yescharacteristic
170Q8—472no—
171Q8—941no—
172Q8—942no—
173Q8—942no—
174Q8—1881no—
175Q8—1881no—
176D4—472no—
177D4—942no—
178D4—942no—
179D4—941no—
180C2×C4—941no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4C2×C4×D4711yescharacteristic
188C2×C4C2×D18811yescharacteristic
189C2×C4#1062535011yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C8—22no—
194C8—22no—
195C8—41no—
196C8—942no—
197C22—41no—
198C22—942no—
199C22—3761no—
200C22#1309398611yescharacteristic
201C22#1309399911yescharacteristic
202C22#1309400911yescharacteristic
203C4—942no—
204C4—3761no—
205C4—1882no—
206C4C22⋊C4×D4711yescharacteristic
207C4C4×D18811yescharacteristic
208C4#1309399411yescharacteristic
209C4#1309399711yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—1882no—
214C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#338C2
socleC2×C47#386
hypercenter#338D47
hypocenterC47#1902
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
4. #15689133C2semidirect
5. C2×#13093942C2semidirect
6. #15688894C2semidirect
7. C47×#338C2semidirect
12. C2×Dic188C4semidirect
13. C2×#10625325C4semidirect
114. #338D47semidirect
115. C47#1902semidirect