Finite Group Databasebeta

← #20243869

Subgroups — #20243869

Order 6016.

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

normal subgroups only

This group has 324 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×#13094052C211yesmaximal, characteristic
2#15689889C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic, complemented
4#15689129C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688894C211yesmaximal, characteristic, complemented
7C47×#338C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×D188C2211yescharacteristic
10#13094052—22no—
11#13094052—22no—
12C2×#10625325C412yescomplemented
13C2×D376C412yescomplemented
14#13094032—22no—
15#13094030—22no—
16C2×#10625329C2211yescharacteristic
17M16×D47—22no—
18#13093983C2211yescharacteristic
19#13093950—22no—
20#13093946—22no—
21#13093940—22no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C23×D47—21no—
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350D412yes—
31#10625350D412yes—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188C2×C412yes—
38C2×D188C2×C411yescharacteristic
39C2×C4×D47—21no—
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—
56D376—24no—
57#10625325—24no—
58#10625324—24no—
59C8×D47—24no—
60C23×C47#4111yescharacteristic
61C22×D47—21no—
62C22×D47—22no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—82no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C22⋊D47—22no—
73C22⋊D47—22no—
74C2×Dic47—21no—
75C2×Dic47—41no—
76D188—22no—
77D188—21no—
78D188—22no—
79D188—41no—
80D188—41no—
81D188C22⋊C412yes—
82C4×D47—22no—
83C4×D47—22no—
84Dic94—21no—
85Dic94C22⋊C412yes—
86C8×C47—22no—
87C8×C47—22no—
88C8×C47—41no—
89C47⋊C8—22no—
90C22×C47—41no—
91C22×C47C4×D411yescharacteristic
92C22×C47#12111yescharacteristic
93C22×C47#12311yescharacteristic
94C2×D47—22no—
95C2×D47—42no—
96C2×D47—81no—
97C2×D47—82no—
98C2×D47—82no—
99C2×D47—82no—
100C4×C47C2×C22⋊C411yescharacteristic
101C4×C47C4×D411yescharacteristic
102C4×C47#12011yescharacteristic
103C4×C47#12111yescharacteristic
104Dic47—22no—
105Dic47—81no—
106#1903—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—21no—
110C2×C47#38611yescharacteristic
111D47—42no—
112D47—82no—
113C2×AGL(1,ℤ/8)—471no—
114#568—471no—
115#421—471no—
116#418—471no—
117C2×#100—471no—
118#344—471no—
119#338D4711yescharacteristic, complemented
120C47#190311yescharacteristic, complemented, Sylow
121C2×#41—471no—
122C22×D4—471no—
123AGL(1,ℤ/8)—942no—
124AGL(1,ℤ/8)—942no—
125C2×SD16—472no—
126C2×D8—472no—
127#131—942no—
128#131—942no—
129C2×M16—471no—
130C2×M16—942no—
131C2×M16C2×D4711yescharacteristic
132C2×M16C2×D4711yescharacteristic
133C2×M16C2×D4711yescharacteristic
134#117—471no—
135#104—942no—
136#102—942no—
137#100—942no—
138C24—941no—
139#41—472no—
140#41—472no—
141#41—941no—
142#41—941no—
143C2×Q8—471no—
144C2×D4—471no—
145C2×D4—472no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C2×D4—941no—
151C2×D4—941no—
152C22×C4—941no—
153C22×C4C22×D4711yescharacteristic
154SD16—944no—
155D8—944no—
156M16—21no—
157M16—21no—
158M16—21no—
159M16—21no—
160M16—21no—
161M16—21no—
162M16—472no—
163M16—944no—
164M16—941no—
165C2×C8—21no—
166C2×C8—944no—
167C2×C8—941no—
168C2×C8C4×D4712yes—
169C2×C8D18812yes—
170C4⋊C4—941no—
171C22⋊C4—941no—
172C42—941no—
173C23—941no—
174C23—942no—
175C23—3762no—
176C23—1881no—
177C23—1881no—
178C23#1062535411yescharacteristic
179Q8—472no—
180Q8—941no—
181D4—472no—
182D4—942no—
183D4—942no—
184D4—942no—
185D4—941no—
186D4—942no—
187D4—1881no—
188D4—1881no—
189C2×C4—941no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—1881no—
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4C2×D18811yescharacteristic
195C2×C4#1062535011yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4D4×D4711yescharacteristic
198C2×C4D4×D4711yescharacteristic
199C8—22no—
200C8—22no—
201C8—41no—
202C8—942no—
203C22—41no—
204C22—942no—
205C22—3762no—
206C22—3762no—
207C22—3762no—
208C22—3761no—
209C22—1882no—
210C22#1309398611yescharacteristic
211C22#1309399911yescharacteristic
212C22#1309400911yescharacteristic
213C4—942no—
214C4—3761no—
215C4C22⋊C4×D4711yescharacteristic
216C4C4×D18811yescharacteristic
217C4#1309399411yescharacteristic
218C4#1309399711yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—3762no—
223C2—1882no—
224C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#338C2
socleC2×C47#386
hypercenter#338D47
hypocenterC47#1903
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
2. #15689889C2semidirect
3. #15689139C2semidirect
4. #15689129C2semidirect
5. C2×#13093940C2semidirect
6. #15688894C2semidirect
7. C47×#338C2semidirect
12. C2×#10625325C4semidirect
13. C2×D376C4semidirect
119. #338D47semidirect
120. C47#1903semidirect