Finite Group Databasebeta

← #20243912

Subgroups — #20243912

Order 6016.

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

normal subgroups only

This group has 344 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#15689889C211yesmaximal, characteristic, complemented
2#15689690C211yesmaximal, characteristic
3#15689128C211yesmaximal, characteristic, complemented
4#15689096C211yesmaximal, characteristic, complemented
5#15688880C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#418C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12M16×D47—22no—
13#13094020C412yescomplemented
14#13094011C412yescomplemented
15#13093995—22no—
16#13093993—22no—
17#13093983C2211yescharacteristic
18#13093983C2211yescharacteristic
19#13093945—22no—
20#13093938—22no—
21C22×D4×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#102×C47—22no—
25C24×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47C2×C412yes—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—24no—
34C2×C22⋊D47D412yes—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39C2×D188C2×C411yescharacteristic
40C2×C4×D47D412yes—
41C2×Dic94C2×C411yescharacteristic
42M16×C47—21no—
43M16×C47—21no—
44C2×C8×C47D412yescomplemented
45C4⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C42×C47—21no—
48C22⋊Dic47—21no—
49C22⋊Dic47—24no—
50C22⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4×Dic47—21no—
54C4×Dic47C2×C412yes—
55#10625329—21no—
56#10625329—21no—
57C2×C47⋊C8D412yescomplemented
58#10625324—24no—
59C8×D47—24no—
60C23×C47—22no—
61C23×C47—41no—
62C23×C47—41no—
63C23×C47—82no—
64C23×C47C2×D411yescharacteristic
65C22×D47C22⋊C412yes—
66D4×C47—22no—
67D4×C47—22no—
68D4×C47—41no—
69D4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C22⋊D47—22no—
78C22⋊D47—22no—
79C22⋊D47—84no—
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47C22⋊C412yes—
83D188—21no—
84D188—21no—
85C4×D47—22no—
86C4×D47—22no—
87Dic94—21no—
88Dic94—21no—
89C8×C47—22no—
90C47⋊C8—22no—
91C22×C47—41no—
92C22×C47—44no—
93C22×C47—42no—
94C22×C47—82no—
95C22×C47—82no—
96C22×C47C2×C22⋊C411yescharacteristic
97C22×C47#12111yescharacteristic
98C22×C47#12111yescharacteristic
99C2×D47—22no—
100C2×D47—42no—
101C4×C47—81no—
102C4×C47C4×D411yescharacteristic
103C4×C47C4×D411yescharacteristic
104C4×C47#12011yescharacteristic
105C4×C47#12311yescharacteristic
106Dic47—22no—
107Dic47—42no—
108Dic47—81no—
109#1910—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—82no—
114C2×C47#38611yescharacteristic
115D47—42no—
116#568—471no—
117#535—471no—
118#418—471no—
119#418D4711yescharacteristic, complemented
120#410—471no—
121H(3,ℤ/4)—471no—
122H(3,ℤ/4)—471no—
123C47#191011yescharacteristic, complemented, Sylow
124C2×#41—471no—
125C22×D4C2×D4711yescharacteristic
126#131—942no—
127#131—942no—
128C2×M16—471no—
129C2×M16—942no—
130C2×M16C2×D4711yescharacteristic
131#127—472no—
132#124—472no—
133#121—942no—
134#120—942no—
135#117—471no—
136#117—471no—
137#117C2×D4711yescharacteristic
138#102—22no—
139#102—942no—
140#99—942no—
141C24—21no—
142#41—941no—
143#41—941no—
144#41—941no—
145#41—941no—
146C2×Q8—471no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—472no—
153C2×D4—471no—
154C2×D4—944no—
155C2×D4C4×D4712yes—
156C22×C4—472no—
157C22×C4C22×D4711yescharacteristic
158M16—21no—
159M16—21no—
160M16—944no—
161M16—941no—
162M16—941no—
163C2×C8—472no—
164C2×C8—944no—
165C2×C8C22⋊D4712yescomplemented
166C4⋊C4—21no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—21no—
170C22⋊C4—944no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C42—21no—
174C42—472no—
175C42—941no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—82no—
180C23—472no—
181C23D4×D4711yescharacteristic
182Q8—941no—
183Q8—941no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—942no—
189D4—942no—
190D4—941no—
191D4—941no—
192D4—3764no—
193C2×C4—41no—
194C2×C4—472no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—1881no—
199C2×C4C2×C4×D4711yescharacteristic
200C2×C4#1062535011yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4#1062535211yescharacteristic
204C2×C4C2×C22⋊D4711yescharacteristic
205C8—22no—
206C8—942no—
207C22—41no—
208C22—44no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—942no—
213C22—1882no—
214C22C22⋊C4×D4711yescharacteristic
215C22#1309399511yescharacteristic
216C22#1309399711yescharacteristic
217C4—81no—
218C4—942no—
219C4—3761no—
220C4—1882no—
221C4(C22⋊D47)⋊C411yescharacteristic
222C4C4×C22⋊D4711yescharacteristic
223C4#1309399211yescharacteristic
224C4#1309400611yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—82no—
229C2—1882no—
230C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#418C2
socleC2×C47#386
hypercenter#418D47
hypocenterC47#1910
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689889C2semidirect
3. #15689128C2semidirect
4. #15689096C2semidirect
5. #15688880C2semidirect
6. #15688879C2semidirect
7. C47×#418C2semidirect
13. #13094020C4semidirect
14. #13094011C4semidirect
44. C2×C8×C47D4semidirect
57. C2×C47⋊C8D4semidirect
119. #418D47semidirect
123. C47#1910semidirect
165. C2×C8C22⋊D47semidirect