Finite Group Databasebeta

← #20253712

Subgroups — #20253712

Order 6016.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689678C211yesmaximal, characteristic, complemented
2#15689674C211yesmaximal, characteristic
3#15689479C214yesmaximal, complemented
4#15689473C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689118C214yesmaximal, complemented
8C4×C8×D47C211yesmaximal, characteristic, complemented
9C47×#487C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×C8×D47C2212yes—
12#13094024C2211yescharacteristic
13#13094021C2211yescharacteristic
14#13094015C2212yes—
15#13094013C2212yes—
16#13094004—21no—
17#13094000—21no—
18#13093999—21no—
19#13093999—21no—
20Q8×Dic47—21no—
21#13093989—21no—
22#13093986—21no—
23#13093986—21no—
24#13093982C2212yes—
25C42×D47C2211yescharacteristic
26#13093948C2214yes—
27#13093946C2214yes—
28#13093944C2214yes—
29C4×C47⋊C8C2211yescharacteristic
30C8×Dic47C2212yes—
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#103×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47C2312yes—
37#10625354—28no—
38C2×D188—22no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188C2312yes—
42C2×C4×D47—22no—
43C2×C4×D47D411yescharacteristic
44C2×C4×D47D411yescharacteristic
45C2×C4×D47C2311yescharacteristic
46C2×Dic94—21no—
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2312yes—
52C42×C47C2311yescharacteristic
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C4×Dic47D411yescharacteristic
62C4×Dic47D411yescharacteristic
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2312yes—
65C8×D47—24no—
66C22×D47—22no—
67C22×D47C2×D411yescharacteristic
68Q8×C47—24no—
69Q8×C47—42no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47C2×D411yescharacteristic
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79D188—24no—
80D188—44no—
81D188—42no—
82D188—42no—
83C4×D47—22no—
84C4×D47—22no—
85C4×D47—44no—
86C4×D47#4114yes—
87Dic94—42no—
88C8×C47—22no—
89C47⋊C8—22no—
90C22×C47C22×D411yescharacteristic
91C2×D47—21no—
92C2×D47—21no—
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47#12412yes—
97C4×C47—42no—
98C4×C47—42no—
99C4×C47#13512yes—
100C4×C47#13512yes—
101C4×C47C2×#4112yes—
102Dic47—21no—
103Dic47—21no—
104Dic47—42no—
105Dic47#12412yes—
106#3131—471nomaximal, Sylow
107C2×C47C2×#12411yescharacteristic
108C2×C47C2×#13511yescharacteristic
109C2×C47C2×#13511yescharacteristic
110D47—22no—
111D47—82no—
112#533—471no—
113#532—471no—
114#488—474no—
115#487—471no—
116#487D4711yescharacteristic, complemented
117#486—471no—
118#486—471no—
119#416—474no—
120C2×C4×C8—471no—
121C47#313111yescharacteristic, complemented, Sylow
122C2×#41—472no—
123C22×C8—472no—
124C4⋊Q8—471no—
125C4⋊Q8C2×D4711yescharacteristic
126C4⋊Q8C2×D4711yescharacteristic
127#127—471no—
128#125—472no—
129#124—472no—
130C22⋊Q8—941no—
131C22⋊Q8—941no—
132#121—941no—
133#121—941no—
134C4×Q8—941no—
135C4×Q8—941no—
136C4×D4—941no—
137C4×D4—941no—
138#117—472no—
139C2×C42—471no—
140#103—474no—
141#103C2×D4714yes—
142#102—474no—
143#102—474no—
144C4×C8—472no—
145C4×C8—471no—
146C4×C8C2×D4711yescharacteristic
147#41—948no—
148C2×Q8—21no—
149C2×Q8—941no—
150C2×Q8C22×D4712yes—
151C2×D4—472no—
152C2×D4—942no—
153C2×D4—941no—
154C2×D4—941no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—942no—
159C2×C8—472no—
160C2×C8—944no—
161C2×C8C22×D4712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—941no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C42—471no—
174C42—471no—
175C42—471no—
176C42—942no—
177C42C22×D4711yescharacteristic
178C23—471no—
179C23—942no—
180Q8—24no—
181Q8—42no—
182Q8—1882no—
183D4—944no—
184D4—1884no—
185D4—1882no—
186D4—1882no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—471no—
190C2×C4—474no—
191C2×C4—471no—
192C2×C4—471no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—1884no—
197C2×C4D4×D4711yescharacteristic
198C2×C4D4×D4711yescharacteristic
199C2×C4C23×D4711yescharacteristic
200C8—22no—
201C8—942no—
202C22—472no—
203C22—941no—
204C22—941no—
205C22—1882no—
206C22—1882no—
207C22—1882no—
208C22C2×D4×D4711yescharacteristic
209C4—42no—
210C4—42no—
211C4—472no—
212C4—941no—
213C4—941no—
214C4—1882no—
215C4#1309404512yes—
216C4#1309404712yes—
217C4#41×D4712yes—
218C2—942no—
219C2—3762no—
220C2#124×D4711yescharacteristic
221C2C2×#1309404511yescharacteristic
222C2C2×#1309404711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3131
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689479C2semidirect
4. #15689473C2semidirect
5. #15689471C2semidirect
6. #15689470C2semidirect
7. #15689118C2semidirect
8. C4×C8×D47C2semidirect
9. C47×#487C2semidirect
116. #487D47semidirect
121. C47#3131semidirect