Finite Group Databasebeta

← #20254526

Subgroups — #20254526

Order 6016.

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

normal subgroups only

This group has 370 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#15689680C211yesmaximal, characteristic, complemented
2#15689673C211yesmaximal, characteristic
3#15689528C211yesmaximal, characteristic, complemented
4#15689521C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689448C214yesmaximal, complemented
8#15689424C214yesmaximal, complemented
9C47×#431C211yesmaximal, characteristic, complemented
10C2×#10625350—21no—
11#13094024C2211yescharacteristic
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094021C2211yescharacteristic
15#13094016C2212yes—
16#13094012—21no—
17#13094003—21no—
18#13094003—21no—
19#13093998—21no—
20#13093998C2212yes—
21C4×Dic94—21no—
22C4×Dic94—21no—
23C4×D188—21no—
24C4×D188C2212yes—
25#13093983C2212yes—
26#13093958C2214yes—
27#13093956C2214yes—
28#13093946C2214yes—
29#13093946C2214yes—
30C2×C42×C47C2211yescharacteristic
31C4⋊C8×C47C2212yes—
32C22⋊C8×C47C2212yes—
33C4×C8×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—22no—
39#10625350—44no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×C8×C47C2312yes—
48C2×C8×C47C2312yes—
49C42×C47D411yescharacteristic
50C42×C47D411yescharacteristic
51C42×C47C2311yescharacteristic
52C42×C47C2311yescharacteristic
53C22⋊Dic47—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60C4⋊Dic47C2312yes—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2411yescharacteristic
76C22⋊D47—44no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80D188—24no—
81D188—42no—
82D188—42no—
83C4×D47—44no—
84Dic94—42no—
85Dic94—42no—
86Dic94—42no—
87C8×C47—22no—
88C8×C47—22no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47C22×D411yescharacteristic
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47#13512yes—
100C4×C47AGL(1,ℤ/8)12yes—
101C4×C472−1+412yes—
102Dic47—42no—
103Dic47—42no—
104Dic47—42no—
105#3228—471nomaximal, Sylow
106C2×C47—41no—
107C2×C47#53611yescharacteristic
108C2×C47C2×#13511yescharacteristic
109C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
110D47—82no—
111#533—471no—
112#532—471no—
113#500—471no—
114#498—471no—
115#486—471no—
116#486—471no—
117#482—474no—
118#478—474no—
119#431D4711yescharacteristic, complemented
120C47#322811yescharacteristic, complemented, Sylow
121C2×#41—941no—
122C4⋊Q8—471no—
123C4⋊Q8—471no—
124C4⋊Q8—471no—
125#127—471no—
126#125—472no—
127#124—941no—
128C22⋊Q8—941no—
129C22⋊Q8—941no—
130#121—472no—
131#121—941no—
132C4×Q8—941no—
133C4×Q8—941no—
134C4×D4—472no—
135C4×D4—941no—
136#117—472no—
137C2×C42C2×D4711yescharacteristic
138#107—474no—
139#106—474no—
140C4⋊C8C2×D4712yes—
141#102—474no—
142#102—474no—
143C22⋊C8C2×D4712yes—
144C4×C8C2×D4711yescharacteristic
145C4×C8C2×D4711yescharacteristic
146#41—1884no—
147C2×Q8—941no—
148C2×Q8—941no—
149C2×Q8—941no—
150C2×D4—472no—
151C2×D4—942no—
152C2×D4—941no—
153C2×D4—941no—
154C22×C4—942no—
155C22×C4D18811yescharacteristic
156C22×C4D18811yescharacteristic
157C22×C4C22×D4711yescharacteristic
158C2×C8C22×D4712yes—
159C2×C8C22×D4712yes—
160C4⋊C4—472no—
161C4⋊C4—472no—
162C4⋊C4—472no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C22⋊C4—942no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C42—942no—
172C42D18811yescharacteristic
173C42D18811yescharacteristic
174C42C22×D4711yescharacteristic
175C42C22×D4711yescharacteristic
176C23—942no—
177C23C2×D18811yescharacteristic
178Q8—1882no—
179Q8—1882no—
180Q8—1882no—
181D4—944no—
182D4—1884no—
183D4—1882no—
184D4—1882no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—1884no—
192C2×C4C2×D18811yescharacteristic
193C2×C4C2×D18811yescharacteristic
194C2×C4C2×D18811yescharacteristic
195C2×C4C2×D18811yescharacteristic
196C2×C4C2×D18811yescharacteristic
197C2×C4C23×D4711yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C22×D18811yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—1882no—
211C4—1882no—
212C4—1882no—
213C4#1309404612yes—
214C4#1309405212yes—
215C4#1309407112yes—
216C2—41no—
217C2—3762no—
218C2#1568969911yescharacteristic
219C2C2×#1309404611yescharacteristic
220C2C2×#1309405211yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3228
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689528C2semidirect
4. #15689521C2semidirect
5. #15689470C2semidirect
6. #15689470C2semidirect
7. #15689448C2semidirect
8. #15689424C2semidirect
9. C47×#431C2semidirect
119. #431D47semidirect
120. C47#3228semidirect