Finite Group Databasebeta

← #20254586

Subgroups — #20254586

Order 6016.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689673C211yesmaximal, characteristic
2#15689533C212yesmaximal, complemented
3#15689489C212yesmaximal, complemented
4#15689447C214yesmaximal, complemented
5#15689410C212yesmaximal, complemented
6#15689400C212yesmaximal, complemented
7#15689180C211yesmaximal, characteristic, complemented
8C47×#533C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10#13094024C2211yescharacteristic
11#13094021C2211yescharacteristic
12#13094012—21no—
13#13093998—21no—
14#13093998C2212yes—
15C4×D188—21no—
16C4×D188C2212yes—
17#13093957C2214yes—
18#13093955C2214yes—
19C4⋊(C47⋊C8)C2212yes—
20#13093944C2214yes—
21#13093944C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yes—
24C4⋊Q8×C47C2211yescharacteristic
25C4⋊Q8×C47C2211yescharacteristic
26#125×C47C2212yes—
27C22⋊Q8×C47—21no—
28C22⋊Q8×C47—21no—
29C4×Q8×C47—21no—
30C4×Q8×C47—21no—
31#117×C47C2212yes—
32C2×C42×C47C2211yescharacteristic
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
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—
45C4⋊C4×C47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47C2312yes—
50C4⋊C4×C47C2312yes—
51C22⋊C4×C47—22no—
52C42×C47—22no—
53C42×C47D411yescharacteristic
54C42×C47D411yescharacteristic
55C42×C47C2311yescharacteristic
56C42×C47C2311yescharacteristic
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47C2312yes—
61C2×C47⋊C8C2314yes—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64Q8×C47—42no—
65Q8×C47—42no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—44no—
78C2×Dic47—22no—
79D188—24no—
80D188—42no—
81D188—42no—
82C4×D47—44no—
83Dic94—42no—
84C47⋊C8—24no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47C22×D411yescharacteristic
89C2×D47—42no—
90C2×D47—42no—
91C2×D47—42no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—21no—
96C4×C47—42no—
97C4×C47—42no—
98C4×C47AGL(1,ℤ/8)12yes—
99C4×C472−1+412yes—
100Dic47—42no—
101#3235—471nomaximal, Sylow
102C2×C47—41no—
103C2×C47#53611yescharacteristic
104C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C47#57511yescharacteristic
106D47—82no—
107#533D4711yescharacteristic, complemented
108#532—471no—
109#501—472no—
110#490—472no—
111#482—474no—
112#476—472no—
113#474—472no—
114#432—471no—
115C47#323511yescharacteristic, complemented, Sylow
116C2×#41—941no—
117C4⋊Q8—471no—
118C4⋊Q8C2×D4711yescharacteristic
119C4⋊Q8C2×D4711yescharacteristic
120#127—471no—
121#125C2×D4712yes—
122#124—941no—
123C22⋊Q8—21no—
124C22⋊Q8—21no—
125#121—472no—
126#121—941no—
127C4×Q8—21no—
128C4×Q8—21no—
129C4×D4—472no—
130C4×D4—941no—
131#117C2×D4712yes—
132C2×C42C2×D4711yescharacteristic
133#107—474no—
134#106—474no—
135C4⋊C8—472no—
136#102—474no—
137#102—474no—
138C22⋊C8—472no—
139#97—472no—
140#41—1884no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—941no—
144C2×D4—472no—
145C2×D4—942no—
146C2×D4—941no—
147C2×D4—941no—
148C22×C4—942no—
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22⋊D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C2×C8—474no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—472no—
158C4⋊C4—941no—
159C4⋊C4C22×D4712yes—
160C4⋊C4C22×D4712yes—
161C22⋊C4—22no—
162C22⋊C4—942no—
163C22⋊C4—942no—
164C42—22no—
165C42C22⋊D4711yescharacteristic
166C42C22⋊D4711yescharacteristic
167C42C22×D4711yescharacteristic
168C42C22×D4711yescharacteristic
169C23—942no—
170C23C2×C22⋊D4711yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—1882no—
174D4—944no—
175D4—1882no—
176D4—1882no—
177D4—1884no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—942no—
184C2×C4—1884no—
185C2×C4C2×C22⋊D4711yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C2×C4C2×C22⋊D4711yescharacteristic
190C2×C4C23×D4711yescharacteristic
191C8—944no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—1882no—
196C22—1882no—
197C22—1882no—
198C22C22×C22⋊D4711yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—1882no—
206C4#1309404912yes—
207C4#1309407212yes—
208C2—41no—
209C2—3762no—
210C2#1568969711yescharacteristic
211C2C2×#1309404911yescharacteristic
212C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3235
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689489C2semidirect
4. #15689447C2semidirect
5. #15689410C2semidirect
6. #15689400C2semidirect
7. #15689180C2semidirect
8. C47×#533C2semidirect
107. #533D47semidirect
115. C47#3235semidirect