Finite Group Databasebeta

← #20252868

Subgroups — #20252868

Order 6016.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094049C212yesmaximal, complemented
2C2×#13094021C211yesmaximal, characteristic, complemented
3#15689323C214yesmaximal, complemented
4#15689318C214yesmaximal, complemented
5#15689147C211yesmaximal, characteristic, complemented
6#15689127C212yesmaximal, complemented
7C4×#41×C47C211yesmaximal, characteristic, complemented
8C22×D188—22no—
9C22×D188C2212yes—
10#13094049—28no—
11C2×#10625336C2214yescomplemented
12C2×#10625334C2214yescomplemented
13C2×#10625329C2212yes—
14#13094021—21no—
15#13094021—21no—
16#13094021C2214yes—
17C4⋊(C47⋊C8)C2214yescomplemented
18#13093944C2218yescomplemented
19C2×#41×C47C2211yescharacteristic
20C4×Q8×C47C2212yescomplemented
21C4×D4×C47—22no—
22C4×D4×C47C2212yescomplemented
23#117×C47—21no—
24#117×C47C2211yescharacteristic
25C2×C42×C47—21no—
26C2×C42×C47C2211yescharacteristic
27C23×D47—22no—
28#41×C47—22no—
29#41×C47D414yescomplemented
30C2×Q8×C47C2311yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47C2311yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47—22no—
35C22×C4×C47D412yes—
36C22×C4×C47C2311yescharacteristic
37C2×D188—24no—
38C2×D188—24no—
39C2×D188—22no—
40C2×D188—24no—
41C2×D188—24no—
42C2×D188—48no—
43C2×D188C2314yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47C2312yes—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—22no—
48C42×C47—21no—
49C42×C47—22no—
50C42×C47D411yescharacteristic
51C42×C47D411yescharacteristic
52C42×C47C2312yes—
53#10625336—28no—
54#10625334—28no—
55#10625329—24no—
56C2×C47⋊C8C2314yes—
57C23×C47—21no—
58C23×C47C2×D411yescharacteristic
59C22×D47—24no—
60C22×D47—48no—
61C22×D47—44no—
62Q8×C47—21no—
63Q8×C47C2×D412yescomplemented
64D4×C47—24no—
65D4×C47—21no—
66D4×C47C2×D412yescomplemented
67C2×C4×C47—21no—
68C2×C4×C47—24no—
69C2×C4×C47—24no—
70C2×C4×C47—22no—
71C2×C4×C47—44no—
72C2×C4×C47C2×D412yes—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D412yes—
76C2×C4×C47#4112yes—
77C2×C4×C47C2411yescharacteristic
78D188—24no—
79D188—24no—
80D188—48no—
81D188—44no—
82D188—48no—
83C47⋊C8—24no—
84C22×C47—22no—
85C22×C47—22no—
86C22×C47—42no—
87C22×C47#12112yes—
88C22×C47C22×D411yescharacteristic
89C2×D47—44no—
90C2×D47—48no—
91C2×D47—88no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—42no—
95C4×C47#12112yes—
96C4×C47AGL(1,ℤ/8)14yescomplemented
97C4×C47C22×D411yescharacteristic
98C4×C47C2×#4111yescharacteristic
99#3038—471nomaximal, Sylow
100C2×C47—22no—
101C2×C47—42no—
102C2×C47C2×#12111yescharacteristic
103C2×C47C2×AGL(1,ℤ/8)12yes—
104D47—84no—
105C2×AGL(1,ℤ/8)—472no—
106C2×#127—471no—
107C4×#41D4711yescharacteristic, complemented
108#460—474no—
109#459—474no—
110#423—471no—
111#418—472no—
112C47#303811yescharacteristic, complemented, Sylow
113C2×#41C2×D4711yescharacteristic
114C22×D4—472no—
115C22×D4—942no—
116AGL(1,ℤ/8)—948no—
117C2×SD16—474no—
118C2×D8—474no—
119C2×M16—472no—
120#127—474no—
121#127—941no—
122#127—941no—
123C4×Q8C2×D4712yescomplemented
124C4×D4—22no—
125C4×D4C2×D4712yescomplemented
126#117—21no—
127#117C2×D4711yescharacteristic
128C2×C42—21no—
129C2×C42C2×D4711yescharacteristic
130C4⋊C8—474no—
131#102—478no—
132C24—942no—
133#41—22no—
134#41D18814yescomplemented
135C2×Q8C22×D4711yescharacteristic
136C2×D4—21no—
137C2×D4—474no—
138C2×D4—944no—
139C2×D4—944no—
140C2×D4—944no—
141C2×D4—944no—
142C2×D4—942no—
143C2×D4—1888no—
144C2×D4C22×D4711yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22⋊D4712yes—
148C22×C4C22×D4711yescharacteristic
149SD16—948no—
150D8—948no—
151M16—944no—
152C2×C8—474no—
153C4⋊C4—22no—
154C4⋊C4C22×D4712yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42C22⋊D4711yescharacteristic
160C42C22⋊D4711yescharacteristic
161C42C22×D4712yes—
162C23—21no—
163C23—944no—
164C23—1888no—
165C23—1884no—
166C23C2×C22⋊D4711yescharacteristic
167Q8—21no—
168Q8C2×D18812yescomplemented
169D4—24no—
170D4—21no—
171D4—944no—
172D4—944no—
173D4—1888no—
174D4—1884no—
175D4—1888no—
176D4C2×D18812yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D18812yes—
183C2×C4#1062535012yes—
184C2×C4C2×C22⋊D4712yes—
185C2×C4C2×C22⋊D4711yescharacteristic
186C2×C4C2×C22⋊D4712yes—
187C2×C4C23×D4711yescharacteristic
188C8—944no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—3768no—
193C22—1884no—
194C22—1888no—
195C22#1309399812yes—
196C22C22×C22⋊D4711yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#1309399812yes—
201C4#1309404914yescomplemented
202C4C22×D18811yescharacteristic
203C4C2×#1062535011yescharacteristic
204C2—22no—
205C2—42no—
206C2—3764no—
207C2C2×#1309399811yescharacteristic
208C2C2×#1309404912yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×#41×C47C2
socleC22×C47C22×D4
hypercenterC4×#41D47
hypocenterC47#3038
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. C2×#13094021C2semidirect
3. #15689323C2semidirect
4. #15689318C2semidirect
5. #15689147C2semidirect
6. #15689127C2semidirect
7. C4×#41×C47C2semidirect
11. C2×#10625336C22semidirect
12. C2×#10625334C22semidirect
17. C4⋊(C47⋊C8)C22semidirect
18. #13093944C22semidirect
20. C4×Q8×C47C22semidirect
22. C4×D4×C47C22semidirect
29. #41×C47D4semidirect
63. Q8×C47C2×D4semidirect
66. D4×C47C2×D4semidirect
96. C4×C47AGL(1,ℤ/8)semidirect
107. C4×#41D47semidirect
112. C47#3038semidirect
123. C4×Q8C2×D47semidirect
125. C4×D4C2×D47semidirect
134. #41D188semidirect
168. Q8C2×D188semidirect
176. D4C2×D188semidirect
201. C4#13094049semidirect