Finite Group Databasebeta

← #20243352

Subgroups — #20243352

Order 6016.

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

normal subgroups only

This group has 548 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#15689140C212yesmaximal, complemented
2#15689119C212yesmaximal, complemented
3#15689097C211yesmaximal, characteristic, complemented
4#15689090C211yesmaximal, characteristic, complemented
5C47×#585C211yesmaximal, characteristic
6C2×#10625329C2211yescharacteristic, complemented
7C22×C47⋊C8C2211yescharacteristic, complemented
8#13093983C2212yescomplemented
9#13093951—24no—
10#13093948—22no—
11#13093945—22no—
12#13093939—22no—
13C22⋊(C47⋊C8)—22no—
142−1+4×C47—22no—
152−1+4×C47C412yescomplemented
16H(5,𝔽2)×C47—22no—
17H(5,𝔽2)×C47—22no—
18H(5,𝔽2)×C47C412yescomplemented
19C2×#41×C47—24no—
20C2×#41×C47—22no—
21C2×#41×C47C2212yes—
22C2×#41×C47C2211yescharacteristic
23#41×C47—24no—
24#41×C47—28no—
25#41×C47—24no—
26#41×C47—24no—
27#41×C47—24no—
28#41×C47—24no—
29#41×C47—22no—
30#41×C47—22no—
31#41×C47—22no—
32#41×C47—22no—
33#41×C47C2×C414yes—
34#41×C47D414yes—
35C2×Q8×C47—22no—
36C2×Q8×C47—24no—
37C2×Q8×C47C2×C411yescharacteristic
38C2×Q8×C47D412yes—
39C2×D4×C47—28no—
40C2×D4×C47—22no—
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C2×D4×C47—24no—
44C2×D4×C47C2×C411yescharacteristic
45C2×D4×C47D412yes—
46C2×D4×C47D412yes—
47C22×C4×C47—24no—
48C22×C4×C47—22no—
49C22×C4×C47D412yes—
50C22×C4×C47C2311yescharacteristic
51C22⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4×Dic47—22no—
54#10625329—22no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—22no—
58C23×C47—24no—
59C23×C47—22no—
60C23×C47C22⋊C412yes—
61C23×C47C2×D411yescharacteristic
62Q8×C47—24no—
63Q8×C47—22no—
64Q8×C47—22no—
65Q8×C47C22⋊C414yes—
66D4×C47—28no—
67D4×C47—24no—
68D4×C47—24no—
69D4×C47—24no—
70D4×C47—24no—
71D4×C47—22no—
72D4×C47—22no—
73D4×C47C22⋊C414yes—
74C2×C4×C47—24no—
75C2×C4×C47—28no—
76C2×C4×C47—22no—
77C2×C4×C47—24no—
78C2×C4×C47—24no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C22⋊C412yes—
82C2×C4×C47C22×C411yescharacteristic
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D411yescharacteristic
86C2×Dic47—42no—
87C47⋊C8—41no—
88C47⋊C8—41no—
89C22×C47—22no—
90C22×C47—24no—
91C22×C47—41no—
92C22×C47—42no—
93C22×C47—82no—
94C22×C47—84no—
95C22×C47C2×C22⋊C411yescharacteristic
96C22×C47#12012yes—
97C4×C47—24no—
98C4×C47—22no—
99C4×C47C2×C22⋊C412yes—
100C4×C47#12011yescharacteristic
101C4×C47#12011yescharacteristic
102Dic47—82no—
103#1794—471nomaximal, Sylow
104C2×C47—22no—
105C2×C47—21no—
106C2×C47—42no—
107C2×C47—44no—
108C2×C47#37911yescharacteristic
109#585D4711yescharacteristic
110#421—472no—
111#416—472no—
112#410—471no—
113#408—471no—
114C47#179411yescharacteristic, complemented, Sylow
1152−1+4—22no—
1162−1+4Dic4712yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)Dic4712yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C2×D4712yes—
123C2×#41C2×D4711yescharacteristic
124C2×M16—471no—
125C22×C8—471no—
126#117—472no—
127#104—944no—
128#103—942no—
129#102—942no—
130#99—942no—
131C22⋊C8—942no—
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—24no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—22no—
142#41C2×Dic4714yes—
143#41C22⋊D4714yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×Dic4711yescharacteristic
147C2×Q8C22⋊D4712yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×Dic4711yescharacteristic
154C2×D4C22⋊D4712yes—
155C2×D4C22⋊D4712yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4C22⋊D4712yes—
159C22×C4C22×D4711yescharacteristic
160M16—942no—
161C2×C8—941no—
162C2×C8—941no—
163C2×C8—942no—
164C4⋊C4—942no—
165C22⋊C4—942no—
166C42—942no—
167C23—24no—
168C23—22no—
169C23C22⋊Dic4712yes—
170C23C2×C22⋊D4711yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊Dic4714yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊Dic4714yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—1882no—
191C2×C4C22⋊Dic4712yes—
192C2×C4C22×Dic4711yescharacteristic
193C2×C4C2×C22⋊D4712yes—
194C2×C4C2×C22⋊D4712yes—
195C2×C4C2×C22⋊D4711yescharacteristic
196C8—1881no—
197C8—1881no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊Dic4711yescharacteristic
205C22#1309399312yes—
206C4—24no—
207C4—22no—
208C4—3762no—
209C4C2×C22⋊Dic4712yes—
210C4#1309399311yescharacteristic
211C4#1309399311yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#1568897911yescharacteristic
subgroupG/H
centerC4#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#585C2
socleC2×C47#379
hypercenter#585D47
hypocenterC47#1794
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #15689140C2semidirect
2. #15689119C2semidirect
3. #15689097C2semidirect
4. #15689090C2semidirect
6. C2×#10625329C22semidirect
7. C22×C47⋊C8C22semidirect
8. #13093983C22semidirect
15. 2−1+4×C47C4semidirect
18. H(5,𝔽2)×C47C4semidirect
114. C47#1794semidirect
116. 2−1+4Dic47semidirect
119. H(5,𝔽2)Dic47semidirect