Finite Group Databasebeta

← #20242512

Subgroups — #20242512

Order 6016.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689793C211yesmaximal, characteristic
2#15689415C211yesmaximal, characteristic, complemented
3#15689410C211yesmaximal, characteristic, complemented
4#15688867C211yesmaximal, characteristic, complemented
5#15688855C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×#492C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9#13094020—21no—
10#13093996—22no—
11#13093995—21no—
12C4×Dic94C2211yescharacteristic
13C4×D188C2211yescharacteristic
14D4×Dic47—21no—
15#13093957—21no—
16#13093955—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093947—21no—
20#13093944—21no—
21C2×SD16×C47—22no—
22C4⋊Q8×C47C2211yescharacteristic
23#127×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47D412yes—
29C2×C22⋊D47—22no—
30C2×C22⋊D47—22no—
31C22×Dic47—22no—
32#10625352—42no—
33#10625352—42no—
34C2×D188D411yescharacteristic
35C2×C4×D47—21no—
36C2×Dic94D411yescharacteristic
37SD16×C47—44no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C42×C47C2311yescharacteristic
42C22⋊Dic47—22no—
43(C2×D47)⋊C4—21no—
44C4⋊Dic47D411yescharacteristic
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—22no—
51C22×D47—21no—
52Q8×C47—42no—
53D4×C47—42no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—41no—
57D4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C22⋊D47—44no—
63C22⋊D47—82no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—44no—
68D188—21no—
69D188—21no—
70C4×D47—41no—
71C4×D47—41no—
72Dic94—21no—
73Dic94SD1612yescomplemented
74C8×C47—22no—
75C47⋊C8—41no—
76C47⋊C8—41no—
77C22×C47—42no—
78C22×C47—42no—
79C22×C47—42no—
80C22×C47#12011yescharacteristic
81C2×D47—41no—
82C2×D47—41no—
83C2×D47—41no—
84C4×C47—21no—
85C4×C47—81no—
86C4×C47C2×SD1611yescharacteristic
87C4×C47#13511yescharacteristic
88C4×C47AGL(1,ℤ/8)11yescharacteristic
89C4×C47#13711yescharacteristic
90Dic47—22no—
91Dic47—41no—
92Dic47—41no—
93#1631—471nomaximal, Sylow
94C2×C47—82no—
95C2×C47#45011yescharacteristic
96C2×C47#45211yescharacteristic
97C2×C47#45311yescharacteristic
98D47—81no—
99#550—471no—
100#492D4711yescharacteristic, complemented
101#477—471no—
102#476—471no—
103#331—471no—
104Q8⋊C8—471no—
105D4⋊C8—471no—
106C47#163111yescharacteristic, complemented, Sylow
107C2×#41—941no—
108C2×SD16—22no—
109C4⋊Q8C2×D4711yescharacteristic
110#127—941no—
111#127C2×D4711yescharacteristic
112#121—941no—
113#121—942no—
114C4×Q8—471no—
115C4×D4—471no—
116C4×D4—941no—
117#107—941no—
118#106—941no—
119C4⋊C8—471no—
120C4⋊C8—471no—
121#103—941no—
122#102—941no—
123C4×C8C2×D4711yescharacteristic
124#41—1882no—
125#41—1882no—
126C2×Q8—21no—
127C2×Q8—471no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—471no—
131C2×D4—942no—
132C2×D4—942no—
133C2×D4C22⋊D4712yes—
134C22×C4—942no—
135C22×C4—941no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—941no—
139C2×C8—941no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—471no—
143C4⋊C4—471no—
144C4⋊C4—941no—
145C22⋊C4—942no—
146C22⋊C4—941no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—22no—
150C23—941no—
151Q8—42no—
152Q8—472no—
153Q8—941no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—941no—
160D4—941no—
161D4—3762no—
162D4—1884no—
163C2×C4—41no—
164C2×C4—941no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—1884no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4D4×D4711yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—22no—
174C8—1881no—
175C8—1881no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1881no—
180C22—1881no—
181C22—1881no—
182C22#1309399211yescharacteristic
183C4—21no—
184C4—81no—
185C4—942no—
186C4—1881no—
187C4—1881no—
188C4SD16×D4711yescharacteristic
189C4#1309404511yescharacteristic
190C4#1309405111yescharacteristic
191C4#1309405311yescharacteristic
192C2—82no—
193C2—3761no—
194C2#1568927211yescharacteristic
195C2#1568928211yescharacteristic
196C2#1568929011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#492C2
socleC22×C47#120
hypercenter#492D47
hypocenterC47#1631
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #15689415C2semidirect
3. #15689410C2semidirect
4. #15688867C2semidirect
5. #15688855C2semidirect
6. #15688852C2semidirect
7. C47×#492C2semidirect
73. Dic94SD16semidirect
100. #492D47semidirect
106. C47#1631semidirect