Finite Group Databasebeta

← #20242586

Subgroups — #20242586

Order 6016.

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

normal subgroups only

This group has 250 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#15689794C211yesmaximal, characteristic
2#15689471C211yesmaximal, characteristic, complemented
3#15689405C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#461C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9#13094021C2211yescharacteristic
10#13094020—21no—
11#13093998—21no—
12#13093997—22no—
13C4×Dic94C2211yescharacteristic
14#13093986—21no—
15#13093955—21no—
16C4⋊(C47⋊C8)C2211yescharacteristic
17#13093947—21no—
18#13093944—22no—
19C4×C47⋊C8C2211yescharacteristic
20C2×SD16×C47—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#103×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C2×C22⋊D47—22no—
29C2×C22⋊D47—22no—
30#10625350—42no—
31#10625350—42no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188D412yes—
35C2×C4×D47—22no—
36C2×Dic94D411yescharacteristic
37SD16×C47—42no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47D411yescharacteristic
42C22⋊C4×C47—21no—
43C42×C47C2311yescharacteristic
44(C2×D47)⋊C4—22no—
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—21no—
51C22×D47—22no—
52Q8×C47—41no—
53Q8×C47—41no—
54D4×C47—21no—
55D4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C22⋊D47—44no—
64C22⋊D47—82no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67D188—42no—
68D188—41no—
69D188—41no—
70D188—41no—
71D188—41no—
72C4×D47—44no—
73Dic94—21no—
74Dic94SD1612yescomplemented
75C8×C47—41no—
76C47⋊C8—41no—
77C47⋊C8—41no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47#12011yescharacteristic
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47—81no—
88C4×C47C2×SD1611yescharacteristic
89C4×C47#13511yescharacteristic
90C4×C47AGL(1,ℤ/8)11yescharacteristic
91C4×C47AGL(1,ℤ/8)11yescharacteristic
92Dic47—22no—
93Dic47—41no—
94#1642—471nomaximal, Sylow
95C2×C47—81no—
96C2×C47#44911yescharacteristic
97C2×C47#45011yescharacteristic
98C2×C47#45511yescharacteristic
99D47—82no—
100#550—471no—
101#486—471no—
102#475—471no—
103#461D4711yescharacteristic, complemented
104#331—471no—
105Q8⋊C8—471no—
106D4⋊C8—471no—
107C47#164211yescharacteristic, complemented, Sylow
108C2×#41—941no—
109C2×SD16—21no—
110C4⋊Q8C2×D4711yescharacteristic
111#127—471no—
112#127—941no—
113#121—942no—
114#121—941no—
115C4×Q8—471no—
116C4×D4—941no—
117C4×D4C2×D4711yescharacteristic
118#106—941no—
119C4⋊C8—471no—
120C4⋊C8C2×D4711yescharacteristic
121#103—21no—
122#103—941no—
123#102—942no—
124C4×C8—471no—
125#41—1882no—
126#41—1882no—
127C2×Q8—21no—
128C2×Q8—471no—
129C2×D4—472no—
130C2×D4—942no—
131C2×D4—942no—
132C2×D4—941no—
133C2×D4—941no—
134C2×D4C22⋊D4711yescharacteristic
135C22×C4—21no—
136C22×C4—942no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—471no—
144C4⋊C4—941no—
145C4⋊C4C22⋊D4711yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—942no—
148C42—941no—
149C42C22×D4711yescharacteristic
150C23—21no—
151C23—942no—
152Q8—41no—
153Q8—41no—
154Q8—472no—
155Q8—941no—
156D4—21no—
157D4—21no—
158D4—3762no—
159D4—1882no—
160D4—1884no—
161D4—1881no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—1884no—
172C2×C4D4×D4711yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C8—41no—
176C8—1881no—
177C8—1881no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1882no—
182C22—1882no—
183C22—1882no—
184C22#1309399211yescharacteristic
185C4—21no—
186C4—41no—
187C4—81no—
188C4—942no—
189C4—1881no—
190C4SD16×D4711yescharacteristic
191C4#1309404411yescharacteristic
192C4#1309405011yescharacteristic
193C4#1309405111yescharacteristic
194C2—81no—
195C2—3762no—
196C2#1568926611yescharacteristic
197C2#1568927211yescharacteristic
198C2#1568929911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#461C2
socleC22×C47#120
hypercenter#461D47
hypocenterC47#1642
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #15689471C2semidirect
3. #15689405C2semidirect
4. #15688866C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×#461C2semidirect
74. Dic94SD16semidirect
103. #461D47semidirect
107. C47#1642semidirect