Finite Group Databasebeta

← #20242613

Subgroups — #20242613

Order 6016.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689839C211yesmaximal, characteristic
2#15689400C211yesmaximal, characteristic, complemented
3#15689325C211yesmaximal, characteristic, complemented
4#15688872C211yesmaximal, characteristic, complemented
5#15688852C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×#487C211yesmaximal, characteristic, complemented
8C2×#10625336—21no—
9#13094013—22no—
10#13093999—21no—
11#13093999—21no—
12C4×D188C2211yescharacteristic
13C4×D188C2211yescharacteristic
14#13093982—21no—
15#13093982—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093948—21no—
20#13093944—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#103×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×Q8×C47D412yes—
27C2×D188—22no—
28C2×D188D411yescharacteristic
29C2×D188D411yescharacteristic
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C42×C47C2311yescharacteristic
38#10625336—42no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D411yescharacteristic
45C4×Dic47—22no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C22×D47—21no—
49C22×D47—21no—
50Q8×C47—42no—
51Q8×C47—41no—
52Q8×C47—41no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—21no—
60D188—21no—
61D188—21no—
62D188—21no—
63D188—21no—
64D188—82no—
65C4×D47—41no—
66C4×D47—41no—
67C4×D47—41no—
68C4×D47—41no—
69C8×C47—41no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47#12011yescharacteristic
73C2×D47—41no—
74C2×D47—41no—
75C2×D47—41no—
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—41no—
79C4×C47—21no—
80C4×C47—42no—
81C4×C47—81no—
82C4×C47#13511yescharacteristic
83C4×C47#13511yescharacteristic
84C4×C47AGL(1,ℤ/8)11yescharacteristic
85C4×C47#13711yescharacteristic
86Dic47—41no—
87Dic47—41no—
88#1646—471nomaximal, Sylow
89C2×C47#44911yescharacteristic
90C2×C47#45211yescharacteristic
91C2×C47#45511yescharacteristic
92D47—81no—
93D47—81no—
94#555—471no—
95#487D4711yescharacteristic, complemented
96#474—471no—
97#461—471no—
98#333—471no—
99D4⋊C8—471no—
100D4⋊C8—471no—
101C47#164611yescharacteristic, complemented, Sylow
102C2×SD16—941no—
103C4⋊Q8C2×D4711yescharacteristic
104C4⋊Q8C2×D4711yescharacteristic
105#124—942no—
106#121—941no—
107#121—941no—
108C4×D4—471no—
109C4×D4—471no—
110#117—941no—
111#117—941no—
112#107—941no—
113C4⋊C8—471no—
114C4⋊C8—471no—
115#103—22no—
116#103—941no—
117#102—941no—
118C4×C8C2×D4711yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D4712yes—
121C2×D4—471no—
122C2×D4—471no—
123C2×D4—942no—
124C22×C4—941no—
125C22×C4—941no—
126SD16—1882no—
127C2×C8—21no—
128C2×C8—941no—
129C2×C8—941no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—471no—
135C4⋊C4—471no—
136C22⋊C4—942no—
137C22⋊C4—942no—
138C22⋊C4—941no—
139C22⋊C4—941no—
140C42—942no—
141C42C22×D4711yescharacteristic
142C23—941no—
143C23—941no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—941no—
148D4—941no—
149D4—941no—
150D4—941no—
151D4—3762no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4D4×D4711yescharacteristic
161C2×C4D4×D4711yescharacteristic
162C2×C4C2×C22⋊D4711yescharacteristic
163C8—41no—
164C8—1881no—
165C8—1881no—
166C22—1881no—
167C22—1881no—
168C22—1881no—
169C22—1881no—
170C22—1881no—
171C22—1881no—
172C22#1309399211yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—1881no—
177C4—1881no—
178C4#1309404511yescharacteristic
179C4#1309404711yescharacteristic
180C4#1309405111yescharacteristic
181C4#1309405611yescharacteristic
182C2—3761no—
183C2—3761no—
184C2#1568926711yescharacteristic
185C2#1568928411yescharacteristic
186C2#1568930011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#487C2
socleC22×C47#120
hypercenter#487D47
hypocenterC47#1646
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #15689400C2semidirect
3. #15689325C2semidirect
4. #15688872C2semidirect
5. #15688852C2semidirect
6. #15688852C2semidirect
7. C47×#487C2semidirect
95. #487D47semidirect
101. C47#1646semidirect