Finite Group Databasebeta

← #20242517

Subgroups — #20242517

Order 6016.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689795C211yesmaximal, characteristic
2#15689496C211yesmaximal, characteristic, complemented
3#15689418C211yesmaximal, characteristic, complemented
4#15689414C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625354—21no—
9C2×#10625325—22no—
10#13094024C2211yescharacteristic
11#13094021—21no—
12#13094021C2211yescharacteristic
13#13093999—22no—
14#13093999—21no—
15C4×D188—21no—
16C4×D188C2211yescharacteristic
17#13093957—21no—
18#13093956—21no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093948—21no—
21#13093946—21no—
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47D411yescharacteristic
26#10625354—42no—
27#10625354—42no—
28C2×D188—22no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188—22no—
32C2×D188D411yescharacteristic
33C2×D188D412yes—
34C2×C4×D47—22no—
35C2×C4×D47—21no—
36C2×Dic94—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47D411yescharacteristic
41C42×C47—21no—
42C42×C47C2311yescharacteristic
43(C2×D47)⋊C4—22no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47D411yescharacteristic
48C2×C47⋊C8—21no—
49#10625325—44no—
50C22×D47—21no—
51C22×D47—22no—
52Q8×C47—21no—
53Q8×C47SD1612yescomplemented
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×Dic47—21no—
60C2×Dic47—41no—
61D188—21no—
62D188—21no—
63D188—42no—
64D188—44no—
65D188—41no—
66D188—41no—
67D188—41no—
68D188—41no—
69D188—82no—
70C4×D47—44no—
71C4×D47—41no—
72C4×D47—41no—
73Dic94—42no—
74C8×C47—22no—
75C8×C47—41no—
76C47⋊C8—41no—
77C22×C47#12011yescharacteristic
78C2×D47—42no—
79C2×D47—41no—
80C2×D47—41no—
81C2×D47—42no—
82C2×D47—42no—
83C2×D47—41no—
84C4×C47—22no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47C2×SD1611yescharacteristic
88C4×C47#13511yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47#13711yescharacteristic
91Dic47—41no—
92Dic47—81no—
93#1631—471nomaximal, Sylow
94C2×C47#45011yescharacteristic
95C2×C47#45211yescharacteristic
96C2×C47#45311yescharacteristic
97D47—81no—
98D47—82no—
99#550—471no—
100#492—471no—
101#477—471no—
102#476—471no—
103#331—471no—
104Q8⋊C8D4711yescharacteristic, complemented
105D4⋊C8—471no—
106C47#163111yescharacteristic, complemented, Sylow
107C2×#41—941no—
108C2×SD16—942no—
109C4⋊Q8—471no—
110#127—471no—
111#127—941no—
112#121—942no—
113#121—941no—
114C4×Q8C2×D4711yescharacteristic
115C4×D4—471no—
116C4×D4—941no—
117#107—941no—
118#106—941no—
119C4⋊C8—471no—
120C4⋊C8C2×D4711yescharacteristic
121#103—941no—
122#102—941no—
123C4×C8C2×D4711yescharacteristic
124#41—1882no—
125#41—1882no—
126C2×Q8—941no—
127C2×Q8D18811yescharacteristic
128C2×D4—471no—
129C2×D4—472no—
130C2×D4—942no—
131C2×D4—942no—
132C2×D4—941no—
133C2×D4—941no—
134C22×C4—942no—
135C22×C4—941no—
136SD16—1884no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—941no—
140C4⋊C4—21no—
141C4⋊C4—471no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4D18811yescharacteristic
145C22⋊C4—942no—
146C22⋊C4—941no—
147C42—21no—
148C42C22×D4711yescharacteristic
149C23—941no—
150C23—942no—
151Q8—21no—
152Q8—1882no—
153Q8#1062532512yescomplemented
154D4—941no—
155D4—941no—
156D4—3762no—
157D4—1882no—
158D4—1884no—
159D4—1881no—
160D4—1881no—
161D4—1881no—
162D4—1881no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—941no—
166C2×C4—1884no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4C2×D18811yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4D4×D4711yescharacteristic
173C8—22no—
174C8—41no—
175C8—1881no—
176C22—1882no—
177C22—1881no—
178C22—1881no—
179C22—1882no—
180C22—1881no—
181C22—1882no—
182C22#1309399411yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—3761no—
187C4—1881no—
188C4C2×#1062532511yescharacteristic
189C4#1309404511yescharacteristic
190C4#1309405211yescharacteristic
191C4#1309405611yescharacteristic
192C2—3761no—
193C2—3762no—
194C2#1568927611yescharacteristic
195C2#1568928811yescharacteristic
196C2#1568929211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1631
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689496C2semidirect
3. #15689418C2semidirect
4. #15689414C2semidirect
5. #15688866C2semidirect
6. #15688852C2semidirect
7. C47×Q8⋊C8C2semidirect
53. Q8×C47SD16semidirect
104. Q8⋊C8D47semidirect
106. C47#1631semidirect
153. Q8#10625325semidirect