Finite Group Databasebeta

← #20242587

Subgroups — #20242587

Order 6016.

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

normal subgroups only

This group has 250 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#15689471C211yesmaximal, characteristic, complemented
3#15689325C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#475C211yesmaximal, characteristic, complemented
8C2×#10625354—21no—
9C2×#10625336—21no—
10#13094021—21no—
11#13094021C2211yescharacteristic
12#13093999—22no—
13#13093999—21no—
14C4×D188—21no—
15C4×D188C2211yescharacteristic
16C4⋊(C47⋊C8)C2211yescharacteristic
17#13093948—21no—
18#13093944—22no—
19C4×C47⋊C8C2211yescharacteristic
20C4⋊Q8×C47C2211yescharacteristic
21C4×Q8×C47C2211yescharacteristic
22#106×C47—21no—
23C4⋊C8×C47C2211yescharacteristic
24#103×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47D411yescharacteristic
27#10625354—42no—
28#10625354—42no—
29C2×D188—22no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—22no—
33C2×D188D411yescharacteristic
34C2×D188D412yes—
35C2×C4×D47—22no—
36C2×C4×D47—21no—
37C2×C8×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47D411yescharacteristic
42C42×C47—21no—
43C42×C47C2311yescharacteristic
44#10625336—42no—
45(C2×D47)⋊C4—22no—
46(C2×D47)⋊C4—21no—
47C4⋊Dic47D411yescharacteristic
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C22×D47—21no—
51C22×D47—22no—
52Q8×C47—21no—
53Q8×C47—41no—
54Q8×C47—41no—
55Q8×C47SD1612yescomplemented
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×Dic47—21no—
63D188—21no—
64D188—21no—
65D188—42no—
66D188—44no—
67D188—41no—
68D188—41no—
69D188—41no—
70D188—41no—
71D188—82no—
72C4×D47—44no—
73C4×D47—41no—
74C4×D47—41no—
75C8×C47—41no—
76C47⋊C8—41no—
77C47⋊C8—41no—
78C22×C47#12011yescharacteristic
79C2×D47—41no—
80C2×D47—42no—
81C2×D47—42no—
82C2×D47—41no—
83C2×D47—42no—
84C2×D47—41no—
85C4×C47—22no—
86C4×C47—21no—
87C4×C47—41no—
88C4×C47—81no—
89C4×C47C2×SD1611yescharacteristic
90C4×C47#13511yescharacteristic
91C4×C47AGL(1,ℤ/8)11yescharacteristic
92C4×C47AGL(1,ℤ/8)11yescharacteristic
93Dic47—41no—
94#1642—471nomaximal, Sylow
95C2×C47#44911yescharacteristic
96C2×C47#45011yescharacteristic
97C2×C47#45511yescharacteristic
98D47—81no—
99D47—82no—
100#550—471no—
101#486—471no—
102#475D4711yescharacteristic, complemented
103#461—471no—
104#331—471no—
105Q8⋊C8—471no—
106D4⋊C8—471no—
107C47#164211yescharacteristic, complemented, Sylow
108C2×#41—941no—
109C2×SD16—941no—
110C4⋊Q8C2×D4711yescharacteristic
111#127—471no—
112#127—941no—
113#121—942no—
114#121—941no—
115C4×Q8C2×D4711yescharacteristic
116C4×D4—471no—
117C4×D4—941no—
118#106—21no—
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×Q8C22⋊D4711yescharacteristic
129C2×D4—471no—
130C2×D4—472no—
131C2×D4—942no—
132C2×D4—942no—
133C2×D4—941no—
134C2×D4—941no—
135C22×C4—942no—
136C22×C4—941no—
137SD16—1882no—
138C2×C8—21no—
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—471no—
145C4⋊C4C22⋊D4711yescharacteristic
146C22⋊C4—942no—
147C22⋊C4—941no—
148C42—21no—
149C42C22×D4711yescharacteristic
150C23—941no—
151C23—942no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1062533612yescomplemented
156D4—941no—
157D4—941no—
158D4—3762no—
159D4—1882no—
160D4—1884no—
161D4—1881no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—941no—
169C2×C4—1884no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4D4×D4711yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C8—41no—
176C8—1881no—
177C8—1881no—
178C22—1881no—
179C22—1882no—
180C22—1882no—
181C22—1881no—
182C22—1881no—
183C22—1882no—
184C22#1309399211yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—81no—
189C4—1881no—
190C4C2×#1062533611yescharacteristic
191C4#1309404511yescharacteristic
192C4#1309404911yescharacteristic
193C4#1309405111yescharacteristic
194C2—3761no—
195C2—3762no—
196C2#1568926711yescharacteristic
197C2#1568927311yescharacteristic
198C2#1568929911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#475C2
socleC22×C47#120
hypercenter#475D47
hypocenterC47#1642
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #15689471C2semidirect
3. #15689325C2semidirect
4. #15688866C2semidirect
5. Q8⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#475C2semidirect
55. Q8×C47SD16semidirect
102. #475D47semidirect
107. C47#1642semidirect
155. Q8#10625336semidirect