Finite Group Databasebeta

← #20242092

Subgroups — #20242092

Order 6016.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689674C211yesmaximal, characteristic
2#15689179C211yesmaximal, characteristic, complemented
3#15689175C211yesmaximal, characteristic, complemented
4#15688869C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic, complemented
6#15688866C211yesmaximal, characteristic, complemented
7C47×#332C211yesmaximal, characteristic, complemented
8C2×#10625354—21no—
9#13094021C2211yescharacteristic
10#13094013—21no—
11#13093999—21no—
12#13093999C412yes—
13#13093986—21no—
14#13093986C412yes—
15C42×D47C2211yescharacteristic
16C4⋊(C47⋊C8)C2211yescharacteristic
17C4⋊(C47⋊C8)C2211yescharacteristic
18(C2×D47)⋊C8—21no—
19(C2×D47)⋊C8—21no—
20#13093934—21no—
21C8×Dic47—21no—
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26#10625354—42no—
27#10625354—42no—
28C2×D188—22no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188C2×C412yes—
32C2×C4×D47—22no—
33C2×C4×D47C2×C411yescharacteristic
34C2×C4×D47D411yescharacteristic
35C2×C4×D47D411yescharacteristic
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47C2×C412yes—
40C42×C47C2311yescharacteristic
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—22no—
43C4×Dic47C2×C411yescharacteristic
44C4×Dic47D411yescharacteristic
45C4×Dic47D411yescharacteristic
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C22×D47—22no—
49C22×D47C22⋊C411yescharacteristic
50Q8×C47—41no—
51Q8×C47—41no—
52C2×C4×C47—22no—
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47C22⋊C411yescharacteristic
57C2×Dic47C22⋊C411yescharacteristic
58C2×Dic47C22⋊C411yescharacteristic
59D188—42no—
60D188—44no—
61D188—41no—
62D188—41no—
63D188—41no—
64D188—41no—
65C4×D47—21no—
66C4×D47—21no—
67C4×D47—21no—
68C4×D47—21no—
69C4×D47—41no—
70C4×D47—44no—
71C8×C47—41no—
72C8×C47—41no—
73C47⋊C8—41no—
74C47⋊C8—41no—
75C22×C47C2×C22⋊C411yescharacteristic
76C2×D47—21no—
77C2×D47—21no—
78C2×D47—21no—
79C2×D47—42no—
80C2×D47—42no—
81C2×D47—42no—
82C4×C47—21no—
83C4×C47—42no—
84C4×C47#13511yescharacteristic
85C4×C47#13511yescharacteristic
86C4×C47AGL(1,ℤ/8)11yescharacteristic
87C4×C47AGL(1,ℤ/8)11yescharacteristic
88Dic47—21no—
89Dic47—21no—
90Dic47—21no—
91#1553—471nomaximal, Sylow
92C2×C47#41311yescharacteristic
93C2×C47#41611yescharacteristic
94C2×C47#41811yescharacteristic
95D47—41no—
96D47—82no—
97#532—471no—
98#432—471no—
99#431—471no—
100#332—471no—
101#332D4711yescharacteristic, complemented
102#331—471no—
103#331—471no—
104C47#155311yescharacteristic, complemented, Sylow
105C2×#41—941no—
106C4⋊Q8C2×D4711yescharacteristic
107#127—471no—
108#124—941no—
109#121—472no—
110#121—941no—
111C4×D4—472no—
112C4×D4—941no—
113C2×C42—471no—
114C4⋊C8—471no—
115C4⋊C8—471no—
116C4⋊C8C2×D4711yescharacteristic
117C4⋊C8C2×D4711yescharacteristic
118C22⋊C8—941no—
119C22⋊C8—941no—
120#97—941no—
121C4×C8—941no—
122#41—1882no—
123#41—1882no—
124C2×Q8—21no—
125C2×D4—472no—
126C2×D4—942no—
127C2×D4—941no—
128C2×D4—941no—
129C22×C4—471no—
130C22×C4—471no—
131C22×C4—471no—
132C22×C4—942no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—941no—
136C2×C8—941no—
137C4⋊C4—21no—
138C4⋊C4C4×D4712yes—
139C22⋊C4—942no—
140C22⋊C4—942no—
141C42—471no—
142C42—471no—
143C42—471no—
144C42C22×D4711yescharacteristic
145C23—471no—
146C23—942no—
147Q8—41no—
148Q8—41no—
149D4—1882no—
150D4—1884no—
151D4—1881no—
152D4—1881no—
153D4—1881no—
154D4—1881no—
155C2×C4—22no—
156C2×C4—471no—
157C2×C4—471no—
158C2×C4—471no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—1881no—
164C2×C4—1884no—
165C2×C4C2×C4×D4711yescharacteristic
166C2×C4D4×D4711yescharacteristic
167C2×C4D4×D4711yescharacteristic
168C8—41no—
169C8—41no—
170C8—1881no—
171C8—1881no—
172C22—941no—
173C22—941no—
174C22—941no—
175C22—1882no—
176C22—1882no—
177C22—1882no—
178C22C22⋊C4×D4711yescharacteristic
179C4—21no—
180C4—42no—
181C4—941no—
182C4—941no—
183C4—941no—
184C4#1309404511yescharacteristic
185C4#1309404711yescharacteristic
186C4#1309404811yescharacteristic
187C4#1309405111yescharacteristic
188C2—3762no—
189C2—1881no—
190C2#1568910611yescharacteristic
191C2#1568911811yescharacteristic
192C2#1568912611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47C2×C22⋊C4
hypercenter#332D47
hypocenterC47#1553
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #15689179C2semidirect
3. #15689175C2semidirect
4. #15688869C2semidirect
5. #15688866C2semidirect
6. #15688866C2semidirect
7. C47×#332C2semidirect
101. #332D47semidirect
104. C47#1553semidirect