Finite Group Databasebeta

← #20242577

Subgroups — #20242577

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#15689858C211yesmaximal, characteristic
2#15689470C211yesmaximal, characteristic
3#15689408C211yesmaximal, characteristic, complemented
4#15689334C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic
6#15688855C211yesmaximal, characteristic, complemented
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Dic188—21no—
9#13094024C2211yescharacteristic
10#13094021C2211yescharacteristic
11#13094013—21no—
12#13094012—21no—
13#13094009—22no—
14C4×Dic94C2211yescharacteristic
15C4×D188—21no—
16#13093986—21no—
17#13093955—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—21no—
20#13093948—21no—
21#13093946—22no—
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47D411yescharacteristic
26C2×D188—21no—
27C2×D188—21no—
28C2×D188D412yes—
29C2×C4×D47—22no—
30C2×Dic94—21no—
31C2×Dic94D411yescharacteristic
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D411yescharacteristic
36C42×C47—21no—
37C42×C47C2311yescharacteristic
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47Dic188—42no—
48C22×D47—22no—
49Q8×C47—21no—
50Q8×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—21no—
57C2×Dic47—21no—
58C2×Dic47—41no—
59D188—42no—
60D188—41no—
61D188—41no—
62D188—41no—
63D188—41no—
64C4×D47—82no—
65Dic94—21no—
66Dic94—21no—
67Dic94—41no—
68Dic94—41no—
69C8×C47—41no—
70C8×C47—41no—
71C47⋊C8—41no—
72C22×C47#12011yescharacteristic
73C2×D47—42no—
74C2×D47—42no—
75C2×D47—42no—
76C4×C47—21no—
77C4×C47—41no—
78C4×C47—41no—
79C4×C47#13511yescharacteristic
80C4×C47#13511yescharacteristic
81C4×C47AGL(1,ℤ/8)11yescharacteristic
82C4×C47#13711yescharacteristic
83Dic47—41no—
84Dic47—41no—
85Dic47—81no—
86#1640—471nomaximal, Sylow
87C2×C47#44911yescharacteristic
88C2×C47#45211yescharacteristic
89C2×C47#45511yescharacteristic
90D47—82no—
91#559—471no—
92#486—471no—
93#475—471no—
94#462—471no—
95#331—471no—
96Q8⋊C8—471no—
97Q8⋊C8D4711yescharacteristic, complemented
98C47#164011yescharacteristic, complemented, Sylow
99C2×Q16—941no—
100C4⋊Q8—471no—
101#127—471no—
102#124—941no—
103#124—941no—
104#123—942no—
105C4×Q8—471no—
106C4×Q8C2×D4711yescharacteristic
107C4×D4—941no—
108C4×D4—941no—
109#106—941no—
110C4⋊C8—471no—
111C4⋊C8C2×D4711yescharacteristic
112#103—941no—
113#103—941no—
114#102—942no—
115C4×C8C2×D4711yescharacteristic
116C2×Q8—471no—
117C2×Q8—941no—
118C2×Q8D18811yescharacteristic
119C2×D4—472no—
120C2×D4—941no—
121C2×D4—941no—
122C22×C4—942no—
123Q16—1882no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—941no—
127C4⋊C4—21no—
128C4⋊C4—471no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C4⋊C4D18811yescharacteristic
133C22⋊C4—942no—
134C22⋊C4—942no—
135C22⋊C4—942no—
136C42—21no—
137C42—941no—
138C42C22×D4711yescharacteristic
139C23—942no—
140Q8—21no—
141Q8—21no—
142Q8—941no—
143Q8—941no—
144Q8—1881no—
145Q8—1881no—
146D4—1882no—
147D4—1881no—
148D4—1881no—
149D4—1881no—
150D4—1881no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—3762no—
156C2×C4—1881no—
157C2×C4C2×D18811yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C2×C4D4×D4711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1881no—
163C22—1882no—
164C22—1882no—
165C22—1882no—
166C22#1309399411yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—3761no—
171C4—1881no—
172C4—1881no—
173C4#1309404611yescharacteristic
174C4#1309404711yescharacteristic
175C4#1309405111yescharacteristic
176C4#1309405711yescharacteristic
177C2—3762no—
178C2#1568927111yescharacteristic
179C2#1568928711yescharacteristic
180C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1640
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
3. #15689408C2semidirect
4. #15689334C2semidirect
6. #15688855C2semidirect
7. C47×Q8⋊C8C2semidirect
97. Q8⋊C8D47semidirect
98. C47#1640semidirect