Finite Group Databasebeta

← #20242660

Subgroups — #20242660

Order 6016.

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

normal subgroups only

This group has 200 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#15689846C211yesmaximal, characteristic
2#15689521C211yesmaximal, characteristic, complemented
3#15689404C211yesmaximal, characteristic
4#15689333C211yesmaximal, characteristic, complemented
5#15688870C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625337—21no—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094019—22no—
12#13094012—21no—
13#13094000—21no—
14C4×Dic94—21no—
15C4×D188C2211yescharacteristic
16#13093982—21no—
17#13093958—21no—
18#13093956—22no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093947—21no—
21#13093946—21no—
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47D411yescharacteristic
26C2×D188D411yescharacteristic
27C2×C4×D47—21no—
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47D411yescharacteristic
34C42×C47—21no—
35C42×C47C2311yescharacteristic
36#10625337—42no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D412yes—
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—22no—
46C4×Dic47—22no—
47C2×C47⋊C8—21no—
48C22×D47—21no—
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—22no—
58C2×Dic47—41no—
59D188—21no—
60D188—21no—
61C4×D47—41no—
62C4×D47—41no—
63Dic94—41no—
64Dic94—41no—
65Dic94—41no—
66Dic94—41no—
67C8×C47—22no—
68C8×C47—41no—
69C47⋊C8—41no—
70C22×C47#12011yescharacteristic
71C2×D47—41no—
72C2×D47—41no—
73C2×D47—41no—
74C4×C47—21no—
75C4×C47—41no—
76C4×C47—41no—
77C4×C47#13511yescharacteristic
78C4×C47#13511yescharacteristic
79C4×C47AGL(1,ℤ/8)11yescharacteristic
80C4×C47#13711yescharacteristic
81Dic47—41no—
82Dic47—42no—
83Dic47—81no—
84#1652—471nomaximal, Sylow
85C2×C47#44911yescharacteristic
86C2×C47#45211yescharacteristic
87C2×C47#45611yescharacteristic
88D47—81no—
89#556—471no—
90#498—471no—
91#474—471no—
92#462—471no—
93#332—471no—
94Q8⋊C8D4711yescharacteristic, complemented
95D4⋊C8—471no—
96C47#165211yescharacteristic, complemented, Sylow
97C2×Q16—941no—
98C4⋊Q8—471no—
99C4⋊Q8—471no—
100#126—942no—
101#124—941no—
102C22⋊Q8—941no—
103C4×Q8—941no—
104C4×Q8C2×D4711yescharacteristic
105C4×D4—471no—
106#117—941no—
107#107—941no—
108#106—942no—
109C4⋊C8—471no—
110C4⋊C8C2×D4711yescharacteristic
111#103—941no—
112#102—941no—
113C4×C8C2×D4711yescharacteristic
114C2×Q8—941no—
115C2×Q8—941no—
116C2×Q8D18811yescharacteristic
117C2×D4—471no—
118C22×C4—941no—
119Q16—1882no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—941no—
123C4⋊C4—21no—
124C4⋊C4—472no—
125C4⋊C4—471no—
126C4⋊C4—942no—
127C4⋊C4—941no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4D18811yescharacteristic
131C22⋊C4—942no—
132C22⋊C4—942no—
133C22⋊C4—941no—
134C42—21no—
135C42—942no—
136C42C22×D4711yescharacteristic
137C23—941no—
138Q8—21no—
139Q8—21no—
140Q8—1881no—
141Q8—1881no—
142Q8—1881no—
143Q8—1881no—
144D4—941no—
145D4—941no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—941no—
149C2×C4—942no—
150C2×C4—1881no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4C2×D18811yescharacteristic
154C2×C4D4×D4711yescharacteristic
155C2×C4D4×D4711yescharacteristic
156C8—22no—
157C8—41no—
158C8—1881no—
159C22—1881no—
160C22—1881no—
161C22—1881no—
162C22#1309399411yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—3761no—
167C4—1881no—
168C4—1882no—
169C4#1309404511yescharacteristic
170C4#1309404611yescharacteristic
171C4#1309405211yescharacteristic
172C4#1309405611yescharacteristic
173C2—3761no—
174C2#1568927011yescharacteristic
175C2#1568928811yescharacteristic
176C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1652
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. #15689521C2semidirect
4. #15689333C2semidirect
5. #15688870C2semidirect
7. C47×Q8⋊C8C2semidirect
94. Q8⋊C8D47semidirect
96. C47#1652semidirect