Finite Group Databasebeta

← #20242563

Subgroups — #20242563

Order 6016.

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

normal subgroups only

This group has 194 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#15689474C211yesmaximal, characteristic, complemented
3#15689418C211yesmaximal, characteristic, complemented
4#15689414C211yesmaximal, characteristic
5#15688870C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8#13094024C2211yescharacteristic
9#13094024C2211yescharacteristic
10#13094019—22no—
11#13094012—21no—
12#13094000—21no—
13C4×Dic94—21no—
14C4×D188C2211yescharacteristic
15#13093982—21no—
16#13093957—21no—
17#13093956—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—22no—
20#13093948—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(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47D412yes—
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—22no—
45C4×Dic47—22no—
46C2×C47⋊C8—21no—
47C22×D47—21no—
48Q8×C47—21no—
49Q8×C47—21no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×Dic47—21no—
56C2×Dic47—22no—
57C2×Dic47—41no—
58D188—21no—
59D188—21no—
60C4×D47—41no—
61C4×D47—41no—
62Dic94—41no—
63Dic94—41no—
64Dic94—42no—
65C8×C47—41no—
66C8×C47—41no—
67C47⋊C8—41no—
68C22×C47#12011yescharacteristic
69C2×D47—41no—
70C2×D47—41no—
71C2×D47—41no—
72C4×C47—21no—
73C4×C47—41no—
74C4×C47—41no—
75C4×C47#13511yescharacteristic
76C4×C47#13511yescharacteristic
77C4×C47#13711yescharacteristic
78C4×C47#13711yescharacteristic
79Dic47—42no—
80Dic47—41no—
81Dic47—81no—
82#1638—471nomaximal, Sylow
83C2×C47#45211yescharacteristic
84C2×C47#45211yescharacteristic
85C2×C47#45411yescharacteristic
86D47—81no—
87#556—471no—
88#487—471no—
89#477—471no—
90#476—471no—
91#332—471no—
92Q8⋊C8D4711yescharacteristic, complemented
93D4⋊C8—471no—
94C47#163811yescharacteristic, complemented, Sylow
95C4⋊Q8—471no—
96C4⋊Q8—471no—
97#126—942no—
98#124—941no—
99C22⋊Q8—941no—
100C4×Q8—941no—
101C4×Q8C2×D4711yescharacteristic
102C4×D4—471no—
103#117—941no—
104#107—941no—
105#106—941no—
106C4⋊C8—471no—
107C4⋊C8C2×D4711yescharacteristic
108#103—942no—
109#103—941no—
110#102—941no—
111C4×C8C2×D4711yescharacteristic
112C2×Q8—941no—
113C2×Q8—941no—
114C2×Q8D18811yescharacteristic
115C2×D4—471no—
116C22×C4—941no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—941no—
120C4⋊C4—21no—
121C4⋊C4—472no—
122C4⋊C4—471no—
123C4⋊C4—942no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4D18811yescharacteristic
128C22⋊C4—942no—
129C22⋊C4—942no—
130C22⋊C4—941no—
131C42—21no—
132C42—942no—
133C42C22×D4711yescharacteristic
134C23—941no—
135Q8—21no—
136Q8—21no—
137Q8—1882no—
138Q8—1881no—
139Q8—1881no—
140D4—941no—
141D4—941no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—941no—
145C2×C4—942no—
146C2×C4—1881no—
147C2×C4—1881no—
148C2×C4—1881no—
149C2×C4C2×D18811yescharacteristic
150C2×C4D4×D4711yescharacteristic
151C2×C4D4×D4711yescharacteristic
152C8—41no—
153C8—41no—
154C8—1881no—
155C22—1881no—
156C22—1881no—
157C22—1881no—
158C22#1309399411yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—3761no—
163C4—1881no—
164C4—1882no—
165C4#1309404511yescharacteristic
166C4#1309404611yescharacteristic
167C4#1309405611yescharacteristic
168C4#1309405711yescharacteristic
169C2—3761no—
170C2#1568928711yescharacteristic
171C2#1568928811yescharacteristic
172C2#1568929711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1638
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. #15689474C2semidirect
3. #15689418C2semidirect
5. #15688870C2semidirect
7. C47×Q8⋊C8C2semidirect
92. Q8⋊C8D47semidirect
94. C47#1638semidirect