Finite Group Databasebeta

← #20242596

Subgroups — #20242596

Order 6016.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689834C211yesmaximal, characteristic
2#15689473C211yesmaximal, characteristic, complemented
3#15689409C211yesmaximal, characteristic, complemented
4#15689329C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic
7C47×#333C211yesmaximal, characteristic, complemented
8C2×#10625325—21no—
9#13094024C2211yescharacteristic
10#13094015—21no—
11#13094004—21no—
12#13094000—22no—
13C4×Dic94C2211yescharacteristic
14C4×D188C2211yescharacteristic
15#13093986—21no—
16C4⋊C4×D47—21no—
17#13093956—21no—
18#13093949—21no—
19#13093949—21no—
20#13093948—22no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47D412yes—
26C2×D188D411yescharacteristic
27C2×C4×D47—21no—
28C2×C4×D47—22no—
29C2×Dic94—21no—
30C2×Dic94D411yescharacteristic
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C42×C47C2311yescharacteristic
36(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—21no—
38C4⋊Dic47—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47D411yescharacteristic
42C4⋊Dic47D411yescharacteristic
43Dic47⋊C4—22no—
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47#10625325—42no—
48C22×D47—21no—
49Q8×C47—42no—
50C2×C4×C47—22no—
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×Dic47—21no—
55C2×Dic47—21no—
56C2×Dic47—21no—
57C2×Dic47—41no—
58D188—21no—
59D188SD1612yes—
60C4×D47—41no—
61C4×D47—41no—
62C4×D47—82no—
63Dic94—21no—
64Dic94—21no—
65Dic94—41no—
66Dic94—41no—
67C8×C47—41no—
68C8×C47—41no—
69C47⋊C8—41no—
70C22×C47#12011yescharacteristic
71C2×D47—22no—
72C2×D47—41no—
73C2×D47—41no—
74C4×C47—21no—
75C4×C47—42no—
76C4×C47C2×SD1611yescharacteristic
77C4×C47#13511yescharacteristic
78C4×C47#13711yescharacteristic
79C4×C47#13711yescharacteristic
80Dic47—41no—
81Dic47—41no—
82Dic47—41no—
83Dic47—81no—
84#1643—471nomaximal, Sylow
85C2×C47#44811yescharacteristic
86C2×C47#45211yescharacteristic
87C2×C47#45511yescharacteristic
88D47—42no—
89#554—471no—
90#487—471no—
91#475—471no—
92#461—471no—
93#333D4711yescharacteristic, complemented
94Q8⋊C8—471no—
95D4⋊C8—471no—
96C47#164311yescharacteristic, complemented, Sylow
97C2×SD16—941no—
98C4⋊Q8—471no—
99C4⋊Q8C2×D4711yescharacteristic
100#125—941no—
101C22⋊Q8—941no—
102C22⋊Q8—942no—
103C4×Q8—471no—
104C4×D4—471no—
105C4×D4—941no—
106C2×C4⋊C4—941no—
107#106—941no—
108C4⋊C8C2×D4711yescharacteristic
109C4⋊C8C2×D4711yescharacteristic
110#103—941no—
111#103—941no—
112#103—942no—
113C4×C8—471no—
114C2×Q8—471no—
115C2×Q8—941no—
116C2×Q8D18812yes—
117C2×D4—471no—
118C22×C4—942no—
119C22×C4—941no—
120SD16—1882no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—941no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—471no—
127C4⋊C4—471no—
128C4⋊C4—942no—
129C4⋊C4—942no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C22⋊C4—942no—
134C22⋊C4—941no—
135C42—941no—
136C42C22×D4711yescharacteristic
137C23—941no—
138Q8—42no—
139Q8—941no—
140Q8—941no—
141Q8—1881no—
142Q8—1881no—
143D4—472no—
144D4—941no—
145C2×C4—22no—
146C2×C4—941no—
147C2×C4—941no—
148C2×C4—941no—
149C2×C4—3762no—
150C2×C4—1881no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4C2×D18811yescharacteristic
154C2×C4D4×D4711yescharacteristic
155C2×C4D4×D4711yescharacteristic
156C8—41no—
157C8—41no—
158C8—1881no—
159C22—942no—
160C22—1881no—
161C22—1881no—
162C22#1309399411yescharacteristic
163C4—21no—
164C4—42no—
165C4—3761no—
166C4—1881no—
167C4—1881no—
168C4—1881no—
169C4SD16×D4711yescharacteristic
170C4#1309404511yescharacteristic
171C4#1309405611yescharacteristic
172C4#1309405611yescharacteristic
173C2—1882no—
174C2#1568926311yescharacteristic
175C2#1568928811yescharacteristic
176C2#1568930311yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#333C2
socleC22×C47#120
hypercenter#333D47
hypocenterC47#1643
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #15689473C2semidirect
3. #15689409C2semidirect
5. #15688853C2semidirect
7. C47×#333C2semidirect
93. #333D47semidirect
96. C47#1643semidirect