Finite Group Databasebeta

← #17993712

Subgroups — #17993712

Order 4736.

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

normal subgroups only

This group has 314 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#14557905C211yesmaximal, characteristic, complemented
2#14557823C212yesmaximal, complemented
3#14557277C211yesmaximal, characteristic, complemented
4D4⋊#64436C212yesmaximal, complemented
5D42×C37C211yesmaximal, characteristic
6C2×#10596940—22no—
7#11924536C2211yescharacteristic, complemented
8#11924467—22no—
9C4⋊#64436C2212yescomplemented
10#11924457—22no—
11C4×#64436C2211yescharacteristic, complemented
12C22×D4×C37—22no—
13#127×C37C2211yescharacteristic
14#121×C37—22no—
15#120×C37—22no—
16C4×D4×C37C2212yes—
17C24×C37—22no—
18C2×D4×C37—24no—
19C2×D4×C37—22no—
20C2×D4×C37—44no—
21C2×D4×C37—44no—
22C2×D4×C37D412yes—
23C2×D4×C37D412yes—
24C22×C4×C37—22no—
25C2×Dic74—21no—
26C4⋊C4×C37D412yes—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C42×C37C2311yescharacteristic
30#10596940—44no—
31C4⋊Dic37—22no—
32C2×#64436—21no—
33C2×#64436—22no—
34C23×C37—22no—
35C23×C37—22no—
36C23×C37—48no—
37C23×C37—82no—
38D4×C37—22no—
39D4×C37—42no—
40D4×C37—48no—
41D4×C37—42no—
42D4×C37—42no—
43D4×C37SD1614yescomplemented
44C2×C4×C37—22no—
45C2×C4×C37—42no—
46C2×C4×C37—42no—
47C2×C4×C37C2×D411yescharacteristic
48C2×C4×C37C2×D412yes—
49C2×Dic37—41no—
50Dic74—42no—
51#64436—22no—
52#64436—42no—
53C22×C37—24no—
54C22×C37—42no—
55C22×C37—42no—
56C22×C37—44no—
57C22×C37—42no—
58C22×C37—88no—
59C22×C37#12011yescharacteristic
60C4×C37—21no—
61C4×C37—42no—
62C4×C37C2×SD1612yes—
63C4×C37AGL(1,ℤ/8)12yes—
64Dic37—81no—
65#1629—371nomaximal, Sylow
66C2×C37—44no—
67C2×C37—82no—
68C2×C37#45012yes—
69C2×C37#45311yescharacteristic
70D42D3711yescharacteristic
71#492—371no—
72#476—372no—
73#331—371no—
74D4⋊C8—372no—
75C37#162911yescharacteristic, complemented, Sylow
76C22×D4—22no—
77C2×SD16—742no—
78C4⋊Q8—371no—
79#127C2×D3711yescharacteristic
80#121—22no—
81#120—22no—
82C4×D4C2×D3712yes—
83#106—742no—
84C4⋊C8—372no—
85#102—742no—
86C4×C8—371no—
87C24—22no—
88C2×Q8—741no—
89C2×D4—24no—
90C2×D4—22no—
91C2×D4—44no—
92C2×D4—44no—
93C2×D4C22⋊D3712yes—
94C2×D4C22⋊D3712yes—
95C22×C4—22no—
96SD16—1484no—
97C2×C8—741no—
98C2×C8—742no—
99C4⋊C4—742no—
100C4⋊C4C22⋊D3712yes—
101C22⋊C4—22no—
102C22⋊C4—22no—
103C42C22×D3711yescharacteristic
104C23—22no—
105C23—22no—
106C23—48no—
107C23—82no—
108Q8—1482no—
109D4—22no—
110D4—42no—
111D4—48no—
112D4—42no—
113D4—42no—
114D4#1059694014yescomplemented
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—1481no—
119C2×C4C2×C22⋊D3711yescharacteristic
120C2×C4C2×C22⋊D3712yes—
121C8—742no—
122C8—1482no—
123C22—24no—
124C22—42no—
125C22—42no—
126C22—42no—
127C22—44no—
128C22—88no—
129C22#1192450511yescharacteristic
130C4—21no—
131C4—42no—
132C4—2961no—
133C4C2×#1059694012yes—
134C4#1192456212yes—
135C2—44no—
136C2—82no—
137C2#1455768412yes—
138C2#1455770111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalD42×C37C2
socleC22×C37#120
hypercenterD42D37
hypocenterC37#1629
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14557905C2semidirect
2. #14557823C2semidirect
3. #14557277C2semidirect
4. D4⋊#64436C2semidirect
7. #11924536C22semidirect
9. C4⋊#64436C22semidirect
11. C4×#64436C22semidirect
43. D4×C37SD16semidirect
75. C37#1629semidirect
114. D4#10596940semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145579052
#145578232
#145572772
D4⋊#644362
D42×C372
#162937