Finite Group Databasebeta

← #18009591

Subgroups — #18009591

Order 4736.

162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 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#14558411C211yesmaximal, characteristic
2#14558377C211yesmaximal, characteristic
3#14557444C211yesmaximal, characteristic
4C2×C22⋊#3866—21no—
5C22⋊#64438—21no—
6C2×#10596938—21no—
7C2×#10596938C2211yescharacteristic
8#11924443—21no—
9#11924443C411yescharacteristic, complemented
10C22×Q8×C37C411yescharacteristic, complemented
11C23×D37D411yescharacteristic
12C22×#3866—41no—
13C2×Q8×C37—42no—
14C2×Q8×C37—41no—
15C22×C4×C37—21no—
16C22×C4×C37C2×C411yescharacteristic
17C22×Dic37—21no—
18C22×Dic37D411yescharacteristic
19C22⋊#3866—22no—
20C22⋊#3866—41no—
21C2×#64438—41no—
22#10596938—41no—
23#10596938—42no—
24C23×C37C22⋊C411yescharacteristic
25C22×D37—21no—
26C22×D37—21no—
27C22×D37—41no—
28C22×D37—41no—
29C22×D37SD1611yescharacteristic
30C22×D37Q1611yescharacteristic
31C2×#3866—42no—
32C2×#3866—81no—
33C2×#3866—81no—
34Q8×C37—42no—
35Q8×C37—42no—
36C2×C4×C37—22no—
37C2×C4×C37—21no—
38C2×C4×C37—41no—
39C2×C4×C37—41no—
40C2×C4×C37—41no—
41C2×Dic37—21no—
42C2×Dic37—41no—
43C2×Dic37—41no—
44C2×Dic37—41no—
45C2×Dic37—41no—
46#64438—81no—
47C22×C37—21no—
48C22×C37—21no—
49C22×C37#9911yescharacteristic
50C22×C37#10311yescharacteristic
51C22×C37#10411yescharacteristic
52C2×D37—21no—
53C2×D37—21no—
54C2×D37—41no—
55C2×D37—41no—
56C2×D37—41no—
57C2×D37—41no—
58C2×D37—81no—
59#3866—82no—
60C4×C37—42no—
61C4×C37—41no—
62Dic37—41no—
63Dic37—81no—
64#1351—371nomaximal, Sylow
65C2×C37—21no—
66C2×C37—21no—
67C2×C37#32811yescharacteristic
68C2×C37AΣL(1,𝔽16)11yescharacteristic
69C2×C37#35411yescharacteristic
70D37—41no—
71D37—41no—
72#393—371no—
73#342—371no—
74#323—371no—
75C37#135111yescharacteristic, complemented, Sylow
76C22×Q8#386611yescharacteristic, complemented
77C2×C22⋊C4—371no—
78C2×C22⋊C4—741no—
79C2×C22⋊C4—741no—
80C22⋊C8—741no—
81#95—371no—
82#95—741no—
83C24—371no—
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—371no—
88C22×C4—741no—
89C22×C4—1481no—
90C22×C4C2×#386611yescharacteristic
91C2×C8—1481no—
92C22⋊C4—742no—
93C22⋊C4—1481no—
94C22⋊C4—1482no—
95C22⋊C4—1481no—
96C23—371no—
97C23—371no—
98C23—741no—
99C23—741no—
100C23—1481no—
101C23—1481no—
102C23C22⋊#386611yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—2961no—
111C2×C4—2961no—
112C2×C4—741no—
113C2×C4—1481no—
114C2×C4—1481no—
115C2×C4—1482no—
116C2×C4—1481no—
117C2×C4—1481no—
118C8—2961no—
119C22—21no—
120C22—21no—
121C22—2961no—
122C22—741no—
123C22—741no—
124C22—1481no—
125C22—1481no—
126C22—1481no—
127C22—1481no—
128C22#1192459411yescharacteristic
129C22#1192459911yescharacteristic
130C22#1192460111yescharacteristic
131C4—42no—
132C4—41no—
133C4—2961no—
134C4—2962no—
135C4—1481no—
136C2—21no—
137C2—21no—
138C2—1481no—
139C2—1481no—
140C2#1455838711yescharacteristic
141C2#1455843311yescharacteristic
142C2#1455843911yescharacteristic
subgroupG/H
centerC22#11924594
commutatorC22×C4×C37C2×C4
FrattiniC22×C4C2×#3866
FittingC22×Q8×C37C4
socleC22×C37#99
prime radicalC23×D37D4
cosocleC2×#10596938C22
hypercenterC22×Q8#3866
hypocenterC37#1351
LCSG ▷ C22×C4×C37 ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. #11924443C4semidirect
10. C22×Q8×C37C4semidirect
75. C37#1351semidirect
76. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145584112
#145583772
#145574442
#135137