Finite Group Databasebeta

← #18009686

Subgroups — #18009686

Order 4736.

158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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#14558520C211yesmaximal, characteristic
2#14558506C211yesmaximal, characteristic
3#14557514C211yesmaximal, characteristic
4C2×#10596957—21no—
5C2×#10596957C411yescharacteristic
6C22×#64438C411yescharacteristic
7#11924597—21no—
8#11924596C412yes—
9#11924593—21no—
10C22⋊#64438—21no—
11C2×#10596964C2211yescharacteristic
12M16×D37—21no—
13#11924454—21no—
14#11924453C411yescharacteristic
15#100×C37C411yescharacteristic
16C2×D4×C37C2×C411yescharacteristic
17C2×C22⋊D37C2×C411yescharacteristic
18C2×C22⋊D37Q811yescharacteristic
19C22×Dic37C2×C411yescharacteristic
20C22×Dic37D411yescharacteristic
21#10596964—41no—
22#10596964—41no—
23C2×C4×D37D411yescharacteristic
24C2×Dic74D411yescharacteristic
25#10596957—22no—
26#10596957—41no—
27#10596957—41no—
28C2×#64438—21no—
29C2×#64438—21no—
30C2×#64438—41no—
31C2×#64438—41no—
32M16×C37—21no—
33#10596934—21no—
34#10596929—41no—
35C8×D37—41no—
36C23×C37C4211yescharacteristic
37C23×C37C4⋊C411yescharacteristic
38C22×D37C4⋊C411yescharacteristic
39D4×C37—41no—
40C2×C4×C37C22⋊C411yescharacteristic
41C22⋊D37—41no—
42C22⋊D37—41no—
43C2×Dic37—21no—
44C2×Dic37—21no—
45C2×Dic37—21no—
46C2×Dic37—21no—
47C2×Dic37C22⋊C411yescharacteristic
48C2×Dic37C22⋊C411yescharacteristic
49C2×Dic37C4⋊C411yescharacteristic
50C4×D37—21no—
51C4×D37—21no—
52Dic74—41no—
53#64438—42no—
54#64438—41no—
55#64438—41no—
56C8×C37—41no—
57#64436—41no—
58C22×C37—21no—
59C22×C37—21no—
60C22×C37—41no—
61C22×C37—41no—
62C22×C37#9511yescharacteristic
63C2×D37—21no—
64C2×D37—41no—
65C4×C37—21no—
66Dic37—21no—
67Dic37—21no—
68Dic37#9911yescharacteristic
69Dic37#9911yescharacteristic
70#1392—371nomaximal, Sylow
71C2×C37—21no—
72C2×C37—41no—
73C2×C37—41no—
74C2×C37#34211yescharacteristic
75D37—41no—
76#413—371no—
77#413—371no—
78#408—371no—
79C37#139211yescharacteristic, complemented, Sylow
80C2×#41—371no—
81C2×M16—371no—
82C2×M16—741no—
83C2×M16—741no—
84C22×C8—371no—
85#101—741no—
86#101—741no—
87#100—372no—
88#100—371no—
89#100#386611yescharacteristic
90C22⋊C8—741no—
91C22⋊C8—741no—
92#41—1481no—
93#41—1481no—
94C2×Q8—371no—
95C2×D4—371no—
96C2×D4—371no—
97C2×D4C2×#386611yescharacteristic
98C22×C4—371no—
99C22×C4—371no—
100C22×C4—371no—
101M16—21no—
102M16—742no—
103M16—741no—
104M16—1481no—
105M16—1481no—
106M16—1481no—
107C2×C8—741no—
108C2×C8—741no—
109C2×C8—1481no—
110C2×C8—1481no—
111C2×C8—1481no—
112C23—371no—
113C23C4×#386611yescharacteristic
114C23C4⋊#386611yescharacteristic
115Q8—1481no—
116D4—41no—
117D4—1481no—
118D4—1481no—
119C2×C4—371no—
120C2×C4—371no—
121C2×C4—371no—
122C2×C4—741no—
123C2×C4—741no—
124C2×C4—741no—
125C2×C4—741no—
126C2×C4—741no—
127C2×C4—741no—
128C2×C4C22⋊#386611yescharacteristic
129C8—41no—
130C8—1481no—
131C8—1481no—
132C8—1481no—
133C8—1482no—
134C22—21no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—741no—
139C22—1481no—
140C22(C2×#3866)⋊C411yescharacteristic
141C4—21no—
142C4—371no—
143C4—371no—
144C4—741no—
145C4—741no—
146C2—21no—
147C2—41no—
148C2—41no—
149C2—1481no—
150C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC23×C37C42
FrattiniC2×D4C2×#3866
Fitting#100×C37C4
socleC2×C37#342
prime radical, cosocleC2×#10596964C22
hypercenter#100#3866
hypocenterC37#1392
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
79. C37#1392semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145585062
#145575142
#139237