Finite Group Databasebeta

← #17994062

Subgroups — #17994062

Order 4736.

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

normal subgroups only

This group has 182 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#14557906C211yesmaximal, characteristic, complemented
2#14557814C211yesmaximal, characteristic, complemented
3#14557729C211yesmaximal, characteristic
4#14557612C211yesmaximal, characteristic, complemented
5#14557278C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#335C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×#10596930—21no—
10C2×D296—21no—
11C2×#10596929—21no—
12#11924536C2211yescharacteristic
13#11924533C2211yescharacteristic
14C4×D148C2211yescharacteristic
15#11924470—21no—
16C4⋊#64436C2211yescharacteristic
17#11924458—21no—
18#11924458—21no—
19#11924448—21no—
20C4⋊C8×C37C2211yescharacteristic
21C4⋊C8×C37C2211yescharacteristic
22C4×C8×C37C2211yescharacteristic
23C2×D148—21no—
24C2×D148—21no—
25C2×D148—21no—
26C2×D148D411yescharacteristic
27C2×C4×D37—21no—
28C2×Dic74—21no—
29C2×C8×C37—21no—
30C2×C8×C37—21no—
31C2×C8×C37D411yescharacteristic
32C2×C8×C37D411yescharacteristic
33C42×C37C2311yescharacteristic
34#10596938—21no—
35C4⋊Dic37—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37D411yescharacteristic
38C2×#64436—21no—
39D296—42no—
40#10596930—42no—
41#10596930—42no—
42#10596929—42no—
43C22×D37—21no—
44C22×D37—41no—
45C2×C4×C37C2×D411yescharacteristic
46C2×C4×C37C2×D411yescharacteristic
47C2×C4×C37#4111yescharacteristic
48C2×Dic37—21no—
49C2×Dic37—41no—
50D148—21no—
51D148—21no—
52D148—41no—
53D148—41no—
54D148—41no—
55D148—41no—
56D148—81no—
57C4×D37—41no—
58C4×D37—41no—
59Dic74—41no—
60Dic74—41no—
61C8×C37—21no—
62C8×C37—41no—
63C8×C37—41no—
64C8×C37D812yescomplemented
65#64436—41no—
66C22×C37#12111yescharacteristic
67C2×D37—41no—
68C2×D37—41no—
69C2×D37—41no—
70C2×D37—81no—
71C2×D37—81no—
72C2×D37—81no—
73C4×C37—21no—
74C4×C37C2×D811yescharacteristic
75C4×C37AGL(1,ℤ/8)11yescharacteristic
76C4×C37AGL(1,ℤ/8)11yescharacteristic
77C4×C37#13711yescharacteristic
78Dic37—41no—
79Dic37—81no—
80#1685—371nomaximal, Sylow
81C2×C37#45911yescharacteristic
82C2×C37#46811yescharacteristic
83C2×C37#47111yescharacteristic
84D37—81no—
85D37—161no—
86#492—371no—
87#474—371no—
88#459—371no—
89#436—371no—
90#335D3711yescharacteristic, complemented
91#332—371no—
92#331—371no—
93C37#168511yescharacteristic, complemented, Sylow
94C2×SD16—741no—
95C2×SD16—741no—
96C2×D8—741no—
97C2×M16—741no—
98C4⋊Q8—371no—
99#127—371no—
100C4×D4—371no—
101#107—741no—
102C4⋊C8—371no—
103C4⋊C8C2×D3711yescharacteristic
104C4⋊C8C2×D3711yescharacteristic
105#102—741no—
106#102—741no—
107C22⋊C8—741no—
108C4×C8C2×D3711yescharacteristic
109C2×Q8—741no—
110C2×D4—371no—
111C2×D4—741no—
112C2×D4—741no—
113C2×D4—741no—
114C22×C4—741no—
115SD16—1482no—
116SD16—1482no—
117D8—1482no—
118M16—1482no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—741no—
122C2×C8D14811yescharacteristic
123C2×C8D14811yescharacteristic
124C4⋊C4—371no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C22⋊C4—741no—
128C42C22×D3711yescharacteristic
129C23—741no—
130C23—1481no—
131Q8—1481no—
132Q8—1481no—
133D4—2961no—
134D4—741no—
135D4—741no—
136D4—1481no—
137D4—1481no—
138D4—1481no—
139D4—1481no—
140C2×C4—741no—
141C2×C4—1481no—
142C2×C4—1481no—
143C2×C4—1481no—
144C2×C4C2×D14811yescharacteristic
145C2×C4D4×D3711yescharacteristic
146C2×C4#1059696611yescharacteristic
147C8—21no—
148C8—41no—
149C8—41no—
150C8—1481no—
151C8D29612yescomplemented
152C22—2961no—
153C22—2961no—
154C22—2961no—
155C22—1481no—
156C22—1481no—
157C22—1481no—
158C22#1192451111yescharacteristic
159C4—21no—
160C4—2961no—
161C4—1481no—
162C4C2×D29611yescharacteristic
163C4#1192456011yescharacteristic
164C4#1192456411yescharacteristic
165C4#1192456811yescharacteristic
166C2—2961no—
167C2—5921no—
168C2#1455772911yescharacteristic
169C2#1455778011yescharacteristic
170C2#1455779711yescharacteristic
subgroupG/H
centerC22#11924511
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#335C2
socleC22×C37#121
prime radical#14557729C2
hypercenter#335D37
hypocenterC37#1685
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
1. #14557906C2semidirect
2. #14557814C2semidirect
4. #14557612C2semidirect
5. #14557278C2semidirect
6. #14557276C2semidirect
7. C37×#335C2semidirect
64. C8×C37D8semidirect
90. #335D37semidirect
93. C37#1685semidirect
151. C8D296semidirect

Maximal subgroups

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

subgroupindex
#145579062
#145578142
#145577292
#145576122
#145572782
#145572762
C37×#3352
#168537