Finite Group Databasebeta

← #17994060

Subgroups — #17994060

Order 4736.

182 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 51 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#14557814C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic
4#14557610C211yesmaximal, characteristic, complemented
5#14557285C211yesmaximal, characteristic, complemented
6#14557280C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596940—21no—
9C2×#10596940—21no—
10C2×#10596939—21no—
11C2×#10596929—21no—
12#11924536C2211yescharacteristic
13C4×D148C2211yescharacteristic
14#11924470—21no—
15C4⋊#64436C2211yescharacteristic
16#11924458—21no—
17#11924457—21no—
18#11924448—21no—
19C4×#64436C2211yescharacteristic
20#127×C37C2211yescharacteristic
21C4⋊C8×C37C2211yescharacteristic
22C4⋊C8×C37C2211yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37—21no—
25C2×D4×C37—21no—
26C2×D148D411yescharacteristic
27C2×C4×D37—21no—
28C2×Dic74—21no—
29C2×C8×C37—21no—
30C2×C8×C37—21no—
31C42×C37C2311yescharacteristic
32#10596940—42no—
33#10596940—42no—
34#10596939—42no—
35#10596938—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37D411yescharacteristic
39C2×#64436—21no—
40C2×#64436D411yescharacteristic
41C2×#64436D411yescharacteristic
42#10596929—42no—
43C23×C37—41no—
44C22×D37—21no—
45D4×C37—41no—
46D4×C37—41no—
47D4×C37—41no—
48D4×C37—41no—
49D4×C37—81no—
50C2×C4×C37C2×D411yescharacteristic
51C2×C4×C37C2×D411yescharacteristic
52C2×C4×C37#4111yescharacteristic
53C2×Dic37—21no—
54C2×Dic37—41no—
55D148—21no—
56D148—21no—
57C4×D37—41no—
58C4×D37—41no—
59Dic74—41no—
60Dic74—41no—
61C8×C37—41no—
62C8×C37—41no—
63#64436—21no—
64#64436—41no—
65#64436D812yescomplemented
66C22×C37—81no—
67C22×C37—81no—
68C22×C37—81no—
69C22×C37#12111yescharacteristic
70C2×D37—41no—
71C2×D37—41no—
72C2×D37—41no—
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—161no—
82C2×C37#45911yescharacteristic
83C2×C37#46811yescharacteristic
84C2×C37#47111yescharacteristic
85D37—81no—
86#492—371no—
87#474—371no—
88#459—371no—
89#436—371no—
90#335—371no—
91#332—371no—
92#331D3711yescharacteristic, complemented
93C37#168511yescharacteristic, complemented, Sylow
94C2×SD16—741no—
95C2×SD16—741no—
96C2×D8—741no—
97C2×M16—741no—
98C4⋊Q8—371no—
99#127C2×D3711yescharacteristic
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×C8—371no—
109C2×Q8—741no—
110C2×D4—21no—
111C2×D4—21no—
112C2×D4—21no—
113C2×D4—371no—
114C22×C4—741no—
115SD16—1482no—
116SD16—1482no—
117D8—1482no—
118M16—1482no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—371no—
122C2×C8—371no—
123C2×C8—741no—
124C4⋊C4—371no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C22⋊C4—741no—
128C42C22×D3711yescharacteristic
129C23—41no—
130C23—741no—
131Q8—1481no—
132Q8—1481no—
133D4—41no—
134D4—41no—
135D4—41no—
136D4—41no—
137D4—81no—
138D4—741no—
139D4—741no—
140C2×C4—741no—
141C2×C4—1481no—
142C2×C4—1481no—
143C2×C4—1481no—
144C2×C4#1059696211yescharacteristic
145C2×C4D4×D3711yescharacteristic
146C2×C4D4×D3711yescharacteristic
147C8—41no—
148C8—41no—
149C8—372no—
150C8—741no—
151C8—1481no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—1481no—
156C22—1481no—
157C22—1481no—
158C22#1192450911yescharacteristic
159C4—21no—
160C4—2961no—
161C4—1481no—
162C4D8×D3711yescharacteristic
163C4#1192456011yescharacteristic
164C4#1192456311yescharacteristic
165C4#1192456511yescharacteristic
166C2—161no—
167C2—2961no—
168C2#1455772711yescharacteristic
169C2#1455777811yescharacteristic
170C2#1455779511yescharacteristic
subgroupG/H
centerC22#11924509
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37#121
prime radical#14557725C2
hypercenter#331D37
hypocenterC37#1685
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #14557905C2semidirect
2. #14557814C2semidirect
4. #14557610C2semidirect
5. #14557285C2semidirect
6. #14557280C2semidirect
7. C37×#331C2semidirect
65. #64436D8semidirect
92. #331D37semidirect
93. C37#1685semidirect

Maximal subgroups

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

subgroupindex
#145579052
#145578142
#145577252
#145576102
#145572852
#145572802
C37×#3312
#168537