Finite Group Databasebeta

← #17993940

Subgroups — #17993940

Order 4736.

188 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 53 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#14557907C211yesmaximal, characteristic, complemented
2#14557810C211yesmaximal, characteristic, complemented
3#14557729C211yesmaximal, characteristic
4#14557598C211yesmaximal, characteristic, complemented
5#14557283C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9C2×#10596941—21no—
10C2×D296—21no—
11C2×C8×D37—21no—
12#11924533C2211yescharacteristic
13C4×D148C2211yescharacteristic
14#11924469—21no—
15C4⋊#64436C2211yescharacteristic
16#11924458—21no—
17#11924456—21no—
18#11924448—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4⋊C8×C37C2211yescharacteristic
22C4⋊C8×C37C2211yescharacteristic
23C2×Q8×C37—21no—
24C2×D148—21no—
25C2×D148—21no—
26C2×D148—21no—
27C2×D148D411yescharacteristic
28C2×C4×D37—21no—
29C2×C8×C37—21no—
30C2×C8×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C42×C37C2311yescharacteristic
34#10596941—42no—
35#10596941—42no—
36#10596938—21no—
37C4⋊Dic37D411yescharacteristic
38C2×#64436—21no—
39C2×#64436D411yescharacteristic
40C2×#64436D411yescharacteristic
41D296—42no—
42C8×D37—42no—
43C22×D37—21no—
44C22×D37—41no—
45Q8×C37—41no—
46Q8×C37—41no—
47C2×C4×C37—41no—
48C2×C4×C37C2×D411yescharacteristic
49C2×C4×C37C2×D411yescharacteristic
50C2×C4×C37#4111yescharacteristic
51C2×Dic37—21no—
52D148—21no—
53D148—41no—
54D148—41no—
55D148—41no—
56D148—41no—
57D148—81no—
58D148SD1612yescomplemented
59C4×D37—41no—
60C4×D37—41no—
61C8×C37—41no—
62C8×C37—41no—
63#64436—21no—
64#64436—41no—
65#64436D812yescomplemented
66C22×C37#12111yescharacteristic
67C2×D37—22no—
68C2×D37—41no—
69C2×D37—41no—
70C2×D37—81no—
71C2×D37—81no—
72C2×D37—81no—
73C4×C37—21no—
74C4×C37—81no—
75C4×C37C2×D811yescharacteristic
76C4×C37C2×SD1611yescharacteristic
77C4×C37#13511yescharacteristic
78C4×C37AGL(1,ℤ/8)11yescharacteristic
79Dic37—41no—
80#1665—371nomaximal, Sylow
81C2×C37#45911yescharacteristic
82C2×C37#46511yescharacteristic
83C2×C37#47111yescharacteristic
84D37—42no—
85D37—161no—
86#492—371no—
87#474—371no—
88#459—371no—
89C8×D4—371no—
90#334—371no—
91#332D3711yescharacteristic, complemented
92#331—371no—
93C37#166511yescharacteristic, complemented, Sylow
94C2×SD16—741no—
95C2×SD16—741no—
96C2×D8—741no—
97C22×C8—741no—
98C4⋊Q8C2×D3711yescharacteristic
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×C8—371no—
109C2×Q8—21no—
110C2×D4—371no—
111C2×D4—741no—
112C2×D4—741no—
113C2×D4—741no—
114C22×C4—741no—
115SD16—1482no—
116SD16—1482no—
117D8—1482no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—371no—
121C2×C8—371no—
122C2×C8—741no—
123C2×C8—1482no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—371no—
127C22⋊C4—741no—
128C42C22×D3711yescharacteristic
129C23—741no—
130C23—1481no—
131Q8—41no—
132Q8—41no—
133D4—372no—
134D4—2961no—
135D4—741no—
136D4—1481no—
137D4—1481no—
138D4—1481no—
139D4—1481no—
140C2×C4—41no—
141C2×C4—741no—
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—2961no—
153C22—2961no—
154C22—2961no—
155C22—742no—
156C22—1481no—
157C22—1481no—
158C22#1192450911yescharacteristic
159C4—21no—
160C4—81no—
161C4—1481no—
162C4D8×D3711yescharacteristic
163C4SD16×D3711yescharacteristic
164C4#1192455911yescharacteristic
165C4#1192456311yescharacteristic
166C2—5921no—
167C2—1482no—
168C2#1455772711yescharacteristic
169C2#1455776511yescharacteristic
170C2#1455779911yescharacteristic
subgroupG/H
centerC22#11924509
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#121
prime radical#14557729C2
hypercenter#332D37
hypocenterC37#1665
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14557907C2semidirect
2. #14557810C2semidirect
4. #14557598C2semidirect
5. #14557283C2semidirect
6. #14557276C2semidirect
7. C37×#332C2semidirect
58. D148SD16semidirect
65. #64436D8semidirect
91. #332D37semidirect
93. C37#1665semidirect

Maximal subgroups

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

subgroupindex
#145579072
#145578102
#145577292
#145575982
#145572832
#145572762
C37×#3322
#166537