Finite Group Databasebeta

← #17994074

Subgroups — #17994074

Order 4736.

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

normal subgroups only

This group has 198 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#14557909C211yesmaximal, characteristic, complemented
2#14557729C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic, complemented
4#14557610C211yesmaximal, characteristic, complemented
5#14557283C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×D296—21no—
9C2×#10596939—21no—
10C2×#10596939—21no—
11C2×#10596939—21no—
12C2×#10596929—21no—
13#11924533C2211yescharacteristic
14C4×D148C2211yescharacteristic
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×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×C8×C37—21no—
32C2×C8×C37—21no—
33C42×C37C2311yescharacteristic
34#10596939—42no—
35#10596939—42no—
36#10596939—42no—
37#10596938—21no—
38C4⋊Dic37D411yescharacteristic
39C2×#64436—21no—
40C2×#64436D411yescharacteristic
41C2×#64436D411yescharacteristic
42D296—42no—
43#10596929—42no—
44C23×C37—41no—
45C22×D37—21no—
46C22×D37—41no—
47D4×C37—41no—
48D4×C37—41no—
49D4×C37—41no—
50D4×C37—41no—
51D4×C37—81no—
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37#4111yescharacteristic
55C2×Dic37—21no—
56D148—21no—
57D148—21no—
58D148—41no—
59D148—41no—
60D148—41no—
61D148—41no—
62D148—81no—
63C4×D37—41no—
64C4×D37—41no—
65C8×C37—41no—
66C8×C37—41no—
67#64436—21no—
68#64436—41no—
69#64436D812yescomplemented
70C22×C37—81no—
71C22×C37—81no—
72C22×C37—81no—
73C22×C37#12111yescharacteristic
74C2×D37—41no—
75C2×D37—41no—
76C2×D37—41no—
77C2×D37—81no—
78C2×D37—81no—
79C2×D37—81no—
80C4×C37—21no—
81C4×C37C2×D811yescharacteristic
82C4×C37AGL(1,ℤ/8)11yescharacteristic
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37AGL(1,ℤ/8)11yescharacteristic
85Dic37—41no—
86#1687—371nomaximal, Sylow
87C2×C37—161no—
88C2×C37#45911yescharacteristic
89C2×C37#46911yescharacteristic
90C2×C37#47211yescharacteristic
91D37—81no—
92D37—161no—
93#493—371no—
94#459—371no—
95#459—371no—
96#436—371no—
97#334—371no—
98#331—371no—
99#331D3711yescharacteristic, complemented
100C37#168711yescharacteristic, complemented, Sylow
101C2×D8—741no—
102C2×D8—741no—
103C2×D8—741no—
104C2×D8—741no—
105C2×M16—741no—
106#127—371no—
107#127C2×D3711yescharacteristic
108C4×D4—371no—
109C4⋊C8—371no—
110C4⋊C8C2×D3711yescharacteristic
111C4⋊C8C2×D3711yescharacteristic
112#102—741no—
113#102—741no—
114C22⋊C8—741no—
115C4×C8—371no—
116C2×D4—21no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—371no—
120C2×D4—741no—
121C2×D4—741no—
122C2×D4—741no—
123C22×C4—741no—
124D8—1482no—
125D8—1482no—
126D8—1482no—
127D8—1482no—
128M16—1482no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—371no—
132C2×C8—371no—
133C2×C8—741no—
134C4⋊C4—371no—
135C22⋊C4—741no—
136C42C22×D3711yescharacteristic
137C23—41no—
138C23—741no—
139C23—1481no—
140D4—41no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—81no—
145D4—2961no—
146D4—741no—
147D4—741no—
148D4—1481no—
149D4—1481no—
150D4—1481no—
151D4—1481no—
152C2×C4—741no—
153C2×C4—1481no—
154C2×C4—1481no—
155C2×C4#1059696211yescharacteristic
156C2×C4D4×D3711yescharacteristic
157C2×C4D4×D3711yescharacteristic
158C8—41no—
159C8—41no—
160C8—372no—
161C8—741no—
162C8—1481no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22—2961no—
167C22—2961no—
168C22—2961no—
169C22—1481no—
170C22—1481no—
171C22—1481no—
172C22#1192450911yescharacteristic
173C4—21no—
174C4—1481no—
175C4D8×D3711yescharacteristic
176C4#1192456011yescharacteristic
177C4#1192456311yescharacteristic
178C4#1192456311yescharacteristic
179C2—161no—
180C2—2961no—
181C2—5921no—
182C2#1455772711yescharacteristic
183C2#1455778511yescharacteristic
184C2#1455780211yescharacteristic
subgroupG/H
centerC22#11924509
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37#121
hypercenter#331D37
hypocenterC37#1687
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. #14557909C2semidirect
2. #14557729C2semidirect
3. #14557725C2semidirect
4. #14557610C2semidirect
5. #14557283C2semidirect
6. #14557276C2semidirect
7. C37×#331C2semidirect
69. #64436D8semidirect
99. #331D37semidirect
100. C37#1687semidirect

Maximal subgroups

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

subgroupindex
#145579092
#145577292
#145577252
#145576102
#145572832
#145572762
C37×#3312
#168737