Finite Group Databasebeta

← #17993635

Subgroups — #17993635

Order 4736.

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

normal subgroups only

This group has 246 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#14558114C211yesmaximal, characteristic
2#14557852C212yesmaximal, complemented
3#14557472C211yesmaximal, characteristic, complemented
4#14557268C212yesmaximal, complemented
5C37×#324C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7#11924516—22no—
8#11924511—22no—
9#11924510—21no—
10#11924510C2212yes—
11C2×C4⋊Dic37C2211yescharacteristic
12#11924468—22no—
13#11924458—22no—
14#11924443—21no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C22×C4×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24C22×Dic37—21no—
25#10596962—42no—
26#10596962—42no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D412yes—
30C2×C4×D37—22no—
31C2×Dic74—21no—
32C2×C8×C37—22no—
33C4⋊C4×C37—22no—
34#10596938—22no—
35#10596938—22no—
36C4⋊Dic37—21no—
37C4⋊Dic37—22no—
38C4⋊Dic37D412yes—
39C23×C37C2×D411yescharacteristic
40C22×D37—22no—
41C2×C4×C37—21no—
42C2×C4×C37—21no—
43C2×C4×C37—21no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37SD1612yes—
47C2×C4×C37C2×D412yes—
48C22⋊D37—42no—
49C22⋊D37—42no—
50C2×Dic37—22no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37—42no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56D148—42no—
57D148—42no—
58D148—81no—
59C4×D37—44no—
60Dic74—42no—
61C8×C37—42no—
62C22×C37—21no—
63C22×C37—21no—
64C22×C37#12011yescharacteristic
65C22×C37C2×SD1611yescharacteristic
66C22×C37AGL(1,ℤ/8)11yescharacteristic
67C2×D37—42no—
68C2×D37—42no—
69C2×D37—42no—
70C4×C37—22no—
71C4×C37—22no—
72C4×C37—41no—
73Dic37—42no—
74Dic37—81no—
75Dic37—81no—
76#1616—371nomaximal, Sylow
77C2×C37—21no—
78C2×C37—21no—
79C2×C37#45011yescharacteristic
80C2×C37#45411yescharacteristic
81C2×C37#45811yescharacteristic
82D37—82no—
83#537—371no—
84#481—372no—
85#400—371no—
86#327—372no—
87#324D3711yescharacteristic, complemented
88C37#161611yescharacteristic, complemented, Sylow
89C2×#41—741no—
90C22⋊Q8—742no—
91#121—372no—
92#121—742no—
93#121—741no—
94C2×C4⋊C4—371no—
95C2×C4⋊C4C2×D3711yescharacteristic
96#106—742no—
97#102—742no—
98C22⋊C8C2×D3712yes—
99#95—371no—
100#95—741no—
101#95—741no—
102#41—1482no—
103#41—1482no—
104C2×Q8—741no—
105C2×D4—372no—
106C2×D4—741no—
107C2×D4—741no—
108C2×D4—742no—
109C22×C4—742no—
110C22×C4—741no—
111C22×C4—741no—
112C22×C4D14811yescharacteristic
113C22×C4D14811yescharacteristic
114C22×C4C22×D3711yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—372no—
118C4⋊C4—741no—
119C4⋊C4—742no—
120C22⋊C4—742no—
121C22⋊C4—742no—
122C23—742no—
123C23C2×D14811yescharacteristic
124Q8—1482no—
125D4—2961no—
126D4—1482no—
127D4—1482no—
128D4—1482no—
129D4—1482no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—742no—
136C2×C4—1484no—
137C2×C4—1481no—
138C2×C4—1481no—
139C2×C4—1482no—
140C2×C4—1481no—
141C2×C4—1481no—
142C2×C4#1059693012yes—
143C2×C4D4×D3712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—1482no—
148C22—1482no—
149C22—1482no—
150C22#1192450611yescharacteristic
151C22C2×#1059693011yescharacteristic
152C22#1192456411yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—2961no—
157C4—2961no—
158C4—1482no—
159C2—21no—
160C2—21no—
161C2—2962no—
162C2#1455768611yescharacteristic
163C2#1455770811yescharacteristic
164C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37#120
prime radical#14558114C2
hypercenter#324D37
hypocenterC37#1616
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14557852C2semidirect
3. #14557472C2semidirect
4. #14557268C2semidirect
5. C37×#324C2semidirect
87. #324D37semidirect
88. C37#1616semidirect

Maximal subgroups

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

subgroupindex
#145581142
#145578522
#145574722
#145572682
C37×#3242
#161637