Finite Group Databasebeta

← #17995124

Subgroups — #17995124

Order 4736.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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#14558300C211yesmaximal, characteristic, complemented
2#14557538C212yesmaximal, complemented
3#14557507C211yesmaximal, characteristic, complemented
4#14557289C212yesmaximal, complemented
5C37×#535C211yesmaximal, characteristic
6#11924543—24no—
7C2×#10596934—22no—
8C2×#10596934C2212yes—
9#11924495C2212yes—
10#11924457—24no—
11#11924451—22no—
12C2×#41×C37C2211yescharacteristic
13C22×D4×C37C2211yescharacteristic
14#127×C37C412yescomplemented
15#124×C37C412yescomplemented
16#121×C37—22no—
17#120×C37—22no—
18#117×C37C2211yescharacteristic
19C24×C37—21no—
20#41×C37—22no—
21#41×C37—22no—
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37—24no—
24C2×D4×C37—22no—
25C2×D4×C37—21no—
26C2×D4×C37—22no—
27C2×D4×C37C2×C412yes—
28C2×D4×C37C2×C411yescharacteristic
29C2×D4×C37D412yes—
30C22×C4×C37D412yes—
31C22×C4×C37C2311yescharacteristic
32C4⋊C4×C37—21no—
33C22⋊C4×C37—21no—
34C22⋊C4×C37—24no—
35C42×C37C2×C412yes—
36C22⋊Dic37—22no—
37C4⋊Dic37—22no—
38C4×Dic37—22no—
39#10596934—24no—
40#10596934—22no—
41#10596934—22no—
42C2×#64436—24no—
43C2×#64436D414yescomplemented
44C23×C37—22no—
45C23×C37—42no—
46C23×C37—82no—
47C23×C37C22⋊C412yes—
48C23×C37C2×D411yescharacteristic
49Q8×C37—22no—
50D4×C37—24no—
51D4×C37—22no—
52D4×C37—24no—
53D4×C37—41no—
54D4×C37—41no—
55D4×C37—84no—
56C2×C4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37C22⋊C412yes—
60C2×C4×C37C22×C411yescharacteristic
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37#4112yes—
64C2×Dic37—42no—
65#64436—24no—
66C22×C37—22no—
67C22×C37—41no—
68C22×C37—42no—
69C22×C37—44no—
70C22×C37—42no—
71C22×C37—84no—
72C22×C37C2×C22⋊C411yescharacteristic
73C22×C37#12112yes—
74C4×C37—22no—
75C4×C37—42no—
76C4×C37C4×D412yes—
77C4×C37#12011yescharacteristic
78C4×C37#12311yescharacteristic
79Dic37—82no—
80#1910—371nomaximal, Sylow
81C2×C37—22no—
82C2×C37—21no—
83C2×C37—42no—
84C2×C37—82no—
85C2×C37#38611yescharacteristic
86#568—371no—
87#535D3711yescharacteristic
88#418—372no—
89#410—371no—
90H(3,ℤ/4)—372no—
91C37#191011yescharacteristic, complemented, Sylow
92C2×#41C2×D3711yescharacteristic
93C22×D4C2×D3711yescharacteristic
94#131—744no—
95C2×M16—372no—
96C2×M16—742no—
97#127Dic3712yescomplemented
98#124Dic3712yescomplemented
99#121—22no—
100#120—22no—
101#117—372no—
102#117C2×D3711yescharacteristic
103#102—744no—
104#99—742no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic3711yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4C2×Dic3712yes—
114C2×D4C2×Dic3711yescharacteristic
115C2×D4C22⋊D3712yes—
116C22×C4C22⋊D3712yes—
117C22×C4C22×D3711yescharacteristic
118M16—744no—
119M16—742no—
120M16—742no—
121C2×C8—374no—
122C2×C8—744no—
123C4⋊C4—21no—
124C4⋊C4—742no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—742no—
128C42—742no—
129C42C2×Dic3712yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic3712yes—
134C23C2×C22⋊D3711yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—1482no—
146C2×C4C22⋊Dic3712yes—
147C2×C4D4×D3712yes—
148C2×C4#1059696412yes—
149C2×C4C22×Dic3711yescharacteristic
150C2×C4C2×C22⋊D3711yescharacteristic
151C8—744no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic3711yescharacteristic
159C22#1192450812yes—
160C4—22no—
161C4—42no—
162C4—2962no—
163C4D4×Dic3712yes—
164C4#1192450411yescharacteristic
165C4#1192451711yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#1455741311yescharacteristic
subgroupG/H
centerC2#14557413
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#535C2
socleC2×C37#386
cosocleC22×C4×C37C23
hypercenter#535D37
hypocenterC37#1910
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14558300C2semidirect
2. #14557538C2semidirect
3. #14557507C2semidirect
4. #14557289C2semidirect
14. #127×C37C4semidirect
15. #124×C37C4semidirect
43. C2×#64436D4semidirect
91. C37#1910semidirect
97. #127Dic37semidirect
98. #124Dic37semidirect

Maximal subgroups

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

subgroupindex
#145583002
#145575382
#145575072
#145572892
C37×#5352
#191037