Finite Group Databasebeta

← #17995121

Subgroups — #17995121

Order 4736.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#14558097C211yesmaximal, characteristic
3#14557537C212yesmaximal, complemented
4#14557289C212yesmaximal, complemented
5C37×#410C211yesmaximal, characteristic, complemented
6C22×D148C2211yescharacteristic
7#11924543—24no—
8C2×#10596934—22no—
9C2×#10596934C2212yes—
10#11924532C412yescomplemented
11#11924525C412yescomplemented
12#11924510—22no—
13#11924504—22no—
14#11924495C2211yescharacteristic
15#11924456—24no—
16C2×#41×C37C2211yescharacteristic
17#117×C37C2212yes—
18#99×C37—22no—
19C23×D37—21no—
20#41×C37—22no—
21#41×C37—22no—
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C2×D4×C37D412yes—
25C22×C4×C37D412yes—
26C22×C4×C37C2311yescharacteristic
27C2×C22⋊D37—24no—
28C2×D148—22no—
29C2×D148—22no—
30C2×D148—21no—
31C2×D148C2×C412yes—
32C4⋊C4×C37—22no—
33C22⋊C4×C37—22no—
34C42×C37—22no—
35C22⋊Dic37—21no—
36#10596938—24no—
37C4⋊Dic37—21no—
38C4×Dic37C2×C412yes—
39#10596934—24no—
40#10596934—22no—
41#10596934—22no—
42C2×#64436—24no—
43C2×#64436D414yescomplemented
44C23×C37C22⋊C412yes—
45C23×C37C2×D411yescharacteristic
46C22×D37—22no—
47C22×D37—42no—
48C22×D37—82no—
49Q8×C37—22no—
50D4×C37—24no—
51D4×C37—22no—
52C2×C4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37—42no—
55C2×C4×C37C22⋊C412yes—
56C2×C4×C37C22×C411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D412yes—
59C2×C4×C37#4112yes—
60C22⋊D37—84no—
61C2×Dic37—22no—
62D148—24no—
63D148—41no—
64D148—41no—
65#64436—24no—
66C22×C37—22no—
67C22×C37—41no—
68C22×C37—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C22×C37#12112yes—
71C2×D37—44no—
72C2×D37—42no—
73C2×D37—84no—
74C4×C37—22no—
75C4×C37—82no—
76C4×C37C4×D412yes—
77C4×C37#12011yescharacteristic
78C4×C37#12311yescharacteristic
79Dic37—42no—
80#1910—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—22no—
83C2×C37—42no—
84C2×C37#38611yescharacteristic
85D37—82no—
86#568—371no—
87#535—371no—
88#418—372no—
89#410D3711yescharacteristic, complemented
90H(3,ℤ/4)—372no—
91C37#191011yescharacteristic, complemented, Sylow
92C2×#41C2×D3711yescharacteristic
93C22×D4—371no—
94#131—744no—
95C2×M16—372no—
96C2×M16—742no—
97#127—372no—
98#124—372no—
99#121—742no—
100#120—742no—
101#117—371no—
102#117C2×D3712yes—
103#102—744no—
104#99—22no—
105C24—741no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D3711yescharacteristic
109C2×D4—372no—
110C2×D4—744no—
111C2×D4—741no—
112C2×D4—742no—
113C2×D4—742no—
114C2×D4C4×D3711yescharacteristic
115C2×D4C22⋊D3712yes—
116C22×C4D14812yes—
117C22×C4C22×D3711yescharacteristic
118M16—744no—
119M16—742no—
120M16—742no—
121C2×C8—374no—
122C2×C8—744no—
123C4⋊C4—22no—
124C4⋊C4—741no—
125C22⋊C4—22no—
126C22⋊C4—741no—
127C22⋊C4—744no—
128C42—22no—
129C42—372no—
130C23—2962no—
131C23—742no—
132C23—1482no—
133C23#1059693812yes—
134C23C2×C22⋊D3711yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—2964no—
139D4—744no—
140D4—1481no—
141D4—1481no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—742no—
146C2×C4#1059693812yes—
147C2×C4C2×C4×D3711yescharacteristic
148C2×C4C2×D14811yescharacteristic
149C2×C4D4×D3712yes—
150C2×C4#1059696412yes—
151C8—744no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—2964no—
156C22—1484no—
157C22—1482no—
158C22C2×#1059693811yescharacteristic
159C22#1192450812yes—
160C4—22no—
161C4—82no—
162C4—1482no—
163C4#1192449612yes—
164C4#1192450611yescharacteristic
165C4#1192452011yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—2962no—
170C2#1455741011yescharacteristic
subgroupG/H
centerC2#14557410
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#410C2
socleC2×C37#386
prime radical#14558097C2
cosocleC22×C4×C37C23
hypercenter#410D37
hypocenterC37#1910
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14558300C2semidirect
3. #14557537C2semidirect
4. #14557289C2semidirect
5. C37×#410C2semidirect
10. #11924532C4semidirect
11. #11924525C4semidirect
43. C2×#64436D4semidirect
89. #410D37semidirect
91. C37#1910semidirect

Maximal subgroups

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

subgroupindex
#145583002
#145580972
#145575372
#145572892
C37×#4102
#191037