Finite Group Databasebeta

← #17995128

Subgroups — #17995128

Order 4736.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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#14558100C211yesmaximal, characteristic
2#14557551C212yesmaximal, complemented
3C2×#11924453C211yesmaximal, characteristic, complemented
4#14557289C212yesmaximal, complemented
5C37×#518C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7C2×#10596934C2212yes—
8#11924532C412yescomplemented
9#11924523C412yescomplemented
10#11924507—22no—
11#11924505—22no—
12#11924495C2211yescharacteristic
13#11924464—24no—
14#11924453—22no—
15C22×D4×C37C2211yescharacteristic
16C4×D4×C37—24no—
17#117×C37C2212yes—
18C2×C22⋊C4×C37—22no—
19C24×C37D412yes—
20C2×D4×C37—22no—
21C2×D4×C37—22no—
22C2×D4×C37C2×C412yes—
23C2×D4×C37D412yes—
24C22×C4×C37—24no—
25C22×C4×C37C2311yescharacteristic
26C2×C22⋊D37—21no—
27C2×C22⋊D37—24no—
28#10596962—22no—
29#10596962—22no—
30C2×D148C2×C411yescharacteristic, complemented
31C2×C4×D37—21no—
32C2×Dic74C2×C411yescharacteristic, complemented
33C4⋊C4×C37—22no—
34C22⋊C4×C37—24no—
35C22⋊C4×C37—22no—
36C42×C37D414yescomplemented
37C22⋊Dic37—24no—
38C22⋊Dic37—21no—
39C4⋊Dic37—21no—
40C4×Dic37C2×C412yescomplemented
41#10596934—22no—
42#10596934—22no—
43C2×#64436—22no—
44C23×C37—22no—
45C23×C37—22no—
46C23×C37—82no—
47C23×C37C22⋊C414yes—
48C23×C37C2×D411yescharacteristic
49C22×D37—21no—
50D4×C37—24no—
51D4×C37—24no—
52C2×C4×C37—24no—
53C2×C4×C37—84no—
54C2×C4×C37C22×C411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D412yes—
57C2×C4×C37#4112yes—
58C22⋊D37—41no—
59C22⋊D37—41no—
60C22⋊D37—84no—
61C2×Dic37—22no—
62C2×Dic37—21no—
63D148—22no—
64C4×D37—42no—
65Dic74—22no—
66#64436—42no—
67C22×C37—24no—
68C22×C37—41no—
69C22×C37—44no—
70C22×C37—44no—
71C22×C37—82no—
72C22×C37C2×C22⋊C411yescharacteristic
73C22×C37#12011yescharacteristic
74C22×C37#12311yescharacteristic
75C2×D37—42no—
76C2×D37—41no—
77C4×C37—44no—
78C4×C37C4×D412yes—
79C4×C37#12112yes—
80Dic37—42no—
81Dic37—41no—
82#1911—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37—21no—
86C2×C37—44no—
87C2×C37#38611yescharacteristic
88D37—81no—
89#535—371no—
90#518D3711yescharacteristic, complemented
91#421—372no—
92C2×#100—371no—
93H(3,ℤ/4)—372no—
94C37#191111yescharacteristic, complemented, Sylow
95C2×#41—371no—
96C22×D4C2×D3711yescharacteristic
97C2×M16—372no—
98#127—372no—
99#124—372no—
100#121—742no—
101#120—742no—
102C4×D4—24no—
103#117—371no—
104#117C2×D3712yes—
105C2×C22⋊C4—22no—
106#104—744no—
107#100—742no—
108C24C22⋊D3712yes—
109#41—742no—
110#41—742no—
111C2×Q8—371no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—371no—
115C2×D4—744no—
116C2×D4—741no—
117C2×D4C4×D3712yes—
118C2×D4D14812yes—
119C22×C4—24no—
120C22×C4—741no—
121C22×C4C22×D3711yescharacteristic
122M16—742no—
123M16—742no—
124C2×C8—742no—
125C4⋊C4—22no—
126C4⋊C4—741no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—744no—
130C22⋊C4—741no—
131C42—372no—
132C42C22⋊D3714yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—741no—
137C23#1059693814yes—
138C23C2×C22⋊D3711yescharacteristic
139Q8—742no—
140D4—24no—
141D4—24no—
142D4—2964no—
143D4—742no—
144D4—1481no—
145D4—1481no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—742no—
149C2×C4—741no—
150C2×C4—1482no—
151C2×C4C2×C4×D3711yescharacteristic
152C2×C4C2×D14811yescharacteristic
153C2×C4#1059696212yes—
154C2×C4C2×C22⋊D3712yes—
155C8—1482no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—1482no—
162C22—1481no—
163C22C2×#1059693811yescharacteristic
164C22#1192450511yescharacteristic
165C22#1192451911yescharacteristic
166C4—44no—
167C4—1482no—
168C4—1481no—
169C4C4×C22⋊D3712yes—
170C4#1192451012yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—2961no—
176C2#1455741211yescharacteristic
subgroupG/H
centerC2#14557412
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#518C2
socleC2×C37#386
prime radical#14558100C2
cosocleC22×C4×C37C23
hypercenter#518D37
hypocenterC37#1911
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #14557551C2semidirect
3. C2×#11924453C2semidirect
4. #14557289C2semidirect
5. C37×#518C2semidirect
8. #11924532C4semidirect
9. #11924523C4semidirect
30. C2×D148C2×C4semidirect
32. C2×Dic74C2×C4semidirect
36. C42×C37D4semidirect
40. C4×Dic37C2×C4semidirect
90. #518D37semidirect
94. C37#1911semidirect
132. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145581002
#145575512
C2×#119244532
#145572892
C37×#5182
#191137