Finite Group Databasebeta

← #17995012

Subgroups — #17995012

Order 4736.

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

normal subgroups only

This group has 342 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#14558040C211yesmaximal, characteristic
3#14557496C212yesmaximal, complemented
4#14557305C212yesmaximal, complemented
5C37×#413C211yesmaximal, characteristic, complemented
6C22×C4×D37C2211yescharacteristic
7#11924543—24no—
8C2×#10596934—22no—
9C2×#10596934C2212yes—
10#11924517C412yes—
11#11924512—21no—
12#11924507—21no—
13#11924504C412yes—
14C4×C22⋊D37—22no—
15#11924495C2211yescharacteristic
16#11924448—24no—
17C2×#41×C37C2211yescharacteristic
18C2×M16×C37C2212yes—
19#101×C37—21no—
20#100×C37—21no—
21C23×D37C2×C411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37D411yescharacteristic
25C2×D4×C37C2×C412yes—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37D412yes—
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30C22×Dic37C2×C411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37—22no—
34C2×C4×D37—22no—
35M16×C37—22no—
36M16×C37—22no—
37C2×C8×C37—22no—
38C22⋊Dic37—22no—
39C22⋊Dic37C2×C412yes—
40#10596938—22no—
41C4⋊Dic37—21no—
42#10596936—22no—
43C4×Dic37—21no—
44#10596934—24no—
45#10596934—22no—
46#10596934—22no—
47C2×#64436—24no—
48C2×#64436D414yescomplemented
49C23×C37C22⋊C412yes—
50C23×C37C22×C411yescharacteristic
51C22×D37—21no—
52C22×D37—22no—
53C22×D37—42no—
54Q8×C37—22no—
55D4×C37—24no—
56D4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37C22⋊C412yes—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37#4112yes—
64C22⋊D37—44no—
65C2×Dic37—22no—
66C2×Dic37—21no—
67C2×Dic37—22no—
68C4×D37—41no—
69C4×D37—42no—
70C4×D37—41no—
71C8×C37—42no—
72#64436—24no—
73C22×C37—22no—
74C22×C37—41no—
75C22×C37—42no—
76C22×C37C2×C22⋊C411yescharacteristic
77C22×C37C4×D412yes—
78C2×D37—22no—
79C2×D37—24no—
80C2×D37—41no—
81C2×D37—42no—
82C2×D37—41no—
83C4×C37—22no—
84C4×C37#12011yescharacteristic
85C4×C37#12112yes—
86C4×C37#12311yescharacteristic
87Dic37—42no—
88Dic37—41no—
89#1891—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37—22no—
92C2×C37—42no—
93C2×C37#38611yescharacteristic
94D37—42no—
95#568—371no—
96#525—371no—
97#413D3711yescharacteristic, complemented
98#407—372no—
99#344—372no—
100C37#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D3711yescharacteristic
102C23×C4—371no—
103#131—744no—
104C2×M16—372no—
105C2×M16—742no—
106C2×M16C2×D3712yes—
107#123—372no—
108C22⋊Q8—741no—
109#121—741no—
110#120—372no—
111C4×D4—742no—
112#117—371no—
113#101—21no—
114#100—21no—
115C22⋊C8—744no—
116C24—371no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D3711yescharacteristic
120C2×D4—742no—
121C2×D4C4×D3712yes—
122C2×D4C22⋊D3711yescharacteristic
123C22×C4—371no—
124C22×C4—741no—
125C22×C4—742no—
126C22×C4—742no—
127C22×C4—741no—
128C22×C4D14812yes—
129C22×C4C22×D3711yescharacteristic
130M16—22no—
131M16—22no—
132M16—744no—
133M16—742no—
134M16—742no—
135C2×C8—22no—
136C2×C8—374no—
137C2×C8—744no—
138C4⋊C4—742no—
139C4⋊C4—741no—
140C22⋊C4—372no—
141C22⋊C4—742no—
142C22⋊C4—742no—
143C42—741no—
144C23—741no—
145C23—742no—
146C23—1482no—
147C23#1059693812yes—
148C23C2×C4×D3711yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—1484no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—742no—
156C2×C4—741no—
157C2×C4—742no—
158C2×C4—1481no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4#1059693812yes—
162C2×C4C2×D14811yescharacteristic
163C2×C4D4×D3712yes—
164C2×C4#1059696412yes—
165C2×C4C2×C22⋊D3711yescharacteristic
166C8—42no—
167C8—744no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—742no—
172C22—744no—
173C22—1481no—
174C22—1482no—
175C22—1481no—
176C22C2×#1059693811yescharacteristic
177C22#1192449612yes—
178C4—22no—
179C4—1482no—
180C4—1481no—
181C4#1192450611yescharacteristic
182C4#1192450812yes—
183C4#1192452011yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—1482no—
188C2#1455741011yescharacteristic
subgroupG/H
centerC4#11924506
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#413C2
socleC2×C37#386
prime radical#14558040C2
cosocleC22×C4×C37C23
hypercenter#413D37
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #14558300C2semidirect
3. #14557496C2semidirect
4. #14557305C2semidirect
5. C37×#413C2semidirect
48. C2×#64436D4semidirect
97. #413D37semidirect
100. C37#1891semidirect

Maximal subgroups

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

subgroupindex
#145583002
#145580402
#145574962
#145573052
C37×#4132
#189137