Finite Group Databasebeta

← #18010119

Subgroups — #18010119

Order 4736.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558556C211yesmaximal, characteristic, complemented
2#14558551C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6#11924603C2212yes—
7#11924603C2212yes—
8#11924593—21no—
9#11924593—21no—
10#11924591—21no—
11C4×#64438—21no—
12C2×#10596962—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924511C411yescharacteristic
17#11924509—21no—
18#11924507C411yescharacteristic
19C4×D148C411yescharacteristic
20C4×C22⋊D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C22×C4×C37—21no—
25C2×C22⋊D37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28#10596962—44no—
29C2×D148—21no—
30C2×D148C2×C411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37C2×C411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×Dic74—21no—
36C2×#64438—22no—
37C2×#64438—22no—
38C4⋊C4×C37C2×C411yescharacteristic
39C22⋊C4×C37—21no—
40C42×C37C2×C411yescharacteristic
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37C2×C411yescharacteristic
45#10596936—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C23×C37—21no—
50C22×D37—21no—
51C22×D37C22⋊C411yescharacteristic
52D4×C37—41no—
53C2×C4×C37—21no—
54C2×C4×C37—42no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C22⋊D37—42no—
59C22⋊D37—42no—
60C22⋊D37—42no—
61C2×Dic37—21no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65D148—41no—
66D148—42no—
67C4×D37—22no—
68C4×D37—22no—
69C4×D37—41no—
70C4×D37—42no—
71Dic74—42no—
72#64438—42no—
73#64438—42no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—21no—
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—41no—
82C2×D37—41no—
83C2×D37—41no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—21no—
87C4×C37—41no—
88Dic37—21no—
89Dic37—41no—
90Dic37#13512yes—
91Dic37AGL(1,ℤ/8)12yes—
92#1553—371nomaximal, Sylow
93C2×C37—81no—
94C2×C37#41311yescharacteristic
95C2×C37#41611yescharacteristic
96C2×C37#41811yescharacteristic
97D37—41no—
98D37—81no—
99#532—371no—
100#432—371no—
101#431—371no—
102#332—372no—
103#331—372no—
104C37#155311yescharacteristic, complemented, Sylow
105C2×#41—741no—
106C4⋊Q8—371no—
107#127—371no—
108#124—741no—
109#121—371no—
110#121—371no—
111#121—741no—
112C4×D4—371no—
113C4×D4—741no—
114C4×D4#386611yescharacteristic
115C2×C42—371no—
116C4⋊C8—372no—
117C4⋊C8—372no—
118C22⋊C8—741no—
119C22⋊C8—741no—
120#97—741no—
121C4×C8—741no—
122#41—1484no—
123C2×Q8—741no—
124C2×D4—371no—
125C2×D4—741no—
126C2×D4—741no—
127C2×D4—741no—
128C2×D4—741no—
129C2×D4C2×#386611yescharacteristic
130C22×C4—21no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—741no—
135C2×C8—742no—
136C2×C8—742no—
137C4⋊C4—371no—
138C4⋊C4—741no—
139C4⋊C4C2×#386611yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—741no—
142C22⋊C4—741no—
143C22⋊C4—741no—
144C42—371no—
145C42—371no—
146C42—371no—
147C42C2×#386611yescharacteristic
148C23—21no—
149C23—371no—
150C23—741no—
151Q8—1482no—
152D4—41no—
153D4—1481no—
154D4—1482no—
155D4—1482no—
156D4—1482no—
157D4—1482no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—371no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—742no—
164C2×C4—742no—
165C2×C4—741no—
166C2×C4—1481no—
167C2×C4—1482no—
168C2×C4C22⋊#386611yescharacteristic
169C2×C4C22⋊#386611yescharacteristic
170C2×C4C22×#386611yescharacteristic
171C8—1482no—
172C8—1482no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—741no—
177C22—741no—
178C22—741no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22C2×C22⋊#386611yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—372no—
188C4—372no—
189C4—741no—
190C4—1481no—
191C2—81no—
192C2—2961no—
193C2—1481no—
194C2#1455851911yescharacteristic
195C2#1455852311yescharacteristic
196C2#1455852511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC4×Dic37C23
hypercenterC4×D4#3866
hypocenterC37#1553
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558556C2semidirect
2. #14558551C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
104. C37#1553semidirect

Maximal subgroups

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

subgroupindex
#145585562
#145585512
#145583922
#145583912
#145580802
#155337