Finite Group Databasebeta

← #18010015

Subgroups — #18010015

Order 4736.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558555C211yesmaximal, characteristic, complemented
2#14558478C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6C4⋊#64438—21no—
7#11924593C2212yes—
8#11924591—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12C2×#10596962—21no—
13#11924535C411yescharacteristic, complemented
14#11924532C411yescharacteristic, complemented
15#11924522—21no—
16#11924511C2211yescharacteristic
17#11924509—21no—
18#11924507C2211yescharacteristic
19C4×D148C411yescharacteristic, complemented
20C4×C22⋊D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29#10596962—44no—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37C2311yescharacteristic
36C2×Dic74—21no—
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×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C23×C37—21no—
50C22×D37—21no—
51C22×D37C2×D411yescharacteristic
52C2×#3866—42no—
53C2×#3866—42no—
54C2×#3866—42no—
55D4×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37—42no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C22⋊D37—42no—
62C22⋊D37—42no—
63C22⋊D37—42no—
64C2×Dic37—21no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68D148—41no—
69D148—42no—
70C4×D37—22no—
71C4×D37—41no—
72C4×D37—41no—
73C4×D37—42no—
74Dic74—42no—
75#64438—42no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37C2×C22⋊C411yescharacteristic
80C2×D37—21no—
81C2×D37—21no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37AGL(1,ℤ/8)12yes—
86#3866—82no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—21no—
90C4×C37—41no—
91Dic37—21no—
92Dic37—21no—
93Dic37—21no—
94Dic37—41no—
95#1514—371nomaximal, Sylow
96C2×C37—81no—
97C2×C37#41011yescharacteristic
98C2×C37#41811yescharacteristic
99C2×C37#42111yescharacteristic
100D37—22no—
101D37—81no—
102#532—371no—
103#432—371no—
104#383—371no—
105#327—372no—
106#327—372no—
107C37#151411yescharacteristic, complemented, Sylow
108C2×#41—741no—
109C4⋊Q8—371no—
110#127—371no—
111#124—741no—
112#121—371no—
113#121—371no—
114#121—741no—
115C4×D4—371no—
116C4×D4—741no—
117C4×D4#386611yescharacteristic, complemented
118C2×C42—371no—
119C4⋊C8—741no—
120C22⋊C8—372no—
121#97—741no—
122#95—372no—
123#95—741no—
124#95—741no—
125#41—1484no—
126C2×Q8—741no—
127C2×D4—371no—
128C2×D4—741no—
129C2×D4—741no—
130C2×D4—741no—
131C2×D4—741no—
132C2×D4C2×#386611yescharacteristic
133C22×C4—21no—
134C22×C4—371no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—741no—
138C22×C4—742no—
139C2×C8—742no—
140C4⋊C4—371no—
141C4⋊C4—741no—
142C4⋊C4C2×#386611yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C42—371no—
148C42—371no—
149C42—371no—
150C42C2×#386611yescharacteristic
151C23—21no—
152C23—371no—
153C23—741no—
154Q8—1482no—
155D4—41no—
156D4—1481no—
157D4—1482no—
158D4—1482no—
159D4—1482no—
160D4—1482no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—371no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—742no—
167C2×C4—741no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4—1482no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4C22⋊#386611yescharacteristic
175C2×C4C22⋊#386611yescharacteristic
176C2×C4C22×#386611yescharacteristic
177C8—1482no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—372no—
182C22—741no—
183C22—741no—
184C22—1481no—
185C22—1481no—
186C22—1481no—
187C22C2×C22⋊#386611yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—2962no—
193C4—741no—
194C4—741no—
195C4—741no—
196C4—1481no—
197C2—81no—
198C2—2961no—
199C2—742no—
200C2#1455851211yescharacteristic
201C2#1455852511yescharacteristic
202C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC2×C4×D37C23
hypercenterC4×D4#3866
hypocenterC37#1514
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. #14558555C2semidirect
2. #14558478C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
13. #11924535C4semidirect
14. #11924532C4semidirect
19. C4×D148C4semidirect
22. C4×D4×C37C4semidirect
107. C37#1514semidirect
117. C4×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585552
#145584782
#145583852
#145583842
#145580802
#151437