Finite Group Databasebeta

← #18010131

Subgroups — #18010131

Order 4736.

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

normal subgroups only

This group has 202 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
2#14558538C211yesmaximal, characteristic
3#14558393C212yesmaximal, complemented
4#14558392C212yesmaximal, complemented
5#14558087C211yesmaximal, characteristic
6C2×#10596953—21no—
7#11924603—21no—
8#11924603C2212yes—
9#11924603C2212yes—
10#11924593—21no—
11#11924591—21no—
12#11924535C2211yescharacteristic
13#11924534C2211yescharacteristic
14#11924526—21no—
15#11924516C411yescharacteristic
16#11924514—21no—
17#11924512C411yescharacteristic
18C4×Dic74—21no—
19C4×Dic74C411yescharacteristic
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×C4×D37C2×C411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×C4×D37D411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×#64438—22no—
30C2×#64438—22no—
31#10596953—42no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C42×C37—21no—
35C42×C37C2×C411yescharacteristic
36#10596938—21no—
37#10596938—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45C4×Dic37—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C22×D37C22⋊C411yescharacteristic
50Q8×C37—41no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22×C411yescharacteristic
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37C22⋊C411yescharacteristic
59C2×Dic37C2×D411yescharacteristic
60C2×Dic37C2×D411yescharacteristic
61C4×D37—21no—
62C4×D37—21no—
63C4×D37—22no—
64C4×D37—41no—
65Dic74—41no—
66Dic74—41no—
67Dic74—41no—
68#64438—42no—
69#64438—42no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—21no—
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79Dic37—21no—
80Dic37—41no—
81Dic37—41no—
82Dic37AGL(1,ℤ/8)11yescharacteristic
83Dic37#13711yescharacteristic
84Dic37#13712yes—
85#1559—371nomaximal, Sylow
86C2×C37#41311yescharacteristic
87C2×C37#41711yescharacteristic
88C2×C37#41911yescharacteristic
89D37—41no—
90#533—371no—
91#432—371no—
92#423—371no—
93#333—372no—
94#332—372no—
95C37#155911yescharacteristic, complemented, Sylow
96C2×M16—741no—
97C4⋊Q8—371no—
98C4⋊Q8—371no—
99#125—741no—
100C22⋊Q8—371no—
101C22⋊Q8—371no—
102C22⋊Q8—741no—
103C4×Q8—371no—
104C4×Q8—741no—
105C4×Q8#386611yescharacteristic
106#117—741no—
107C2×C42—371no—
108C4⋊C8—372no—
109C4⋊C8—372no—
110C4⋊C8—741no—
111C22⋊C8—741no—
112#97—741no—
113C2×Q8—371no—
114C2×Q8—741no—
115C2×Q8C2×#386611yescharacteristic
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119M16—1482no—
120C2×C8—742no—
121C2×C8—742no—
122C4⋊C4—21no—
123C4⋊C4—371no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4C2×#386611yescharacteristic
131C22⋊C4—741no—
132C22⋊C4—741no—
133C42—21no—
134C42—371no—
135C42—371no—
136C42—371no—
137C42—741no—
138C42C2×#386611yescharacteristic
139C23—371no—
140Q8—41no—
141Q8—1481no—
142Q8—1481no—
143Q8—1481no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—371no—
147C2×C4—371no—
148C2×C4—371no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4—742no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—1481no—
155C2×C4C22⋊#386611yescharacteristic
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22×#386611yescharacteristic
158C8—1482no—
159C8—1482no—
160C22—741no—
161C22—741no—
162C22—741no—
163C22C2×C22⋊#386611yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—371no—
170C4—371no—
171C4—372no—
172C4—741no—
173C4—1481no—
174C4—1481no—
175C2—1481no—
176C2#1455851911yescharacteristic
177C2#1455852411yescharacteristic
178C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenterC4×Q8#3866
hypocenterC37#1559
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #14558393C2semidirect
4. #14558392C2semidirect
95. C37#1559semidirect

Maximal subgroups

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

subgroupindex
#145585562
#145585382
#145583932
#145583922
#145580872
#155937