Finite Group Databasebeta

← #18010118

Subgroups — #18010118

Order 4736.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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
2D37⋊(C4⋊C8)C211yesmaximal, characteristic
3#14558392C212yesmaximal, complemented
4#14558392C212yesmaximal, complemented
5#14558089C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7#11924603C2212yes—
8#11924603C2212yes—
9C4⋊#64438—21no—
10#11924593—21no—
11#11924591—21no—
12#11924535C2211yescharacteristic
13#11924535C2211yescharacteristic
14#11924528C411yescharacteristic
15#11924514—21no—
16#11924514—21no—
17#11924501—21no—
18#11924501—21no—
19#11924494C411yescharacteristic
20#11924494C411yescharacteristic
21C42×D37C2211yescharacteristic
22#125×C37C411yescharacteristic
23C2×C4×D37C2×C411yescharacteristic
24C2×C4×D37D411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×Dic74—21no—
27C2×Dic74—21no—
28C2×#64438—22no—
29C2×#64438—22no—
30D37⋊C8—42no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C4⋊C4×C37C2×C411yescharacteristic
35C42×C37C2×C411yescharacteristic
36#10596938—21no—
37#10596938—21no—
38C4⋊Dic37C2×C411yescharacteristic
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C22×D37C22⋊C411yescharacteristic
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59C2×Dic37C2×D411yescharacteristic
60C4×D37—22no—
61C4×D37—22no—
62C4×D37—21no—
63C4×D37—21no—
64Dic74—42no—
65Dic74—41no—
66Dic74—41no—
67#64438—42no—
68#64438—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—21no—
72C2×D37#10112yes—
73C4×C37—21no—
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—41no—
77C4×C37—41no—
78Dic37—21no—
79Dic37—41no—
80Dic37—41no—
81Dic37#13512yes—
82Dic37AGL(1,ℤ/8)11yescharacteristic
83Dic37#13711yescharacteristic
84#1552—371nomaximal, Sylow
85C2×C37C2×#10111yescharacteristic
86C2×C37#41611yescharacteristic
87C2×C37#41711yescharacteristic
88D37—22no—
89#533—371no—
90#432—371no—
91C2×C4⋊C8—371no—
92#332—372no—
93#332—372no—
94C37#155211yescharacteristic, complemented, Sylow
95C22×C8—741no—
96C4⋊Q8—371no—
97C4⋊Q8—371no—
98#125—371no—
99#125#386611yescharacteristic
100C22⋊Q8—741no—
101C22⋊Q8—741no—
102C4×Q8—741no—
103C4×Q8—741no—
104#117—371no—
105#117—371no—
106C2×C42—371no—
107C4⋊C8—372no—
108C4⋊C8—372no—
109C4⋊C8—741no—
110C22⋊C8—741no—
111#97—741no—
112C2×Q8—741no—
113C2×Q8—741no—
114C22×C4—371no—
115C22×C4—371no—
116C22×C4—371no—
117C2×C8—742no—
118C2×C8—742no—
119C2×C8—1482no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—371no—
123C4⋊C4—371no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4C2×#386611yescharacteristic
129C4⋊C4C2×#386611yescharacteristic
130C22⋊C4—741no—
131C22⋊C4—741no—
132C42—371no—
133C42—371no—
134C42—371no—
135C42—741no—
136C42—741no—
137C42C2×#386611yescharacteristic
138C23—371no—
139Q8—1482no—
140Q8—1481no—
141Q8—1481no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—371no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—741no—
148C2×C4—742no—
149C2×C4—741no—
150C2×C4—742no—
151C2×C4—741no—
152C2×C4—741no—
153C2×C4C22⋊#386611yescharacteristic
154C2×C4C22⋊#386611yescharacteristic
155C2×C4C22×#386611yescharacteristic
156C8—1482no—
157C8—1482no—
158C22—372no—
159C22—741no—
160C22—741no—
161C22C2×C22⋊#386611yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—372no—
168C4—371no—
169C4—371no—
170C4—741no—
171C4—1481no—
172C4—1481no—
173C2—742no—
174C2D37⋊#10111yescharacteristic
175C2#1455852311yescharacteristic
176C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#125×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenter#125#3866
hypocenterC37#1552
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #14558392C2semidirect
4. #14558392C2semidirect
94. C37#1552semidirect

Maximal subgroups

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

subgroupindex
#145585562
D37⋊(C4⋊C8)2
#145583922
#145580892
#155237