Finite Group Databasebeta

← #17993059

Subgroups — #17993059

Order 4736.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#14558067C211yesmaximal, characteristic
2#14557586C211yesmaximal, characteristic, complemented
3#14557263C212yesmaximal, complemented
4#14557260C212yesmaximal, complemented
5C37×#423C211yesmaximal, characteristic, complemented
6#11924530—21no—
7#11924528C411yescharacteristic
8#11924524C411yescharacteristic
9#11924519—21no—
10#11924515C411yescharacteristic
11#11924510C411yescharacteristic
12C4×Dic74C2211yescharacteristic
13C4×D148C2211yescharacteristic
14C4×C22⋊D37—21no—
15#11924493—21no—
16C4⋊#64436—21no—
17C22⋊#64436—21no—
18C4×#64436C2212yes—
19C2×M16×C37—21no—
20C2×C42×C37C2211yescharacteristic
21C4⋊C8×C37—21no—
22C4⋊C8×C37C2212yes—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C2×C22⋊D37—21no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×Dic74C2×C411yescharacteristic
30M16×C37—42no—
31C2×C8×C37—22no—
32C42×C37C2×C411yescharacteristic
33C42×C37D411yescharacteristic
34C42×C37D411yescharacteristic
35C42×C37C2311yescharacteristic
36C22⋊Dic37—21no—
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—22no—
49C23×C37C22⋊C411yescharacteristic
50C22×D37—21no—
51C2×C4×C37—22no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C22⋊D37—42no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65D148—22no—
66C4×D37—41no—
67C4×D37—41no—
68Dic74—22no—
69C8×C37—42no—
70#64436—42no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—41no—
76C2×D37—41no—
77C2×D37—41no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37#13112yes—
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—41no—
86Dic37—41no—
87Dic37—41no—
88#1495—371nomaximal, Sylow
89C2×C37—41no—
90C2×C37#40811yescharacteristic
91C2×C37#41711yescharacteristic
92C2×C37#42111yescharacteristic
93D37—81no—
94#529—371no—
95#431—371no—
96#423D3711yescharacteristic, complemented
97Q8⋊C8—372no—
98D4⋊C8—372no—
99C37#149511yescharacteristic, complemented, Sylow
100C2×M16—21no—
101#126—741no—
102#125—371no—
103#124—371no—
104#123—741no—
105C22⋊Q8—371no—
106#121—371no—
107C4×Q8—371no—
108C4×D4—371no—
109C4×D4—741no—
110#117—741no—
111C2×C42C2×D3711yescharacteristic
112C4⋊C8—21no—
113C4⋊C8—741no—
114C4⋊C8C2×D3712yes—
115C22⋊C8—741no—
116C4×C8—372no—
117C2×Q8—371no—
118C2×D4—371no—
119C2×D4—741no—
120C22×C4—741no—
121C22×C4C4×D3711yescharacteristic
122C22×C4D14811yescharacteristic
123C22×C4C22⋊D3711yescharacteristic
124M16—42no—
125C2×C8—22no—
126C2×C8—742no—
127C4⋊C4—371no—
128C4⋊C4—371no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C22⋊C4—741no—
136C22⋊C4—741no—
137C22⋊C4—741no—
138C42—741no—
139C42C4×D3711yescharacteristic
140C42D14811yescharacteristic
141C42C22⋊D3711yescharacteristic
142C42C22×D3711yescharacteristic
143C23—741no—
144C23#1059693811yescharacteristic
145Q8—742no—
146D4—742no—
147D4—1482no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—1481no—
156C2×C4—1481no—
157C2×C4#1059693811yescharacteristic
158C2×C4#1059693811yescharacteristic
159C2×C4#1059693811yescharacteristic
160C2×C4C2×C4×D3711yescharacteristic
161C2×C4C2×D14811yescharacteristic
162C2×C4C2×C22⋊D3711yescharacteristic
163C8—42no—
164C8—1482no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—1481no—
169C22—1481no—
170C22—1481no—
171C22C2×#1059693811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—1481no—
177C4—1481no—
178C4—1481no—
179C4#1192454412yes—
180C4#1192456211yescharacteristic
181C4#1192456711yescharacteristic
182C2—41no—
183C2—2961no—
184C2#1455750111yescharacteristic
185C2#1455753211yescharacteristic
186C2#1455754911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#423C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C4
cosocleC42×C37C23
hypercenter#423D37
hypocenterC37#1495
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #14557586C2semidirect
3. #14557263C2semidirect
4. #14557260C2semidirect
5. C37×#423C2semidirect
96. #423D37semidirect
99. C37#1495semidirect

Maximal subgroups

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

subgroupindex
#145580672
#145575862
#145572632
#145572602
C37×#4232
#149537