Finite Group Databasebeta

← #17993225

Subgroups — #17993225

Order 4736.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#14557590C211yesmaximal, characteristic, complemented
3#14557274C212yesmaximal, complemented
4#14557272C212yesmaximal, complemented
5C37×#432C211yesmaximal, characteristic, complemented
6#11924530—21no—
7#11924528C2211yescharacteristic
8#11924524C2211yescharacteristic
9#11924519—21no—
10#11924515C411yescharacteristic
11#11924510C411yescharacteristic
12C4×Dic74C411yescharacteristic
13C4×D148C411yescharacteristic
14C4×C22⋊D37—21no—
15#11924493—21no—
16C4⋊#64436—21no—
17C22⋊#64436—21no—
18#11924447C2212yes—
19C2×C42×C37C2211yescharacteristic
20C4⋊C8×C37—21no—
21C22⋊C8×C37—21no—
22#97×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
30C2×C8×C37—22no—
31C42×C37C2×C411yescharacteristic
32C42×C37D411yescharacteristic
33C42×C37D411yescharacteristic
34C42×C37C2311yescharacteristic
35C22⋊Dic37—21no—
36#10596938—21no—
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40C4⋊Dic37C2×C411yescharacteristic
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47C2×#64436—22no—
48C23×C37C22⋊C411yescharacteristic
49C22×D37—21no—
50C2×C4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C22⋊D37—42no—
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63D148—41no—
64C4×D37—42no—
65Dic74—41no—
66C8×C37—42no—
67#64436—42no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37C2×C22⋊C411yescharacteristic
72C2×D37—41no—
73C2×D37—41no—
74C2×D37—41no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81Dic37—41no—
82Dic37—41no—
83Dic37—41no—
84#1535—371nomaximal, Sylow
85C2×C37—41no—
86C2×C37#41311yescharacteristic
87C2×C37#42111yescharacteristic
88C2×C37#42111yescharacteristic
89D37—81no—
90#529—371no—
91#432—371no—
92#432D3711yescharacteristic, complemented
93#330—372no—
94#329—372no—
95C37#153511yescharacteristic, complemented, Sylow
96#126—741no—
97#125—371no—
98#124—371no—
99#123—741no—
100C22⋊Q8—371no—
101#121—371no—
102C4×Q8—371no—
103C4×D4—371no—
104C4×D4—741no—
105#117—741no—
106C2×C42C2×D3711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—741no—
109C22⋊C8—21no—
110C22⋊C8—741no—
111#97—372no—
112#97C2×D3712yes—
113C2×Q8—371no—
114C2×D4—371no—
115C2×D4—741no—
116C22×C4—741no—
117C22×C4C4×D3711yescharacteristic
118C22×C4D14811yescharacteristic
119C22×C4C22⋊D3711yescharacteristic
120C2×C8—22no—
121C2×C8—742no—
122C4⋊C4—371no—
123C4⋊C4—371no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C22⋊C4—741no—
129C22⋊C4—741no—
130C22⋊C4—741no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C42—741no—
134C42C4×D3711yescharacteristic
135C42D14811yescharacteristic
136C42C22⋊D3711yescharacteristic
137C42C22×D3711yescharacteristic
138C23—741no—
139C23#1059693811yescharacteristic
140Q8—1481no—
141D4—1481no—
142D4—1482no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—741no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—1482no—
150C2×C4#1059693811yescharacteristic
151C2×C4#1059693811yescharacteristic
152C2×C4#1059693811yescharacteristic
153C2×C4C2×C4×D3711yescharacteristic
154C2×C4C2×D14811yescharacteristic
155C2×C4C2×C22⋊D3711yescharacteristic
156C8—42no—
157C8—1482no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—1481no—
162C22—1481no—
163C22—1481no—
164C22C2×#1059693811yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—1481no—
172C4—1481no—
173C4—1481no—
174C2—41no—
175C2—2961no—
176C2#1455751511yescharacteristic
177C2#1455754911yescharacteristic
178C2#1455755111yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#432C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C4
cosocleC42×C37C23
hypercenter#432D37
hypocenterC37#1535
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #14557590C2semidirect
3. #14557274C2semidirect
4. #14557272C2semidirect
5. C37×#432C2semidirect
92. #432D37semidirect
95. C37#1535semidirect

Maximal subgroups

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

subgroupindex
#145580672
#145575902
#145572742
#145572722
C37×#4322
#153537