Finite Group Databasebeta

← #17993128

Subgroups — #17993128

Order 4736.

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

normal subgroups only

This group has 274 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
1C2×#11924515C211yesmaximal, characteristic
2#14557497C211yesmaximal, characteristic
3#14557269C214yesmaximal, complemented
4C37×#381C211yesmaximal, characteristic
5C22×Dic74C411yescharacteristic, complemented
6C2×#10596934—21no—
7#11924515—21no—
8#11924515—21no—
9#11924515C412yescomplemented
10#11924515C2212yes—
11C2×C4⋊Dic37C411yescharacteristic, complemented
12C2×#10596936—21no—
13C2×C22⋊Dic37—21no—
14C22⋊#64436—21no—
15C22⋊#64436C2212yes—
16C23×C4×C37C2211yescharacteristic
17C2×C22⋊C4×C37—21no—
18#95×C37—21no—
19#95×C37C2212yes—
20C24×C37D411yescharacteristic
21C22×C4×C37—22no—
22C22×C4×C37—42no—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37—21no—
31C2×Dic74—21no—
32C2×Dic74—42no—
33C2×Dic74C2×C412yes—
34C22⋊C4×C37—42no—
35C22⋊Dic37—22no—
36C22⋊Dic37—22no—
37C4⋊Dic37—21no—
38C4⋊Dic37C2×C412yes—
39#10596936—22no—
40#10596936—22no—
41#10596934—42no—
42C2×#64436—22no—
43C23×C37—22no—
44C23×C37—22no—
45C23×C37—41no—
46C23×C37C22⋊C411yescharacteristic
47C23×C37C22⋊C411yescharacteristic
48C23×C37C2×D411yescharacteristic
49C2×C4×C37—22no—
50C2×C4×C37—22no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37—42no—
56C2×C4×C37—42no—
57C2×C4×C37—42no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—42no—
65C2×Dic37—42no—
66Dic74—42no—
67Dic74—42no—
68#64436—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—44no—
77C22×C37#9912yes—
78C22×C37C2×C22⋊C411yescharacteristic
79C22×C37#13712yes—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—82no—
85Dic37—42no—
86Dic37—42no—
87#1511—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37—22no—
90C2×C37—41no—
91C2×C37C2×#9911yescharacteristic
92C2×C37#41911yescharacteristic
93C2×C37#42111yescharacteristic
94C2×C22⋊Q8—371no—
95#407—371no—
96#381D3711yescharacteristic
97#328—374no—
98C37#151111yescharacteristic, complemented, Sylow
99C22×Q8—371no—
100C23×C4C2×D3711yescharacteristic
101C2×M16—741no—
102C22⋊Q8—372no—
103C22⋊Q8—372no—
104C22⋊Q8—741no—
105C22⋊Q8—741no—
106C2×C4⋊C4—371no—
107C2×C4⋊C4—741no—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—741no—
110C22⋊C8—372no—
111C22⋊C8—741no—
112#95—21no—
113#95C2×D3712yes—
114C24C22⋊D3711yescharacteristic
115C2×Q8—372no—
116C2×Q8—741no—
117C2×Q8—1482no—
118C22×C4—22no—
119C22×C4—42no—
120C22×C4—741no—
121C22×C4—741no—
122C22×C4C4×D3711yescharacteristic
123C22×C4C4×D3711yescharacteristic
124C22×C4D14811yescharacteristic
125C22×C4D14811yescharacteristic
126C22×C4C22⋊D3711yescharacteristic
127C22×C4C22×D3711yescharacteristic
128M16—1482no—
129C2×C8—742no—
130C4⋊C4—372no—
131C4⋊C4—742no—
132C4⋊C4—741no—
133C4⋊C4—742no—
134C22⋊C4—42no—
135C22⋊C4—742no—
136C22⋊C4—742no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23#1059693811yescharacteristic
141C23#1059693811yescharacteristic
142C23C2×C22⋊D3711yescharacteristic
143Q8—1482no—
144Q8—1482no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—742no—
155C2×C4—742no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4#1059693811yescharacteristic
159C2×C4#1059693811yescharacteristic
160C2×C4C2×C4×D3711yescharacteristic
161C2×C4C2×D14811yescharacteristic
162C8—1482no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1192445012yes—
172C22C2×#1059693811yescharacteristic
173C22#1192456612yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—82no—
179C4—1482no—
180C4—1482no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1192445011yescharacteristic
185C2#1455754111yescharacteristic
186C2#1455755111yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#381C2
socleC22×C37C2×C22⋊C4
prime radicalC24×C37D4
cosocleC22×C4×C37C23
hypercenter#381D37
hypocenterC37#1511
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #14557269C2semidirect
5. C22×Dic74C4semidirect
9. #11924515C4semidirect
11. C2×C4⋊Dic37C4semidirect
98. C37#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
#145574972
#145572692
C37×#3812
#151137