Finite Group Databasebeta

← #17995580

Subgroups — #17995580

Order 4736.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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
2C4×C22⋊Dic37C211yesmaximal, characteristic
3#14557299C214yesmaximal
4C37×#380C211yesmaximal, characteristic
5C22×Dic74C411yescharacteristic, complemented
6#11924515—21no—
7#11924515—21no—
8#11924515—21no—
9#11924515—21no—
10C2×C4⋊Dic37C411yescharacteristic, complemented
11C2×#10596936C412yescomplemented
12C2×C22⋊Dic37C2212yes—
13C2×C22⋊Dic37C2212yes—
14C2×C4×Dic37—21no—
15#11924443—21no—
16C23×C4×C37C2211yescharacteristic
17C2×C4⋊C4×C37—21no—
18C2×C22⋊C4×C37C2212yes—
19#95×C37—21no—
20C24×C37C2311yescharacteristic
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×C37D411yescharacteristic
29C22×Dic37—22no—
30C22×Dic37C2×C412yes—
31C22×Dic37C2×C412yes—
32C2×Dic74—21no—
33C2×Dic74—21no—
34C2×Dic74—42no—
35C4⋊C4×C37—42no—
36C22⋊C4×C37—24no—
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39C22⋊Dic37—22no—
40C22⋊Dic37Q814yescomplemented
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43#10596936—22no—
44#10596936—22no—
45C4×Dic37—42no—
46C23×C37—41no—
47C23×C37—41no—
48C23×C37C22×C411yescharacteristic
49C23×C37C2×D411yescharacteristic
50C23×C37C2×D411yescharacteristic
51C23×C37C2×Q812yes—
52C23×C37#4112yes—
53C2×C4×C37—22no—
54C2×C4×C37—22no—
55C2×C4×C37—22no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—42no—
60C2×C4×C37—42no—
61C2×C4×C37—42no—
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×Dic37—22no—
67C2×Dic37—22no—
68C2×Dic37—24no—
69C2×Dic37—42no—
70C2×Dic37—42no—
71C2×Dic37—42no—
72C2×Dic37—42no—
73Dic74—42no—
74Dic74—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—42no—
82C22×C37—42no—
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37C4×Q812yes—
85C22×C37C22⋊Q812yes—
86C22×C37#12411yescharacteristic
87C22×C37C4⋊Q811yescharacteristic
88C4×C37—21no—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—82no—
92C4×C37#9912yes—
93Dic37—44no—
94Dic37—42no—
95Dic37—42no—
96#1996—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37—21no—
99C2×C37—22no—
100C2×C37—21no—
101C2×C37#39111yescharacteristic
102C2×C37C2×#9911yescharacteristic
103C2×C37#41011yescharacteristic
104C2×C22⋊Q8—371no—
105#380D3711yescharacteristic
106C4×C22⋊C4—371no—
107#342—374no—
108C37#199611yescharacteristic, complemented, Sylow
109C22×Q8—371no—
110C23×C4C2×D3711yescharacteristic
111C22⋊Q8—741no—
112C22⋊Q8—741no—
113C22⋊Q8—741no—
114C22⋊Q8—741no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—372no—
117C2×C4⋊C4—371no—
118C2×C22⋊C4—372no—
119C2×C22⋊C4—372no—
120C2×C22⋊C4C2×D3712yes—
121C2×C42—741no—
122#95—21no—
123#95—741no—
124C24C22×D3711yescharacteristic
125C2×Q8—741no—
126C2×Q8—741no—
127C2×Q8—1482no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—372no—
131C22×C4—372no—
132C22×C4—742no—
133C22×C4C4×D3711yescharacteristic
134C22×C4C4×D3711yescharacteristic
135C22×C4D14811yescharacteristic
136C22×C4D14811yescharacteristic
137C22×C4C22⋊D3711yescharacteristic
138C22×C4C22⋊D3711yescharacteristic
139C4⋊C4—42no—
140C4⋊C4—742no—
141C4⋊C4—742no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C22⋊C4—24no—
145C22⋊C4—374no—
146C22⋊C4—742no—
147C22⋊C4—742no—
148C22⋊C4—742no—
149C42—1482no—
150C23—41no—
151C23—41no—
152C23C2×C4×D3711yescharacteristic
153C23C2×D14811yescharacteristic
154C23#1059696412yes—
155C23Q8×D3712yes—
156C23C2×C22⋊D3711yescharacteristic
157Q8—1482no—
158Q8—1482no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—742no—
169C2×C4—742no—
170C2×C4—744no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4#1059693811yescharacteristic
176C2×C4#1059693811yescharacteristic
177C2×C4#1059693811yescharacteristic
178C2×C4#1059693811yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×#1059693811yescharacteristic
188C22#1192450112yes—
189C22#1192451612yes—
190C22#1192452311yescharacteristic
191C22#1192453411yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—82no—
196C4—1484no—
197C4—1482no—
198C4—1482no—
199C4#1192445012yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#1455743811yescharacteristic
205C2C2×#1192445011yescharacteristic
206C2#1455750611yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#380C2
socleC22×C37C2×C22⋊C4
prime radical, cosocleC24×C37C23
hypercenter#380D37
hypocenterC37#1996
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
5. C22×Dic74C4semidirect
10. C2×C4⋊Dic37C4semidirect
11. C2×#10596936C4semidirect
40. C22⋊Dic37Q8semidirect
108. C37#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
C4×C22⋊Dic372
#145572992
C37×#3802
#199637