Finite Group Databasebeta

← #17995035

Subgroups — #17995035

Order 4736.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22×#10596934C211yesmaximal, characteristic, complemented
2C2×#11924457C212yesmaximal, complemented
3#14557393C211yesmaximal, characteristic, complemented
4#14557295C212yesmaximal, complemented
5C2×#121×C37C211yesmaximal, characteristic
6C2×#10596934—22no—
7C2×#10596934—24no—
8C22×#64436C2212yes—
9C2×C4⋊Dic37C2212yes—
10C2×C22⋊Dic37—21no—
11#11924457—24no—
12#11924443—21no—
13C22×D4×C37—21no—
14C22×D4×C37C2211yescharacteristic
15C23×C4×C37C2211yescharacteristic
16#121×C37—22no—
17#121×C37C414yescomplemented
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37—21no—
20C24×C37—21no—
21C24×C37D411yescharacteristic
22C2×D4×C37—24no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37—22no—
26C2×D4×C37—44no—
27C2×D4×C37C2×C412yes—
28C22×C4×C37—22no—
29C22×C4×C37—22no—
30C22×C4×C37—21no—
31C22×C4×C37C2×C412yes—
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D412yes—
34C22×C4×C37C2311yescharacteristic
35C22×Dic37—22no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C412yes—
38C22⋊C4×C37—24no—
39C22⋊Dic37—42no—
40C4⋊Dic37—22no—
41C4⋊Dic37—22no—
42#10596934—28no—
43C2×#64436—22no—
44C2×#64436—22no—
45C2×#64436D414yescomplemented
46C23×C37—22no—
47C23×C37—21no—
48C23×C37—22no—
49C23×C37—21no—
50C23×C37—22no—
51C23×C37—42no—
52C23×C37—42no—
53C23×C37—41no—
54C23×C37—41no—
55C23×C37C22⋊C412yes—
56C23×C37C2×D411yescharacteristic
57D4×C37—24no—
58D4×C37—48no—
59D4×C37—41no—
60D4×C37—41no—
61C2×C4×C37—22no—
62C2×C4×C37—24no—
63C2×C4×C37—22no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—42no—
67C2×C4×C37C22⋊C412yes—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D412yes—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37#4112yes—
72C2×Dic37—42no—
73C2×Dic37—42no—
74C2×Dic37—42no—
75#64436—24no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37—42no—
83C22×C37—42no—
84C22×C37—82no—
85C22×C37—82no—
86C22×C37C2×C22⋊C411yescharacteristic
87C22×C37#12112yes—
88C22×C37AGL(1,ℤ/8)11yescharacteristic
89C22×C37AGL(1,ℤ/8)12yes—
90C22×C37#13711yescharacteristic
91C4×C37—22no—
92C4×C37—42no—
93C4×C37C4×D412yes—
94C4×C37#12011yescharacteristic
95C4×C37#12311yescharacteristic
96Dic37—82no—
97#1895—371nomaximal, Sylow
98C2×C37—42no—
99C2×C37—82no—
100C2×C37#38611yescharacteristic
101C2×C37#41711yescharacteristic
102C2×C37#41811yescharacteristic
103C2×C37#46812yes—
104C2×C37#46912yes—
105C22×M16—371no—
106C2×#121D3711yescharacteristic
107C2×#102—372no—
108#380—371no—
109#340—372no—
110C37#189511yescharacteristic, complemented, Sylow
111C22×D4—21no—
112C22×D4C2×D3711yescharacteristic
113C23×C4C2×D3711yescharacteristic
114C2×M16—744no—
115C2×M16—742no—
116C22×C8—372no—
117#121—22no—
118#121Dic3714yescomplemented
119C2×C4⋊C4—372no—
120C2×C4⋊C4C2×D3711yescharacteristic
121C2×C22⋊C4—21no—
122C2×C22⋊C4—741no—
123#102—744no—
124#95—741no—
125C24—21no—
126C24C22⋊D3711yescharacteristic
127C2×D4—24no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—44no—
132C2×D4C2×Dic3712yes—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—742no—
137C22×C4C2×Dic3712yes—
138C22×C4C22⋊D3711yescharacteristic
139C22×C4C22⋊D3712yes—
140C22×C4C22×D3711yescharacteristic
141M16—748no—
142C2×C8—374no—
143C2×C8—742no—
144C2×C8—742no—
145C4⋊C4—21no—
146C4⋊C4—742no—
147C4⋊C4—742no—
148C4⋊C4C2×Dic3712yes—
149C22⋊C4—24no—
150C22⋊C4—1482no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—41no—
158C23—42no—
159C23—41no—
160C23C22⋊Dic3712yes—
161C23C2×C22⋊D3711yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4C22⋊Dic3712yes—
176C2×C4D4×D3712yes—
177C2×C4#1059696412yes—
178C2×C4C22×Dic3711yescharacteristic
179C2×C4C2×C22⋊D3711yescharacteristic
180C8—744no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22C2×C22⋊Dic3711yescharacteristic
192C22#1192450812yes—
193C22#1192456111yescharacteristic
194C22#1192456212yes—
195C22#1192456611yescharacteristic
196C4—22no—
197C4—42no—
198C4—2962no—
199C4D4×Dic3712yes—
200C4#1192450411yescharacteristic
201C4#1192451711yescharacteristic
202C2—42no—
203C2—82no—
204C2#1455741311yescharacteristic
205C2#1455753411yescharacteristic
206C2#1455753811yescharacteristic
207C2#1455777712yes—
208C2#1455778412yes—
subgroupG/H
centerC23C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC2×#121×C37C2
socleC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenterC2×#121D37
hypocenterC37#1895
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#10596934C2semidirect
2. C2×#11924457C2semidirect
3. #14557393C2semidirect
4. #14557295C2semidirect
17. #121×C37C4semidirect
45. C2×#64436D4semidirect
110. C37#1895semidirect
118. #121Dic37semidirect

Maximal subgroups

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

subgroupindex
C22×#105969342
C2×#119244572
#145573932
#145572952
C2×#121×C372
#189537