Finite Group Databasebeta

← #17995034

Subgroups — #17995034

Order 4736.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11924510C211yesmaximal, characteristic
2C2×#11924458C212yesmaximal, complemented
3#14557393C211yesmaximal, characteristic, complemented
4#14557296C212yesmaximal, complemented
5C22×M16×C37C211yesmaximal, characteristic, complemented
6C22×D148C2211yescharacteristic
7C22×C22⋊D37—21no—
8#11924510—22no—
9#11924510C414yescomplemented
10C2×C4⋊Dic37C2212yes—
11C2×C4⋊Dic37C2211yescharacteristic
12C2×C22⋊Dic37—21no—
13C2×#10596938—21no—
14#11924458—24no—
15#11924443—21no—
16C23×C4×C37C2211yescharacteristic
17C2×M16×C37—22no—
18C2×M16×C37—24no—
19C22×C8×C37C2212yes—
20C24×C37D411yescharacteristic
21C23×D37—21no—
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37C2×C412yes—
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D412yes—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—24no—
29C2×C22⋊D37—44no—
30C22×Dic37—21no—
31C22×Dic37—22no—
32C2×D148—22no—
33C2×D148—22no—
34C2×D148—21no—
35C2×D148C2×C412yes—
36M16×C37—28no—
37C2×C8×C37—22no—
38C2×C8×C37—22no—
39C2×C8×C37D414yescomplemented
40C22⋊Dic37—42no—
41#10596938—24no—
42C4⋊Dic37—21no—
43C4⋊Dic37—22no—
44C4⋊Dic37—22no—
45C4⋊Dic37C2×C412yes—
46C23×C37—22no—
47C23×C37—21no—
48C23×C37—22no—
49C23×C37—21no—
50C23×C37C22⋊C412yes—
51C23×C37C2×D411yescharacteristic
52C22×D37—22no—
53C22×D37—42no—
54C22×D37—42no—
55C22×D37—41no—
56C22×D37—41no—
57C2×C4×C37—22no—
58C2×C4×C37—24no—
59C2×C4×C37—22no—
60C2×C4×C37—22no—
61C2×C4×C37C22⋊C412yes—
62C2×C4×C37C22×C411yescharacteristic
63C2×C4×C37C2×D412yes—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37#4112yes—
66C22⋊D37—48no—
67C2×Dic37—22no—
68C2×Dic37—42no—
69C2×Dic37—42no—
70C2×Dic37—42no—
71C2×Dic37—42no—
72D148—24no—
73D148—41no—
74D148—41no—
75C8×C37—24no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37C2×C22⋊C411yescharacteristic
82C22×C37#12112yes—
83C22×C37AGL(1,ℤ/8)11yescharacteristic
84C22×C37AGL(1,ℤ/8)12yes—
85C22×C37#13711yescharacteristic
86C2×D37—42no—
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—82no—
90C2×D37—82no—
91C4×C37—22no—
92C4×C37C4×D412yes—
93C4×C37#12011yescharacteristic
94C4×C37#12311yescharacteristic
95Dic37—42no—
96Dic37—82no—
97#1895—371nomaximal, Sylow
98C2×C37—42no—
99C2×C37#38611yescharacteristic
100C2×C37#41711yescharacteristic
101C2×C37#41811yescharacteristic
102C2×C37#46812yes—
103C2×C37#46912yes—
104D37—82no—
105C22×M16D3711yescharacteristic, complemented
106C2×#121—371no—
107C2×#102—372no—
108#380—371no—
109#340—372no—
110C37#189511yescharacteristic, complemented, Sylow
111C22×D4—371no—
112C22×D4—741no—
113C23×C4C2×D3711yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D3712yes—
117#121—374no—
118#121—742no—
119C2×C4⋊C4—371no—
120C2×C4⋊C4—372no—
121C2×C22⋊C4—741no—
122C2×C22⋊C4—741no—
123#102—744no—
124#95—741no—
125C24—741no—
126C24D14811yescharacteristic
127C2×D4—372no—
128C2×D4—744no—
129C2×D4—742no—
130C2×D4—742no—
131C2×D4—741no—
132C2×D4—1484no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—741no—
136C22×C4—742no—
137C22×C4C4×D3712yes—
138C22×C4D14811yescharacteristic
139C22×C4C22⋊D3712yes—
140C22×C4C22×D3711yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D3714yescomplemented
145C4⋊C4—372no—
146C4⋊C4—741no—
147C4⋊C4—742no—
148C4⋊C4—742no—
149C22⋊C4—744no—
150C22⋊C4—1482no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—742no—
156C23—1482no—
157C23—1482no—
158C23—1481no—
159C23—1481no—
160C23#1059693812yes—
161C23C2×D14811yescharacteristic
162D4—744no—
163D4—1488no—
164D4—1481no—
165D4—1481no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—742no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4#1059693812yes—
176C2×C4C2×C4×D3711yescharacteristic
177C2×C4#1059696212yes—
178C2×C4C2×C22⋊D3712yes—
179C2×C4C2×C22⋊D3711yescharacteristic
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—2962no—
187C22—2962no—
188C22—1482no—
189C22—1482no—
190C22—1482no—
191C22C2×#1059693811yescharacteristic
192C22#1192451012yes—
193C22#1192456412yes—
194C22#1192456411yescharacteristic
195C22#1192456911yescharacteristic
196C4—22no—
197C4—2962no—
198C4—1482no—
199C4C4×C22⋊D3712yes—
200C4#1192450511yescharacteristic
201C4#1192451911yescharacteristic
202C2—42no—
203C2—2962no—
204C2#1455741211yescharacteristic
205C2#1455753511yescharacteristic
206C2#1455753911yescharacteristic
207C2#1455777912yes—
208C2#1455778612yes—
subgroupG/H
centerC23C2×D148
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC22×M16×C37C2
socleC23×C37C2×D4
prime radicalC2×#11924510C2
cosocleC22×C4×C37C23
hypercenterC22×M16D37
hypocenterC37#1895
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#11924458C2semidirect
3. #14557393C2semidirect
4. #14557296C2semidirect
5. C22×M16×C37C2semidirect
9. #11924510C4semidirect
39. C2×C8×C37D4semidirect
105. C22×M16D37semidirect
110. C37#1895semidirect
144. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245102
C2×#119244582
#145573932
#145572962
C22×M16×C372
#189537