Finite Group Databasebeta

← #17994891

Subgroups — #17994891

Order 4736.

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

normal subgroups only

This group has 408 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
1C22×#10596934C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D37C211yesmaximal, characteristic
3C2×#11924448C212yesmaximal, complemented
4#14557287C212yesmaximal, complemented
5C2×C22⋊C8×C37C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C411yescharacteristic
7C22×C4×D37C2211yescharacteristic
8C2×#10596934—22no—
9C2×#10596934—24no—
10C22×#64436C2212yes—
11C4×C22⋊D37—22no—
12C4×C22⋊D37—22no—
13C2×#10596936C411yescharacteristic
14C2×C22⋊Dic37C411yescharacteristic
15C2×#10596938C411yescharacteristic
16C2×C4×Dic37C2211yescharacteristic
17#11924448—24no—
18C23×C4×C37C2211yescharacteristic
19C22×C8×C37C2212yes—
20C22⋊C8×C37—22no—
21C24×C37C2×C411yescharacteristic
22C23×D37C2×C411yescharacteristic
23C22×C4×C37—22no—
24C22×C4×C37—22no—
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37D412yes—
27C22×C4×C37D412yes—
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—22no—
38C2×C4×D37—22no—
39C2×C8×C37—22no—
40C2×C8×C37—22no—
41C2×C8×C37—22no—
42C22⋊Dic37—22no—
43#10596938—22no—
44#10596936—22no—
45C4×Dic37—21no—
46C4×Dic37—21no—
47#10596934—28no—
48C2×#64436—22no—
49C2×#64436—22no—
50C2×#64436D414yescomplemented
51C23×C37—22no—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37—22no—
55C23×C37C22⋊C412yes—
56C23×C37C22×C411yescharacteristic
57C22×D37—21no—
58C22×D37—22no—
59C22×D37—21no—
60C22×D37—22no—
61C22×D37M1612yescomplemented
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—24no—
65C2×C4×C37—22no—
66C2×C4×C37C22⋊C412yes—
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D412yes—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37#4112yes—
71C22⋊D37—28no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37M1612yescomplemented
79C4×D37—41no—
80C4×D37—42no—
81C4×D37—41no—
82C8×C37—42no—
83#64436—24no—
84C22×C37—22no—
85C22×C37—22no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37C2×C22⋊C411yescharacteristic
90C22×C37C4×D412yes—
91C22×C37C2×M1611yescharacteristic
92C22×C37C2×M1611yescharacteristic
93C22×C37#13112yes—
94C2×D37—22no—
95C2×D37—24no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—22no—
100C4×C37#12011yescharacteristic
101C4×C37#12112yes—
102C4×C37#12311yescharacteristic
103Dic37—22no—
104Dic37—41no—
105Dic37—41no—
106#1870—371nomaximal, Sylow
107C2×C37—42no—
108C2×C37#38611yescharacteristic
109C2×C37#40711yescharacteristic
110C2×C37#40811yescharacteristic
111C2×C37#43512yes—
112C2×C37#43612yes—
113D37—42no—
114C22×M16—371no—
115C2×C4×D4—371no—
116C2×C22⋊C8—372no—
117C2×C22⋊C8D3711yescharacteristic, complemented
118#336—372no—
119C37#187011yescharacteristic, complemented, Sylow
120C22×D4—371no—
121C23×C4—371no—
122C23×C4C2×D3711yescharacteristic
123C2×M16—744no—
124C2×M16—742no—
125C22×C8—372no—
126C22×C8C2×D3712yes—
127C4×D4—742no—
128C4×D4—742no—
129C2×C4⋊C4—371no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4—371no—
132C2×C42—371no—
133C22⋊C8—22no—
134C22⋊C8—744no—
135C24—371no—
136C24C4×D3711yescharacteristic
137C2×D4—742no—
138C2×D4—742no—
139C2×D4—742no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—741no—
146C22×C4—742no—
147C22×C4—742no—
148C22×C4—741no—
149C22×C4C4×D3711yescharacteristic
150C22×C4D14812yes—
151C22×C4C22⋊D3712yes—
152C22×C4C22×D3711yescharacteristic
153M16—748no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—374no—
158C2×C8—742no—
159C2×C8—742no—
160C4⋊C4—742no—
161C22⋊C4—742no—
162C22⋊C4—742no—
163C42—741no—
164C42—741no—
165C23—22no—
166C23—21no—
167C23—21no—
168C23—22no—
169C23—372no—
170C23—741no—
171C23—742no—
172C23—741no—
173C23—742no—
174C23#1059693812yes—
175C23C2×C4×D3711yescharacteristic
176D4—748no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—372no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—1481no—
189C2×C4—1482no—
190C2×C4—1481no—
191C2×C4#1059693812yes—
192C2×C4C2×D14811yescharacteristic
193C2×C4D4×D3712yes—
194C2×C4#1059696412yes—
195C2×C4C2×C22⋊D3711yescharacteristic
196C8—42no—
197C8—744no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—742no—
204C22—744no—
205C22—1481no—
206C22—1482no—
207C22—1481no—
208C22C2×#1059693811yescharacteristic
209C22#1192449612yes—
210C22M16×D3711yescharacteristic
211C22M16×D3711yescharacteristic
212C22#1192454212yes—
213C4—22no—
214C4—742no—
215C4—1481no—
216C4—1481no—
217C4#1192450611yescharacteristic
218C4#1192450812yes—
219C4#1192452011yescharacteristic
220C2—42no—
221C2—1482no—
222C2#1455741011yescharacteristic
223C2#1455749611yescharacteristic
224C2#1455749911yescharacteristic
225C2#1455760712yes—
226C2#1455760812yes—
subgroupG/H
center, FrattiniC22×C4C22×D37
commutator, socleC23×C37C22×C4
FittingC2×C22⋊C8×C37C2
prime radicalC22×C22⋊D37C4
cosocleC22×C4×C37C23
hypercenterC2×C22⋊C8D37
hypocenterC37#1870
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#10596934C2semidirect
3. C2×#11924448C2semidirect
4. #14557287C2semidirect
5. C2×C22⋊C8×C37C2semidirect
50. C2×#64436D4semidirect
61. C22×D37M16semidirect
78. C2×Dic37M16semidirect
117. C2×C22⋊C8D37semidirect
119. C37#1870semidirect

Maximal subgroups

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

subgroupindex
C22×#105969342
C2×C4×C22⋊D372
C2×#119244482
#145572872
C2×C22⋊C8×C372
#187037