Finite Group Databasebeta

← #17995052

Subgroups — #17995052

Order 4736.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11924519C211yesmaximal, characteristic
2C2×#11924495C211yesmaximal, characteristic, complemented
3C2×#11924450C212yesmaximal
4#14557299C212yesmaximal, complemented
5C37×#381C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C2211yescharacteristic
7#11924519—21no—
8#11924519—21no—
9#11924519—22no—
10#11924495—24no—
11C2×C4⋊Dic37—21no—
12C2×#10596936C412yescomplemented
13C2×C22⋊Dic37C2211yescharacteristic
14C2×C22⋊Dic37C2212yes—
15C2×#10596938C412yescomplemented
16C2×C4×Dic37—21no—
17#11924450—24no—
18C23×C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37C2212yes—
20#95×C37—22no—
21C24×C37C2311yescharacteristic
22C23×D37C2×C411yescharacteristic
23C22×C4×C37—22no—
24C22×C4×C37—22no—
25C22×C4×C37—22no—
26C22×C4×C37C2×C412yes—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D412yes—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C2×C22⋊D37—22no—
33C2×C22⋊D37—22no—
34C22×Dic37—22no—
35C22×Dic37C2×C411yescharacteristic
36C22×Dic37C2×C412yes—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C22⋊Dic37—22no—
40C22⋊Dic37—21no—
41C22⋊Dic37—21no—
42C22⋊Dic37D414yes—
43#10596938—22no—
44#10596938—22no—
45C4⋊Dic37—24no—
46#10596936—22no—
47#10596936—22no—
48C4×Dic37—24no—
49C23×C37—42no—
50C23×C37C22×C411yescharacteristic
51C23×C37C2×D411yescharacteristic
52C23×C37C2×D412yes—
53C23×C37C2×D411yescharacteristic
54C23×C37#4112yes—
55C22×D37—21no—
56C22×D37—22no—
57C22×D37—42no—
58C2×C4×C37—24no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—24no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—44no—
65C2×C4×C37—42no—
66C2×C4×C37C22⋊C412yes—
67C2×C4×C37C22⋊C412yes—
68C22⋊D37—41no—
69C22⋊D37—42no—
70C22⋊D37—41no—
71C2×Dic37—21no—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—24no—
75C2×Dic37—44no—
76C2×Dic37—42no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—22no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37C2×C22⋊C411yescharacteristic
83C22×C37C4×D412yes—
84C22×C37#12011yescharacteristic
85C22×C37#12112yes—
86C22×C37#12311yescharacteristic
87C2×D37—41no—
88C2×D37—42no—
89C2×D37—82no—
90C4×C37—22no—
91C4×C37—22no—
92C4×C37—82no—
93Dic37—44no—
94Dic37—41no—
95Dic37—42no—
96#1899—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—22no—
99C2×C37—22no—
100C2×C37—21no—
101C2×C37#38611yescharacteristic
102C2×C37#41012yes—
103D37—81no—
104C2×#123—371no—
105C2×#117—371no—
106C2×#99—372no—
107#381D3711yescharacteristic, complemented
108#342—372no—
109C37#189911yescharacteristic, complemented, Sylow
110C22×D4—371no—
111C23×C4C2×D3711yescharacteristic
112#123—741no—
113#123—741no—
114#123—742no—
115#117—744no—
116C2×C4⋊C4—372no—
117C2×C4⋊C4—741no—
118C2×C22⋊C4—372no—
119C2×C22⋊C4—371no—
120C2×C22⋊C4—372no—
121C2×C22⋊C4C2×D3712yes—
122C2×C42—741no—
123#99—744no—
124#95—22no—
125C24—371no—
126C24C22×D3711yescharacteristic
127C2×D4—741no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—741no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—371no—
135C22×C4—372no—
136C22×C4—742no—
137C22×C4C4×D3712yes—
138C22×C4D14811yescharacteristic
139C22×C4D14811yescharacteristic
140C22×C4C22⋊D3712yes—
141C4⋊C4—744no—
142C4⋊C4—742no—
143C4⋊C4—742no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—374no—
147C22⋊C4—741no—
148C22⋊C4—742no—
149C22⋊C4—741no—
150C22⋊C4—742no—
151C22⋊C4—742no—
152C42—744no—
153C23—42no—
154C23—742no—
155C23—741no—
156C23—1482no—
157C23C2×C4×D3711yescharacteristic
158C23C2×D14811yescharacteristic
159C23D4×D3712yes—
160C23#1059696412yes—
161C23C2×C22⋊D3711yescharacteristic
162D4—1481no—
163D4—1482no—
164D4—1481no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—742no—
176C2×C4—744no—
177C2×C4—1484no—
178C2×C4—1482no—
179C2×C4#1059693812yes—
180C2×C4#1059693812yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—2962no—
187C22—1482no—
188C22—1481no—
189C22C2×#1059693811yescharacteristic
190C22#1192449612yes—
191C22#1192450611yescharacteristic
192C22#1192450812yes—
193C22#1192452011yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—1484no—
198C4—1482no—
199C4—1481no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—2961no—
205C2#1455741011yescharacteristic
206C2#1455750612yes—
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#381C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#381D37
hypocenterC37#1899
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11924495C2semidirect
4. #14557299C2semidirect
5. C37×#381C2semidirect
12. C2×#10596936C4semidirect
15. C2×#10596938C4semidirect
107. #381D37semidirect
109. C37#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#119245192
C2×#119244952
C2×#119244502
#145572992
C37×#3812
#189937