Finite Group Databasebeta

← #18010432

Subgroups — #18010432

Order 4736.

584 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11924597C212yesmaximal, complemented
2C2×#11924596C212yesmaximal, complemented
3#14558505C212yesmaximal, complemented
4C22×#10596962C211yesmaximal, characteristic
5C2×#10596957C2214yes—
6#11924597—24no—
7#11924596—24no—
8#11924593—24no—
9C2×#10596962—24no—
10C2×#10596962—24no—
11C2×#10596962—24no—
12C22×Dic74C2211yescharacteristic
13C22×D148C411yescharacteristic
14C22×C22⋊D37C411yescharacteristic
15C22×C22⋊D37C2211yescharacteristic
16C22×C4×D37C411yescharacteristic
17C22×C4×D37C2211yescharacteristic
18C23×C4×C37C411yescharacteristic
19C24×C37C2×C411yescharacteristic
20C23×D37C2×C411yescharacteristic
21C23×D37C2×C411yescharacteristic
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37—22no—
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C2×C22⋊D37—22no—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32C2×C22⋊D37D414yes—
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37C2311yescharacteristic
35#10596962—232no—
36C2×D148—22no—
37C2×D148—22no—
38C2×D148—22no—
39C2×C4×D37—22no—
40C2×C4×D37—22no—
41C2×C4×D37—22no—
42C2×C4×D37—22no—
43C2×C4×D37—22no—
44C2×C4×D37D414yes—
45C2×Dic74—22no—
46C2×Dic74—22no—
47C2×Dic74D414yes—
48#10596957—24no—
49#10596957—24no—
50C2×#64438—24no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37—42no—
54C23×C37C22⋊C412yes—
55C23×C37C22×C411yescharacteristic
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—21no—
59C22×D37—21no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37C22⋊C412yes—
63C22×D37C22⋊C412yes—
64C2×C4×C37—28no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37C22⋊C412yes—
70C2×C4×C37C22⋊C412yes—
71C22⋊D37—28no—
72C22⋊D37—28no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37C22⋊C412yes—
76C2×Dic37C2×D412yes—
77C2×Dic37C2×D412yes—
78C2×Dic37C2×D412yes—
79D148—28no—
80C4×D37—28no—
81C4×D37—28no—
82Dic74—28no—
83#64438—44no—
84C22×C37—22no—
85C22×C37—22no—
86C22×C37—42no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37C2×C22⋊C411yescharacteristic
90C22×C37C2×C22⋊C411yescharacteristic
91C22×C37C2×C22⋊C411yescharacteristic
92C2×D37—22no—
93C2×D37—22no—
94C2×D37—24no—
95C2×D37—42no—
96C2×D37—42no—
97C2×D37—42no—
98C2×D37—42no—
99C2×D37—42no—
100C4×C37—22no—
101C4×C37—22no—
102Dic37—22no—
103Dic37#12014yes—
104#1785—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—21no—
107C2×C37—42no—
108C2×C37#37911yescharacteristic
109C2×C37#41312yes—
110D37—42no—
111D37—42no—
112C22×#41—371no—
113C2×#101—372no—
114C2×#100—372no—
115#407—372no—
116C37#178511yescharacteristic, complemented, Sylow
117C2×#41—744no—
118C2×#41—744no—
119C2×#41—744no—
120C22×Q8—371no—
121C22×D4—371no—
122C22×D4—371no—
123C22×D4—371no—
124C23×C4—371no—
125C23×C4—371no—
126C23×C4#386611yescharacteristic
127C2×M16—374no—
128#101—744no—
129#100—744no—
130C22⋊C8—744no—
131C24—371no—
132C24—371no—
133C24C2×#386611yescharacteristic
134#41—7432no—
135C2×Q8—374no—
136C2×Q8—742no—
137C2×Q8—742no—
138C2×D4—374no—
139C2×D4—742no—
140C2×D4—742no—
141C2×D4—742no—
142C2×D4—742no—
143C2×D4—742no—
144C2×D4—742no—
145C2×D4—742no—
146C2×D4—742no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—374no—
153C22×C4—742no—
154C22×C4—742no—
155C22×C4—742no—
156C22×C4—742no—
157C22×C4—742no—
158C22×C4C2×#386611yescharacteristic
159C22×C4C2×#386611yescharacteristic
160M16—744no—
161M16—744no—
162C2×C8—744no—
163C23—21no—
164C23—21no—
165C23—42no—
166C23—372no—
167C23—372no—
168C23—741no—
169C23—741no—
170C23—741no—
171C23—741no—
172C23—1482no—
173C23—1482no—
174C23C22⋊#386612yes—
175C23C22×#386611yescharacteristic
176Q8—748no—
177D4—748no—
178D4—748no—
179D4—748no—
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—372no—
186C2×C4—372no—
187C2×C4—372no—
188C2×C4—372no—
189C2×C4—748no—
190C2×C4—748no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4C22⋊#386612yes—
194C2×C4C22⋊#386612yes—
195C8—1484no—
196C22—22no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—742no—
202C22—742no—
203C22—744no—
204C22—1482no—
205C22—1482no—
206C22—1482no—
207C22—1482no—
208C22—1482no—
209C22C2×C22⋊#386611yescharacteristic
210C22C2×C22⋊#386611yescharacteristic
211C22C2×C22⋊#386611yescharacteristic
212C4—22no—
213C4—22no—
214C4—374no—
215C4—742no—
216C2—21no—
217C2—21no—
218C2—42no—
219C2—1482no—
220C2—1482no—
221C2#1455847411yescharacteristic
222C2#1455851912yes—
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×#10596962C2
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37#1785
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924597C2semidirect
2. C2×#11924596C2semidirect
3. #14558505C2semidirect
116. C37#1785semidirect

Maximal subgroups

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

subgroupindex
C2×#119245972
C2×#119245962
#145585052
C22×#105969622
#178537