Finite Group Databasebeta

← #18010622

Subgroups — #18010622

Order 4736.

390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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×D37⋊M16C211yesmaximal, characteristic, complemented
2C2×#11924596C212yesmaximal, complemented
3#14558505C211yesmaximal, characteristic, complemented
4#14558413C212yesmaximal, complemented
5C2×#11924509C211yesmaximal, characteristic
6C2×#10596953—21no—
7D37⋊M16—24no—
8C2×#10596957C2212yes—
9C2×#10596957C2212yes—
10C2×D37⋊C8—21no—
11#11924596—24no—
12#11924593—21no—
13#11924593—21no—
14C22×D148C411yescharacteristic
15C22×C22⋊D37C411yescharacteristic
16C22×C22⋊D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18#11924509—21no—
19#11924509—21no—
20#11924509—21no—
21#11924509—21no—
22C2×#10596936C2211yescharacteristic
23C2×#10596938C411yescharacteristic
24C2×C22⋊C4×C37C411yescharacteristic
25C24×C37C2×C411yescharacteristic
26C23×D37C2×C411yescharacteristic
27C23×D37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—22no—
35C2×C22⋊D37—22no—
36C2×C22⋊D37—42no—
37C22×Dic37C2×C411yescharacteristic
38C22×Dic37C2311yescharacteristic
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—42no—
42C2×C4×D37—22no—
43C2×C4×D37—22no—
44C2×C4×D37D411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37D411yescharacteristic
47C2×C4×D37D411yescharacteristic
48#10596957—22no—
49#10596957—22no—
50#10596957—22no—
51#10596957D414yescomplemented
52C2×#64438—22no—
53C2×#64438—22no—
54#10596953—24no—
55D37⋊C8—24no—
56C22⋊C4×C37—21no—
57C22⋊C4×C37—21no—
58#10596938—21no—
59#10596938—21no—
60#10596936—21no—
61#10596936—21no—
62C23×C37—21no—
63C23×C37—22no—
64C23×C37—41no—
65C23×C37—41no—
66C23×C37C22×C411yescharacteristic
67C22×D37—22no—
68C22×D37—22no—
69C22×D37—21no—
70C22×D37—22no—
71C22×D37—41no—
72C22×D37—41no—
73C22×D37—41no—
74C22×D37C22⋊C411yescharacteristic
75C22×D37C22⋊C411yescharacteristic
76C2×C4×C37—22no—
77C2×C4×C37—21no—
78C2×C4×C37—41no—
79C2×C4×C37C22⋊C411yescharacteristic
80C2×C4×C37C22⋊C411yescharacteristic
81C22⋊D37—42no—
82C22⋊D37—42no—
83C22⋊D37—41no—
84C22⋊D37—42no—
85C22⋊D37—41no—
86C2×Dic37—21no—
87C2×Dic37—41no—
88C2×Dic37C2×D412yes—
89C2×Dic37C2×D411yescharacteristic
90C2×Dic37C2×D411yescharacteristic
91C2×Dic37#4112yes—
92D148—42no—
93D148—42no—
94C4×D37—21no—
95C4×D37—21no—
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—21no—
99C4×D37—21no—
100#64438—24no—
101#64438—42no—
102C22×C37—21no—
103C22×C37—21no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37—82no—
108C22×C37C2×C22⋊C411yescharacteristic
109C22×C37C4×D412yes—
110C2×D37—21no—
111C2×D37—21no—
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—44no—
116C2×D37—41no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—82no—
120C2×D37#10012yescomplemented
121C4×C37—21no—
122C4×C37—21no—
123C4×C37—41no—
124Dic37—41no—
125Dic37#12011yescharacteristic
126Dic37#12112yes—
127Dic37#12311yescharacteristic
128#1900—371nomaximal, Sylow
129C2×C37—22no—
130C2×C37—81no—
131C2×C37#38611yescharacteristic
132C2×C37C2×#10011yescharacteristic
133C2×C37#41311yescharacteristic
134D37—22no—
135D37—41no—
136D37—81no—
137C22×M16—371no—
138C2×#121—371no—
139C2×#100—372no—
140#407—371no—
141#343—372no—
142C37#190011yescharacteristic, complemented, Sylow
143C22×D4—371no—
144C22×D4—371no—
145C22×D4—371no—
146C23×C4—371no—
147C2×M16—372no—
148C2×M16—372no—
149C2×M16—744no—
150C2×M16—741no—
151C22×C8—741no—
152#121—741no—
153#121—741no—
154#121—741no—
155#121—741no—
156C2×C4⋊C4—371no—
157C2×C22⋊C4—371no—
158C2×C22⋊C4#386611yescharacteristic
159#100—744no—
160C22⋊C8—741no—
161C22⋊C8—741no—
162C24—371no—
163C24—371no—
164C24C2×#386611yescharacteristic
165C2×D4—741no—
166C2×D4—741no—
167C2×D4—742no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—742no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—1482no—
174C2×D4—1482no—
175C22×C4—371no—
176C22×C4—371no—
177C22×C4—371no—
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—742no—
182C22×C4—742no—
183C22×C4C2×#386611yescharacteristic
184C22×C4C2×#386611yescharacteristic
185M16—374no—
186M16—742no—
187M16—744no—
188M16—742no—
189M16—742no—
190C2×C8—742no—
191C2×C8—744no—
192C2×C8—742no—
193C4⋊C4—741no—
194C4⋊C4—741no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—741no—
198C22⋊C4—741no—
199C23—21no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—371no—
204C23—371no—
205C23—742no—
206C23—742no—
207C23—742no—
208C23—741no—
209C23—1481no—
210C23—1481no—
211C23—1481no—
212C23C22×#386611yescharacteristic
213D4—1482no—
214D4—1482no—
215D4—1481no—
216D4—1482no—
217D4—1481no—
218D4—1482no—
219D4—1482no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—371no—
224C2×C4—371no—
225C2×C4—372no—
226C2×C4—372no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—742no—
230C2×C4—742no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—741no—
234C2×C4—1481no—
235C2×C4C22⋊#386611yescharacteristic
236C2×C4C22⋊#386611yescharacteristic
237C8—744no—
238C8—1482no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—372no—
246C22—2962no—
247C22—741no—
248C22—741no—
249C22—741no—
250C22—741no—
251C22—741no—
252C22—1484no—
253C22—1481no—
254C22—1481no—
255C22—1481no—
256C22C2×C22⋊#386611yescharacteristic
257C22D4×#386612yes—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—371no—
262C4—372no—
263C4—371no—
264C4—1481no—
265C2—22no—
266C2—81no—
267C2—2961no—
268C2—742no—
269C2—1481no—
270C2#1455848111yescharacteristic
271C2D37⋊#10011yescharacteristic
272C2#1455851911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924509C2
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1900
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D37⋊M16C2semidirect
2. C2×#11924596C2semidirect
3. #14558505C2semidirect
4. #14558413C2semidirect
51. #10596957D4semidirect
120. C2×D37#100semidirect
142. C37#1900semidirect

Maximal subgroups

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

subgroupindex
C2×D37⋊M162
C2×#119245962
#145585052
#145584132
C2×#119245092
#190037