Finite Group Databasebeta

← C2×#14557785 #18004191

Subgroups — C2×#14557785 #18004191

Order 4736.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10596939C211yesmaximal, characteristic, complemented
2C22×#10596929C211yesmaximal, characteristic, complemented
3C2×#11924511C211yesmaximal, characteristic, complemented
4C2×#11924507C211yesmaximal, characteristic, complemented
5#14557785C218yesmaximal, direct product factor
6C2×#11924467C211yesmaximal, characteristic, complemented
7C2×#11924458C211yesmaximal, characteristic, complemented
8C2×#102×C37C211yesmaximal, characteristic, complemented
9C22×D148—21no—
10C22×D148C2211yescharacteristic
11C22×C22⋊D37—21no—
12C22×C4×D37C2211yescharacteristic
13C2×#10596939—24no—
14C2×#10596939C2214yescomplemented
15C2×#10596929—24no—
16C2×#10596929C2214yescomplemented
17C22×#64436C2211yescharacteristic
18#11924511—22no—
19#11924511C2214yescomplemented
20#11924507—22no—
21#11924507C2214yescomplemented
22C2×C4⋊Dic37C2211yescharacteristic
23C2×C22⋊Dic37—21no—
24C2×#10596938—21no—
25#11924467C2214yescomplemented
26#11924458C2214yescomplemented
27C22×D4×C37C2211yescharacteristic
28C22×C8×C37C2211yescharacteristic
29C2×C4⋊C4×C37C2211yescharacteristic
30#102×C37C2214yescomplemented
31C24×C37—21no—
32C23×D37—21no—
33C23×D37D411yescharacteristic
34C2×D4×C37—22no—
35C2×D4×C37—21no—
36C2×D4×C37—22no—
37C2×D4×C37C2312yes—
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—24no—
41C2×C22⋊D37—44no—
42C22×Dic37—21no—
43C22×Dic37D411yescharacteristic
44C2×D148—22no—
45C2×D148—22no—
46C2×D148—24no—
47C2×D148—21no—
48C2×D148—44no—
49C2×D148C2312yes—
50C2×C4×D37—22no—
51C2×C4×D37—22no—
52C2×C4×D37D412yes—
53C2×C4×D37C2312yes—
54C2×C8×C37—22no—
55C2×C8×C37C2312yes—
56C4⋊C4×C37—21no—
57C4⋊C4×C37C2312yes—
58C22⋊Dic37—24no—
59#10596939—28no—
60#10596938—24no—
61C4⋊Dic37—21no—
62C4⋊Dic37C2312yes—
63C2×#64436D414yescomplemented
64C2×#64436C2312yes—
65#10596929—28no—
66C23×C37—22no—
67C23×C37—42no—
68C23×C37—42no—
69C23×C37—42no—
70C23×C37C2×D411yescharacteristic
71C22×D37—22no—
72C22×D37—22no—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37—42no—
76C22×D37—42no—
77C22×D37—42no—
78C22×D37C2×D412yes—
79D4×C37—22no—
80D4×C37—22no—
81D4×C37—42no—
82C2×C4×C37—22no—
83C2×C4×C37—42no—
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D412yes—
86C2×C4×C37#4112yes—
87C2×C4×C37C2411yescharacteristic
88C22⋊D37—48no—
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—42no—
92C2×Dic37C2×D412yes—
93D148—22no—
94D148—22no—
95D148—48no—
96D148—42no—
97C4×D37—24no—
98C4×D37—22no—
99C4×D37—22no—
100C8×C37—22no—
101#64436C2×D414yescomplemented
102C22×C37—42no—
103C22×C37—42no—
104C22×C37—42no—
105C22×C37—84no—
106C22×C37#12112yes—
107C22×C37AGL(1,ℤ/8)12yes—
108C22×C37AGL(1,ℤ/8)12yes—
109C22×C37C22×D411yescharacteristic
110C2×D37—22no—
111C2×D37—22no—
112C2×D37—22no—
113C2×D37—44no—
114C2×D37—42no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—84no—
118C4×C37—42no—
119C4×C37#12112yes—
120C4×C37C22×D411yescharacteristic
121C4×C37C2×#4111yescharacteristic
122Dic37—22no—
123Dic37—42no—
124C2×#469—371nomaximal, Sylow
125C2×C37—82no—
126C2×C37#46914yescomplemented
127C2×C37C2×#12111yescharacteristic
128C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
130D37—42no—
131D37—82no—
132C22×D8—371no—
133C22×M16—371no—
134C2×#121—371no—
135C2×#121—371no—
136#469—378no—
137C2×#106—371no—
138C2×#102—371no—
139C2×#102D3711yescharacteristic, complemented
140C37C2×#46911yescharacteristic, complemented, Sylow
141C22×D4—371no—
142C22×D4—741no—
143C22×D4—741no—
144C22×D4C2×D3711yescharacteristic
145C23×C4—371no—
146C2×D8—374no—
147C2×D8—744no—
148C2×M16—374no—
149C2×M16—744no—
150C22×C8—371no—
151C22×C8C2×D3711yescharacteristic
152#121—374no—
153#121—374no—
154#121—742no—
155#121—742no—
156C2×C4⋊C4—371no—
157C2×C4⋊C4C2×D3711yescharacteristic
158C2×C22⋊C4—741no—
159C2×C22⋊C4—741no—
160#106—374no—
161#102—374no—
162#102C2×D3714yescomplemented
163C24—21no—
164C24—371no—
165C24—741no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—21no—
169C2×D4—372no—
170C2×D4—744no—
171C2×D4—744no—
172C2×D4—742no—
173C2×D4—742no—
174C2×D4—741no—
175C2×D4—1484no—
176C2×D4—1484no—
177C2×D4C22×D3712yes—
178C22×C4—21no—
179C22×C4—371no—
180C22×C4—372no—
181C22×C4—372no—
182C22×C4—742no—
183C22×C4—742no—
184C22×C4—741no—
185C22×C4C22×D3711yescharacteristic
186D8—748no—
187M16—748no—
188C2×C8—22no—
189C2×C8—374no—
190C2×C8—372no—
191C2×C8C22×D3712yes—
192C4⋊C4—21no—
193C4⋊C4—372no—
194C4⋊C4—741no—
195C4⋊C4C22×D3712yes—
196C22⋊C4—744no—
197C22⋊C4—744no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—372no—
203C23—742no—
204C23—742no—
205C23—742no—
206C23—742no—
207C23—1482no—
208C23—1482no—
209C23—1482no—
210C23D4×D3711yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—742no—
215D4—742no—
216D4—1488no—
217D4—1488no—
218D4—1482no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—372no—
222C2×C4—742no—
223C2×C4—744no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—742no—
227C2×C4—1482no—
228C2×C4#1059696212yes—
229C2×C4D4×D3711yescharacteristic
230C2×C4D4×D3712yes—
231C2×C4C23×D3711yescharacteristic
232C8—22no—
233C8—374no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—2964no—
239C22—742no—
240C22—742no—
241C22—742no—
242C22—1482no—
243C22—1482no—
244C22—1482no—
245C22—1484no—
246C22#1192450912yes—
247C22#1192456012yes—
248C22#1192456312yes—
249C22C2×D4×D3711yescharacteristic
250C4—42no—
251C4—742no—
252C4—1482no—
253C4#1192450912yes—
254C4C2×D4×D3711yescharacteristic
255C4C2×#1059696211yescharacteristic
256C2—82no—
257C2—2962no—
258C2—1482no—
259C2#1455778514yesdirect product factor
260C2C2×#1192450911yescharacteristic
261C2C2×#1192456011yescharacteristic
262C2C2×#1192456311yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC23×C37C2×D4
hypercenterC2×#102D37
hypocenterC37C2×#469
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#10596939C2semidirect
2. C22×#10596929C2semidirect
3. C2×#11924511C2semidirect
4. C2×#11924507C2semidirect
5. #14557785C2direct (N × H)
6. C2×#11924467C2semidirect
7. C2×#11924458C2semidirect
8. C2×#102×C37C2semidirect
14. C2×#10596939C22semidirect
16. C2×#10596929C22semidirect
19. #11924511C22semidirect
21. #11924507C22semidirect
25. #11924467C22semidirect
26. #11924458C22semidirect
30. #102×C37C22semidirect
63. C2×#64436D4semidirect
101. #64436C2×D4semidirect
126. C2×C37#469semidirect
139. C2×#102D37semidirect
140. C37C2×#469semidirect
162. #102C2×D37semidirect
259. C2#14557785direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969392
C22×#105969292
C2×#119245112
C2×#119245072
#145577852
C2×#119244672
C2×#119244582
C2×#102×C372
C2×#46937