Finite Group Databasebeta

← C2×#14557764 #18004158

Subgroups — C2×#14557764 #18004158

Order 4736.

564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10596941C211yesmaximal, characteristic, complemented
2C23×#64436C211yesmaximal, characteristic, complemented
3C2×#11924510C211yesmaximal, characteristic
4#14557764C218yesmaximal, direct product factor
5C2×#11924467C211yesmaximal, characteristic, complemented
6C2×#11924460C211yesmaximal, characteristic, complemented
7C2×#11924456C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C37C211yesmaximal, characteristic, complemented
9C22×D148C2211yescharacteristic
10C22×C22⋊D37—21no—
11C2×#10596941—24no—
12C2×#10596941C2214yescomplemented
13C22×#64436—24no—
14C22×#64436C2211yescharacteristic
15C22×#64436C2211yescharacteristic
16C22×#64436C2214yescomplemented
17#11924510—22no—
18#11924510C2214yes—
19C2×C4⋊Dic37C2211yescharacteristic
20C2×#10596938—21no—
21#11924467C2214yescomplemented
22#11924460C2214yescomplemented
23#11924456C2214yescomplemented
24C22×Q8×C37C2211yescharacteristic
25C23×C4×C37C2211yescharacteristic
26C22⋊Q8×C37—22no—
27C22⋊Q8×C37C2214yescomplemented
28C2×C4⋊C4×C37—21no—
29C2×C4⋊C4×C37C2211yescharacteristic
30C2×C22⋊C4×C37—21no—
31C24×C37D411yescharacteristic
32C23×D37—21no—
33C2×Q8×C37—21no—
34C2×Q8×C37—22no—
35C2×Q8×C37—22no—
36C2×Q8×C37C2312yes—
37C22×C4×C37—22no—
38C22×C4×C37—22no—
39C22×C4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37D411yescharacteristic
42C22×C4×C37D412yes—
43C22×C4×C37C2312yes—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—24no—
46C2×C22⋊D37—44no—
47C22×Dic37—21no—
48C2×D148—22no—
49C2×D148—22no—
50C2×D148—21no—
51C2×D148C2312yes—
52C4⋊C4×C37—24no—
53C4⋊C4×C37—21no—
54C4⋊C4×C37C2312yes—
55C22⋊C4×C37—24no—
56#10596941—28no—
57#10596938—24no—
58C4⋊Dic37—21no—
59C4⋊Dic37C2312yes—
60C2×#64436—22no—
61C2×#64436—28no—
62C2×#64436D414yescomplemented
63C2×#64436C2312yes—
64C2×#64436C2312yes—
65C23×C37—22no—
66C23×C37—22no—
67C23×C37SD1614yescomplemented
68C23×C37C2×D412yes—
69C23×C37C2×D411yescharacteristic
70C22×D37—22no—
71C22×D37—42no—
72C22×D37—42no—
73C22×D37—42no—
74Q8×C37—22no—
75Q8×C37—22no—
76Q8×C37—42no—
77C2×C4×C37—22no—
78C2×C4×C37—24no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—42no—
84C2×C4×C37—42no—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D412yes—
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37#4112yes—
89C2×C4×C37C2411yescharacteristic
90C22⋊D37—48no—
91C2×Dic37—22no—
92C2×Dic37—42no—
93D148—22no—
94D148—22no—
95D148—42no—
96#64436—22no—
97#64436C2×D414yescomplemented
98C22×C37—22no—
99C22×C37—22no—
100C22×C37—28no—
101C22×C37#12112yes—
102C22×C37C2×SD1612yes—
103C22×C37C2×SD1614yescomplemented
104C22×C37#13512yes—
105C22×C37C22×D411yescharacteristic
106C2×D37—42no—
107C2×D37—42no—
108C2×D37—42no—
109C2×D37—84no—
110C4×C37—22no—
111C4×C37—42no—
112C4×C37—42no—
113C4×C37#12112yes—
114C4×C37C22×D411yescharacteristic
115C4×C37C2×#4111yescharacteristic
116Dic37—42no—
117C2×#465—371nomaximal, Sylow
118C2×C37—24no—
119C2×C37#46514yescomplemented
120C2×C37C2×#12111yescharacteristic
121C2×C37C22×SD1611yescharacteristic
122C2×C37C2×#13511yescharacteristic
123D37—82no—
124C22×SD16—371no—
125C23×C8—371no—
126C2×C22⋊Q8D3711yescharacteristic, complemented
127C2×#121—371no—
128#465—378no—
129C2×#106—371no—
130C2×#103—371no—
131C2×#102—371no—
132C37C2×#46511yescharacteristic, complemented, Sylow
133C22×Q8C2×D3711yescharacteristic
134C22×D4—371no—
135C22×D4—741no—
136C23×C4C2×D3711yescharacteristic
137C2×SD16—374no—
138C2×SD16—744no—
139C22×C8—371no—
140C22×C8—371no—
141C22×C8—374no—
142C22×C8—744no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D3714yescomplemented
145#121—374no—
146#121—742no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—741no—
152#106—374no—
153#103—374no—
154#102—374no—
155C24—741no—
156C24C22⋊D3711yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D3712yes—
161C2×D4—372no—
162C2×D4—744no—
163C2×D4—742no—
164C2×D4—742no—
165C2×D4—741no—
166C2×D4—1484no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—741no—
172C22×C4C22⋊D3712yes—
173C22×C4C22⋊D3711yescharacteristic
174C22×C4C22×D3712yes—
175C22×C4C22×D3711yescharacteristic
176SD16—748no—
177C2×C8—374no—
178C2×C8—372no—
179C2×C8—372no—
180C2×C8—748no—
181C2×C8—742no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—372no—
185C4⋊C4—741no—
186C4⋊C4C22×D3712yes—
187C22⋊C4—24no—
188C22⋊C4—744no—
189C23—22no—
190C23—22no—
191C23—742no—
192C23—1482no—
193C23—1482no—
194C23—1482no—
195C23#1059694114yescomplemented
196C23C2×C22⋊D3712yes—
197C23C2×C22⋊D3711yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—742no—
202D4—742no—
203D4—1488no—
204D4—1482no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—742no—
214C2×C4—1482no—
215C2×C4D4×D3712yes—
216C2×C4#1059696412yes—
217C2×C4C2×C22⋊D3712yes—
218C2×C4C2×C22⋊D3711yescharacteristic
219C2×C4C23×D3711yescharacteristic
220C8—374no—
221C8—742no—
222C22—28no—
223C22—22no—
224C22—22no—
225C22—2964no—
226C22—1482no—
227C22—1482no—
228C22—1482no—
229C22#1192450812yes—
230C22C2×#1059694112yes—
231C22C2×#1059694114yescomplemented
232C22#1192455612yes—
233C22C22×C22⋊D3711yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—1482no—
238C4#1192450812yes—
239C4C2×D4×D3711yescharacteristic
240C4C2×#1059696411yescharacteristic
241C2—24no—
242C2—2962no—
243C2#1455776414yesdirect product factor
244C2C2×#1192450811yescharacteristic
245C2C22×#1059694111yescharacteristic
246C2C2×#1192455611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C22⋊Q8×C37C2
socleC23×C37C2×D4
prime radicalC2×#11924510C2
hypercenterC2×C22⋊Q8D37
hypocenterC37C2×#465
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10596941C2semidirect
2. C23×#64436C2semidirect
4. #14557764C2direct (N × H)
5. C2×#11924467C2semidirect
6. C2×#11924460C2semidirect
7. C2×#11924456C2semidirect
8. C2×C22⋊Q8×C37C2semidirect
12. C2×#10596941C22semidirect
16. C22×#64436C22semidirect
21. #11924467C22semidirect
22. #11924460C22semidirect
23. #11924456C22semidirect
27. C22⋊Q8×C37C22semidirect
62. C2×#64436D4semidirect
67. C23×C37SD16semidirect
97. #64436C2×D4semidirect
103. C22×C37C2×SD16semidirect
119. C2×C37#465semidirect
126. C2×C22⋊Q8D37semidirect
132. C37C2×#465semidirect
144. C22⋊Q8C2×D37semidirect
195. C23#10596941semidirect
231. C22C2×#10596941semidirect
243. C2#14557764direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969412
C23×#644362
C2×#119245102
#145577642
C2×#119244672
C2×#119244602
C2×#119244562
C2×C22⋊Q8×C372
C2×#46537