Finite Group Databasebeta

← C2×#14557850 #18004494

Subgroups — C2×#14557850 #18004494

Order 4736.

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

normal subgroups only

This group has 512 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
1C2×#11924507C211yesmaximal, characteristic
2C2×C4⋊C4×D37C211yesmaximal, characteristic, complemented
3#14557850C218yesmaximal, direct product factor
4C2×#11924468C211yesmaximal, characteristic, complemented
5C2×#11924467C211yesmaximal, characteristic, complemented
6C2×#11924457C211yesmaximal, characteristic, complemented
7C2×#11924448C211yesmaximal, characteristic, complemented
8C2×#102×C37C211yesmaximal, characteristic, complemented
9C22×C22⋊D37—21no—
10C22×C4×D37—21no—
11C22×C4×D37C2211yescharacteristic
12C22×#64436C2211yescharacteristic
13#11924507—22no—
14#11924507C2214yes—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936—21no—
18C4⋊C4×D37—22no—
19C4⋊C4×D37C2214yescomplemented
20C2×C22⋊Dic37—21no—
21#11924468C2214yescomplemented
22#11924467C2214yescomplemented
23#11924457C2214yescomplemented
24#11924448C2214yescomplemented
25C22×D4×C37C2211yescharacteristic
26C22×C8×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28#102×C37C2214yescomplemented
29C24×C37—21no—
30C23×D37D411yescharacteristic
31C2×D4×C37—21no—
32C2×D4×C37—22no—
33C2×D4×C37—22no—
34C2×D4×C37C2312yes—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—24no—
38C2×C22⋊D37—44no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41C22×Dic37D411yescharacteristic
42C2×C4×D37—22no—
43C2×C4×D37—22no—
44C2×C4×D37—24no—
45C2×C4×D37—44no—
46C2×C4×D37D412yes—
47C2×C4×D37C2312yes—
48C2×C8×C37—22no—
49C2×C8×C37C2312yes—
50C4⋊C4×C37—21no—
51C4⋊C4×C37C2312yes—
52C22⋊Dic37—24no—
53C4⋊Dic37—21no—
54C4⋊Dic37—21no—
55C4⋊Dic37C2312yes—
56C4⋊Dic37C2312yes—
57#10596936—24no—
58C2×#64436—22no—
59C2×#64436C2312yes—
60C23×C37—22no—
61C23×C37—42no—
62C23×C37—42no—
63C23×C37—42no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66C22×D37—22no—
67C22×D37SD1614yes—
68C22×D37C2×D412yes—
69D4×C37—22no—
70D4×C37—22no—
71D4×C37—42no—
72C2×C4×C37—22no—
73C2×C4×C37—42no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37#4112yes—
76C2×C4×C37#4112yes—
77C2×C4×C37C2411yescharacteristic
78C22⋊D37—48no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—42no—
83C2×Dic37—42no—
84C2×Dic37C2×D412yes—
85C4×D37—24no—
86C4×D37—22no—
87C4×D37—22no—
88C4×D37—48no—
89C8×C37—22no—
90#64436—22no—
91C22×C37—42no—
92C22×C37—42no—
93C22×C37—42no—
94C22×C37—84no—
95C22×C37#12312yes—
96C22×C37C2×SD1612yes—
97C22×C37AGL(1,ℤ/8)12yes—
98C22×C37C22×D411yescharacteristic
99C2×D37—22no—
100C2×D37—22no—
101C2×D37—28no—
102C2×D37C2×SD1614yes—
103C4×C37—42no—
104C4×C37#12312yes—
105C4×C37C2×#4111yescharacteristic
106C4×C37C2×#4111yescharacteristic
107Dic37—22no—
108Dic37—42no—
109Dic37—42no—
110C2×#481—371nomaximal, Sylow
111C2×C37—82no—
112C2×C37#48114yescomplemented
113C2×C37C2×#12311yescharacteristic
114C2×C37C22×SD1611yescharacteristic
115C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
116D37—24no—
117C2×#121—371no—
118C22×C4⋊C4—371no—
119#481—378no—
120C2×#106—371no—
121C2×#106—371no—
122C2×#102—371no—
123C2×#102D3711yescharacteristic, complemented
124C2×C22⋊C8—371no—
125C37C2×#48111yescharacteristic, complemented, Sylow
126C22×D4—741no—
127C22×D4C2×D3711yescharacteristic
128C23×C4—371no—
129C23×C4—741no—
130C22×C8—371no—
131C22×C8C2×D3711yescharacteristic
132#121—374no—
133#121—742no—
134C2×C4⋊C4—371no—
135C2×C4⋊C4—371no—
136C2×C4⋊C4—374no—
137C2×C4⋊C4—742no—
138C2×C4⋊C4—741no—
139C2×C4⋊C4C2×D3711yescharacteristic
140C2×C22⋊C4—741no—
141#106—374no—
142#106—374no—
143#102—374no—
144#102C2×D3714yescomplemented
145C22⋊C8—374no—
146C24—21no—
147C24—371no—
148C2×D4—22no—
149C2×D4—21no—
150C2×D4—22no—
151C2×D4—744no—
152C2×D4—1484no—
153C2×D4C22×D3712yes—
154C22×C4—21no—
155C22×C4—371no—
156C22×C4—372no—
157C22×C4—372no—
158C22×C4—744no—
159C22×C4—742no—
160C22×C4—742no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—1484no—
164C22×C4C22×D3711yescharacteristic
165C2×C8—22no—
166C2×C8—372no—
167C2×C8—742no—
168C2×C8C22×D3712yes—
169C4⋊C4—21no—
170C4⋊C4—372no—
171C4⋊C4—372no—
172C4⋊C4—744no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C4⋊C4C22×D3712yes—
176C22⋊C4—744no—
177C23—22no—
178C23—42no—
179C23—42no—
180C23—42no—
181C23—374no—
182C23—372no—
183C23—742no—
184C23—742no—
185C23D4×D3711yescharacteristic
186D4—22no—
187D4—22no—
188D4—42no—
189D4—1488no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—372no—
193C2×C4—742no—
194C2×C4—744no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—1488no—
200C2×C4—1482no—
201C2×C4—1482no—
202C2×C4#1059696212yes—
203C2×C4D4×D3711yescharacteristic
204C2×C4#1059696412yes—
205C2×C4C23×D3711yescharacteristic
206C8—22no—
207C8—742no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—84no—
212C22—374no—
213C22—742no—
214C22—742no—
215C22—748no—
216C22#1192451812yes—
217C22SD16×D3712yes—
218C22#1192456012yes—
219C22C2×D4×D3711yescharacteristic
220C4—42no—
221C4—742no—
222C4—1482no—
223C4—1482no—
224C4#1192451812yes—
225C4C2×#1059696411yescharacteristic
226C4C2×#1059696211yescharacteristic
227C2—82no—
228C2—744no—
229C2#1455785014yesdirect product factor
230C2C2×#1192451811yescharacteristic
231C2C2×SD16×D3711yescharacteristic
232C2C2×#1192456011yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC23×C37C2×D4
prime radicalC2×#11924507C2
hypercenterC2×#102D37
hypocenterC37C2×#481
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
2. C2×C4⋊C4×D37C2semidirect
3. #14557850C2direct (N × H)
4. C2×#11924468C2semidirect
5. C2×#11924467C2semidirect
6. C2×#11924457C2semidirect
7. C2×#11924448C2semidirect
8. C2×#102×C37C2semidirect
19. C4⋊C4×D37C22semidirect
21. #11924468C22semidirect
22. #11924467C22semidirect
23. #11924457C22semidirect
24. #11924448C22semidirect
28. #102×C37C22semidirect
112. C2×C37#481semidirect
123. C2×#102D37semidirect
125. C37C2×#481semidirect
144. #102C2×D37semidirect
229. C2#14557850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245072
C2×C4⋊C4×D372
#145578502
C2×#119244682
C2×#119244672
C2×#119244572
C2×#119244482
C2×#102×C372
C2×#48137