Finite Group Databasebeta

← #18004060

Subgroups — #18004060

Order 4736.

548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11924562C212yesmaximal, complemented
2#14558083C211yesmaximal, characteristic, complemented
3#14557748C214yesmaximal, complemented
4#14557738C212yesmaximal, complemented
5#14557728C212yesmaximal, complemented
6#14557557C211yesmaximal, characteristic, complemented
7#14557532C212yesmaximal, complemented
8C2×C4×D4×C37C211yesmaximal, characteristic, complemented
9C2×#10596962C2212yes—
10#11924562—28no—
11C2×#10596940C2214yes—
12C2×#10596939C2214yes—
13C2×#10596934C2212yes—
14#11924536C2211yescharacteristic, complemented
15#11924533C2211yescharacteristic, complemented
16#11924524C2212yescomplemented
17#11924510—21no—
18#11924510—21no—
19C4×D148—21no—
20C4×D148—21no—
21C4⋊#64436C2212yescomplemented
22C4⋊#64436C2212yescomplemented
23#11924459C2214yescomplemented
24#11924456C2214yescomplemented
25C22×D4×C37C2211yescharacteristic
26C23×C4×C37—21no—
27C4×D4×C37—21no—
28C4×D4×C37—21no—
29C4×D4×C37C2212yes—
30C4×D4×C37C2212yes—
31C2×C4⋊C4×C37C2211yescharacteristic
32C2×C22⋊C4×C37—21no—
33C2×C42×C37C2211yescharacteristic
34C24×C37—21no—
35C2×D4×C37—21no—
36C2×D4×C37—22no—
37C2×D4×C37D414yescomplemented
38C2×D4×C37C2312yes—
39C22×C4×C37—21no—
40C22×C4×C37—22no—
41C22×C4×C37—22no—
42C22×C4×C37—44no—
43C22×C4×C37D411yescharacteristic
44C22×C4×C37D411yescharacteristic
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—22no—
47#10596962—24no—
48#10596962—24no—
49C2×D148—21no—
50C2×D148—21no—
51C2×D148C2312yes—
52C2×C4×D37—22no—
53C2×Dic74C2312yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37C2312yes—
56C22⋊C4×C37—22no—
57C22⋊C4×C37—22no—
58C42×C37D411yescharacteristic
59C42×C37D411yescharacteristic
60C42×C37C2311yescharacteristic
61C42×C37C2311yescharacteristic
62#10596940—28no—
63#10596939—28no—
64#10596938—22no—
65#10596938—22no—
66C4⋊Dic37—21no—
67C4⋊Dic37—21no—
68#10596934—24no—
69C2×#64436C2314yes—
70C23×C37—24no—
71C23×C37—22no—
72C23×C37—42no—
73C23×C37—42no—
74C23×C37C2×D411yescharacteristic
75C22×D37—22no—
76D4×C37—24no—
77D4×C37—22no—
78D4×C37C2×D414yes—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—41no—
82C2×C4×C37—44no—
83C2×C4×C37—42no—
84C2×C4×C37—44no—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37#4112yes—
92C2×C4×C37C2411yescharacteristic
93C22⋊D37—44no—
94C2×Dic37—22no—
95D148—22no—
96D148—22no—
97D148—42no—
98D148—42no—
99C4×D37—44no—
100Dic74—22no—
101Dic74—22no—
102#64436—24no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37—24no—
106C22×C37—48no—
107C22×C37—42no—
108C22×C37—42no—
109C22×C37#12112yes—
110C22×C37C22×D411yescharacteristic
111C2×D37—42no—
112C2×D37—42no—
113C2×D37—42no—
114C4×C37—21no—
115C4×C37—21no—
116C4×C37—21no—
117C4×C37—42no—
118C4×C37#12112yes—
119C4×C37AGL(1,ℤ/8)12yescomplemented
120C4×C37C22×D411yescharacteristic
121C4×C37C2×#4111yescharacteristic
122Dic37—42no—
123#3036—371nomaximal, Sylow
124C2×C37—22no—
125C2×C37—44no—
126C2×C37C2×#12111yescharacteristic
127C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C37#57511yescharacteristic
129D37—82no—
130C2×AGL(1,ℤ/8)—372no—
131#532—371no—
132C2×C4×D4D3711yescharacteristic, complemented
133#463—374no—
134#461—372no—
135#459—372no—
136#423—371no—
137#417—372no—
138C37#303611yescharacteristic, complemented, Sylow
139C2×#41—372no—
140C22×D4C2×D3711yescharacteristic
141C23×C4—21no—
142AGL(1,ℤ/8)—748no—
143C2×SD16—374no—
144C2×D8—374no—
145C2×M16—372no—
146C4⋊Q8—371no—
147#127—371no—
148#124—372no—
149#121—741no—
150#121—741no—
151C4×D4—21no—
152C4×D4—21no—
153C4×D4—741no—
154C4×D4—741no—
155C4×D4C2×D3712yes—
156C4×D4C2×D3712yes—
157C2×C4⋊C4C2×D3711yescharacteristic
158C2×C22⋊C4—21no—
159C2×C42C2×D3711yescharacteristic
160C4⋊C8—372no—
161C4⋊C8—372no—
162#103—374no—
163#102—374no—
164C24—21no—
165#41—744no—
166#41—744no—
167C2×Q8—372no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—372no—
171C2×D4—742no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4D14814yescomplemented
175C2×D4C22×D3712yes—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—44no—
180C22×C4—742no—
181C22×C4C22⋊D3711yescharacteristic
182C22×C4C22⋊D3711yescharacteristic
183C22×C4C22×D3711yescharacteristic
184SD16—748no—
185D8—748no—
186M16—744no—
187C2×C8—374no—
188C4⋊C4—21no—
189C4⋊C4—741no—
190C4⋊C4—741no—
191C4⋊C4C22×D3712yes—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—742no—
195C22⋊C4—742no—
196C42C22⋊D3711yescharacteristic
197C42C22⋊D3711yescharacteristic
198C42C22×D3711yescharacteristic
199C42C22×D3711yescharacteristic
200C23—24no—
201C23—22no—
202C23—42no—
203C23—42no—
204C23—742no—
205C23C2×C22⋊D3711yescharacteristic
206Q8—742no—
207Q8—742no—
208D4—24no—
209D4—22no—
210D4—742no—
211D4—742no—
212D4—1482no—
213D4—1484no—
214D4—1482no—
215D4C2×D14814yes—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—742no—
223C2×C4—1484no—
224C2×C4C2×D14812yes—
225C2×C4#1059696212yes—
226C2×C4C2×C22⋊D3711yescharacteristic
227C2×C4C2×C22⋊D3711yescharacteristic
228C2×C4C2×C22⋊D3711yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C2×C4C2×C22⋊D3711yescharacteristic
231C2×C4C23×D3711yescharacteristic
232C8—744no—
233C22—21no—
234C22—21no—
235C22—24no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—1482no—
240C22—1482no—
241C22—1482no—
242C22#1192451012yes—
243C22C22×C22⋊D3711yescharacteristic
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—1482no—
249C4#1192451012yes—
250C4#1192456212yescomplemented
251C4C22×D14811yescharacteristic
252C4C2×#1059696211yescharacteristic
253C2—22no—
254C2—44no—
255C2—2962no—
256C2C2×#1192451011yescharacteristic
257C2C2×#1192456211yescharacteristic
258C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C4×D4×C37C2
socleC22×C37C22×D4
hypercenterC2×C4×D4D37
hypocenterC37#3036
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. #14558083C2semidirect
3. #14557748C2semidirect
4. #14557738C2semidirect
5. #14557728C2semidirect
6. #14557557C2semidirect
7. #14557532C2semidirect
8. C2×C4×D4×C37C2semidirect
14. #11924536C22semidirect
15. #11924533C22semidirect
16. #11924524C22semidirect
21. C4⋊#64436C22semidirect
22. C4⋊#64436C22semidirect
23. #11924459C22semidirect
24. #11924456C22semidirect
37. C2×D4×C37D4semidirect
119. C4×C37AGL(1,ℤ/8)semidirect
132. C2×C4×D4D37semidirect
138. C37#3036semidirect
174. C2×D4D148semidirect
250. C4#11924562semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145580832
#145577482
#145577382
#145577282
#145575572
#145575322
C2×C4×D4×C372
#303637