Finite Group Databasebeta

← #18004768

Subgroups — #18004768

Order 4736.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#14558069C211yesmaximal, characteristic
2C2×Q8×Dic37C211yesmaximal, characteristic, complemented
3#14557866C211yesmaximal, characteristic, complemented
4#14557852C211yesmaximal, characteristic
5#14557838C212yesmaximal, complemented
6#14557757C212yesmaximal, complemented
7#14557672C211yesmaximal, characteristic
8#14557640C212yesmaximal, complemented
9#14557636C212yesmaximal, complemented
10#14557587C211yesmaximal, characteristic, complemented
11C37×#451C211yesmaximal, characteristic, complemented
12C2×#10596941C2212yes—
13#11924531—21no—
14#11924527C2211yescharacteristic
15#11924525C2211yescharacteristic
16#11924520—21no—
17#11924510C2211yescharacteristic
18Q8×Dic37—21no—
19Q8×Dic37—21no—
20Q8×Dic37C2212yes—
21Q8×Dic37C2212yes—
22Q8×Dic37C2211yescharacteristic
23#11924498C2211yescharacteristic
24#11924496—21no—
25#11924494—21no—
26C2×C4⋊Dic37—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×C4×Dic37—21no—
29C2×C4×Dic37C2211yescharacteristic
30#11924469C2212yes—
31#11924468C2212yes—
32#11924465C2212yes—
33#11924460C2212yes—
34#11924460C2212yes—
35#11924458C2212yes—
36C22⋊#64436C2211yescharacteristic
37#11924446C2212yes—
38C22×Q8×C37C2211yescharacteristic
39C2×Q16×C37C2212yes—
40C22⋊Q8×C37C2211yescharacteristic
41#103×C37C2212yes—
42C22⋊C8×C37C2211yescharacteristic
43C2×Q8×C37—24no—
44C2×Q8×C37—21no—
45C2×Q8×C37C2311yescharacteristic
46C2×Q8×C37C2312yes—
47C22×C4×C37—21no—
48C22×C4×C37C2311yescharacteristic
49C2×C22⋊D37—21no—
50C22×Dic37—21no—
51C22×Dic37D411yescharacteristic
52C22×Dic37D411yescharacteristic
53C2×D148C2311yescharacteristic
54C2×C4×D37—21no—
55Q16×C37—24no—
56C2×C8×C37C2312yes—
57C4⋊C4×C37—21no—
58C4⋊C4×C37C2311yescharacteristic
59C22⋊C4×C37—21no—
60#10596941—24no—
61#10596938—21no—
62#10596938—21no—
63#10596938—21no—
64#10596938—21no—
65C4⋊Dic37—21no—
66C4⋊Dic37—22no—
67C4⋊Dic37—22no—
68C4⋊Dic37—21no—
69C4⋊Dic37—21no—
70C4⋊Dic37C2312yes—
71C4⋊Dic37C2311yescharacteristic
72#10596936—21no—
73C4×Dic37—22no—
74C4×Dic37—22no—
75C4×Dic37—21no—
76C4×Dic37D411yescharacteristic
77C4×Dic37D411yescharacteristic
78C4×Dic37C2311yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81C23×C37C2×D411yescharacteristic
82C22×D37—21no—
83Q8×C37—24no—
84Q8×C37—22no—
85Q8×C37—22no—
86Q8×C37#4114yes—
87C2×C4×C37—24no—
88C2×C4×C37—22no—
89C2×C4×C37—22no—
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—42no—
95C2×Dic37—22no—
96C2×Dic37—22no—
97C2×Dic37—21no—
98C2×Dic37—41no—
99C2×Dic37—42no—
100C2×Dic37C2×D411yescharacteristic
101C2×Dic37C2×D411yescharacteristic
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D411yescharacteristic
104D148—22no—
105C4×D37—42no—
106C8×C37—22no—
107#64436—22no—
108C22×C37—21no—
109C22×C37—21no—
110C22×C37#13712yes—
111C22×C37C22×D411yescharacteristic
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C4×C37—24no—
116C4×C37—21no—
117C4×C37—41no—
118C4×C37—41no—
119C4×C37C2×#4112yes—
120Dic37—21no—
121Dic37—21no—
122Dic37—21no—
123Dic37—21no—
124Dic37—41no—
125Dic37—42no—
126#3117—371nomaximal, Sylow
127C2×C37—22no—
128C2×C37#52511yescharacteristic
129C2×C37C2×#13711yescharacteristic
130C2×C37#57511yescharacteristic
131D37—81no—
132#529—371no—
133C2×C4×Q8—371no—
134#484—371no—
135#481—371no—
136#479—372no—
137#464—372no—
138#451D3711yescharacteristic, complemented
139#448—371no—
140#441—372no—
141#440—372no—
142#432—371no—
143C37#311711yescharacteristic, complemented, Sylow
144C22×Q8C2×D3711yescharacteristic
145C2×Q16C2×D3712yes—
146C2×SD16—372no—
147#126—741no—
148#125—371no—
149#124—371no—
150#123—741no—
151C22⋊Q8C2×D3711yescharacteristic
152#121—371no—
153C4×Q8—372no—
154C4×Q8—372no—
155C4×Q8—371no—
156C4×Q8—741no—
157C4×Q8—741no—
158C4×D4—371no—
159C4×D4—741no—
160#117—741no—
161C2×C4⋊C4—371no—
162C2×C4⋊C4—741no—
163C2×C42—371no—
164C2×C42—741no—
165#107—372no—
166#106—372no—
167C4⋊C8—372no—
168#103—372no—
169#103—372no—
170#103C2×D3712yes—
171#102—372no—
172C22⋊C8—371no—
173C22⋊C8C2×D3711yescharacteristic
174#97—372no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8C22×D3711yescharacteristic
178C2×Q8C22×D3712yes—
179C2×D4—371no—
180C2×D4—741no—
181C22×C4—21no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4C22×D3711yescharacteristic
187Q16—24no—
188SD16—744no—
189C2×C8—372no—
190C2×C8C22×D3712yes—
191C4⋊C4—21no—
192C4⋊C4—372no—
193C4⋊C4—371no—
194C4⋊C4—741no—
195C4⋊C4—742no—
196C4⋊C4—742no—
197C4⋊C4—741no—
198C4⋊C4—741no—
199C4⋊C4—741no—
200C4⋊C4C22×D3711yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C22⋊C4—741no—
206C42—371no—
207C42—371no—
208C42—371no—
209C42—371no—
210C42—742no—
211C42—742no—
212C42—741no—
213C23—741no—
214C23D4×D3711yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—22no—
218Q8#1059696414yes—
219D4—742no—
220D4—1482no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—371no—
227C2×C4—371no—
228C2×C4—371no—
229C2×C4—371no—
230C2×C4—742no—
231C2×C4—742no—
232C2×C4—741no—
233C2×C4—1482no—
234C2×C4—1481no—
235C2×C4—1482no—
236C2×C4D4×D3711yescharacteristic
237C2×C4C23×D3711yescharacteristic
238C8—22no—
239C8—742no—
240C22—21no—
241C22—21no—
242C22—1481no—
243C22—1481no—
244C22—1481no—
245C22#1192456812yes—
246C22C2×D4×D3711yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—41no—
251C4—741no—
252C4—741no—
253C4—741no—
254C4—741no—
255C4—1481no—
256C4—1482no—
257C4C2×#1059696412yes—
258C2—22no—
259C2—2961no—
260C2#1455803911yescharacteristic
261C2C2×#1192456811yescharacteristic
262C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#451C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#451D37
hypocenterC37#3117
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic37C2semidirect
3. #14557866C2semidirect
5. #14557838C2semidirect
6. #14557757C2semidirect
8. #14557640C2semidirect
9. #14557636C2semidirect
10. #14557587C2semidirect
11. C37×#451C2semidirect
138. #451D37semidirect
143. C37#3117semidirect

Maximal subgroups

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

subgroupindex
#145580692
C2×Q8×Dic372
#145578662
#145578522
#145578382
#145577572
#145576722
#145576402
#145576362
#145575872
C37×#4512
#311737