Finite Group Databasebeta

← #18007245

Subgroups — #18007245

Order 4736.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558256C211yesmaximal, characteristic, complemented
2#14557890C212yesmaximal, complemented
3#14557885C211yesmaximal, characteristic, complemented
4#14557837C212yesmaximal, complemented
5#14557820C211yesmaximal, characteristic, complemented
6#14557748C212yesmaximal
7#14557738C211yesmaximal, characteristic, complemented
8Q8×#64436C211yesmaximal, characteristic, complemented
9C4×#10596940C212yesmaximal, complemented
10C4×#10596939C211yesmaximal, characteristic
11C37×#554C211yesmaximal, characteristic, complemented
12C2×#10596940C2212yes—
13C2×#10596939C2211yescharacteristic
14#11924536C2211yescharacteristic
15#11924531—22no—
16#11924524C2212yes—
17#11924512—21no—
18C4×Dic74C2212yes—
19C4×D148C2211yescharacteristic
20#11924494—21no—
21#11924469C2211yescharacteristic
22#11924467C2212yes—
23C4⋊#64436C2211yescharacteristic
24C4⋊#64436C2212yes—
25#11924459C2212yes—
26#11924459C2212yes—
27#11924459C2212yes—
28#11924457C2211yescharacteristic
29#11924456C2212yes—
30#11924456C2211yescharacteristic
31C4×#64436C2211yescharacteristic
32C4×#64436C2212yes—
33C4⋊Q8×C37C2211yescharacteristic
34#125×C37C2212yes—
35C22⋊Q8×C37—21no—
36C22⋊Q8×C37—22no—
37C4×Q8×C37C2211yescharacteristic
38C4×D4×C37C2211yescharacteristic
39C4×D4×C37C2212yes—
40C2×C4⋊C4×C37—21no—
41C2×Q8×C37—21no—
42C2×Q8×C37D411yescharacteristic
43C2×D4×C37C2311yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37—22no—
46C2×D148C2311yescharacteristic
47C2×C4×D37—21no—
48C2×Dic74C2312yes—
49C4⋊C4×C37—22no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37—22no—
52C4⋊C4×C37D411yescharacteristic
53C4⋊C4×C37D412yes—
54C4⋊C4×C37C2311yescharacteristic
55C4⋊C4×C37C2312yes—
56C22⋊C4×C37—21no—
57C22⋊C4×C37—22no—
58C42×C37C2311yescharacteristic
59C42×C37C2312yes—
60#10596940—24no—
61#10596939—22no—
62#10596938—22no—
63#10596938—21no—
64#10596938—22no—
65C4⋊Dic37—21no—
66C4⋊Dic37—21no—
67C4⋊Dic37C2311yescharacteristic
68#10596936—22no—
69C4×Dic37—22no—
70C2×#64436C2311yescharacteristic
71C2×#64436C2312yes—
72C2×#64436C2311yescharacteristic
73C23×C37—21no—
74C22×D37—21no—
75Q8×C37—22no—
76Q8×C37—81no—
77D4×C37—21no—
78D4×C37#4112yes—
79C2×C4×C37—21no—
80C2×C4×C37—22no—
81C2×C4×C37—42no—
82C2×C4×C37—82no—
83C2×C4×C37C2×D412yes—
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2411yescharacteristic
88C2×Dic37—21no—
89C2×Dic37—22no—
90D148—21no—
91D148—21no—
92C4×D37—42no—
93Dic74—22no—
94Dic74—22no—
95#64436—21no—
96#64436—22no—
97#64436—21no—
98C22×C37—22no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37C22×D411yescharacteristic
102C2×D37—41no—
103C2×D37—41no—
104C2×D37—41no—
105C4×C37—22no—
106C4×C37—22no—
107C4×C37—21no—
108C4×C37—41no—
109C4×C37—42no—
110C4×C37#13512yes—
111C4×C37C2×#4111yescharacteristic
112C4×C372−1+411yescharacteristic
113Dic37—42no—
114Dic37—41no—
115#3360—371nomaximal, Sylow
116C2×C37—42no—
117C2×C37#54811yescharacteristic
118C2×C37C2×#13511yescharacteristic
119C2×C37#57711yescharacteristic
120D37—81no—
121#556—371no—
122#554D3711yescharacteristic, complemented
123#488—372no—
124#487—371no—
125#479—372no—
126#476—371no—
127#463—372no—
128#461—371no—
129C8×Q8—371no—
130C4×SD16—372no—
131C4×D8—371no—
132C37#336011yescharacteristic, complemented, Sylow
133C2×SD16—372no—
134C2×D8—371no—
135C4⋊Q8—371no—
136C4⋊Q8C2×D3711yescharacteristic
137#126—742no—
138#125C2×D3712yes—
139#124—372no—
140C22⋊Q8—21no—
141C22⋊Q8—22no—
142C22⋊Q8—741no—
143C4×Q8—372no—
144C4×Q8C2×D3711yescharacteristic
145C4×D4—371no—
146C4×D4C2×D3711yescharacteristic
147C4×D4C2×D3712yes—
148#117—741no—
149C2×C4⋊C4—21no—
150#107—371no—
151#106—372no—
152C4⋊C8—371no—
153C4⋊C8—372no—
154#103—372no—
155#103—372no—
156#103—372no—
157#102—371no—
158#102—371no—
159#102—372no—
160C4×C8—371no—
161C4×C8—372no—
162C2×Q8—21no—
163C2×Q8—372no—
164C2×Q8C22⋊D3711yescharacteristic
165C2×D4—371no—
166C2×D4C22×D3711yescharacteristic
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—741no—
170SD16—744no—
171D8—742no—
172C2×C8—371no—
173C2×C8—372no—
174C2×C8—371no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—371no—
179C4⋊C4—742no—
180C4⋊C4—741no—
181C4⋊C4—741no—
182C4⋊C4C22⋊D3711yescharacteristic
183C4⋊C4C22⋊D3712yes—
184C4⋊C4C22×D3712yes—
185C4⋊C4C22×D3711yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—742no—
189C22⋊C4—741no—
190C22⋊C4—742no—
191C42—742no—
192C42C22×D3711yescharacteristic
193C42C22×D3712yes—
194C23—21no—
195C23—741no—
196Q8—22no—
197Q8—81no—
198Q8—742no—
199Q8—742no—
200D4—21no—
201D4—741no—
202D4—741no—
203D4#1059696612yes—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4—741no—
209C2×C4—742no—
210C2×C4—1482no—
211C2×C4C2×C22⋊D3712yes—
212C2×C4C2×C22⋊D3712yes—
213C2×C4C2×C22⋊D3711yescharacteristic
214C2×C4C2×C22⋊D3711yescharacteristic
215C2×C4C23×D3711yescharacteristic
216C8—741no—
217C8—742no—
218C8—741no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1481no—
223C22—1481no—
224C22—1481no—
225C22C22×C22⋊D3711yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—1481no—
232C4—1482no—
233C4#1192455612yes—
234C4C2×#1059696611yescharacteristic
235C4#1192458411yescharacteristic
236C2—42no—
237C2—2961no—
238C2#1455819411yescharacteristic
239C2C2×#1192455611yescharacteristic
240C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#554C2
socleC22×C37C22×D4
prime radicalC2×#10596939C22
hypercenter#554D37
hypocenterC37#3360
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #14558256C2semidirect
2. #14557890C2semidirect
3. #14557885C2semidirect
4. #14557837C2semidirect
5. #14557820C2semidirect
7. #14557738C2semidirect
8. Q8×#64436C2semidirect
9. C4×#10596940C2semidirect
11. C37×#554C2semidirect
122. #554D37semidirect
132. C37#3360semidirect

Maximal subgroups

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

subgroupindex
#145582562
#145578902
#145578852
#145578372
#145578202
#145577482
#145577382
Q8×#644362
C4×#105969402
C4×#105969392
C37×#5542
#336037