Finite Group Databasebeta

← #18007249

Subgroups — #18007249

Order 4736.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558257C211yesmaximal, characteristic, complemented
2#14558240C211yesmaximal, characteristic, complemented
3#14557889C212yesmaximal, complemented
4#14557883C211yesmaximal, characteristic, complemented
5#14557838C212yesmaximal, complemented
6#14557824C211yesmaximal, characteristic, complemented
7#14557750C212yesmaximal
8#14557657C211yesmaximal, characteristic, complemented
9SD16×Dic37C212yesmaximal, complemented
10C4×#10596939C211yesmaximal, characteristic
11C37×#461C211yesmaximal, characteristic, complemented
12C2×#10596939C2211yescharacteristic
13#11924536C2211yescharacteristic
14#11924531—22no—
15#11924527C2212yes—
16#11924525C2212yes—
17#11924516—21no—
18#11924515—21no—
19#11924513—22no—
20Q8×Dic37C2212yes—
21C4×Dic74C2211yescharacteristic
22C4×D148C2211yescharacteristic
23D4×Dic37C2212yes—
24#11924494—21no—
25C2×C4⋊Dic37—21no—
26#11924469C2211yescharacteristic
27#11924468C2212yes—
28#11924465C2212yes—
29#11924460C2212yes—
30#11924460C2212yes—
31#11924458C2212yes—
32#11924457C2211yescharacteristic
33#11924456C2211yescharacteristic
34C4×#64436C2211yescharacteristic
35C8×Dic37C2212yes—
36C2×SD16×C37C2212yes—
37C4⋊Q8×C37C2211yescharacteristic
38C4×D4×C37C2211yescharacteristic
39C4⋊C8×C37C2211yescharacteristic
40#103×C37C2212yes—
41C2×Q8×C37C2312yes—
42C2×D4×C37C2311yescharacteristic
43C22×C4×C37—21no—
44C22×Dic37—22no—
45C2×D148C2311yescharacteristic
46C2×C4×D37—21no—
47C2×Dic74—21no—
48C2×Dic74D411yescharacteristic
49SD16×C37—24no—
50C2×C8×C37C2312yes—
51C4⋊C4×C37—21no—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2311yescharacteristic
54C22⋊C4×C37—21no—
55C42×C37C2311yescharacteristic
56C22⋊Dic37—22no—
57#10596939—22no—
58#10596938—21no—
59#10596938—22no—
60#10596938—22no—
61C4⋊Dic37—21no—
62C4⋊Dic37—22no—
63C4⋊Dic37—22no—
64C4⋊Dic37D411yescharacteristic
65C4⋊Dic37C2312yes—
66C4⋊Dic37C2311yescharacteristic
67#10596936—22no—
68#10596936D412yes—
69C4×Dic37—22no—
70C4×Dic37C2312yes—
71C2×#64436C2311yescharacteristic
72C2×#64436C2311yescharacteristic
73C23×C37—21no—
74C22×D37—21no—
75Q8×C37—22no—
76Q8×C37—22no—
77D4×C37—21no—
78D4×C37#4112yes—
79C2×C4×C37—22no—
80C2×C4×C37—21no—
81C2×C4×C37—42no—
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2411yescharacteristic
85C2×Dic37—21no—
86C2×Dic37—22no—
87C2×Dic37—82no—
88C2×Dic37C2×D412yes—
89C2×Dic37C2×D412yes—
90D148—21no—
91D148—21no—
92C4×D37—42no—
93Dic74—22no—
94Dic74—81no—
95C8×C37—22no—
96#64436—21no—
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—21no—
106C4×C37—42no—
107C4×C37—41no—
108C4×C37#13512yes—
109C4×C37C2×#4111yescharacteristic
110C4×C372−1+411yescharacteristic
111Dic37—22no—
112Dic37—22no—
113Dic37—41no—
114Dic37—42no—
115#3360—371nomaximal, Sylow
116C2×C37—42no—
117C2×C37#54811yescharacteristic
118C2×C37C2×#13511yescharacteristic
119C2×C37#57711yescharacteristic
120D37—81no—
121#556—371no—
122#554—371no—
123#488—372no—
124#487—371no—
125#479—372no—
126#476—371no—
127#463—372no—
128#461D3711yescharacteristic, complemented
129C8×Q8—371no—
130C4×SD16—372no—
131C4×D8—371no—
132C37#336011yescharacteristic, complemented, Sylow
133C2×SD16C2×D3712yes—
134C2×D8—371no—
135C4⋊Q8—371no—
136C4⋊Q8C2×D3711yescharacteristic
137#126—742no—
138#125—372no—
139#124—372no—
140C22⋊Q8—742no—
141C22⋊Q8—741no—
142C22⋊Q8—741no—
143C4×Q8—371no—
144C4×Q8—372no—
145C4×D4—372no—
146C4×D4—371no—
147C4×D4C2×D3711yescharacteristic
148#117—741no—
149C2×C4⋊C4—741no—
150#107—371no—
151#106—372no—
152C4⋊C8—372no—
153C4⋊C8C2×D3711yescharacteristic
154#103—372no—
155#103—372no—
156#103C2×D3712yes—
157#102—371no—
158#102—372no—
159#102—371no—
160C4×C8—372no—
161C4×C8—371no—
162C2×Q8—371no—
163C2×Q8—741no—
164C2×Q8C22×D3712yes—
165C2×D4—371no—
166C2×D4C22×D3711yescharacteristic
167C22×C4—21no—
168C22×C4—742no—
169C22×C4—741no—
170SD16—24no—
171D8—742no—
172C2×C8—371no—
173C2×C8—371no—
174C2×C8C22×D3712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—372no—
178C4⋊C4—371no—
179C4⋊C4—372no—
180C4⋊C4—371no—
181C4⋊C4—742no—
182C4⋊C4—742no—
183C4⋊C4—742no—
184C4⋊C4—741no—
185C4⋊C4C22×D3711yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C22⋊C4—742no—
190C22⋊C4—741no—
191C42—372no—
192C42—742no—
193C42C22×D3711yescharacteristic
194C23—21no—
195C23—741no—
196Q8—22no—
197Q8—22no—
198Q8—2961no—
199Q8—742no—
200D4—21no—
201D4—741no—
202D4—741no—
203D4#1059696412yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—372no—
208C2×C4—372no—
209C2×C4—2962no—
210C2×C4—741no—
211C2×C4—742no—
212C2×C4—1482no—
213C2×C4D4×D3711yescharacteristic
214C2×C4D4×D3711yescharacteristic
215C2×C4C23×D3711yescharacteristic
216C8—22no—
217C8—741no—
218C8—741no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1481no—
223C22—1481no—
224C22—1481no—
225C22C2×D4×D3711yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—742no—
230C4—742no—
231C4—1481no—
232C4—1482no—
233C4#1192455712yes—
234C4C2×#1059696411yescharacteristic
235C4#1192458311yescharacteristic
236C2—42no—
237C2—2961no—
238C2#1455818911yescharacteristic
239C2C2×#1192455711yescharacteristic
240C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#461C2
socleC22×C37C22×D4
prime radicalC2×#10596939C22
hypercenter#461D37
hypocenterC37#3360
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14558257C2semidirect
2. #14558240C2semidirect
3. #14557889C2semidirect
4. #14557883C2semidirect
5. #14557838C2semidirect
6. #14557824C2semidirect
8. #14557657C2semidirect
9. SD16×Dic37C2semidirect
11. C37×#461C2semidirect
128. #461D37semidirect
132. C37#3360semidirect

Maximal subgroups

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

subgroupindex
#145582572
#145582402
#145578892
#145578832
#145578382
#145578242
#145577502
#145576572
SD16×Dic372
C4×#105969392
C37×#4612
#336037