Finite Group Databasebeta

← #18006460

Subgroups — #18006460

Order 4736.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#14558198C211yesmaximal, characteristic, complemented
2#14558186C211yesmaximal, characteristic
3#14557862C212yesmaximal, complemented
4#14557815C211yesmaximal, characteristic, complemented
5#14557765C212yesmaximal, complemented
6#14557735C211yesmaximal, characteristic, complemented
7#14557673C212yesmaximal, complemented
8C4×#10596930C211yesmaximal, characteristic, complemented
9C8×D148C211yesmaximal, characteristic, complemented
10#103×D37C212yesmaximal, complemented
11C37×#487C211yesmaximal, characteristic, complemented
12C2×#10596966—21no—
13C2×Q8×D37C2212yes—
14C2×#10596930C2211yescharacteristic
15C2×#10596941C2212yes—
16C2×C8×D37C2212yes—
17#11924535—21no—
18#11924521—22no—
19#11924514—22no—
20#11924512—21no—
21#11924512C2212yes—
22#11924511C2212yes—
23C4×Dic74C2211yescharacteristic
24C4×D148C2211yescharacteristic
25C4×D148C2211yescharacteristic
26#11924498—21no—
27C4⋊C4×D37C2212yes—
28#11924468C2211yescharacteristic
29#11924467C2212yes—
30C4⋊#64436C2211yescharacteristic
31#11924461C2211yescharacteristic
32#11924460C2212yes—
33#11924459C2212yes—
34#11924458C2211yescharacteristic
35#11924448C2212yes—
36C4⋊Q8×C37C2211yescharacteristic
37C4⋊Q8×C37C2211yescharacteristic
38#103×C37C2212yes—
39#103×C37C2212yes—
40C4×C8×C37C2211yescharacteristic
41C2×Q8×C37—21no—
42C2×Q8×C37C2312yes—
43#10596966—44no—
44Q8×D37—24no—
45Q8×D37—42no—
46C2×D148—22no—
47C2×D148D411yescharacteristic
48C2×D148C2311yescharacteristic
49C2×C4×D37—22no—
50C2×C4×D37—22no—
51C2×C4×D37—21no—
52C2×C4×D37C2312yes—
53C2×Dic74—22no—
54C2×Dic74C2311yescharacteristic
55C2×C8×C37C2311yescharacteristic
56C2×C8×C37C2311yescharacteristic
57C4⋊C4×C37—21no—
58C4⋊C4×C37—21no—
59C4⋊C4×C37—21no—
60C4⋊C4×C37C2312yes—
61C42×C37C2311yescharacteristic
62#10596941—42no—
63#10596938—22no—
64#10596938—21no—
65#10596938—22no—
66#10596938D412yes—
67C4⋊Dic37D411yescharacteristic
68C4⋊Dic37C2311yescharacteristic
69C4⋊Dic37C2311yescharacteristic
70#10596936—21no—
71#10596936—22no—
72#10596936—22no—
73C4×Dic37—21no—
74C2×#64436C2312yes—
75#10596930—22no—
76C8×D37—42no—
77C22×D37—21no—
78C22×D37C2×D412yes—
79Q8×C37—22no—
80Q8×C37—22no—
81Q8×C37—42no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2411yescharacteristic
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37C2×D412yes—
91D148—21no—
92D148—21no—
93D148—44no—
94D148SD1614yescomplemented
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—44no—
98C4×D37—44no—
99C4×D37—42no—
100Dic74—21no—
101Dic74—44no—
102Dic74#4112yescomplemented
103C8×C37—21no—
104C8×C37—21no—
105#64436—22no—
106C22×C37C22×D411yescharacteristic
107C2×D37—22no—
108C2×D37—22no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—41no—
112C2×D37C2×SD1614yes—
113C4×C37—21no—
114C4×C37—42no—
115C4×C37—42no—
116C4×C37C2×SD1612yes—
117C4×C37C2×#4111yescharacteristic
118C4×C37H(5,𝔽2)11yescharacteristic
119Dic37—22no—
120Dic37—22no—
121Dic37—41no—
122Dic37—41no—
123#3298—371nomaximal, Sylow
124C2×C37#54611yescharacteristic
125C2×C37C22×SD1611yescharacteristic
126C2×C37#57811yescharacteristic
127D37—24no—
128D37—81no—
129D4×Q8—371no—
130#547—371no—
131#487D3711yescharacteristic, complemented
132#483—372no—
133#475—371no—
134#465—372no—
135#461—371no—
136#448—372no—
137C4×SD16—371no—
138C8×D4—371no—
139C2×#103—372no—
140C37#329811yescharacteristic, complemented, Sylow
141C2×#41—741no—
142C22×Q8—372no—
143C2×SD16—372no—
144C2×SD16—371no—
145C22×C8—372no—
146C4⋊Q8—741no—
147C4⋊Q8C2×D3711yescharacteristic
148C4⋊Q8C2×D3711yescharacteristic
149#123—742no—
150C22⋊Q8—372no—
151C22⋊Q8—742no—
152C22⋊Q8—741no—
153#121—372no—
154C4×Q8—371no—
155C4×D4—371no—
156C4×D4—371no—
157C4×D4—741no—
158C2×C4⋊C4—372no—
159#106—371no—
160#106—372no—
161C4⋊C8—371no—
162#103—372no—
163#103—371no—
164#103—372no—
165#103C2×D3712yes—
166#103C2×D3712yes—
167#102—371no—
168C22⋊C8—372no—
169C4×C8C2×D3711yescharacteristic
170#41—1484no—
171C2×Q8—21no—
172C2×Q8—371no—
173C2×Q8—742no—
174C2×Q8—744no—
175C2×Q8—1482no—
176C2×Q8C22×D3712yes—
177C2×D4—371no—
178C2×D4—371no—
179C2×D4—742no—
180C22×C4—372no—
181C22×C4—742no—
182C22×C4—742no—
183C22×C4—741no—
184SD16—742no—
185SD16—1482no—
186C2×C8—372no—
187C2×C8—1482no—
188C2×C8C22×D3711yescharacteristic
189C2×C8C22×D3711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—371no—
194C4⋊C4—371no—
195C4⋊C4—371no—
196C4⋊C4—742no—
197C4⋊C4—742no—
198C4⋊C4—741no—
199C4⋊C4C22×D3712yes—
200C22⋊C4—372no—
201C22⋊C4—742no—
202C22⋊C4—742no—
203C22⋊C4—741no—
204C42—741no—
205C42C22×D3711yescharacteristic
206C23—372no—
207C23—741no—
208Q8—22no—
209Q8—22no—
210Q8—42no—
211Q8—372no—
212Q8—741no—
213Q8—1484no—
214D4—374no—
215D4—741no—
216D4—741no—
217D4—1484no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—372no—
221C2×C4—741no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—1484no—
227C2×C4—1484no—
228C2×C4—1482no—
229C2×C4D4×D3711yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4C23×D3711yescharacteristic
232C8—21no—
233C8—21no—
234C8—742no—
235C22—374no—
236C22—742no—
237C22—742no—
238C22—1481no—
239C22—1481no—
240C22—1481no—
241C22C2×D4×D3711yescharacteristic
242C4—21no—
243C4—42no—
244C4—42no—
245C4—742no—
246C4—742no—
247C4—1481no—
248C4—1481no—
249C4SD16×D3712yes—
250C4#41×D3711yescharacteristic
251C4#1192458211yescharacteristic
252C2—2961no—
253C2—744no—
254C2#1455817611yescharacteristic
255C2C2×SD16×D3711yescharacteristic
256C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#487C2
socleC22×C37C22×D4
prime radical#14558186C2
hypercenter#487D37
hypocenterC37#3298
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14558198C2semidirect
3. #14557862C2semidirect
4. #14557815C2semidirect
5. #14557765C2semidirect
6. #14557735C2semidirect
7. #14557673C2semidirect
8. C4×#10596930C2semidirect
9. C8×D148C2semidirect
10. #103×D37C2semidirect
11. C37×#487C2semidirect
94. D148SD16semidirect
102. Dic74#41semidirect
131. #487D37semidirect
140. C37#3298semidirect

Maximal subgroups

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

subgroupindex
#145581982
#145581862
#145578622
#145578152
#145577652
#145577352
#145576732
C4×#105969302
C8×D1482
#103×D372
C37×#4872
#329837