Finite Group Databasebeta

← #18006463

Subgroups — #18006463

Order 4736.

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

normal subgroups only

This group has 420 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
1Q8×D148C211yesmaximal, characteristic, complemented
2#14558188C211yesmaximal, characteristic
3#14557884C211yesmaximal, characteristic, complemented
4#14557865C212yesmaximal, complemented
5#14557818C211yesmaximal, characteristic, complemented
6#14557761C212yesmaximal, complemented
7#14557738C211yesmaximal, characteristic, complemented
8#14557670C212yesmaximal, complemented
9C8×D148C211yesmaximal, characteristic, complemented
10#103×D37C212yesmaximal, complemented
11C4×SD16×C37C211yesmaximal, characteristic, complemented
12C2×#10596962—21no—
13C2×Q8×D37C2212yes—
14C2×#10596940C2212yes—
15C2×C8×D37C2212yes—
16#11924536—21no—
17#11924536C2211yescharacteristic
18#11924536C2211yescharacteristic
19#11924518—22no—
20#11924516—22no—
21#11924516C2212yes—
22#11924515—21no—
23#11924507C2212yes—
24C4×D148—21no—
25C4×D148C2211yescharacteristic
26C4⋊C4×D37C2212yes—
27#11924467C2212yes—
28C4⋊#64436C2211yescharacteristic
29#11924461C2212yes—
30#11924461C2212yes—
31#11924460C2212yes—
32#11924459C2212yes—
33#11924448C2212yes—
34C2×SD16×C37C2211yescharacteristic
35C4×Q8×C37C2211yescharacteristic
36C4×D4×C37C2211yescharacteristic
37#106×C37C2211yescharacteristic
38#103×C37C2211yescharacteristic
39#102×C37C2211yescharacteristic
40C4×C8×C37C2211yescharacteristic
41C2×Q8×C37C2311yescharacteristic
42C2×D4×C37C2311yescharacteristic
43C22×C4×C37—21no—
44C2×C22⋊D37—22no—
45Q8×D37—24no—
46Q8×D37—42no—
47#10596962—44no—
48C2×D148D411yescharacteristic
49C2×C4×D37—22no—
50C2×C4×D37—22no—
51C2×C4×D37C2312yes—
52C2×Dic74—21no—
53C2×Dic74—22no—
54C2×Dic74C2312yes—
55SD16×C37—22no—
56C2×C8×C37C2311yescharacteristic
57C2×C8×C37C2311yescharacteristic
58C4⋊C4×C37—21no—
59C4⋊C4×C37C2311yescharacteristic
60C4⋊C4×C37C2311yescharacteristic
61C22⋊C4×C37—21no—
62C42×C37—21no—
63C42×C37C2311yescharacteristic
64C22⋊Dic37—22no—
65#10596940—42no—
66#10596938—22no—
67#10596938D412yes—
68C4⋊Dic37—21no—
69C4⋊Dic37—21no—
70C4⋊Dic37—21no—
71C4⋊Dic37—22no—
72C4⋊Dic37D411yescharacteristic
73C4⋊Dic37C2312yes—
74#10596936—22no—
75C2×#64436C2312yes—
76C8×D37—42no—
77C23×C37—21no—
78C22×D37C2×D412yes—
79Q8×C37—21no—
80Q8×C37#4112yescomplemented
81D4×C37—21no—
82D4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—21no—
85C2×C4×C37—21no—
86C2×C4×C37—42no—
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2411yescharacteristic
90C22⋊D37—44no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37C2×D412yes—
94D148SD1614yescomplemented
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—44no—
98C4×D37—44no—
99Dic74—22no—
100Dic74—22no—
101Dic74—44no—
102Dic74—42no—
103C8×C37—21no—
104C8×C37—21no—
105#64436—22no—
106C22×C37—41no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37C22×D411yescharacteristic
110C2×D37—22no—
111C2×D37—22no—
112C2×D37C2×SD1614yes—
113C4×C37—22no—
114C4×C37—21no—
115C4×C37—41no—
116C4×C37—41no—
117C4×C37C2×SD1612yes—
118C4×C37C2×#4111yescharacteristic
119C4×C37H(5,𝔽2)11yescharacteristic
120Dic37—22no—
121Dic37—42no—
122Dic37—42no—
123#3298—371nomaximal, Sylow
124C2×C37—81no—
125C2×C37#54611yescharacteristic
126C2×C37C22×SD1611yescharacteristic
127C2×C37#57811yescharacteristic
128D37—24no—
129D4×Q8—371no—
130#547—371no—
131#487—371no—
132#483—372no—
133#475—371no—
134#465—372no—
135#461—371no—
136#448—372no—
137C4×SD16D3711yescharacteristic, complemented
138C8×D4—371no—
139C2×#103—372no—
140C37#329811yescharacteristic, complemented, Sylow
141C2×#41—741no—
142C22×Q8—372no—
143C2×SD16—372no—
144C2×SD16C2×D3711yescharacteristic
145C22×C8—372no—
146C4⋊Q8—371no—
147C4⋊Q8—371no—
148C4⋊Q8—741no—
149#123—742no—
150C22⋊Q8—372no—
151C22⋊Q8—742no—
152C22⋊Q8—741no—
153#121—372no—
154C4×Q8C2×D3711yescharacteristic
155C4×D4—371no—
156C4×D4—741no—
157C4×D4C2×D3711yescharacteristic
158C2×C4⋊C4—372no—
159#106—372no—
160#106C2×D3711yescharacteristic
161C4⋊C8—371no—
162#103—372no—
163#103—372no—
164#103—372no—
165#103—372no—
166#103C2×D3711yescharacteristic
167#102C2×D3711yescharacteristic
168C22⋊C8—372no—
169C4×C8C2×D3711yescharacteristic
170#41—1484no—
171C2×Q8—372no—
172C2×Q8—742no—
173C2×Q8—741no—
174C2×Q8—744no—
175C2×Q8—1482no—
176C2×Q8C22×D3711yescharacteristic
177C2×D4—371no—
178C2×D4—742no—
179C2×D4C22×D3711yescharacteristic
180C22×C4—21no—
181C22×C4—372no—
182C22×C4—742no—
183C22×C4—742no—
184SD16—22no—
185SD16—1482no—
186C2×C8—372no—
187C2×C8—1482no—
188C2×C8C22×D3711yescharacteristic
189C2×C8C22×D3711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—371no—
192C4⋊C4—372no—
193C4⋊C4—742no—
194C4⋊C4—742no—
195C4⋊C4—741no—
196C4⋊C4—741no—
197C4⋊C4—741no—
198C4⋊C4C22×D3711yescharacteristic
199C4⋊C4C22×D3711yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—372no—
202C22⋊C4—742no—
203C22⋊C4—742no—
204C42—21no—
205C42C22×D3711yescharacteristic
206C23—21no—
207C23—372no—
208Q8—21no—
209Q8—742no—
210Q8—742no—
211Q8—1484no—
212Q8—1482no—
213Q8#1059696212yescomplemented
214D4—21no—
215D4—21no—
216D4—374no—
217D4—1484no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—372no—
223C2×C4—742no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—742no—
227C2×C4—1484no—
228C2×C4—1484no—
229C2×C4D4×D3711yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4C23×D3711yescharacteristic
232C8—21no—
233C8—21no—
234C8—742no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—374no—
239C22—742no—
240C22—742no—
241C22C2×D4×D3711yescharacteristic
242C4—21no—
243C4—22no—
244C4—41no—
245C4—41no—
246C4—742no—
247C4—1482no—
248C4—1482no—
249C4SD16×D3712yes—
250C4C2×#1059696211yescharacteristic
251C4#1192458211yescharacteristic
252C2—81no—
253C2—744no—
254C2#1455817911yescharacteristic
255C2C2×SD16×D3711yescharacteristic
256C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×SD16×C37C2
socleC22×C37C22×D4
prime radical#14558188C2
hypercenterC4×SD16D37
hypocenterC37#3298
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D148C2semidirect
3. #14557884C2semidirect
4. #14557865C2semidirect
5. #14557818C2semidirect
6. #14557761C2semidirect
7. #14557738C2semidirect
8. #14557670C2semidirect
9. C8×D148C2semidirect
10. #103×D37C2semidirect
11. C4×SD16×C37C2semidirect
80. Q8×C37#41semidirect
94. D148SD16semidirect
137. C4×SD16D37semidirect
140. C37#3298semidirect
213. Q8#10596962semidirect

Maximal subgroups

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

subgroupindex
Q8×D1482
#145581882
#145578842
#145578652
#145578182
#145577612
#145577382
#145576702
C8×D1482
#103×D372
C4×SD16×C372
#329837