Finite Group Databasebeta

← #487×D37 #18004904

Subgroups — #487×D37 #18004904

Order 4736.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D37C211yesmaximal, characteristic
2C4⋊Q8×D37C211yesmaximal, characteristic
3#14557885C211yesmaximal, characteristic, complemented
4#14557884C211yesmaximal, characteristic, complemented
5#14557883C211yesmaximal, characteristic, complemented
6#14557882C214yesmaximal, complemented
7#103×D37C214yesmaximal
8C4×C8×D37C211yesmaximal, characteristic
9C37×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D37—21no—
11C2×Q8×D37C2212yes—
12C2×C8×D37C2212yes—
13#11924536C2211yescharacteristic
14#11924536C2211yescharacteristic
15#11924535—21no—
16#11924535—21no—
17#11924535—21no—
18#11924535C2212yes—
19#11924534—21no—
20#11924534C2212yes—
21C4⋊C4×D37—21no—
22C4⋊C4×D37—21no—
23C4⋊C4×D37—21no—
24C4⋊C4×D37C2212yes—
25C42×D37C2211yescharacteristic
26#11924461C2214yes—
27#11924460C2214yes—
28#11924459C2214yes—
29C4×#64436C2211yescharacteristic
30C8×Dic37C2212yes—
31C4⋊Q8×C37C2211yescharacteristic
32C4⋊Q8×C37C2211yescharacteristic
33#103×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×Q8×C37C2312yes—
37Q8×D37—28no—
38Q8×D37—44no—
39C2×C4×D37—22no—
40C2×C4×D37—22no—
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C4×D37C2311yescharacteristic
44C2×Dic74—21no—
45C2×Dic74—22no—
46C2×Dic74—22no—
47C2×Dic74C2312yes—
48C2×C8×C37C2312yes—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37—21no—
52C4⋊C4×C37C2312yes—
53C42×C37C2311yescharacteristic
54C4⋊Dic37—21no—
55C4⋊Dic37—21no—
56C4⋊Dic37—21no—
57C4⋊Dic37C2312yes—
58#10596936—22no—
59#10596936—22no—
60#10596936—22no—
61#10596936—22no—
62C4×Dic37D411yescharacteristic
63C4×Dic37D411yescharacteristic
64C4×Dic37C2311yescharacteristic
65C2×#64436C2312yes—
66C8×D37—24no—
67C22×D37C2×D411yescharacteristic
68Q8×C37—24no—
69Q8×C37—42no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2411yescharacteristic
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37C2×D411yescharacteristic
78C2×Dic37C2×D411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80C4×D37—44no—
81C4×D37—44no—
82C4×D37SD1614yes—
83C4×D37Q1614yes—
84C4×D37#4114yes—
85Dic74—24no—
86Dic74—42no—
87Dic74—44no—
88Dic74—44no—
89C8×C37—22no—
90#64436—22no—
91C22×C37C22×D411yescharacteristic
92C2×D37#12412yes—
93C2×D37C2×SD1612yes—
94C2×D37C2×Q1612yes—
95C4×C37—42no—
96C4×C37—42no—
97C4×C37C2×SD1612yes—
98C4×C37C2×Q1612yes—
99C4×C37C2×#4112yes—
100Dic37—42no—
101Dic37—42no—
102Dic37#12412yes—
103Dic37C2×SD1612yes—
104Dic37C2×Q1612yes—
105C2×#487—371nomaximal, Sylow
106C2×C37C2×#12411yescharacteristic
107C2×C37C22×SD1611yescharacteristic
108C2×C37C22×Q1611yescharacteristic
109D37#48714yesdirect product factor
110C2×C4⋊Q8—371no—
111C2×C4⋊Q8—371no—
112#487—371no—
113#487—371no—
114#487—374no—
115#487—371no—
116#487D3711yescharacteristic, direct product factor
117C2×#103—374no—
118C2×C4×C8—371no—
119C37C2×#48711yescharacteristic, complemented, Sylow
120C22×Q8—372no—
121C22×Q8—741no—
122C22×C8—372no—
123C4⋊Q8—372no—
124C4⋊Q8—372no—
125C4⋊Q8—371no—
126C4⋊Q8—371no—
127C4⋊Q8—741no—
128C4⋊Q8—741no—
129C4⋊Q8—741no—
130C4⋊Q8—741no—
131C4⋊Q8C2×D3711yescharacteristic
132C4⋊Q8C2×D3711yescharacteristic
133C2×C4⋊C4—372no—
134C2×C4⋊C4—741no—
135C2×C4⋊C4—741no—
136C2×C4⋊C4—741no—
137C2×C42—371no—
138#103—374no—
139#103—374no—
140#103—374no—
141#103C2×D3714yes—
142C4×C8—372no—
143C4×C8—371no—
144C4×C8C2×D3711yescharacteristic
145C2×Q8—21no—
146C2×Q8—372no—
147C2×Q8—742no—
148C2×Q8—742no—
149C2×Q8—748no—
150C2×Q8—741no—
151C2×Q8—1484no—
152C2×Q8C22×D3712yes—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—742no—
157C22×C4—742no—
158C2×C8—372no—
159C2×C8—744no—
160C2×C8C22×D3712yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—372no—
165C4⋊C4—742no—
166C4⋊C4—742no—
167C4⋊C4—742no—
168C4⋊C4—742no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C4⋊C4C22×D3712yes—
173C42—371no—
174C42—371no—
175C42—371no—
176C42C22×D3711yescharacteristic
177C23—371no—
178Q8—24no—
179Q8—42no—
180Q8—744no—
181Q8—1484no—
182Q8—1484no—
183Q8—1482no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—374no—
190C2×C4—374no—
191C2×C4—374no—
192C2×C4—742no—
193C2×C4—742no—
194C2×C4—1484no—
195C2×C4—1484no—
196C2×C4D4×D3711yescharacteristic
197C2×C4D4×D3711yescharacteristic
198C2×C4C23×D3711yescharacteristic
199C8—22no—
200C8—742no—
201C22—372no—
202C22—372no—
203C22—372no—
204C22C2×D4×D3711yescharacteristic
205C4—42no—
206C4—42no—
207C4—372no—
208C4—372no—
209C4—372no—
210C4—1482no—
211C4—1482no—
212C4SD16×D3712yes—
213C4Q16×D3712yes—
214C4#41×D3712yes—
215C2—374no—
216C2#124×D3711yescharacteristic
217C2C2×SD16×D3711yescharacteristic
218C2C2×Q16×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#487C2
socleC22×C37C22×D4
prime radicalC22×D37C2×D4
hypercenter#487D37
hypocenterC37C2×#487
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
3. #14557885C2semidirect
4. #14557884C2semidirect
5. #14557883C2semidirect
6. #14557882C2semidirect
9. C37×#487C2semidirect
109. D37#487direct (N × H)
116. #487D37direct (N × H)
119. C37C2×#487semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D372
#145578852
#145578842
#145578832
#145578822
#103×D372
C4×C8×D372
C37×#4872
C2×#48737