Finite Group Databasebeta

← #17995806

Subgroups — #17995806

Order 4736.

326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558100C211yesmaximal, characteristic
2#14557573C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic, complemented
4#14557532C211yesmaximal, characteristic, complemented
5C2×#11924453C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C37×#390C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11#11924532—21no—
12#11924523—21no—
13#11924507—21no—
14#11924507—21no—
15#11924505—22no—
16#11924495C2211yescharacteristic
17#11924469—21no—
18#11924467—21no—
19#11924464—22no—
20#11924459—21no—
21#11924456—21no—
22#11924453—22no—
23C22×D4×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37—22no—
26C2×C42×C37C2211yescharacteristic
27C24×C37D412yes—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C22×C4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—22no—
39C2×C22⋊D37—22no—
40#10596962—21no—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44C2×D148D411yescharacteristic
45C2×C4×D37—21no—
46C2×Dic74D411yescharacteristic
47C4⋊C4×C37—21no—
48C4⋊C4×C37—21no—
49C22⋊C4×C37—44no—
50C42×C37—21no—
51C42×C37—21no—
52C22⋊Dic37—22no—
53C22⋊Dic37—22no—
54C22⋊Dic37—21no—
55C4⋊Dic37D411yescharacteristic
56C4⋊Dic37D411yescharacteristic
57C4×Dic37—21no—
58#10596934—21no—
59#10596934—21no—
60#10596934—21no—
61#10596934D412yescomplemented
62C2×#64436—21no—
63C2×#64436—21no—
64C23×C37—22no—
65C23×C37—22no—
66C23×C37—22no—
67C23×C37—42no—
68C23×C37—42no—
69C23×C37C2×D411yescharacteristic
70C22×D37—21no—
71D4×C37—41no—
72D4×C37—41no—
73D4×C37—41no—
74D4×C37—41no—
75C2×C4×C37—22no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—42no—
79C2×C4×C37—41no—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C2×C4×C37#4111yescharacteristic
86C22⋊D37—41no—
87C22⋊D37—41no—
88C22⋊D37—82no—
89C22⋊D37—82no—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93D148—21no—
94D148—21no—
95C4×D37—41no—
96C4×D37—41no—
97Dic74—21no—
98Dic74—21no—
99#64436—22no—
100#64436—41no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—44no—
104C22×C37—42no—
105C22×C37—42no—
106C22×C37—42no—
107C22×C37—82no—
108C22×C37#12011yescharacteristic
109C22×C37#12111yescharacteristic
110C22×C37#12311yescharacteristic
111C2×D37—41no—
112C2×D37—41no—
113C2×D37—41no—
114C4×C37—42no—
115C4×C37—81no—
116C4×C37#12111yescharacteristic
117C4×C37#12111yescharacteristic
118C4×C37#12311yescharacteristic
119C4×C37#12411yescharacteristic
120Dic37—41no—
121Dic37—41no—
122Dic37—41no—
123#2037—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37—82no—
127C2×C37#39411yescharacteristic
128C2×C37#45311yescharacteristic
129C2×C37#45511yescharacteristic
130D37—81no—
131#535—371no—
132#428—371no—
133C2×#104—371no—
134#417—371no—
135C2×#100—371no—
136#390D3711yescharacteristic, complemented
137#339—371no—
138C37#203711yescharacteristic, complemented, Sylow
139C2×#41—371no—
140C22×D4C2×D3711yescharacteristic
141C2×M16—371no—
142C2×M16—371no—
143#127—741no—
144#124—741no—
145#121—741no—
146#121—741no—
147#120—742no—
148#117—371no—
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—22no—
151C2×C42C2×D3711yescharacteristic
152#107—741no—
153#106—741no—
154#104—742no—
155#103—741no—
156#102—741no—
157#100—742no—
158C24C22⋊D3712yes—
159#41—741no—
160#41—741no—
161#41—741no—
162#41—741no—
163C2×Q8—371no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—371no—
171C2×D4—742no—
172C2×D4—742no—
173C2×D4—741no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178M16—372no—
179M16—741no—
180M16—741no—
181M16—741no—
182C2×C8—741no—
183C2×C8—741no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—371no—
187C4⋊C4—371no—
188C22⋊C4—44no—
189C22⋊C4—742no—
190C22⋊C4—742no—
191C22⋊C4—741no—
192C42—21no—
193C42—21no—
194C42—741no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—741no—
201C23C2×C22⋊D3711yescharacteristic
202Q8—741no—
203Q8—741no—
204D4—41no—
205D4—41no—
206D4—41no—
207D4—41no—
208D4—2962no—
209D4—2962no—
210D4—741no—
211D4—741no—
212D4—1481no—
213D4—1481no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—1481no—
223C2×C4—1481no—
224C2×C4#1059696211yescharacteristic
225C2×C4#1059696211yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4D4×D3711yescharacteristic
228C2×C4D4×D3711yescharacteristic
229C2×C4#1059696411yescharacteristic
230C8—742no—
231C8—1481no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22#1192450411yescharacteristic
243C22#1192450811yescharacteristic
244C22#1192451911yescharacteristic
245C4—42no—
246C4—81no—
247C4—1481no—
248C4—1481no—
249C4—1481no—
250C4#1192450911yescharacteristic
251C4#1192450911yescharacteristic
252C4#1192451811yescharacteristic
253C4#1192452211yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—2961no—
258C2#1455744811yescharacteristic
259C2#1455770011yescharacteristic
260C2#1455771011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#390C2
socleC22×C37#120
prime radical#14558100C2
hypercenter#390D37
hypocenterC37#2037
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #14557573C2semidirect
3. C2×#11924464C2semidirect
4. #14557532C2semidirect
5. C2×#11924453C2semidirect
6. #14557293C2semidirect
7. C37×#390C2semidirect
61. #10596934D4semidirect
136. #390D37semidirect
138. C37#2037semidirect

Maximal subgroups

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

subgroupindex
#145581002
#145575732
C2×#119244642
#145575322
C2×#119244532
#145572932
C37×#3902
#203737