Finite Group Databasebeta

← #17993136

Subgroups — #17993136

Order 4736.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#14558043C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic, complemented
3#14557392C211yesmaximal, characteristic, complemented
4#14557271C211yesmaximal, characteristic, complemented
5#14557269C211yesmaximal, characteristic, complemented
6#14557267C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×#10596964C411yescharacteristic, complemented
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—21no—
11#11924518—21no—
12#11924516C411yescharacteristic, complemented
13#11924515C2211yescharacteristic
14#11924507C411yescharacteristic, complemented
15#11924504—21no—
16D4×Dic37—21no—
17#11924496—21no—
18#11924494C411yescharacteristic, complemented
19C2×#10596936—21no—
20C2×#10596938—21no—
21C22⋊#64436C2211yescharacteristic
22#11924448—21no—
23#11924443C2211yescharacteristic
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C2×D4×C37—21no—
29C2×D4×C37C2×C411yescharacteristic
30C22×C4×C37—21no—
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C22×Dic37D411yescharacteristic
37#10596964—42no—
38C2×C4×D37—42no—
39C2×C4×D37C2×C411yescharacteristic
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×Dic74C2×C411yescharacteristic
44C2×C8×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C22⋊C4×C37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49#10596938—21no—
50#10596938—21no—
51#10596938—42no—
52C4⋊Dic37—21no—
53C4⋊Dic37C2×C411yescharacteristic
54#10596936—21no—
55#10596936—42no—
56C4×Dic37—21no—
57C2×#64436—21no—
58#10596929—42no—
59C23×C37—21no—
60C23×C37C2×D411yescharacteristic
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—41no—
64C22×D37—41no—
65C22×D37C22⋊C411yescharacteristic
66C22×D37C22⋊C411yescharacteristic
67D4×C37—41no—
68D4×C37—41no—
69D4×C37—41no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—41no—
74C2×C4×C37—41no—
75C2×C4×C37C22×C411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C22⋊D37—42no—
78C22⋊D37—42no—
79C2×Dic37—22no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—42no—
83C2×Dic37—41no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37C22⋊C411yescharacteristic
87C2×Dic37C22⋊C411yescharacteristic
88C4×D37—22no—
89C4×D37—22no—
90C4×D37—41no—
91C4×D37—41no—
92Dic74—41no—
93C8×C37—41no—
94#64436—41no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37C2×C22⋊C411yescharacteristic
101C22×C37AGL(1,ℤ/8)11yescharacteristic
102C22×C37#13711yescharacteristic
103C2×D37—21no—
104C2×D37—21no—
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—21no—
108C2×D37—21no—
109C2×D37—42no—
110C2×D37—42no—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—41no—
114C4×C37—81no—
115Dic37—21no—
116Dic37—41no—
117Dic37—41no—
118Dic37—81no—
119Dic37#9912yes—
120#1513—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—21no—
123C2×C37—81no—
124C2×C37C2×#9911yescharacteristic
125C2×C37#41711yescharacteristic
126C2×C37#42111yescharacteristic
127D37—41no—
128D37—41no—
129#525—371no—
130#407—371no—
131#380—371no—
132#328—371no—
133#328—371no—
134#327—371no—
135#327D3711yescharacteristic, complemented
136C37#151311yescharacteristic, complemented, Sylow
137C2×#41—371no—
138C23×C4—371no—
139C2×M16—741no—
140#123—741no—
141C22⋊Q8—371no—
142C22⋊Q8—371no—
143#121—371no—
144#121C2×D3711yescharacteristic
145#120—741no—
146C4×D4—741no—
147C4×D4—741no—
148#117—371no—
149C2×C4⋊C4—741no—
150C2×C22⋊C4—741no—
151C22⋊C8—371no—
152C22⋊C8—741no—
153C22⋊C8C2×D3711yescharacteristic
154#95—371no—
155#95C2×D3711yescharacteristic
156C24—371no—
157#41—1482no—
158C2×Q8—371no—
159C2×D4—21no—
160C2×D4—741no—
161C2×D4—741no—
162C2×D4C4×D3711yescharacteristic
163C22×C4—21no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—371no—
168C22×C4—371no—
169C22×C4—741no—
170C22×C4—741no—
171C22×C4—1482no—
172C22×C4C22×D3711yescharacteristic
173M16—1482no—
174C2×C8—21no—
175C2×C8—741no—
176C4⋊C4—371no—
177C4⋊C4—741no—
178C4⋊C4—741no—
179C4⋊C4—1482no—
180C4⋊C4C4×D3711yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C22⋊C4—741no—
186C22⋊C4—1482no—
187C42—741no—
188C23—21no—
189C23—371no—
190C23—371no—
191C23—741no—
192C23—741no—
193C23—1481no—
194C23—1481no—
195C23D4×D3711yescharacteristic
196Q8—1481no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—1482no—
201D4—1482no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—371no—
208C2×C4—371no—
209C2×C4—742no—
210C2×C4—742no—
211C2×C4—742no—
212C2×C4—741no—
213C2×C4—741no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1482no—
217C2×C4—1481no—
218C2×C4—1481no—
219C2×C4—1481no—
220C2×C4C2×C4×D3711yescharacteristic
221C2×C4D4×D3711yescharacteristic
222C8—41no—
223C8—1481no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—741no—
230C22—741no—
231C22—741no—
232C22—741no—
233C22—741no—
234C22—741no—
235C22—1482no—
236C22—1482no—
237C22C22⋊C4×D3711yescharacteristic
238C22#1192456011yescharacteristic
239C22#1192456511yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—81no—
244C4—372no—
245C4—2961no—
246C4—741no—
247C4—1481no—
248C4—1481no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—1481no—
253C2—1481no—
254C2#99×D3711yescharacteristic
255C2#1455753111yescharacteristic
256C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37C2×C22⋊C4
prime radical#14558043C2
cosocleC22×C4×C37C23
hypercenter#327D37
hypocenterC37#1513
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14557495C2semidirect
3. #14557392C2semidirect
4. #14557271C2semidirect
5. #14557269C2semidirect
6. #14557267C2semidirect
7. C37×#327C2semidirect
8. C2×#10596964C4semidirect
12. #11924516C4semidirect
14. #11924507C4semidirect
18. #11924494C4semidirect
135. #327D37semidirect
136. C37#1513semidirect

Maximal subgroups

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

subgroupindex
#145580432
#145574952
#145573922
#145572712
#145572692
#145572672
C37×#3272
#151337