Finite Group Databasebeta

← #17993123

Subgroups — #17993123

Order 4736.

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

normal subgroups only

This group has 326 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#121×D37C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic, complemented
3#14557395C211yesmaximal, characteristic, complemented
4#14557268C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic, complemented
6#14557266C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×D4×D37—21no—
9C2×D4×D37C411yescharacteristic, complemented
10C22×C4×D37C2211yescharacteristic
11C2×#10596929—21no—
12#11924511C411yescharacteristic, complemented
13#11924510C2211yescharacteristic
14#11924509—21no—
15#11924508—21no—
16#11924507C411yescharacteristic, complemented
17C4⋊C4×D37C411yescharacteristic, complemented
18C2×#10596938—21no—
19C22⋊C4×D37—21no—
20C22⋊#64436C2211yescharacteristic, complemented
21#11924448—21no—
22#11924443—21no—
23#11924443C2211yescharacteristic, complemented
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic, complemented
26#95×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C23×D37D411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37C2×C411yescharacteristic
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C22×Dic37—21no—
37C22×Dic37D411yescharacteristic
38D4×D37—42no—
39D4×D37—42no—
40D4×D37—42no—
41C2×D148—21no—
42C2×D148C2×C411yescharacteristic
43C2×C4×D37—21no—
44C2×C4×D37—42no—
45C2×C4×D37C2×C411yescharacteristic
46C2×C4×D37C2×C411yescharacteristic
47C2×C4×D37D411yescharacteristic
48C2×C4×D37D411yescharacteristic
49C2×C8×C37—21no—
50C4⋊C4×C37C2×C411yescharacteristic
51C22⋊C4×C37—21no—
52C22⋊Dic37—21no—
53#10596938—21no—
54#10596938—21no—
55#10596938—42no—
56C4⋊Dic37C2×C411yescharacteristic
57#10596936—21no—
58C2×#64436—21no—
59#10596929—42no—
60C23×C37—21no—
61C23×C37C2×D411yescharacteristic
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—22no—
65C22×D37—21no—
66C22×D37—41no—
67C22×D37—42no—
68C22×D37—42no—
69C22×D37—42no—
70C22×D37C22⋊C411yescharacteristic
71C22×D37C22⋊C411yescharacteristic
72D4×C37—41no—
73D4×C37—41no—
74D4×C37—41no—
75C2×C4×C37—21no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37—41no—
80C2×C4×C37C22×C411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C22⋊D37—42no—
83C22⋊D37—42no—
84C22⋊D37—41no—
85C22⋊D37—41no—
86C2×Dic37—21no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37C22⋊C411yescharacteristic
92C2×Dic37C22⋊C411yescharacteristic
93D148—41no—
94D148—42no—
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—41no—
98C4×D37—41no—
99C4×D37—42no—
100C8×C37—41no—
101#64436—41no—
102C22×C37—21no—
103C22×C37—21no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37C2×C22⋊C411yescharacteristic
108C22×C37AGL(1,ℤ/8)11yescharacteristic
109C22×C37AGL(1,ℤ/8)11yescharacteristic
110C2×D37—21no—
111C2×D37—21no—
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—84no—
121C2×D37#9912yes—
122C4×C37—21no—
123C4×C37—21no—
124C4×C37—41no—
125C4×C37—81no—
126Dic37—21no—
127Dic37—21no—
128Dic37—41no—
129Dic37—81no—
130#1510—371nomaximal, Sylow
131C2×C37—21no—
132C2×C37—21no—
133C2×C37—81no—
134C2×C37C2×#9911yescharacteristic
135C2×C37#41811yescharacteristic
136C2×C37#42111yescharacteristic
137D37—22no—
138D37—41no—
139D37—81no—
140C2×#121—371no—
141#407—371no—
142#381—371no—
143#327—371no—
144#327—371no—
145#327—371no—
146#327D3711yescharacteristic, complemented
147C37#151011yescharacteristic, complemented, Sylow
148C22×D4—371no—
149C22×D4—741no—
150C23×C4—371no—
151C2×M16—741no—
152#121—371no—
153#121—371no—
154#121—371no—
155#121—741no—
156#121—741no—
157#121C2×D3711yescharacteristic
158C2×C4⋊C4—371no—
159C2×C22⋊C4—741no—
160C2×C22⋊C4—741no—
161C22⋊C8—371no—
162C22⋊C8—741no—
163C22⋊C8C2×D3711yescharacteristic, complemented
164#95—371no—
165#95—741no—
166#95C2×D3711yescharacteristic, complemented
167C24—371no—
168C24—741no—
169C2×D4—21no—
170C2×D4—371no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4—741no—
175C2×D4—1482no—
176C2×D4—1482no—
177C2×D4—1482no—
178C2×D4C4×D3711yescharacteristic
179C22×C4—21no—
180C22×C4—371no—
181C22×C4—371no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—371no—
185C22×C4—741no—
186C22×C4—741no—
187C22×C4—1482no—
188C22×C4C22×D3711yescharacteristic
189M16—1482no—
190C2×C8—21no—
191C2×C8—741no—
192C4⋊C4—371no—
193C4⋊C4—741no—
194C4⋊C4C4×D3711yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—741no—
197C22⋊C4—741no—
198C22⋊C4—741no—
199C22⋊C4—1482no—
200C23—21no—
201C23—371no—
202C23—371no—
203C23—742no—
204C23—741no—
205C23—741no—
206C23—741no—
207C23—1481no—
208C23—1482no—
209C23—1482no—
210C23—1482no—
211C23D4×D3711yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—1481no—
216D4—1482no—
217D4—1482no—
218D4—1482no—
219D4—1481no—
220D4—1481no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—371no—
227C2×C4—371no—
228C2×C4—742no—
229C2×C4—742no—
230C2×C4—741no—
231C2×C4—1481no—
232C2×C4—1481no—
233C2×C4—1482no—
234C2×C4—1481no—
235C2×C4—1481no—
236C2×C4—1481no—
237C2×C4—1481no—
238C2×C4C2×C4×D3711yescharacteristic
239C2×C4D4×D3711yescharacteristic
240C8—41no—
241C8—1481no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—372no—
248C22—2964no—
249C22—741no—
250C22—741no—
251C22—741no—
252C22—741no—
253C22—741no—
254C22—1482no—
255C22—1482no—
256C22—1481no—
257C22—1481no—
258C22—1481no—
259C22C22⋊C4×D3711yescharacteristic
260C22#1192456011yescharacteristic
261C22#1192456311yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—2961no—
267C4—741no—
268C4—741no—
269C4—1481no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—2961no—
274C2—742no—
275C2—1481no—
276C2#99×D3711yescharacteristic
277C2#1455753611yescharacteristic
278C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37C2×C22⋊C4
prime radical#121×D37C2
cosocleC22×C4×C37C23
hypercenter#327D37
hypocenterC37#1510
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. #14557395C2semidirect
4. #14557268C2semidirect
5. #14557267C2semidirect
6. #14557266C2semidirect
7. C37×#327C2semidirect
9. C2×D4×D37C4semidirect
12. #11924511C4semidirect
16. #11924507C4semidirect
17. C4⋊C4×D37C4semidirect
20. C22⋊#64436C22semidirect
23. #11924443C22semidirect
25. C22⋊C8×C37C22semidirect
26. #95×C37C22semidirect
146. #327D37semidirect
147. C37#1510semidirect
163. C22⋊C8C2×D37semidirect
166. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
#121×D372
#145574952
#145573952
#145572682
#145572672
#145572662
C37×#3272
#151037