Finite Group Databasebeta

← #17993549

Subgroups — #17993549

Order 4736.

308 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 51 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#14558091C211yesmaximal, characteristic
2#14557674C211yesmaximal, characteristic, complemented
3#14557671C211yesmaximal, characteristic, complemented
4#14557446C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic, complemented
9C2×D4×D37—21no—
10C2×#10596930—21no—
11C2×#10596940—21no—
12#11924521—21no—
13#11924518—21no—
14#11924510C2211yescharacteristic
15#11924508—21no—
16#11924506—21no—
17#11924504—21no—
18C2×#10596938—21no—
19C2×#10596938C2211yescharacteristic
20#11924461—21no—
21#11924459—21no—
22C22⋊#64436C2211yescharacteristic, complemented
23#11924443—21no—
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic, complemented
26#95×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C23×D37D411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37D411yescharacteristic
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—
40C2×D148—21no—
41C2×D148D411yescharacteristic
42C2×C4×D37—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—42no—
46C2×C8×C37—21no—
47C4⋊C4×C37D411yescharacteristic
48C22⋊C4×C37—21no—
49C22⋊Dic37—21no—
50#10596940—42no—
51#10596938—21no—
52#10596938—21no—
53#10596938—21no—
54#10596938—21no—
55#10596938—42no—
56C4⋊Dic37D411yescharacteristic
57#10596936—21no—
58C2×#64436—21no—
59#10596930—42no—
60C23×C37—21no—
61C23×C37C2×D411yescharacteristic
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—42no—
66C22×D37—41no—
67C22×D37—41no—
68C22×D37—81no—
69C22×D37—81no—
70C22×D37SD1612yescomplemented
71D4×C37—41no—
72D4×C37—41no—
73D4×C37—41no—
74C2×C4×C37—21no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C22⋊D37—42no—
82C22⋊D37—41no—
83C22⋊D37—41no—
84C22⋊D37—81no—
85C2×Dic37—22no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91D148—41no—
92D148—42no—
93C4×D37—42no—
94Dic74—22no—
95Dic74—22no—
96Dic74—41no—
97Dic74—41no—
98C8×C37—41no—
99#64436—41no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—41no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37#12011yescharacteristic
106C22×C37C2×SD1611yescharacteristic
107C22×C37AGL(1,ℤ/8)11yescharacteristic
108C2×D37—22no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—42no—
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C2×D37—81no—
116C2×D37—84no—
117C4×C37—21no—
118C4×C37—21no—
119C4×C37—41no—
120C4×C37—81no—
121Dic37—41no—
122Dic37—41no—
123Dic37—42no—
124#1601—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—81no—
128C2×C37#45011yescharacteristic
129C2×C37#45511yescharacteristic
130C2×C37B(4,𝔽2)11yescharacteristic
131D37—42no—
132D37—81no—
133#534—371no—
134#448—371no—
135#448—371no—
136#393—371no—
137#327—371no—
138#327D3711yescharacteristic, complemented
139#323—371no—
140C37#160111yescharacteristic, complemented, Sylow
141C22×Q8—371no—
142C22×D4—741no—
143C2×SD16—741no—
144C2×SD16—741no—
145#123—741no—
146#123—741no—
147#121—371no—
148#121—741no—
149#121C2×D3711yescharacteristic
150#120—741no—
151#120—741no—
152C2×C22⋊C4—371no—
153C2×C22⋊C4—741no—
154#103—741no—
155#103—741no—
156C22⋊C8—371no—
157C22⋊C8C2×D3711yescharacteristic, complemented
158#95—741no—
159#95C2×D3711yescharacteristic, complemented
160C24—371no—
161C24—741no—
162C2×Q8—741no—
163C2×Q8—741no—
164C2×Q8—1482no—
165C2×D4—21no—
166C2×D4—371no—
167C2×D4—741no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—1482no—
172C2×D4—1482no—
173C2×D4D14811yescharacteristic
174C22×C4—21no—
175C22×C4—371no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4C22×D3711yescharacteristic
179SD16—1482no—
180SD16—1482no—
181C2×C8—21no—
182C2×C8—741no—
183C4⋊C4—371no—
184C4⋊C4—741no—
185C4⋊C4D14811yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—741no—
188C22⋊C4—741no—
189C22⋊C4—741no—
190C22⋊C4—741no—
191C22⋊C4—741no—
192C22⋊C4—1482no—
193C23—21no—
194C23—372no—
195C23—2961no—
196C23—2961no—
197C23—741no—
198C23—741no—
199C23—741no—
200C23—1481no—
201C23—1481no—
202C23—1482no—
203C23D4×D3711yescharacteristic
204Q8—742no—
205Q8—742no—
206Q8—1481no—
207Q8—1481no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—2961no—
212D4—1481no—
213D4—1482no—
214D4—1482no—
215D4—1481no—
216D4—1481no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—742no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—1482no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4C2×D14811yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C8—41no—
232C8—1481no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—2961no—
239C22—2964no—
240C22—742no—
241C22—1482no—
242C22—1481no—
243C22—1481no—
244C22—1481no—
245C22—1481no—
246C22—1481no—
247C22#1192450611yescharacteristic
248C22SD16×D3711yescharacteristic
249C22#1192456011yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—1481no—
255C4—1482no—
256C4—1481no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—2961no—
261C2—1482no—
262C2#1455768511yescharacteristic
263C2#1455771211yescharacteristic
264C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37#120
prime radical#14558091C2
hypercenter#327D37
hypocenterC37#1601
LCSG ▷ C22×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. #14557674C2semidirect
3. #14557671C2semidirect
4. #14557446C2semidirect
5. #14557266C2semidirect
6. #14557256C2semidirect
7. C37×#327C2semidirect
8. C22×Dic74C22semidirect
22. C22⋊#64436C22semidirect
25. C22⋊C8×C37C22semidirect
26. #95×C37C22semidirect
70. C22×D37SD16semidirect
138. #327D37semidirect
140. C37#1601semidirect
157. C22⋊C8C2×D37semidirect
159. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580912
#145576742
#145576712
#145574462
#145572662
#145572562
C37×#3272
#160137