Finite Group Databasebeta

← #17992941

Subgroups — #17992941

Order 4736.

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

normal subgroups only

This group has 280 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
1C2×#11924518C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic, complemented
3C22⋊C8×D37C211yesmaximal, characteristic, complemented
4#14557258C211yesmaximal, characteristic, complemented
5#14557258C211yesmaximal, characteristic, complemented
6#14557257C211yesmaximal, characteristic, complemented
7C37×#323C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C411yescharacteristic
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—21no—
11C2×C8×D37—21no—
12#11924518—21no—
13#11924518—21no—
14#11924518—21no—
15#11924518—21no—
16C2×C4⋊Dic37C411yescharacteristic
17C2×#10596936C2211yescharacteristic
18C2×C22⋊Dic37C411yescharacteristic
19C2×#10596938C411yescharacteristic
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22#11924448—21no—
23#11924448—21no—
24C2×C22⋊C4×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26C22⋊C8×C37C2211yescharacteristic
27C24×C37C2×C411yescharacteristic
28C23×D37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—42no—
34C22×Dic37C2×C411yescharacteristic
35C22×Dic37C2×C411yescharacteristic
36C22×Dic37C2×C411yescharacteristic
37C2×C4×D37—42no—
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C8×C37—21no—
43C2×C8×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48#10596938—21no—
49#10596938—21no—
50C4⋊Dic37—21no—
51C4⋊Dic37—21no—
52#10596936—21no—
53#10596936—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—42no—
57C8×D37—42no—
58C23×C37—21no—
59C23×C37—21no—
60C23×C37—21no—
61C23×C37—41no—
62C23×C37—41no—
63C23×C37C22×C411yescharacteristic
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—22no—
67C22×D37—41no—
68C22×D37C22⋊C411yescharacteristic
69C22×D37C22⋊C411yescharacteristic
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C22⋊D37—42no—
76C22⋊D37—42no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—41no—
82C2×Dic37—41no—
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37C22⋊C411yescharacteristic
85C4×D37—22no—
86C4×D37—22no—
87C4×D37—41no—
88C4×D37—41no—
89C8×C37—41no—
90C8×C37—41no—
91#64436—41no—
92#64436—41no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—81no—
99C22×C37—81no—
100C22×C37C2×C22⋊C411yescharacteristic
101C22×C37#13111yescharacteristic
102C22×C37#13111yescharacteristic
103C2×D37—21no—
104C2×D37—21no—
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—21no—
108C2×D37—42no—
109C2×D37—42no—
110C2×D37#9912yes—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—41no—
114Dic37—21no—
115Dic37—21no—
116Dic37—41no—
117Dic37—41no—
118#1468—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—81no—
122C2×C37#40811yescharacteristic
123C2×C37C2×#9911yescharacteristic
124C2×C37#41311yescharacteristic
125D37—22no—
126D37—41no—
127C2×#123—371no—
128#407—371no—
129C2×C22⋊C8—371no—
130#324—371no—
131#324—371no—
132#323—371no—
133#323D3711yescharacteristic, complemented
134C37#146811yescharacteristic, complemented, Sylow
135C22×D4—371no—
136C23×C4—371no—
137C2×M16—741no—
138C22×C8—741no—
139#123—741no—
140#123—741no—
141#123—741no—
142#123—741no—
143C2×C4⋊C4—371no—
144C2×C4⋊C4—371no—
145C2×C22⋊C4—371no—
146C2×C22⋊C4—371no—
147C2×C22⋊C4C2×D3711yescharacteristic
148C22⋊C8—371no—
149C22⋊C8—371no—
150C22⋊C8—741no—
151C22⋊C8—741no—
152C22⋊C8C2×D3711yescharacteristic
153C22⋊C8C2×D3711yescharacteristic
154C24—371no—
155C24C4×D3711yescharacteristic
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—1482no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—1482no—
167C22×C4C4×D3711yescharacteristic
168C22×C4C22×D3711yescharacteristic
169M16—1482no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—741no—
173C2×C8—741no—
174C2×C8—1482no—
175C4⋊C4—741no—
176C4⋊C4—741no—
177C4⋊C4—741no—
178C4⋊C4—741no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—371no—
191C23—371no—
192C23—742no—
193C23—741no—
194C23—741no—
195C23—1481no—
196C23C2×C4×D3711yescharacteristic
197D4—1482no—
198D4—1482no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—742no—
205C2×C4—742no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1481no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4D4×D3711yescharacteristic
215C2×C4D4×D3711yescharacteristic
216C8—41no—
217C8—41no—
218C8—1481no—
219C8—1481no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—372no—
228C22—741no—
229C22—741no—
230C22—741no—
231C22—741no—
232C22—741no—
233C22—1482no—
234C22—1482no—
235C22C22⋊C4×D3711yescharacteristic
236C22#1192454211yescharacteristic
237C22#1192454411yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—741no—
242C4—741no—
243C4—1481no—
244C4—1481no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—742no—
249C2—1481no—
250C2#1455749811yescharacteristic
251C2#99×D3711yescharacteristic
252C2#1455751411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C4
cosocleC22×C4×C37C23
hypercenter#323D37
hypocenterC37#1468
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14557495C2semidirect
3. C22⋊C8×D37C2semidirect
4. #14557258C2semidirect
5. #14557258C2semidirect
6. #14557257C2semidirect
7. C37×#323C2semidirect
133. #323D37semidirect
134. C37#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#119245182
#145574952
C22⋊C8×D372
#145572582
#145572572
C37×#3232
#146837