Finite Group Databasebeta

← #17997856

Subgroups — #17997856

Order 4736.

560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D37C211yesmaximal, characteristic
2C2×#11924495C211yesmaximal, characteristic, complemented
3#14557473C211yesmaximal, characteristic, complemented
4#14557470C211yesmaximal, characteristic, complemented
5#14557465C211yesmaximal, characteristic, complemented
6#14557460C211yesmaximal, characteristic, complemented
7#14557458C212yesmaximal, complemented
8#14557449C212yesmaximal
9C4×C4⋊Dic37C212yesmaximal, complemented
10C4×#10596938C212yesmaximal, complemented
11C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
12C22×C22⋊D37C2211yescharacteristic
13C22×C4×D37C2211yescharacteristic
14C4×C22⋊D37—24no—
15#11924495—24no—
16C2×C4⋊Dic37C2212yes—
17C2×C4⋊Dic37C2212yes—
18C2×C4⋊Dic37C2211yescharacteristic
19C2×C4⋊Dic37C2211yescharacteristic
20C2×#10596936C2211yescharacteristic
21C2×C22⋊Dic37C2212yes—
22C2×C22⋊Dic37C2211yescharacteristic
23C2×#10596938C2212yes—
24C2×#10596938C2212yes—
25C2×#10596938C2211yescharacteristic
26C2×C4×Dic37C2212yes—
27C2×C4×Dic37C2211yescharacteristic
28#11924443C2212yes—
29#11924443C2212yes—
30#11924443C2212yes—
31#11924443C2212yes—
32C23×C4×C37C2211yescharacteristic
33C2×C22⋊C4×C37C2212yes—
34C2×C42×C37C2212yes—
35#95×C37C2211yescharacteristic
36#95×C37C2211yescharacteristic
37C24×C37C2311yescharacteristic
38C23×D37C2311yescharacteristic
39C22×C4×C37—24no—
40C22×C4×C37D414yes—
41C22×C4×C37C2312yes—
42C22×C4×C37C2311yescharacteristic
43C22×C4×C37C2312yes—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—22no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48C22×Dic37C2312yes—
49C22×Dic37C2312yes—
50C22×Dic37C2311yescharacteristic
51C22×Dic37C2311yescharacteristic
52C22×Dic37C2311yescharacteristic
53C2×C4×D37—22no—
54C2×C4×D37—24no—
55C22⋊C4×C37—24no—
56C42×C37—24no—
57C22⋊Dic37—24no—
58C22⋊Dic37—22no—
59#10596938—24no—
60#10596938—22no—
61#10596938—24no—
62C4⋊Dic37—22no—
63C4⋊Dic37—22no—
64C4⋊Dic37—24no—
65C4⋊Dic37—24no—
66#10596936—22no—
67C4×Dic37—24no—
68C4×Dic37—22no—
69C23×C37—22no—
70C23×C37—21no—
71C23×C37—21no—
72C23×C37—22no—
73C23×C37C2×D412yes—
74C23×C37C2411yescharacteristic
75C22×D37—21no—
76C22×D37—22no—
77C22×D37—22no—
78C22×D37—21no—
79C22×D37#4112yes—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—28no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37C2×D412yes—
88C2×C4×C37C2×D412yes—
89C2×C4×C37#4114yes—
90C2×C4×C37#4114yes—
91C22⋊D37—28no—
92C2×Dic37—21no—
93C2×Dic37—21no—
94C2×Dic37—22no—
95C2×Dic37—22no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37—22no—
99C2×Dic37—22no—
100C2×Dic37—22no—
101C2×Dic37—22no—
102C2×Dic37—22no—
103C2×Dic37—22no—
104C2×Dic37#4112yes—
105C4×D37—44no—
106C22×C37—22no—
107C22×C37—22no—
108C22×C37—22no—
109C22×C37—42no—
110C22×C37—42no—
111C22×C37C22×D411yescharacteristic
112C22×C37C2×#4111yescharacteristic
113C22×C37C2×#4111yescharacteristic
114C22×C37C2×#4112yes—
115C22×C37C2×#4112yes—
116C2×D37—22no—
117C2×D37—24no—
118C2×D37—41no—
119C2×D37—42no—
120C2×D37—41no—
121C4×C37—22no—
122C4×C37—24no—
123C4×C37—42no—
124C4×C37#12314yes—
125Dic37—22no—
126Dic37—41no—
127Dic37—42no—
128Dic37—42no—
129Dic37—41no—
130#2395—371nomaximal, Sylow
131C2×C37—42no—
132C2×C37C2×#12311yescharacteristic
133C2×C37#52511yescharacteristic
134C2×C37#52912yes—
135C2×C37#52912yes—
136C2×C37#53211yescharacteristic
137D37—42no—
138C2×C4×D4—371no—
139C2×#117—371no—
140#400—371no—
141#399—371no—
142#398—371no—
143#397—372no—
144#397—371no—
145#394—372no—
146C4×C4⋊C4—372no—
147C4×C22⋊C4—372no—
148C4×C22⋊C4D3711yescharacteristic, complemented
149C37#239511yescharacteristic, complemented, Sylow
150C22×D4—371no—
151C23×C4—371no—
152C23×C4C2×D3711yescharacteristic
153C4×D4—744no—
154#117—744no—
155C2×C4⋊C4—371no—
156C2×C4⋊C4—371no—
157C2×C4⋊C4—371no—
158C2×C4⋊C4—372no—
159C2×C4⋊C4—372no—
160C2×C22⋊C4—372no—
161C2×C22⋊C4—371no—
162C2×C22⋊C4—371no—
163C2×C22⋊C4—372no—
164C2×C22⋊C4—372no—
165C2×C22⋊C4C2×D3712yes—
166C2×C42—372no—
167C2×C42—371no—
168C2×C42C2×D3712yes—
169#95—372no—
170#95—372no—
171#95—372no—
172#95—372no—
173#95C2×D3711yescharacteristic
174#95C2×D3711yescharacteristic
175C24—371no—
176C24C22×D3711yescharacteristic
177C2×D4—742no—
178C2×D4—742no—
179C2×D4—742no—
180C22×C4—24no—
181C22×C4—371no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—372no—
185C22×C4—372no—
186C22×C4—742no—
187C22×C4—744no—
188C22×C4D14814yes—
189C22×C4C22×D3712yes—
190C22×C4C22×D3711yescharacteristic
191C22×C4C22×D3712yes—
192C22×C4C22×D3711yescharacteristic
193C4⋊C4—744no—
194C4⋊C4—742no—
195C4⋊C4—742no—
196C4⋊C4—742no—
197C4⋊C4—744no—
198C22⋊C4—24no—
199C22⋊C4—744no—
200C22⋊C4—744no—
201C22⋊C4—742no—
202C22⋊C4—742no—
203C22⋊C4—744no—
204C42—24no—
205C42—744no—
206C42—742no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—372no—
212C23—741no—
213C23—741no—
214C23—742no—
215C23—742no—
216C23C2×D14812yes—
217C23C23×D3711yescharacteristic
218D4—748no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—372no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—741no—
230C2×C4—742no—
231C2×C4—742no—
232C2×C4—741no—
233C2×C4—742no—
234C2×C4—742no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—742no—
239C2×C4—1484no—
240C2×C4C2×D14812yes—
241C2×C4C2×D14812yes—
242C2×C4#1059696214yes—
243C2×C4#1059696414yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—742no—
250C22—744no—
251C22—1481no—
252C22—1482no—
253C22—1481no—
254C22C22×D14811yescharacteristic
255C22#41×D3711yescharacteristic
256C22#41×D3711yescharacteristic
257C22C2×#1059696412yes—
258C22C2×#1059696212yes—
259C4—22no—
260C4—24no—
261C4—42no—
262C4—742no—
263C4—1481no—
264C4—1482no—
265C4—1481no—
266C4—1482no—
267C4#1192452014yes—
268C2—42no—
269C2—1482no—
270C2C2×#1192452011yescharacteristic
271C2#1455804511yescharacteristic
272C2#1455806312yes—
273C2#1455806512yes—
274C2#1455808311yescharacteristic
subgroupG/H
centerC22×C4C22×D37
commutator, socle, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC4×C22⋊C4×C37C2
prime radicalC22×C22⋊D37C22
hypercenterC4×C22⋊C4D37
hypocenterC37#2395
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11924495C2semidirect
3. #14557473C2semidirect
4. #14557470C2semidirect
5. #14557465C2semidirect
6. #14557460C2semidirect
7. #14557458C2semidirect
9. C4×C4⋊Dic37C2semidirect
10. C4×#10596938C2semidirect
11. C4×C22⋊C4×C37C2semidirect
148. C4×C22⋊C4D37semidirect
149. C37#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D372
C2×#119244952
#145574732
#145574702
#145574652
#145574602
#145574582
#145574492
C4×C4⋊Dic372
C4×#105969382
C4×C22⋊C4×C372
#239537