Finite Group Databasebeta

← #17997861

Subgroups — #17997861

Order 4736.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11924496C211yesmaximal, characteristic
2C2×#11924494C211yesmaximal, characteristic, complemented
3#14557471C211yesmaximal, characteristic, complemented
4#14557465C211yesmaximal, characteristic, complemented
5#14557459C212yesmaximal, complemented
6#14557458C211yesmaximal, characteristic, complemented
7#14557449C212yesmaximal
8C4⋊C4×Dic37C212yesmaximal, complemented
9C22⋊C4×Dic37C212yesmaximal, complemented
10#14557380C211yesmaximal, characteristic, complemented
11C37×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D37C2211yescharacteristic
13C23×Dic37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15#11924496—24no—
16#11924494—24no—
17C2×C4⋊Dic37C2212yes—
18C2×C4⋊Dic37C2211yescharacteristic
19C2×#10596936C2211yescharacteristic
20C2×C22⋊Dic37C2212yes—
21C2×#10596938C2212yes—
22C2×#10596938C2212yes—
23C2×#10596938C2211yescharacteristic
24C2×C4×Dic37C2212yes—
25C2×C4×Dic37C2211yescharacteristic
26C2×C4×Dic37C2212yes—
27#11924443C2212yes—
28#11924443C2212yes—
29#11924443C2211yescharacteristic
30#11924443C2212yes—
31#11924443C2212yes—
32C2×C4⋊C4×C37C2212yes—
33C2×C4⋊C4×C37C2211yescharacteristic
34C2×C22⋊C4×C37C2212yes—
35C2×C22⋊C4×C37C2211yescharacteristic
36#95×C37C2211yescharacteristic
37C24×C37C2311yescharacteristic
38C23×D37C2311yescharacteristic
39C22×C4×C37C2311yescharacteristic
40C22×C4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C22×C4×C37C2312yes—
43C2×C22⋊D37—22no—
44C2×C22⋊D37—22no—
45C2×C22⋊D37—22no—
46C22×Dic37—22no—
47C22×Dic37—24no—
48C22×Dic37C2312yes—
49C22×Dic37C2312yes—
50C22×Dic37C2311yescharacteristic
51C22×Dic37C2311yescharacteristic
52C22×Dic37C2311yescharacteristic
53C2×C4×D37—24no—
54C2×C4×D37D414yes—
55C4⋊C4×C37—22no—
56C4⋊C4×C37—24no—
57C22⋊C4×C37—22no—
58C22⋊C4×C37—24no—
59C22⋊Dic37—24no—
60#10596938—24no—
61#10596938—22no—
62#10596938—24no—
63C4⋊Dic37—22no—
64C4⋊Dic37—24no—
65#10596936—22no—
66C4×Dic37—24no—
67C4×Dic37—22no—
68C4×Dic37—24no—
69C23×C37—21no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—21no—
73C23×C37#4112yes—
74C23×C37C2411yescharacteristic
75C22×D37—22no—
76C22×D37—22no—
77C22×D37—21no—
78C22×D37—21no—
79C22×D37C2×D412yes—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—21no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37C2×D412yes—
89C2×C4×C37#4114yes—
90C22⋊D37—28no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—22no—
94C2×Dic37—21no—
95C2×Dic37—22no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—22no—
99C2×Dic37—22no—
100C2×Dic37—22no—
101C2×Dic37—44no—
102C2×Dic37C2×D412yes—
103C2×Dic37#4112yes—
104C2×Dic37#4114yes—
105C4×D37—28no—
106C22×C37—22no—
107C22×C37—24no—
108C22×C37—41no—
109C22×C37—42no—
110C22×C37—41no—
111C22×C37C22×D411yescharacteristic
112C22×C37C2×#4112yes—
113C22×C37C2×#4111yescharacteristic
114C22×C37C2×#4112yes—
115C22×C37C2×#4111yescharacteristic
116C2×D37—22no—
117C2×D37—22no—
118C2×D37—22no—
119C2×D37—42no—
120C2×D37—42no—
121C4×C37—22no—
122C4×C37—24no—
123C4×C37—41no—
124C4×C37—42no—
125Dic37—22no—
126Dic37—41no—
127Dic37—42no—
128Dic37—42no—
129Dic37#12314yes—
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#399D3711yescharacteristic, complemented
142#398—371no—
143#397—372no—
144#397—371no—
145#394—372no—
146C4×C4⋊C4—372no—
147C4×C22⋊C4—372no—
148C4×C22⋊C4—371no—
149C37#239511yescharacteristic, complemented, Sylow
150C22×D4—371no—
151C23×C4—371no—
152C23×C4—371no—
153C4×D4—744no—
154#117—744no—
155C2×C4⋊C4—371no—
156C2×C4⋊C4—371no—
157C2×C4⋊C4—372no—
158C2×C4⋊C4C2×D3711yescharacteristic
159C2×C4⋊C4C2×D3712yes—
160C2×C22⋊C4—372no—
161C2×C22⋊C4—372no—
162C2×C22⋊C4—371no—
163C2×C22⋊C4—372no—
164C2×C22⋊C4C2×D3711yescharacteristic
165C2×C22⋊C4C2×D3712yes—
166C2×C42—372no—
167C2×C42—371no—
168C2×C42—372no—
169#95—372no—
170#95—371no—
171#95—372no—
172#95—372no—
173#95—372no—
174#95C2×D3711yescharacteristic
175C24—371no—
176C24C22×D3711yescharacteristic
177C2×D4—742no—
178C2×D4—742no—
179C2×D4—742no—
180C22×C4—371no—
181C22×C4—371no—
182C22×C4—374no—
183C22×C4—372no—
184C22×C4—371no—
185C22×C4—372no—
186C22×C4—744no—
187C22×C4—742no—
188C22×C4—744no—
189C22×C4C22×D3711yescharacteristic
190C22×C4C22×D3712yes—
191C22×C4C22×D3711yescharacteristic
192C22×C4C22×D3712yes—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—744no—
196C4⋊C4—742no—
197C4⋊C4—742no—
198C22⋊C4—22no—
199C22⋊C4—24no—
200C22⋊C4—744no—
201C22⋊C4—742no—
202C22⋊C4—744no—
203C22⋊C4—744no—
204C42—744no—
205C42—744no—
206C42—742no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—22no—
211C23—372no—
212C23—742no—
213C23—741no—
214C23—742no—
215C23—741no—
216C23#1059696612yes—
217C23C23×D3711yescharacteristic
218D4—748no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—372no—
228C2×C4—374no—
229C2×C4—372no—
230C2×C4—748no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—742no—
234C2×C4—741no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—742no—
239C2×C4—742no—
240C2×C4—742no—
241C2×C4—1484no—
242C2×C4D4×D3712yes—
243C2×C4#1059696414yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—42no—
248C22—41no—
249C22—742no—
250C22—742no—
251C22—742no—
252C22—1482no—
253C22—1482no—
254C22C2×D4×D3711yescharacteristic
255C22#41×D3712yes—
256C22#41×D3711yescharacteristic
257C22C2×#1059696412yes—
258C22C2×#1059696611yescharacteristic
259C4—22no—
260C4—24no—
261C4—41no—
262C4—42no—
263C4—374no—
264C4—742no—
265C4—1481no—
266C4—1482no—
267C4—1482no—
268C2—42no—
269C2—1482no—
270C2#123×D3711yescharacteristic
271C2#1455804611yescharacteristic
272C2#1455806012yes—
273C2#1455806912yes—
274C2#1455808111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#399C2
prime radicalC22×C22⋊D37C22
hypercenter#399D37
hypocenterC37#2395
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#11924494C2semidirect
3. #14557471C2semidirect
4. #14557465C2semidirect
5. #14557459C2semidirect
6. #14557458C2semidirect
8. C4⋊C4×Dic37C2semidirect
9. C22⋊C4×Dic37C2semidirect
10. #14557380C2semidirect
11. C37×#399C2semidirect
141. #399D37semidirect
149. C37#2395semidirect

Maximal subgroups

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

subgroupindex
C2×#119244962
C2×#119244942
#145574712
#145574652
#145574592
#145574582
#145574492
C4⋊C4×Dic372
C22⋊C4×Dic372
#145573802
C37×#3992
#239537