Finite Group Databasebeta

← #17997885

Subgroups — #17997885

Order 4736.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11924501C211yesmaximal, characteristic, complemented
2C2×#11924498C211yesmaximal, characteristic
3#14557471C211yesmaximal, characteristic, complemented
4#14557462C212yesmaximal, complemented
5#14557451C211yesmaximal, characteristic
6#14557450C211yesmaximal, characteristic
7#14557446C212yesmaximal, complemented
8#14557380C212yesmaximal, complemented
9#14557380C212yesmaximal, complemented
10#14557378C211yesmaximal, characteristic, complemented
11C37×#400C211yesmaximal, characteristic, complemented
12C22×Dic74C2211yescharacteristic
13C22×D148C2211yescharacteristic
14C22×C4×D37C2212yes—
15#11924501—24no—
16#11924498—24no—
17C2×#10596936C2211yescharacteristic
18C2×#10596936C2211yescharacteristic
19C2×#10596938C2212yes—
20C2×#10596938C2212yes—
21C2×#10596938C2212yes—
22C2×#10596938C2212yes—
23C2×#10596938C2212yes—
24C2×C4×Dic37C2211yescharacteristic
25C2×C4×Dic37C2211yescharacteristic
26C2×C4×Dic37C2212yes—
27C2×C4×Dic37C2211yescharacteristic
28#11924443C2212yes—
29#11924443C2212yes—
30#11924443C2211yescharacteristic
31#11924443C2212yes—
32C2×C4⋊C4×C37C2211yescharacteristic
33C2×C4⋊C4×C37C2211yescharacteristic
34#95×C37C2212yes—
35#95×C37C2211yescharacteristic
36#95×C37C2212yes—
37C23×D37C2312yes—
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C2312yes—
40C22×C4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C22×C4×C37C2311yescharacteristic
43C22×Dic37C2311yescharacteristic
44C22×Dic37C2312yes—
45C22×Dic37C2311yescharacteristic
46C22×Dic37C2311yescharacteristic
47C22×Dic37C2311yescharacteristic
48C2×D148—24no—
49C2×D148—22no—
50C2×C4×D37—24no—
51C2×C4×D37—24no—
52C2×C4×D37—24no—
53C2×Dic74—22no—
54C2×Dic74—22no—
55C2×Dic74—22no—
56C4⋊C4×C37—22no—
57C4⋊C4×C37—22no—
58#10596938—24no—
59#10596938—24no—
60#10596938—24no—
61#10596938—24no—
62#10596938—24no—
63#10596936—22no—
64#10596936—22no—
65C4×Dic37—22no—
66C4×Dic37—22no—
67C4×Dic37—24no—
68C4×Dic37D414yes—
69C23×C37C2411yescharacteristic
70C22×D37—22no—
71C22×D37—22no—
72C22×D37—22no—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37—22no—
76C22×D37#4114yes—
77C2×C4×C37—21no—
78C2×C4×C37—21no—
79C2×C4×C37—22no—
80C2×C4×C37—21no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37C2×D412yes—
89C2×C4×C37#4112yes—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—21no—
94C2×Dic37—21no—
95C2×Dic37—22no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—22no—
99C2×Dic37C2×D412yes—
100C2×Dic37C2×D412yes—
101C2×Dic37#4112yes—
102C2×Dic37#4114yes—
103D148—28no—
104C4×D37—48no—
105Dic74—28no—
106C22×C37C22×D411yescharacteristic
107C22×C37C2×#4112yes—
108C22×C37C2×#4111yescharacteristic
109C22×C37C2×#4112yes—
110C22×C37C2×#4111yescharacteristic
111C2×D37—24no—
112C2×D37—24no—
113C2×D37—24no—
114C2×D37—42no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—42no—
118C4×C37—22no—
119C4×C37—22no—
120C4×C37—41no—
121C4×C37—42no—
122C4×C37—42no—
123Dic37—22no—
124Dic37—22no—
125Dic37—41no—
126Dic37—42no—
127Dic37#12414yes—
128#2398—371nomaximal, Sylow
129C2×C37#52511yescharacteristic
130C2×C37#52511yescharacteristic
131C2×C37C2×#12411yescharacteristic
132C2×C37#52912yes—
133C2×C37#52912yes—
134D37—44no—
135C2×C4×Q8—371no—
136C2×C4×D4—371no—
137#400—371no—
138#400D3711yescharacteristic, complemented
139#397—372no—
140#394—371no—
141#394—371no—
142#393—372no—
143C4×C22⋊C4—372no—
144C4×C22⋊C4—372no—
145#376—371no—
146C37#239811yescharacteristic, complemented, Sylow
147C22×Q8—371no—
148C22×D4—371no—
149C23×C4—372no—
150C4×Q8—744no—
151C4×D4—744no—
152C2×C4⋊C4—371no—
153C2×C4⋊C4—371no—
154C2×C4⋊C4C2×D3711yescharacteristic
155C2×C4⋊C4C2×D3711yescharacteristic
156C2×C22⋊C4—372no—
157C2×C22⋊C4—372no—
158C2×C22⋊C4—372no—
159C2×C22⋊C4—372no—
160C2×C22⋊C4—372no—
161C2×C42—371no—
162C2×C42—371no—
163C2×C42—371no—
164C2×C42—372no—
165#95—372no—
166#95—371no—
167#95—372no—
168#95—372no—
169#95C2×D3711yescharacteristic
170#95C2×D3712yes—
171#95C2×D3712yes—
172C24—372no—
173C2×Q8—742no—
174C2×Q8—742no—
175C2×Q8—742no—
176C2×D4—744no—
177C2×D4—742no—
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—372no—
182C22×C4—371no—
183C22×C4—744no—
184C22×C4—744no—
185C22×C4—744no—
186C22×C4C22×D3712yes—
187C22×C4C22×D3712yes—
188C22×C4C22×D3711yescharacteristic
189C22×C4C22×D3711yescharacteristic
190C22×C4C22×D3711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—742no—
194C4⋊C4—742no—
195C22⋊C4—744no—
196C22⋊C4—744no—
197C22⋊C4—744no—
198C22⋊C4—744no—
199C22⋊C4—744no—
200C42—374no—
201C42—744no—
202C42—742no—
203C42—742no—
204C23—374no—
205C23—742no—
206C23—742no—
207C23—742no—
208C23—742no—
209C23—742no—
210C23—742no—
211C23C23×D3711yescharacteristic
212Q8—748no—
213D4—748no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—372no—
226C2×C4—374no—
227C2×C4—372no—
228C2×C4—372no—
229C2×C4—741no—
230C2×C4—741no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—741no—
234C2×C4—742no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—1488no—
239C2×C4D4×D3712yes—
240C2×C4#1059696612yes—
241C22—744no—
242C22—744no—
243C22—744no—
244C22—1482no—
245C22—1482no—
246C22—1482no—
247C22—1482no—
248C22C2×D4×D3711yescharacteristic
249C22#41×D3712yes—
250C22#41×D3711yescharacteristic
251C22#41×D3712yes—
252C22C2×#1059696611yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—42no—
258C4—374no—
259C4—742no—
260C4—742no—
261C4—1481no—
262C4—1482no—
263C2—1484no—
264C2#1455804111yescharacteristic
265C2#1455804611yescharacteristic
266C2#124×D3711yescharacteristic
267C2#1455806612yes—
268C2#1455806812yes—
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#400C2
prime radicalC22×D148C22
hypercenter#400D37
hypocenterC37#2398
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#11924501C2semidirect
3. #14557471C2semidirect
4. #14557462C2semidirect
7. #14557446C2semidirect
8. #14557380C2semidirect
9. #14557380C2semidirect
10. #14557378C2semidirect
11. C37×#400C2semidirect
138. #400D37semidirect
146. C37#2398semidirect

Maximal subgroups

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

subgroupindex
C2×#119245012
C2×#119244982
#145574712
#145574622
#145574512
#145574502
#145574462
#145573802
#145573782
C37×#4002
#239837