Finite Group Databasebeta

← #17997881

Subgroups — #17997881

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×#11924496C211yesmaximal, characteristic
3#14557474C212yesmaximal, complemented
4#14557459C211yesmaximal, characteristic, complemented
5#14557448C212yesmaximal
6#14557446C211yesmaximal, characteristic, complemented
7#14557445C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic37C212yesmaximal, complemented
9#14557380C212yesmaximal, complemented
10#14557378C211yesmaximal, characteristic, complemented
11C37×#397C211yesmaximal, characteristic, complemented
12C22×Dic74C2211yescharacteristic
13C22×C22⋊D37C2211yescharacteristic
14C23×Dic37C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924501—24no—
17#11924496—24no—
18C2×#10596936C2212yes—
19C2×#10596936C2211yescharacteristic
20C2×C22⋊Dic37C2212yes—
21C2×#10596938C2212yes—
22C2×#10596938C2211yescharacteristic
23C2×#10596938C2212yes—
24C2×C4×Dic37C2212yes—
25C2×C4×Dic37C2212yes—
26C2×C4×Dic37C2211yescharacteristic
27#11924443C2211yescharacteristic
28#11924443C2212yes—
29#11924443C2212yes—
30#11924443C2212yes—
31#11924443C2212yes—
32C2×C4⋊C4×C37C2211yescharacteristic
33C2×C22⋊C4×C37C2211yescharacteristic
34C2×C22⋊C4×C37C2212yes—
35#95×C37C2211yescharacteristic
36#95×C37C2212yes—
37C24×C37C2311yescharacteristic
38C23×D37C2311yescharacteristic
39C22×C4×C37C2312yes—
40C22×C4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C22×C4×C37C2311yescharacteristic
43C2×C22⋊D37—22no—
44C2×C22⋊D37—22no—
45C2×C22⋊D37—22no—
46C22×Dic37—22no—
47C22×Dic37—24no—
48C22×Dic37C2312yes—
49C22×Dic37C2311yescharacteristic
50C22×Dic37C2311yescharacteristic
51C22×Dic37C2312yes—
52C22×Dic37C2311yescharacteristic
53C2×C4×D37—22no—
54C2×C4×D37—24no—
55C2×Dic74—22no—
56C2×Dic74—24no—
57C4⋊C4×C37—22no—
58C22⋊C4×C37—24no—
59C22⋊C4×C37—22no—
60C22⋊Dic37—24no—
61#10596938—24no—
62#10596938—22no—
63#10596938—24no—
64#10596936—22no—
65#10596936—24no—
66C4×Dic37—24no—
67C4×Dic37—24no—
68C4×Dic37D414yes—
69C23×C37—21no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—21no—
73C23×C37#4112yes—
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—21no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—22no—
89C2×C4×C37C2×D412yes—
90C22⋊D37—28no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37—21no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—22no—
99C2×Dic37—22no—
100C2×Dic37—44no—
101C2×Dic37C2×D412yes—
102C2×Dic37C2×D412yes—
103C2×Dic37#4114yes—
104C2×Dic37#4114yes—
105C4×D37—44no—
106Dic74—28no—
107C22×C37—22no—
108C22×C37—24no—
109C22×C37—41no—
110C22×C37—41no—
111C22×C37—42no—
112C22×C37C22×D411yescharacteristic
113C22×C37C2×#4111yescharacteristic
114C22×C37C2×#4112yes—
115C22×C37C2×#4112yes—
116C22×C37C2×#4111yescharacteristic
117C2×D37—22no—
118C2×D37—24no—
119C2×D37—41no—
120C2×D37—41no—
121C2×D37—42no—
122C4×C37—22no—
123C4×C37—42no—
124C4×C37—41no—
125C4×C37—42no—
126Dic37—24no—
127Dic37—22no—
128Dic37—41no—
129Dic37—42no—
130Dic37#12414yes—
131#2398—371nomaximal, Sylow
132C2×C37—42no—
133C2×C37#52511yescharacteristic
134C2×C37#52511yescharacteristic
135C2×C37C2×#12411yescharacteristic
136C2×C37#52912yes—
137C2×C37#52912yes—
138D37—42no—
139C2×C4×Q8—371no—
140C2×C4×D4—371no—
141#400—372no—
142#397—371no—
143#397D3711yescharacteristic, complemented
144#394—372no—
145#393—371no—
146#393—371no—
147C4×C22⋊C4—372no—
148C4×C22⋊C4—372no—
149#376—371no—
150C37#239811yescharacteristic, complemented, Sylow
151C22×Q8—371no—
152C22×D4—371no—
153C23×C4—371no—
154C23×C4—371no—
155C4×Q8—744no—
156C4×D4—744no—
157C2×C4⋊C4—371no—
158C2×C4⋊C4—372no—
159C2×C4⋊C4C2×D3711yescharacteristic
160C2×C22⋊C4—372no—
161C2×C22⋊C4—371no—
162C2×C22⋊C4—372no—
163C2×C22⋊C4—372no—
164C2×C22⋊C4C2×D3711yescharacteristic
165C2×C22⋊C4C2×D3712yes—
166C2×C42—371no—
167C2×C42—372no—
168C2×C42—372no—
169#95—371no—
170#95—372no—
171#95—372no—
172#95—372no—
173#95—372no—
174#95C2×D3711yescharacteristic
175#95C2×D3712yes—
176C24—371no—
177C24C22×D3711yescharacteristic
178C2×Q8—744no—
179C2×Q8—742no—
180C2×D4—742no—
181C2×D4—742no—
182C2×D4—742no—
183C22×C4—371no—
184C22×C4—372no—
185C22×C4—371no—
186C22×C4—372no—
187C22×C4—371no—
188C22×C4—742no—
189C22×C4—744no—
190C22×C4—742no—
191C22×C4—744no—
192C22×C4C22×D3712yes—
193C22×C4C22×D3711yescharacteristic
194C22×C4C22×D3712yes—
195C22×C4C22×D3711yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—742no—
198C4⋊C4—744no—
199C22⋊C4—24no—
200C22⋊C4—22no—
201C22⋊C4—744no—
202C22⋊C4—744no—
203C22⋊C4—744no—
204C22⋊C4—742no—
205C42—374no—
206C42—744no—
207C42—744no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—372no—
213C23—741no—
214C23—742no—
215C23—742no—
216C23—741no—
217C23#1059696412yes—
218C23C23×D3711yescharacteristic
219Q8—748no—
220D4—748no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—372no—
231C2×C4—374no—
232C2×C4—372no—
233C2×C4—374no—
234C2×C4—742no—
235C2×C4—741no—
236C2×C4—742no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4—742no—
241C2×C4—742no—
242C2×C4—742no—
243C2×C4—1484no—
244C2×C4—1484no—
245C2×C4D4×D3712yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—742no—
252C22—744no—
253C22—1481no—
254C22—1481no—
255C22—1482no—
256C22C2×D4×D3711yescharacteristic
257C22#41×D3712yes—
258C22#41×D3711yescharacteristic
259C22#41×D3712yes—
260C22C2×#1059696411yescharacteristic
261C4—22no—
262C4—42no—
263C4—41no—
264C4—42no—
265C4—374no—
266C4—744no—
267C4—742no—
268C4—1481no—
269C4—1482no—
270C2—42no—
271C2—1482no—
272C2#1455804111yescharacteristic
273C2#1455804311yescharacteristic
274C2#124×D3711yescharacteristic
275C2#1455806012yes—
276C2#1455806612yes—
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#397C2
prime radicalC22×C22⋊D37C22
hypercenter#397D37
hypocenterC37#2398
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#11924501C2semidirect
3. #14557474C2semidirect
4. #14557459C2semidirect
6. #14557446C2semidirect
7. #14557445C2semidirect
8. C22⋊C4×Dic37C2semidirect
9. #14557380C2semidirect
10. #14557378C2semidirect
11. C37×#397C2semidirect
143. #397D37semidirect
150. 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×#119244962
#145574742
#145574592
#145574482
#145574462
#145574452
C22⋊C4×Dic372
#145573802
#145573782
C37×#3972
#239837