Finite Group Databasebeta

← #17997884

Subgroups — #17997884

Order 4736.

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

normal subgroups only

This group has 568 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×#11924501C211yesmaximal, characteristic, complemented
2C2×D4×Dic37C211yesmaximal, characteristic
3#14557473C211yesmaximal, characteristic, complemented
4#14557472C211yesmaximal, characteristic, complemented
5#14557461C212yesmaximal, complemented
6#14557447C211yesmaximal, characteristic
7#14557445C212yesmaximal, complemented
8C22⋊C4×Dic37C212yesmaximal, complemented
9C22⋊C4×Dic37C212yesmaximal, complemented
10#14557378C211yesmaximal, characteristic, complemented
11C37×#394C211yesmaximal, characteristic
12C22×Dic74C2211yescharacteristic
13C23×Dic37C2212yes—
14#11924501—24no—
15D4×Dic37—24no—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C2211yescharacteristic
18C2×#10596936C2211yescharacteristic
19C2×C22⋊Dic37C2212yes—
20C2×C22⋊Dic37C2212yes—
21C2×C22⋊Dic37C2212yes—
22C2×C4×Dic37C2211yescharacteristic
23C2×C4×Dic37C2211yescharacteristic
24C2×C4×Dic37C2212yes—
25C2×C4×Dic37C2211yescharacteristic
26#11924443C2212yes—
27#11924443C2212yes—
28#11924443C2212yes—
29#11924443C2211yescharacteristic
30#11924443C2212yes—
31#11924443C2212yes—
32C22×D4×C37C2211yescharacteristic
33C2×C4⋊C4×C37C2211yescharacteristic
34C2×C22⋊C4×C37C2212yes—
35C2×C22⋊C4×C37C2212yes—
36#95×C37C2211yescharacteristic
37C24×C37C2312yes—
38C2×D4×C37—24no—
39C2×D4×C37—22no—
40C22×C4×C37C2311yescharacteristic
41C22×C4×C37C2312yes—
42C22×C4×C37C2311yescharacteristic
43C22×C4×C37C2311yescharacteristic
44C22×Dic37—24no—
45C22×Dic37—24no—
46C22×Dic37—24no—
47C22×Dic37C2311yescharacteristic
48C22×Dic37C2312yes—
49C22×Dic37C2312yes—
50C22×Dic37C2311yescharacteristic
51C22×Dic37C2311yescharacteristic
52C22×Dic37C2311yescharacteristic
53C2×Dic74—22no—
54C2×Dic74—22no—
55C2×Dic74—22no—
56C4⋊C4×C37—22no—
57C22⋊C4×C37—24no—
58C22⋊C4×C37—24no—
59C22⋊Dic37—24no—
60C22⋊Dic37—24no—
61C22⋊Dic37—24no—
62C4⋊Dic37—22no—
63#10596936—22no—
64#10596936—22no—
65C4×Dic37—22no—
66C4×Dic37—22no—
67C4×Dic37—24no—
68C4×Dic37D414yes—
69C23×C37—22no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37—22no—
74C23×C37—22no—
75C23×C37#4114yes—
76C23×C37C2411yescharacteristic
77D4×C37—28no—
78C2×C4×C37—21no—
79C2×C4×C37—21no—
80C2×C4×C37—22no—
81C2×C4×C37—21no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37C2×D412yes—
87C2×C4×C37#4112yes—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—22no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—22no—
99C2×Dic37—22no—
100C2×Dic37—48no—
101C2×Dic37C2×D412yes—
102C2×Dic37C2×D412yes—
103C2×Dic37#4112yes—
104C2×Dic37#4114yes—
105Dic74—28no—
106C22×C37—24no—
107C22×C37—24no—
108C22×C37—24no—
109C22×C37—42no—
110C22×C37—42no—
111C22×C37—42no—
112C22×C37—42no—
113C22×C37C22×D411yescharacteristic
114C22×C37C2×#4111yescharacteristic
115C22×C37C2×#4112yes—
116C22×C37C2×#4112yes—
117C22×C37C2×#4111yescharacteristic
118C4×C37—22no—
119C4×C37—22no—
120C4×C37—41no—
121C4×C37—42no—
122Dic37—22no—
123Dic37—22no—
124Dic37—41no—
125Dic37—42no—
126Dic37—42no—
127Dic37#12414yes—
128#2398—371nomaximal, Sylow
129C2×C37—44no—
130C2×C37#52511yescharacteristic
131C2×C37#52511yescharacteristic
132C2×C37C2×#12411yescharacteristic
133C2×C37#52912yes—
134C2×C37#52912yes—
135C2×C4×Q8—371no—
136C2×C4×D4—371no—
137#400—371no—
138#400—371no—
139#397—372no—
140#394—371no—
141#394D3711yescharacteristic
142#393—372no—
143C4×C22⋊C4—372no—
144C4×C22⋊C4—372no—
145#376—371no—
146C37#239811yescharacteristic, complemented, Sylow
147C22×Q8—371no—
148C22×D4C2×D3711yescharacteristic
149C23×C4—372no—
150C4×Q8—744no—
151C4×D4—744no—
152C2×C4⋊C4—371no—
153C2×C4⋊C4—371no—
154C2×C4⋊C4—371no—
155C2×C4⋊C4C2×D3711yescharacteristic
156C2×C22⋊C4—372no—
157C2×C22⋊C4—372no—
158C2×C22⋊C4—372no—
159C2×C22⋊C4C2×D3712yes—
160C2×C22⋊C4C2×D3712yes—
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#95—372no—
170#95—372no—
171#95C2×D3711yescharacteristic
172C24C22×D3712yes—
173C2×Q8—742no—
174C2×Q8—742no—
175C2×Q8—742no—
176C2×D4—24no—
177C2×D4—22no—
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—372no—
182C22×C4—372no—
183C22×C4—371no—
184C22×C4—744no—
185C22×C4—744no—
186C22×C4—744no—
187C22×C4C22×D3712yes—
188C22×C4C22×D3711yescharacteristic
189C22×C4C22×D3711yescharacteristic
190C22×C4C22×D3711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—742no—
193C4⋊C4—742no—
194C4⋊C4—742no—
195C22⋊C4—24no—
196C22⋊C4—24no—
197C22⋊C4—744no—
198C22⋊C4—744no—
199C22⋊C4—744no—
200C42—374no—
201C42—744no—
202C42—742no—
203C42—742no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23#1059696414yes—
211C23C23×D3711yescharacteristic
212Q8—748no—
213D4—28no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—372no—
223C2×C4—374no—
224C2×C4—372no—
225C2×C4—372no—
226C2×C4—741no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—741no—
230C2×C4—741no—
231C2×C4—742no—
232C2×C4—742no—
233C2×C4—742no—
234C2×C4—742no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—1488no—
239C2×C4D4×D3712yes—
240C2×C4#1059696412yes—
241C22—24no—
242C22—24no—
243C22—24no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D3711yescharacteristic
249C22#41×D3711yescharacteristic
250C22#41×D3712yes—
251C22C2×#1059696412yes—
252C22C2×#1059696411yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—374no—
258C4—742no—
259C4—742no—
260C4—1481no—
261C4—1482no—
262C4—1482no—
263C2—44no—
264C2#1455803911yescharacteristic
265C2#1455804311yescharacteristic
266C2#124×D3711yescharacteristic
267C2#1455806012yes—
268C2#1455806412yes—
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#394C2
prime radicalC22×D4×C37C22
hypercenter#394D37
hypocenterC37#2398
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#11924501C2semidirect
3. #14557473C2semidirect
4. #14557472C2semidirect
5. #14557461C2semidirect
7. #14557445C2semidirect
8. C22⋊C4×Dic37C2semidirect
9. C22⋊C4×Dic37C2semidirect
10. #14557378C2semidirect
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×D4×Dic372
#145574732
#145574722
#145574612
#145574472
#145574452
C22⋊C4×Dic372
#145573782
C37×#3942
#239837