Finite Group Databasebeta

← #17997863

Subgroups — #17997863

Order 4736.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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×Q8×Dic37C211yesmaximal, characteristic, complemented
2C2×#11924492C211yesmaximal, characteristic
3#14557473C211yesmaximal, characteristic, complemented
4#14557469C211yesmaximal, characteristic
5#14557467C212yesmaximal, complemented
6#14557456C212yesmaximal
7#14557452C211yesmaximal, characteristic, complemented
8#14557384C212yesmaximal, complemented
9#14557384C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic37C212yesmaximal
11C37×#393C211yesmaximal, characteristic
12C23×Dic37C2211yescharacteristic
13Q8×Dic37—24no—
14#11924492—24no—
15C2×C4⋊Dic37C2212yes—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C2212yes—
18C2×#10596936C2211yescharacteristic
19C2×#10596936C2212yes—
20C2×#10596936C2211yescharacteristic
21C2×#10596936C2212yes—
22C2×C22⋊Dic37C2211yescharacteristic
23C2×C22⋊Dic37C2212yes—
24C2×C4×Dic37C2211yescharacteristic
25C2×C4×Dic37C2212yes—
26C2×C4×Dic37C2212yes—
27C2×C4×Dic37C2211yescharacteristic
28#11924443C2212yes—
29#11924443C2211yescharacteristic
30#11924443C2212yes—
31#11924443C2212yes—
32C22×Q8×C37C2211yescharacteristic
33C2×C22⋊C4×C37C2212yes—
34C2×C22⋊C4×C37C2211yescharacteristic
35#95×C37C2212yes—
36#95×C37C2211yescharacteristic
37C24×C37C2311yescharacteristic
38C2×Q8×C37—22no—
39C2×Q8×C37—24no—
40C22×C4×C37C2311yescharacteristic
41C22×C4×C37C2312yes—
42C22×C4×C37C2311yescharacteristic
43C22×C4×C37C2312yes—
44C22×Dic37—22no—
45C22×Dic37—22no—
46C22×Dic37Q814yescomplemented
47C22×Dic37C2311yescharacteristic
48C22×Dic37C2312yes—
49C22×Dic37C2311yescharacteristic
50C22×Dic37C2311yescharacteristic
51C22×Dic37C2312yes—
52C22×Dic37C2311yescharacteristic
53C22⋊C4×C37—22no—
54C22⋊C4×C37—24no—
55C22⋊Dic37—22no—
56C22⋊Dic37—24no—
57C4⋊Dic37—22no—
58C4⋊Dic37—24no—
59#10596936—22no—
60#10596936—24no—
61#10596936—22no—
62#10596936—24no—
63#10596936—24no—
64C4×Dic37—22no—
65C4×Dic37—24no—
66C4×Dic37—24no—
67C4×Dic37D414yes—
68C23×C37—21no—
69C23×C37—22no—
70C23×C37—22no—
71C23×C37—21no—
72C23×C37C2×Q812yes—
73C23×C37C2411yescharacteristic
74Q8×C37—28no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—22no—
78C2×C4×C37—21no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37C2×D412yes—
84C2×C4×C37#4114yes—
85C2×Dic37—21no—
86C2×Dic37—22no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—21no—
90C2×Dic37—28no—
91C2×Dic37—21no—
92C2×Dic37—22no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—22no—
96C2×Dic37C2×D412yes—
97C2×Dic37C2×D412yes—
98C2×Dic37C2×Q812yes—
99C2×Dic37C2×Q812yes—
100C2×Dic37#4114yes—
101C2×Dic37#4112yes—
102C22×C37—22no—
103C22×C37—24no—
104C22×C37—41no—
105C22×C37—42no—
106C22×C37—41no—
107C22×C37C22×D411yescharacteristic
108C22×C37C22×Q811yescharacteristic
109C22×C37C2×#4111yescharacteristic
110C22×C37C2×#4112yes—
111C22×C37C2×#4112yes—
112C4×C37—22no—
113C4×C37—24no—
114C4×C37—42no—
115C4×C37—41no—
116Dic37—22no—
117Dic37—24no—
118Dic37—22no—
119Dic37—41no—
120Dic37—42no—
121Dic37C22⋊Q814yes—
122#2396—371nomaximal, Sylow
123C2×C37—42no—
124C2×C37C2×C22⋊Q811yescharacteristic
125C2×C37#52511yescharacteristic
126C2×C37#52912yes—
127C2×C37#53211yescharacteristic
128C2×C37#53312yes—
129C2×C4×Q8—371no—
130C2×#117—371no—
131#400—371no—
132#399—371no—
133#398—372no—
134#396—372no—
135#395—371no—
136#393D3711yescharacteristic
137C4×C4⋊C4—371no—
138C4×C4⋊C4—372no—
139C4×C22⋊C4—372no—
140C37#239611yescharacteristic, complemented, Sylow
141C22×Q8C2×D3711yescharacteristic
142C23×C4—371no—
143C4×Q8—744no—
144#117—744no—
145C2×C4⋊C4—371no—
146C2×C4⋊C4—371no—
147C2×C4⋊C4—372no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4—372no—
150C2×C4⋊C4—372no—
151C2×C4⋊C4—372no—
152C2×C22⋊C4—371no—
153C2×C22⋊C4—372no—
154C2×C22⋊C4C2×D3711yescharacteristic
155C2×C22⋊C4C2×D3712yes—
156C2×C42—371no—
157C2×C42—371no—
158C2×C42—372no—
159C2×C42—372no—
160#95—372no—
161#95—372no—
162#95—371no—
163#95—372no—
164#95C2×D3712yes—
165#95C2×D3711yescharacteristic
166C24C22×D3711yescharacteristic
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—371no—
170C22×C4—374no—
171C22×C4—371no—
172C22×C4—372no—
173C22×C4—371no—
174C22×C4—371no—
175C22×C4—372no—
176C22×C4—742no—
177C22×C4—742no—
178C22×C4C22×D3712yes—
179C22×C4C22×D3711yescharacteristic
180C22×C4C22×D3711yescharacteristic
181C22×C4C22×D3712yes—
182C4⋊C4—744no—
183C4⋊C4—744no—
184C4⋊C4—742no—
185C4⋊C4—744no—
186C4⋊C4—742no—
187C4⋊C4—742no—
188C4⋊C4—744no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—744no—
192C22⋊C4—742no—
193C42—374no—
194C42—744no—
195C42—742no—
196C42—744no—
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D3712yes—
202C23C23×D3711yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—372no—
213C2×C4—372no—
214C2×C4—372no—
215C2×C4—372no—
216C2×C4—372no—
217C2×C4—374no—
218C2×C4—748no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—742no—
224C2×C4—741no—
225C2×C4—742no—
226C2×C4—742no—
227C2×C4—742no—
228C2×C4—742no—
229C2×C4D4×D3712yes—
230C2×C4#1059696414yes—
231C22—22no—
232C22—24no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D3711yescharacteristic
237C22C2×Q8×D3711yescharacteristic
238C22#41×D3711yescharacteristic
239C22#41×D3712yes—
240C22C2×#1059696412yes—
241C4—22no—
242C4—24no—
243C4—42no—
244C4—41no—
245C4—374no—
246C4—742no—
247C4—744no—
248C4—742no—
249C4—1481no—
250C4—1482no—
251C2—42no—
252C2C22⋊Q8×D3711yescharacteristic
253C2#1455803911yescharacteristic
254C2#1455806212yes—
255C2#1455808211yescharacteristic
256C2#1455808512yes—
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#393C2
prime radicalC24×C37C23
hypercenter#393D37
hypocenterC37#2396
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic37C2semidirect
3. #14557473C2semidirect
5. #14557467C2semidirect
7. #14557452C2semidirect
8. #14557384C2semidirect
9. #14557384C2semidirect
46. C22×Dic37Q8semidirect
140. C37#2396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic372
C2×#119244922
#145574732
#145574692
#145574672
#145574562
#145574522
#145573842
C22⋊C4×Dic372
C37×#3932
#239637