Finite Group Databasebeta

← #17997875

Subgroups — #17997875

Order 4736.

840 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 177 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×C4×D148C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D37C214yesmaximal, complemented
3#14557469C212yesmaximal, complemented
4#14557468C212yesmaximal, complemented
5#14557442C212yesmaximal, complemented
6#14557441C212yesmaximal, complemented
7#14557379C211yesmaximal, characteristic, complemented
8C2×C4×D4×C37C211yesmaximal, characteristic, complemented
9C22×D148C2211yescharacteristic
10C22×C22⋊D37C2214yes—
11C22×C4×D37C2212yes—
12C4×D148—24no—
13C4×C22⋊D37—216no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×#10596936C2214yes—
16C2×C22⋊Dic37C2214yes—
17C2×#10596938C2212yes—
18C2×#10596938C2214yes—
19C2×C4×Dic37C2212yes—
20#11924443C2212yes—
21#11924443C2212yes—
22C22×D4×C37C2211yescharacteristic
23C23×C4×C37C2212yes—
24C4×D4×C37—24no—
25C2×C4⋊C4×C37C2211yescharacteristic
26C2×C22⋊C4×C37C2212yes—
27C2×C42×C37C2211yescharacteristic
28C24×C37C2312yes—
29C23×D37C2312yes—
30C2×D4×C37—24no—
31C2×D4×C37—22no—
32C22×C4×C37—28no—
33C22×C4×C37—24no—
34C22×C4×C37C2312yes—
35C22×C4×C37C2311yescharacteristic
36C22×C4×C37C2311yescharacteristic
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—28no—
39C2×C22⋊D37—28no—
40C2×C22⋊D37—28no—
41C22×Dic37C2312yes—
42C22×Dic37C2314yes—
43C2×D148—24no—
44C2×D148—22no—
45C2×C4×D37—28no—
46C2×C4×D37—24no—
47C4⋊C4×C37—22no—
48C22⋊C4×C37—24no—
49C42×C37D414yescomplemented
50C22⋊Dic37—28no—
51#10596938—24no—
52#10596938—28no—
53C4⋊Dic37—22no—
54#10596936—28no—
55C4×Dic37D418yescomplemented
56C23×C37—24no—
57C23×C37—22no—
58C23×C37—24no—
59C23×C37—22no—
60C23×C37#4114yes—
61C23×C37C2411yescharacteristic
62C22×D37—22no—
63C22×D37—24no—
64C22×D37—22no—
65C22×D37—24no—
66C22×D37#4114yes—
67D4×C37—28no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—24no—
71C2×C4×C37—22no—
72C2×C4×C37—48no—
73C2×C4×C37C2×D414yes—
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2×D412yes—
76C2×C4×C37C2×D412yes—
77C22⋊D37—232no—
78C2×Dic37—24no—
79C2×Dic37—24no—
80C2×Dic37—24no—
81C2×Dic37—22no—
82C2×Dic37C2×D418yes—
83D148—28no—
84C4×D37—48no—
85C22×C37—28no—
86C22×C37—24no—
87C22×C37—42no—
88C22×C37—44no—
89C22×C37—42no—
90C22×C37C22×D412yes—
91C22×C37C22×D411yescharacteristic
92C22×C37C2×#4112yes—
93C22×C37C2×#4112yes—
94C2×D37—24no—
95C2×D37—28no—
96C2×D37—44no—
97C2×D37—42no—
98C2×D37—42no—
99C4×C37—22no—
100C4×C37—22no—
101C4×C37—42no—
102C4×C37#12714yes—
103Dic37—28no—
104Dic37—42no—
105#2397—371nomaximal, Sylow
106C2×C37—44no—
107C2×C37#52511yescharacteristic
108C2×C37#52514yes—
109C2×C37#52511yescharacteristic
110C2×C37C2×#12711yescharacteristic
111D37—44no—
112C2×C4×D4—374no—
113C2×C4×D4—371no—
114C2×C4×D4D3711yescharacteristic, complemented
115#399—372no—
116#399—372no—
117#392—372no—
118#392—372no—
119#376—371no—
120C37#239711yescharacteristic, complemented, Sylow
121C22×D4—374no—
122C22×D4—371no—
123C22×D4C2×D3711yescharacteristic
124C23×C4—372no—
125C23×C4C2×D3712yes—
126C4×D4—24no—
127C4×D4—7416no—
128C4×D4—744no—
129C2×C4⋊C4—374no—
130C2×C4⋊C4—371no—
131C2×C4⋊C4C2×D3711yescharacteristic
132C2×C22⋊C4—374no—
133C2×C22⋊C4—374no—
134C2×C22⋊C4—372no—
135C2×C22⋊C4C2×D3712yes—
136C2×C42—372no—
137C2×C42C2×D3711yescharacteristic
138#95—372no—
139#95—372no—
140C24—372no—
141C24C22×D3712yes—
142C2×D4—24no—
143C2×D4—22no—
144C2×D4—744no—
145C2×D4—748no—
146C2×D4—748no—
147C2×D4—748no—
148C2×D4—742no—
149C22×C4—28no—
150C22×C4—24no—
151C22×C4—374no—
152C22×C4—372no—
153C22×C4—748no—
154C22×C4—744no—
155C22×C4C22×D3712yes—
156C22×C4C22×D3711yescharacteristic
157C22×C4C22×D3711yescharacteristic
158C22×C4C22×D3711yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—748no—
161C4⋊C4—742no—
162C22⋊C4—24no—
163C22⋊C4—748no—
164C22⋊C4—748no—
165C22⋊C4—744no—
166C42—378no—
167C42C22⋊D3714yescomplemented
168C23—24no—
169C23—22no—
170C23—24no—
171C23—22no—
172C23—374no—
173C23—744no—
174C23—742no—
175C23—742no—
176C23—744no—
177C23#1059696214yes—
178C23C23×D3711yescharacteristic
179D4—28no—
180D4—748no—
181D4—7432no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—378no—
188C2×C4—744no—
189C2×C4—744no—
190C2×C4—744no—
191C2×C4—742no—
192C2×C4—1488no—
193C2×C4D4×D3714yes—
194C2×C4C2×C22⋊D3712yes—
195C2×C4C2×C22⋊D3712yes—
196C2×C4C2×C22⋊D3712yes—
197C22—28no—
198C22—24no—
199C22—42no—
200C22—44no—
201C22—42no—
202C22—744no—
203C22—748no—
204C22—1484no—
205C22—1482no—
206C22—1482no—
207C22C2×D4×D3712yes—
208C22C22×C22⋊D3711yescharacteristic
209C22#41×D3712yes—
210C22C2×#1059696212yes—
211C4—22no—
212C4—22no—
213C4—42no—
214C4—748no—
215C4—1482no—
216C4#1192453214yes—
217C2—44no—
218C2—1484no—
219C2#1455804011yescharacteristic
220C2#1455804214yes—
221C2#1455804411yescharacteristic
222C2C2×#1192453211yescharacteristic
subgroupG/H
centerC22×C4C22×D37
commutator, socle, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC2×C4×D4×C37C2
hypercenterC2×C4×D4D37
hypocenterC37#2397
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D148C2semidirect
2. C2×C4×C22⋊D37C2semidirect
3. #14557469C2semidirect
4. #14557468C2semidirect
5. #14557442C2semidirect
6. #14557441C2semidirect
7. #14557379C2semidirect
8. C2×C4×D4×C37C2semidirect
49. C42×C37D4semidirect
55. C4×Dic37D4semidirect
114. C2×C4×D4D37semidirect
120. C37#2397semidirect
167. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D1482
C2×C4×C22⋊D372
#145574692
#145574682
#145574422
#145574412
#145573792
C2×C4×D4×C372
#239737