Finite Group Databasebeta

← #18009872

Subgroups — #18009872

Order 4736.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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
1#14558503C211yesmaximal, characteristic, complemented
2C2×C22⋊#64438C211yesmaximal, characteristic, complemented
3#14558377C212yesmaximal, complemented
4#14558376C212yesmaximal, complemented
5C2×#11924508C211yesmaximal, characteristic
6C2×#10596957—21no—
7C22×#64438—21no—
8C22⋊#64438—21no—
9C22⋊#64438—21no—
10C22⋊#64438C2212yes—
11C22⋊#64438C2212yes—
12C22×C22⋊D37C411yescharacteristic
13C22×C22⋊D37C411yescharacteristic
14C23×Dic37C2211yescharacteristic
15#11924508—21no—
16#11924508—21no—
17#11924508—21no—
18#11924508—21no—
19C2×#10596936C411yescharacteristic
20C2×C22⋊Dic37C2211yescharacteristic
21C2×#10596938C2211yescharacteristic
22C22×D4×C37C411yescharacteristic
23C24×C37C2×C411yescharacteristic
24C24×C37C2×C411yescharacteristic
25C23×D37C2×C411yescharacteristic
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—42no—
29C22×C4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—42no—
35C2×C22⋊D37—42no—
36C22×Dic37—42no—
37C22×Dic37C2×C411yescharacteristic
38C22×Dic37C2×C411yescharacteristic
39C22×Dic37D411yescharacteristic
40C22×Dic37D411yescharacteristic
41C22×Dic37D411yescharacteristic
42C22×Dic37D411yescharacteristic
43C22×Dic37C2311yescharacteristic
44#10596957—42no—
45C2×#64438—22no—
46C2×#64438—22no—
47C2×#64438—42no—
48C22⋊Dic37—21no—
49C22⋊Dic37—21no—
50#10596938—21no—
51#10596938—21no—
52#10596936—21no—
53#10596936—21no—
54C23×C37—22no—
55C23×C37—22no—
56C23×C37—21no—
57C23×C37—22no—
58C23×C37—41no—
59C23×C37—41no—
60C23×C37—41no—
61C23×C37C22⋊C411yescharacteristic
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22×C411yescharacteristic
64C22×D37—21no—
65C22×D37—22no—
66C22×D37—41no—
67C22×D37—41no—
68D4×C37—42no—
69D4×C37—42no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C22⋊D37—42no—
73C22⋊D37—42no—
74C22⋊D37—42no—
75C22⋊D37—42no—
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—21no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37—41no—
83C2×Dic37—41no—
84C2×Dic37C22⋊C411yescharacteristic
85C2×Dic37C22⋊C411yescharacteristic
86C2×Dic37C2×D411yescharacteristic
87C2×Dic37C2×D411yescharacteristic
88#64438—42no—
89#64438—42no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—44no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37—82no—
102C22×C37#10012yes—
103C22×C37C2×C22⋊C411yescharacteristic
104C22×C37#13112yes—
105C2×D37—41no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—82no—
109C4×C37—41no—
110Dic37—21no—
111Dic37—21no—
112Dic37—21no—
113Dic37—41no—
114Dic37#9912yes—
115#1471—371nomaximal, Sylow
116C2×C37—22no—
117C2×C37—22no—
118C2×C37—41no—
119C2×C37—81no—
120C2×C37#40811yescharacteristic
121C2×C37C2×#9911yescharacteristic
122C2×C37C2×#10011yescharacteristic
123D37—81no—
124C2×#121—371no—
125#407—371no—
126C2×C22⋊C8—371no—
127#323—372no—
128#323—372no—
129C37#147111yescharacteristic, complemented, Sylow
130C22×D4—371no—
131C22×D4—371no—
132C22×D4#386611yescharacteristic
133C23×C4—371no—
134C2×M16—741no—
135C22×C8—741no—
136#121—741no—
137#121—741no—
138#121—741no—
139#121—741no—
140C2×C4⋊C4—371no—
141C2×C22⋊C4—371no—
142C2×C22⋊C4—371no—
143C22⋊C8—372no—
144C22⋊C8—372no—
145C22⋊C8—741no—
146C22⋊C8—741no—
147C24—371no—
148C24C2×#386611yescharacteristic
149C24C2×#386611yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C2×D4—741no—
154C2×D4—741no—
155C2×D4—741no—
156C2×D4—741no—
157C2×D4—1482no—
158C2×D4—1482no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—1482no—
167C22×C4C2×#386611yescharacteristic
168M16—1482no—
169C2×C8—742no—
170C2×C8—742no—
171C2×C8—1482no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C22⋊C4—741no—
175C22⋊C4—741no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C23—22no—
179C23—22no—
180C23—21no—
181C23—22no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—742no—
186C23—741no—
187C23—1481no—
188C23—1481no—
189C23C22⋊#386611yescharacteristic
190C23C22⋊#386611yescharacteristic
191C23C22×#386611yescharacteristic
192D4—42no—
193D4—42no—
194D4—1482no—
195D4—1482no—
196D4—1482no—
197D4—1482no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—371no—
201C2×C4—371no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—742no—
205C2×C4—742no—
206C2×C4—742no—
207C2×C4—741no—
208C2×C4—1481no—
209C2×C4—1481no—
210C2×C4—1481no—
211C2×C4—1481no—
212C8—1482no—
213C8—1482no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—44no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—82no—
226C22—2962no—
227C22—1481no—
228C22—1481no—
229C22—1481no—
230C22#1192459612yes—
231C22C2×C22⋊#386611yescharacteristic
232C22#1192462312yes—
233C4—41no—
234C4—372no—
235C4—741no—
236C4—741no—
237C4—741no—
238C4—1481no—
239C2—22no—
240C2—22no—
241C2—41no—
242C2—81no—
243C2—2961no—
244C2#1455850611yescharacteristic
245C2D37⋊#9911yescharacteristic
246C2C2×#1192459611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC22×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924508C2
cosocleC22×Dic37C23
hypercenterC22×D4#3866
hypocenterC37#1471
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558503C2semidirect
2. C2×C22⋊#64438C2semidirect
3. #14558377C2semidirect
4. #14558376C2semidirect
129. C37#1471semidirect

Maximal subgroups

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

subgroupindex
#145585032
C2×C22⋊#644382
#145583772
#145583762
C2×#119245082
#147137