Finite Group Databasebeta

← #18009991

Subgroups — #18009991

Order 4736.

346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558505C211yesmaximal, characteristic, complemented
2C4×C22⋊#3866C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#121×D37C211yesmaximal, characteristic
6C2×#10596957—21no—
7C2×C22⋊#3866—21no—
8C2×C4×#3866—21no—
9#11924593—21no—
10#11924593C2212yescomplemented
11(C2×#3866)⋊C4C2212yescomplemented
12C2×D4×D37—21no—
13C2×D4×D37C411yescharacteristic, complemented
14C22×C4×D37C2211yescharacteristic
15#11924511C2211yescharacteristic
16#11924510C411yescharacteristic, complemented
17#11924509—21no—
18#11924508—21no—
19#11924507C2211yescharacteristic
20C4⋊C4×D37C411yescharacteristic, complemented
21C22⋊C4×D37—21no—
22#121×C37C411yescharacteristic, complemented
23C23×D37—21no—
24C23×D37D411yescharacteristic
25C22×#3866—22no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37D411yescharacteristic
33D4×D37—42no—
34D4×D37—44no—
35C2×D148—21no—
36C2×D148C2×C411yescharacteristic
37C2×C4×D37—21no—
38C2×C4×D37—42no—
39C2×C4×D37C2×C411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37C2311yescharacteristic
43C22⋊#3866—24no—
44#10596957—42no—
45C2×#64438—22no—
46C4×#3866—42no—
47C4⋊C4×C37C2×C411yescharacteristic
48C22⋊C4×C37—21no—
49C22⋊Dic37—21no—
50#10596938—21no—
51#10596938—21no—
52C4⋊Dic37C2×C411yescharacteristic
53#10596936—21no—
54C23×C37—21no—
55C23×C37C22⋊C411yescharacteristic
56C22×D37—22no—
57C22×D37—22no—
58C22×D37—21no—
59C22×D37—41no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37—42no—
63C22×D37C22⋊C411yescharacteristic
64C22×D37C2×D411yescharacteristic
65C2×#3866—24no—
66C2×#3866—42no—
67C2×#3866—42no—
68D4×C37—41no—
69D4×C37—42no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37C22⋊C411yescharacteristic
73C2×C4×C37C22×C411yescharacteristic
74C22⋊D37—42no—
75C22⋊D37—42no—
76C22⋊D37—42no—
77C2×Dic37—22no—
78C2×Dic37—21no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C2×D411yescharacteristic
81D148—41no—
82D148—42no—
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—41no—
86C4×D37—41no—
87C4×D37—42no—
88#64438—42no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37—41no—
95C22×C37C2×C22⋊C411yescharacteristic
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—44no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—41no—
104C2×D37—84no—
105C2×D37#10412yes—
106C2×D37AGL(1,ℤ/8)12yes—
107#3866—44no—
108C4×C37—21no—
109C4×C37—21no—
110C4×C37—41no—
111Dic37—21no—
112Dic37—41no—
113Dic37#9912yes—
114#1507—371nomaximal, Sylow
115C2×C37—41no—
116C2×C37—81no—
117C2×C37C2×#9911yescharacteristic
118C2×C37#41811yescharacteristic
119C2×C37C2×#10411yescharacteristic
120D37—22no—
121D37—22no—
122D37—81no—
123C2×#121—371no—
124#407—371no—
125C4×C22⋊C4—371no—
126#327—372no—
127#327—372no—
128C37#150711yescharacteristic, complemented, Sylow
129C22×D4—371no—
130C22×D4—741no—
131C23×C4—371no—
132C2×M16—741no—
133#121—371no—
134#121—371no—
135#121—371no—
136#121—741no—
137#121—741no—
138#121#386611yescharacteristic, complemented
139C2×C4⋊C4—371no—
140C2×C22⋊C4—741no—
141C2×C22⋊C4—741no—
142C2×C42—741no—
143C22⋊C8—372no—
144C22⋊C8—741no—
145#95—372no—
146C24—371no—
147C24—741no—
148C2×D4—21no—
149C2×D4—371no—
150C2×D4—741no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4—741no—
154C2×D4—1482no—
155C2×D4—1484no—
156C2×D4C2×#386611yescharacteristic
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—741no—
163C22×C4—742no—
164C22×C4—1482no—
165C22×C4C2×#386611yescharacteristic
166M16—1482no—
167C2×C8—742no—
168C4⋊C4—371no—
169C4⋊C4—741no—
170C4⋊C4C2×#386611yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—741no—
173C22⋊C4—741no—
174C22⋊C4—744no—
175C22⋊C4—741no—
176C42—1482no—
177C23—21no—
178C23—371no—
179C23—371no—
180C23—742no—
181C23—742no—
182C23—741no—
183C23—1481no—
184C23—1482no—
185C23—1482no—
186C23—1482no—
187C23C22⋊#386611yescharacteristic
188D4—41no—
189D4—42no—
190D4—1481no—
191D4—1482no—
192D4—1482no—
193D4—1482no—
194D4—1482no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—371no—
198C2×C4—371no—
199C2×C4—742no—
200C2×C4—742no—
201C2×C4—742no—
202C2×C4—744no—
203C2×C4—741no—
204C2×C4—1481no—
205C2×C4—1481no—
206C2×C4—1482no—
207C2×C4—1482no—
208C2×C4—1482no—
209C2×C4C22⋊#386611yescharacteristic
210C2×C4C22×#386611yescharacteristic
211C8—1482no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—372no—
219C22—372no—
220C22—2964no—
221C22—741no—
222C22—741no—
223C22—741no—
224C22—741no—
225C22—1484no—
226C22—1481no—
227C22—1481no—
228C22—1481no—
229C22C2×C22⋊#386611yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—372no—
234C4—741no—
235C4—1484no—
236C4—1481no—
237C2—41no—
238C2—81no—
239C2—2961no—
240C2—742no—
241C2—742no—
242C2D37⋊#9911yescharacteristic
243C2#1455852511yescharacteristic
244C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#121×D37C2
cosocleC2×C4×D37C23
hypercenter#121#3866
hypocenterC37#1507
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558505C2semidirect
2. C4×C22⋊#3866C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
10. #11924593C22semidirect
11. (C2×#3866)⋊C4C22semidirect
13. C2×D4×D37C4semidirect
16. #11924510C4semidirect
20. C4⋊C4×D37C4semidirect
22. #121×C37C4semidirect
128. C37#1507semidirect
138. #121#3866semidirect

Maximal subgroups

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

subgroupindex
#145585052
C4×C22⋊#38662
#145583852
#145583842
#121×D372
#150737