Finite Group Databasebeta

← #18010002

Subgroups — #18010002

Order 4736.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558504C211yesmaximal, characteristic, complemented
2#14558476C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#121×D37C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×C22⋊#3866—21no—
8#11924593C2212yescomplemented
9C22⋊#64438—21no—
10(C2×#3866)⋊C4—21no—
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—42no—
44C2×#64438—22no—
45#10596953—42no—
46C4⋊C4×C37C2×C411yescharacteristic
47C22⋊C4×C37—21no—
48C22⋊Dic37—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37C2×C411yescharacteristic
52#10596936—21no—
53C23×C37—21no—
54C23×C37C22⋊C411yescharacteristic
55C22×D37—22no—
56C22×D37—22no—
57C22×D37—21no—
58C22×D37—41no—
59C22×D37—42no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37C22⋊C411yescharacteristic
63C22×D37C2×D411yescharacteristic
64C2×#3866—42no—
65C2×#3866—42no—
66C2×#3866—42no—
67D4×C37—41no—
68D4×C37—42no—
69C2×C4×C37—21no—
70C2×C4×C37—41no—
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C22×C411yescharacteristic
73C22⋊D37—42no—
74C22⋊D37—42no—
75C22⋊D37—42no—
76C2×Dic37—21no—
77C2×Dic37—41no—
78C2×Dic37C22⋊C411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80D148—41no—
81D148—42no—
82C4×D37—22no—
83C4×D37—22no—
84C4×D37—41no—
85C4×D37—41no—
86C4×D37—42no—
87#64438—42no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37C2×C22⋊C411yescharacteristic
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—44no—
100C2×D37—41no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—84no—
104C2×D37#9912yes—
105C2×D37AGL(1,ℤ/8)12yes—
106#3866—82no—
107C4×C37—21no—
108C4×C37—21no—
109C4×C37—41no—
110Dic37—21no—
111Dic37—21no—
112Dic37—41no—
113#1510—371nomaximal, Sylow
114C2×C37—41no—
115C2×C37—81no—
116C2×C37C2×#9911yescharacteristic
117C2×C37#41811yescharacteristic
118C2×C37#42111yescharacteristic
119D37—22no—
120D37—22no—
121D37—81no—
122C2×#121—371no—
123#407—371no—
124#381—371no—
125#327—372no—
126#327—372no—
127C37#151011yescharacteristic, complemented, Sylow
128C22×D4—371no—
129C22×D4—741no—
130C23×C4—371no—
131C2×M16—741no—
132#121—371no—
133#121—371no—
134#121—371no—
135#121—741no—
136#121—741no—
137#121#386611yescharacteristic, complemented
138C2×C4⋊C4—371no—
139C2×C22⋊C4—741no—
140C2×C22⋊C4—741no—
141C22⋊C8—372no—
142C22⋊C8—741no—
143#95—372no—
144#95—741no—
145C24—371no—
146C24—741no—
147C2×D4—21no—
148C2×D4—371no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4—1482no—
154C2×D4—1484no—
155C2×D4C2×#386611yescharacteristic
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—741no—
162C22×C4—742no—
163C22×C4—1482no—
164C22×C4C2×#386611yescharacteristic
165M16—1482no—
166C2×C8—742no—
167C4⋊C4—371no—
168C4⋊C4—741no—
169C4⋊C4C2×#386611yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C22⋊C4—741no—
174C22⋊C4—1482no—
175C23—21no—
176C23—371no—
177C23—371no—
178C23—742no—
179C23—742no—
180C23—741no—
181C23—1481no—
182C23—1482no—
183C23—1482no—
184C23—1482no—
185C23C22⋊#386611yescharacteristic
186D4—41no—
187D4—42no—
188D4—1481no—
189D4—1482no—
190D4—1482no—
191D4—1482no—
192D4—1482no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—371no—
196C2×C4—371no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—741no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4—1482no—
203C2×C4—1482no—
204C2×C4—1482no—
205C2×C4—1482no—
206C2×C4—1481no—
207C2×C4C22⋊#386611yescharacteristic
208C2×C4C22×#386611yescharacteristic
209C8—1482no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—372no—
217C22—372no—
218C22—2964no—
219C22—741no—
220C22—741no—
221C22—741no—
222C22—741no—
223C22—1484no—
224C22—1481no—
225C22—1481no—
226C22—1481no—
227C22C2×C22⋊#386611yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—2962no—
232C4—741no—
233C4—741no—
234C4—1481no—
235C2—41no—
236C2—81no—
237C2—2961no—
238C2—742no—
239C2—742no—
240C2D37⋊#9911yescharacteristic
241C2#1455852511yescharacteristic
242C2#1455853011yescharacteristic
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#1510
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. #14558504C2semidirect
2. #14558476C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
8. #11924593C22semidirect
11. (C2×#3866)⋊C4C22semidirect
13. C2×D4×D37C4semidirect
16. #11924510C4semidirect
20. C4⋊C4×D37C4semidirect
22. #121×C37C4semidirect
127. C37#1510semidirect
137. #121#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145584762
#145583852
#145583842
#121×D372
#151037