Finite Group Databasebeta

← #18010437

Subgroups — #18010437

Order 4736.

618 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11924600C214yesmaximal, complemented
2#14558504C211yesmaximal, characteristic, complemented
3C4×C22⋊#3866C211yesmaximal, characteristic, complemented
4C22×#10596964C211yesmaximal, characteristic
5C2×#10596953C2212yescomplemented
6C2×C22⋊#3866—21no—
7C2×C4×#3866C2212yescomplemented
8#11924600—28no—
9#11924593—21no—
10C22⋊#64438—21no—
11(C2×#3866)⋊C4—21no—
12C2×#10596964—28no—
13C2×#10596964—21no—
14C2×#10596964—21no—
15C2×#10596964C412yescomplemented
16C2×#10596964C2212yes—
17C22×Dic74C411yescharacteristic, complemented
18C22×C22⋊D37—21no—
19C23×Dic37—21no—
20C22×C4×D37C2211yescharacteristic
21C22×D4×C37C411yescharacteristic, complemented
22C24×C37—21no—
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25C2×D4×C37—24no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C412yes—
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—28no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32C22×Dic37—28no—
33C22×Dic37—21no—
34C22×Dic37—22no—
35C22×Dic37—22no—
36C22×Dic37D411yescharacteristic
37#10596964—28no—
38#10596964—28no—
39#10596964—24no—
40#10596964—24no—
41#10596964—24no—
42#10596964D418yes—
43C2×C4×D37—24no—
44C2×C4×D37C2×C411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37D411yescharacteristic
47C2×C4×D37C2311yescharacteristic
48C2×Dic74—21no—
49C2×Dic74—24no—
50C2×Dic74C2×C412yes—
51C22⋊#3866—24no—
52C2×#64438—22no—
53C4×#3866—24no—
54#10596953—24no—
55C23×C37—24no—
56C23×C37—22no—
57C23×C37—42no—
58C23×C37—42no—
59C23×C37C22⋊C411yescharacteristic
60C22×D37—22no—
61C22×D37—22no—
62C22×D37—41no—
63C22×D37C22⋊C411yescharacteristic
64C22×D37C2×D411yescharacteristic
65C2×#3866—24no—
66C2×#3866—42no—
67C2×#3866—42no—
68D4×C37—24no—
69D4×C37—22no—
70D4×C37C22⋊C414yescomplemented
71C2×C4×C37—22no—
72C2×C4×C37C22⋊C411yescharacteristic
73C2×C4×C37C22×C411yescharacteristic
74C22⋊D37—28no—
75C22⋊D37—28no—
76C2×Dic37—24no—
77C2×Dic37—28no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—28no—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—22no—
86C4×D37C2×D414yes—
87Dic74—24no—
88Dic74—22no—
89Dic74C22⋊C414yescomplemented
90#64438—42no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—24no—
94C22×C37—48no—
95C22×C37—42no—
96C22×C37—42no—
97C22×C37#10412yescomplemented
98C22×C37C2×C22⋊C411yescharacteristic
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—21no—
103C2×D37—21no—
104C2×D37—44no—
105C2×D37#12012yes—
106#3866—44no—
107C4×C37—21no—
108C4×C37C2×C22⋊C412yes—
109Dic37—24no—
110Dic37—21no—
111Dic37#12012yes—
112#1789—371nomaximal, Sylow
113C2×C37—22no—
114C2×C37—44no—
115C2×C37#37911yescharacteristic
116C2×C37C2×#10411yescharacteristic
117C2×C37#42111yescharacteristic
118D37—22no—
119D37—41no—
120C22×#41—371no—
121C2×#104—374no—
122#407—371no—
123C4×C22⋊C4—371no—
124C37#178911yescharacteristic, complemented, Sylow
125C2×#41—372no—
126C2×#41—372no—
127C2×#41—741no—
128C2×#41—741no—
129C2×#41—748no—
130C22×Q8—371no—
131C22×D4—741no—
132C22×D4#386611yescharacteristic, complemented
133C23×C4—371no—
134C23×C4—741no—
135C2×M16—372no—
136C2×C22⋊C4—741no—
137C2×C42—372no—
138#104—748no—
139C22⋊C8—741no—
140C22⋊C8—741no—
141#95—741no—
142C24—21no—
143C24—371no—
144#41—378no—
145#41—744no—
146#41—744no—
147#41—748no—
148#41—748no—
149#41—744no—
150C2×Q8—372no—
151C2×Q8—744no—
152C2×Q8—741no—
153C2×D4—24no—
154C2×D4—21no—
155C2×D4—742no—
156C2×D4—742no—
157C2×D4—748no—
158C2×D4C2×#386612yes—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—744no—
165C22×C4—742no—
166C22×C4—742no—
167C22×C4—748no—
168C22×C4—741no—
169C22×C4—742no—
170C22×C4C2×#386611yescharacteristic
171M16—744no—
172C2×C8—742no—
173C22⋊C4—744no—
174C42—744no—
175C23—24no—
176C23—22no—
177C23—42no—
178C23—42no—
179C23—371no—
180C23—371no—
181C23—742no—
182C23—742no—
183C23—1481no—
184C23C22⋊#386611yescharacteristic
185Q8—374no—
186Q8—744no—
187Q8—742no—
188D4—24no—
189D4—22no—
190D4—748no—
191D4—748no—
192D4C22⋊#386614yescomplemented
193C2×C4—22no—
194C2×C4—371no—
195C2×C4—374no—
196C2×C4—371no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—742no—
200C2×C4—748no—
201C2×C4—744no—
202C2×C4—748no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4—744no—
206C2×C4—1482no—
207C2×C4—1482no—
208C2×C4C22⋊#386611yescharacteristic
209C2×C4C22×#386611yescharacteristic
210C8—1482no—
211C22—21no—
212C22—21no—
213C22—24no—
214C22—48no—
215C22—42no—
216C22—42no—
217C22—372no—
218C22—741no—
219C22—741no—
220C22—741no—
221C22—741no—
222C22—741no—
223C22—1484no—
224C22#1192460012yescomplemented
225C22C2×C22⋊#386611yescharacteristic
226C4—21no—
227C4—372no—
228C4—741no—
229C4—744no—
230C4—1484no—
231C4C2×C22⋊#386612yes—
232C2—22no—
233C2—44no—
234C2—742no—
235C2—1481no—
236C2#1455847411yescharacteristic
237C2C2×#1192460011yescharacteristic
238C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×#10596964C2
cosocleC2×C4×D37C23
hypercenterC22×D4#3866
hypocenterC37#1789
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11924600C2semidirect
2. #14558504C2semidirect
3. C4×C22⋊#3866C2semidirect
5. C2×#10596953C22semidirect
7. C2×C4×#3866C22semidirect
15. C2×#10596964C4semidirect
17. C22×Dic74C4semidirect
21. C22×D4×C37C4semidirect
70. D4×C37C22⋊C4semidirect
89. Dic74C22⋊C4semidirect
97. C22×C37#104semidirect
124. C37#1789semidirect
132. C22×D4#3866semidirect
192. D4C22⋊#3866semidirect
224. C22#11924600semidirect

Maximal subgroups

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

subgroupindex
C2×#119246002
#145585042
C4×C22⋊#38662
C22×#105969642
#178937