Finite Group Databasebeta

← #18009982

Subgroups — #18009982

Order 4736.

334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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
2C2×(C2×#3866)⋊C4C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558040C211yesmaximal, characteristic
6C23×#3866—21no—
7C2×#10596957—21no—
8#11924593—21no—
9#11924593C2212yes—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12C22×C4×D37C2211yescharacteristic
13#11924517—21no—
14#11924512C411yescharacteristic, complemented
15#11924512C2211yescharacteristic
16#11924507C411yescharacteristic, complemented
17#11924507C2211yescharacteristic
18#11924504—21no—
19C4×C22⋊D37—21no—
20C4×C22⋊D37—21no—
21#11924495C411yescharacteristic, complemented
22C2×#41×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—24no—
25C22×#3866—22no—
26C22×#3866—42no—
27C22×#3866—42no—
28#41×C37—42no—
29C2×Q8×C37C2×C411yescharacteristic, complemented
30C2×D4×C37—21no—
31C2×D4×C37C2×C411yescharacteristic, complemented
32C22×C4×C37—21no—
33C22×C4×C37C2×C411yescharacteristic
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C22×Dic37D411yescharacteristic
37C2×C4×D37—42no—
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37C2311yescharacteristic
42#10596957—42no—
43C2×#64438—22no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37C2×C411yescharacteristic, complemented
50C4⋊Dic37C2×C411yescharacteristic, complemented
51#10596936—21no—
52#10596936—21no—
53C4×Dic37—21no—
54C23×C37—21no—
55C23×C37C22⋊C411yescharacteristic
56C22×D37—22no—
57C22×D37—22no—
58C22×D37—21no—
59C22×D37—21no—
60C22×D37C22⋊C411yescharacteristic
61C22×D37C2×D411yescharacteristic
62C2×#3866—24no—
63C2×#3866—48no—
64C2×#3866—42no—
65C2×#3866—42no—
66Q8×C37—41no—
67D4×C37—41no—
68D4×C37—42no—
69C2×C4×C37—22no—
70C2×C4×C37—21no—
71C2×C4×C37—42no—
72C2×C4×C37C22⋊C411yescharacteristic
73C2×C4×C37C22×C411yescharacteristic
74C22⋊D37—42no—
75C22⋊D37—41no—
76C22⋊D37—41no—
77C2×Dic37—22no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C2×D411yescharacteristic
82C4×D37—41no—
83C4×D37—41no—
84C4×D37—41no—
85C4×D37—41no—
86#64438—42no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37#9912yes—
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—24no—
95C2×D37—24no—
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37#10412yes—
101C2×D37AGL(1,ℤ/8)11yescharacteristic
102C2×D37#13711yescharacteristic
103#3866—44no—
104C4×C37—21no—
105C4×C37—21no—
106C4×C37—41no—
107Dic37—21no—
108Dic37—21no—
109Dic37—41no—
110Dic37—41no—
111#1504—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—81no—
114C2×C37C2×#9911yescharacteristic
115C2×C37#41711yescharacteristic
116C2×C37C2×#10411yescharacteristic
117D37—21no—
118D37—22no—
119D37—21no—
120#525—371no—
121#407—371no—
122C2×#95—371no—
123#328—372no—
124#327—372no—
125C37#150411yescharacteristic, complemented, Sylow
126C2×#41#386611yescharacteristic, complemented
127C23×C4—371no—
128C23×C4—741no—
129C2×M16—741no—
130#123—741no—
131C22⋊Q8—371no—
132C22⋊Q8—371no—
133#121—371no—
134#121—371no—
135#120—741no—
136C4×D4—741no—
137C4×D4—741no—
138#117—371no—
139C22⋊C8—372no—
140C22⋊C8—741no—
141#95—372no—
142#95—741no—
143C24—371no—
144#41—42no—
145C2×Q8C2×#386611yescharacteristic, complemented
146C2×D4—21no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4C2×#386611yescharacteristic, complemented
150C22×C4—21no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—742no—
157C22×C4—744no—
158C22×C4—1482no—
159C22×C4—1482no—
160C22×C4—1482no—
161C22×C4C2×#386611yescharacteristic
162M16—1482no—
163C2×C8—742no—
164C4⋊C4—371no—
165C4⋊C4—371no—
166C4⋊C4—741no—
167C4⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C42—741no—
174C23—21no—
175C23—371no—
176C23—371no—
177C23—742no—
178C23—741no—
179C23—741no—
180C23—742no—
181C23C22⋊#386611yescharacteristic
182Q8—41no—
183D4—41no—
184D4—42no—
185D4—1481no—
186D4—1481no—
187D4—1482no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—742no—
194C2×C4—744no—
195C2×C4—741no—
196C2×C4—741no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4—1482no—
202C2×C4—1488no—
203C2×C4—1482no—
204C2×C4C22⋊#386611yescharacteristic
205C2×C4C22×#386611yescharacteristic
206C8—1482no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—371no—
213C22—371no—
214C22—372no—
215C22—744no—
216C22—744no—
217C22—741no—
218C22—741no—
219C22—741no—
220C22—741no—
221C22#1192459412yes—
222C22C2×C22⋊#386611yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—741no—
227C4—741no—
228C4—1484no—
229C4—1481no—
230C4—1481no—
231C2—22no—
232C2—81no—
233C2—741no—
234C2—741no—
235C2—742no—
236C2C2×#1192459411yescharacteristic
237C2#1455852411yescharacteristic
238C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558040C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1504
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558505C2semidirect
2. C2×(C2×#3866)⋊C4C2semidirect
3. #14558387C2semidirect
4. #14558384C2semidirect
14. #11924512C4semidirect
16. #11924507C4semidirect
21. #11924495C4semidirect
22. C2×#41×C37C4semidirect
29. C2×Q8×C37C2×C4semidirect
31. C2×D4×C37C2×C4semidirect
49. C4⋊Dic37C2×C4semidirect
50. C4⋊Dic37C2×C4semidirect
125. C37#1504semidirect
126. C2×#41#3866semidirect
145. C2×Q8C2×#3866semidirect
149. C2×D4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145585052
C2×(C2×#3866)⋊C42
#145583872
#145583842
#145580402
#150437