Finite Group Databasebeta

← #18009983

Subgroups — #18009983

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#14558504C211yesmaximal, characteristic, complemented
2C2×(C2×#3866)⋊C4C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558385C212yesmaximal, complemented
5#14558046C211yesmaximal, characteristic
6C23×#3866—21no—
7C2×#10596953—21no—
8#11924593C2212yes—
9C22⋊#64438—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12C2×#10596966C411yescharacteristic, complemented
13C22×C4×D37C2211yescharacteristic
14#11924521—21no—
15#11924512C2211yescharacteristic
16#11924511C2211yescharacteristic
17#11924510C411yescharacteristic, complemented
18#11924506—21no—
19#11924498—21no—
20#11924496—21no—
21#11924494C411yescharacteristic, complemented
22C22⋊Q8×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—24no—
25C22×#3866—22no—
26C22×#3866—42no—
27C22×#3866—42no—
28C2×Q8×C37C2×C411yescharacteristic, complemented
29C22×C4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37D411yescharacteristic
32#10596966—42no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148C2×C411yescharacteristic, complemented
36C2×C4×D37—21no—
37C2×C4×D37—42no—
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37C2311yescharacteristic
42C2×#64438—22no—
43#10596953—42no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic, complemented
46C22⋊C4×C37—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37C2×C411yescharacteristic, complemented
52#10596936—21no—
53C4×Dic37—21no—
54C23×C37C22⋊C411yescharacteristic
55C22×D37—22no—
56C22×D37—22no—
57C22×D37—21no—
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—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—41no—
70C2×C4×C37C22⋊C411yescharacteristic
71C2×C4×C37C22×C411yescharacteristic
72C22⋊D37—42no—
73C2×Dic37—21no—
74C2×Dic37—41no—
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C2×D411yescharacteristic
77D148—41no—
78D148—42no—
79D148—41no—
80D148—41no—
81C4×D37—22no—
82C4×D37—22no—
83C4×D37—41no—
84C4×D37—41no—
85C4×D37—42no—
86#64438—42no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37#10412yes—
90C22×C37C2×C22⋊C411yescharacteristic
91C2×D37—24no—
92C2×D37—24no—
93C2×D37—21no—
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—41no—
100C2×D37#9912yes—
101C2×D37AGL(1,ℤ/8)11yescharacteristic
102C2×D37#13711yescharacteristic
103#3866—44no—
104C4×C37—21no—
105C4×C37—21no—
106C4×C37—41no—
107C4×C37—41no—
108Dic37—21no—
109Dic37—21no—
110Dic37—41no—
111#1504—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37C2×#9911yescharacteristic
114C2×C37#41711yescharacteristic
115C2×C37C2×#10411yescharacteristic
116D37—21no—
117D37—22no—
118D37—21no—
119D37—81no—
120#525—371no—
121#407—371no—
122C2×#95—371no—
123#328—372no—
124#327—372no—
125C37#150411yescharacteristic, complemented, Sylow
126C2×#41—371no—
127C23×C4—371no—
128C23×C4—741no—
129C2×M16—741no—
130#123—741no—
131C22⋊Q8—371no—
132C22⋊Q8#386611yescharacteristic, complemented
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—1482no—
145C2×Q8C2×#386611yescharacteristic, complemented
146C2×D4—371no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4—741no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—741no—
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—21no—
165C4⋊C4—371no—
166C4⋊C4—741no—
167C4⋊C4C2×#386611yescharacteristic, complemented
168C22⋊C4—21no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C42—741no—
174C23—371no—
175C23—371no—
176C23—742no—
177C23—741no—
178C23—741no—
179C23—742no—
180C23—741no—
181C23C22⋊#386611yescharacteristic
182Q8—41no—
183D4—1481no—
184D4—1482no—
185D4—1481no—
186D4—1481no—
187D4—1482no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—744no—
196C2×C4—741no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1482no—
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—372no—
210C22—371no—
211C22—371no—
212C22—744no—
213C22—744no—
214C22—741no—
215C22—741no—
216C22—741no—
217C22—741no—
218C22—1481no—
219C22—1481no—
220C22—1481no—
221C22#1192460112yes—
222C22C2×C22⋊#386611yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—41no—
227C4—741no—
228C4—741no—
229C4—1484no—
230C4—1481no—
231C2—22no—
232C2—2961no—
233C2—741no—
234C2—742no—
235C2—741no—
236C2D37⋊#9911yescharacteristic
237C2#1455852411yescharacteristic
238C2C2×#1192460111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558046C2
cosocleC2×C4×D37C23
hypercenterC22⋊Q8#3866
hypocenterC37#1504
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14558504C2semidirect
2. C2×(C2×#3866)⋊C4C2semidirect
3. #14558387C2semidirect
4. #14558385C2semidirect
12. C2×#10596966C4semidirect
17. #11924510C4semidirect
21. #11924494C4semidirect
22. C22⋊Q8×C37C4semidirect
28. C2×Q8×C37C2×C4semidirect
35. C2×D148C2×C4semidirect
45. C4⋊C4×C37C2×C4semidirect
51. C4⋊Dic37C2×C4semidirect
125. C37#1504semidirect
132. C22⋊Q8#3866semidirect
145. C2×Q8C2×#3866semidirect
167. C4⋊C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
C2×(C2×#3866)⋊C42
#145583872
#145583852
#145580462
#150437