Finite Group Databasebeta

← #17993011

Subgroups — #17993011

Order 4736.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558080C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic, complemented
3C4×#10596929C211yesmaximal, characteristic, complemented
4#14557262C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596962—21no—
9C2×#10596929—21no—
10#11924535C411yescharacteristic
11#11924532C411yescharacteristic
12#11924522—21no—
13#11924511C411yescharacteristic
14#11924509—21no—
15#11924507C411yescharacteristic
16C4×D148C2211yescharacteristic
17C4×C22⋊D37—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic
20#11924448—21no—
21#11924446—21no—
22C4×#64436C2211yescharacteristic
23C8×Dic37—21no—
24C4×D4×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32#10596962—42no—
33#10596962—42no—
34C2×D148—21no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37—21no—
37C2×C4×D37C2×C411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×Dic74—21no—
41C2×C8×C37—21no—
42C2×C8×C37—21no—
43C4⋊C4×C37C2×C411yescharacteristic
44C22⋊C4×C37—21no—
45C42×C37C2311yescharacteristic
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37C2×C411yescharacteristic
50#10596936—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—24no—
57C23×C37—21no—
58C22×D37—21no—
59C22×D37C22⋊C411yescharacteristic
60D4×C37—21no—
61D4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C22×C411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C22⋊D37—42no—
69C22⋊D37—42no—
70C22⋊D37—42no—
71C2×Dic37—21no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C22⋊C411yescharacteristic
75D148—21no—
76D148—21no—
77D148—42no—
78C4×D37—21no—
79C4×D37—21no—
80C4×D37—21no—
81C4×D37—21no—
82C4×D37—22no—
83C4×D37—41no—
84C4×D37—41no—
85Dic74—42no—
86C8×C37—22no—
87C8×C37—41no—
88#64436—22no—
89#64436—41no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—41no—
100C4×C37—21no—
101C4×C37—41no—
102C4×C37#13111yescharacteristic
103C4×C37#13111yescharacteristic
104C4×C37AGL(1,ℤ/8)11yescharacteristic
105C4×C37AGL(1,ℤ/8)11yescharacteristic
106Dic37—21no—
107Dic37—21no—
108Dic37—41no—
109Dic37#10412yes—
110#1484—371nomaximal, Sylow
111C2×C37—81no—
112C2×C37#40811yescharacteristic
113C2×C37#41811yescharacteristic
114C2×C37C2×#10411yescharacteristic
115D37—41no—
116D37—81no—
117#532—371no—
118#431—371no—
119C4×M16—371no—
120D4⋊C8—371no—
121D4⋊C8—371no—
122D4⋊C8—371no—
123D4⋊C8D3711yescharacteristic, complemented
124C37#148411yescharacteristic, complemented, Sylow
125C2×#41—741no—
126C2×M16—741no—
127C4⋊Q8—371no—
128#127—371no—
129#124—741no—
130#121—371no—
131#121—371no—
132#121—741no—
133C4×D4—371no—
134C4×D4—741no—
135C4×D4C2×D3711yescharacteristic
136C2×C42—371no—
137C4⋊C8—371no—
138C4⋊C8C2×D3711yescharacteristic
139C22⋊C8—741no—
140#97—741no—
141C4×C8—371no—
142C4×C8—741no—
143C4×C8C2×D3711yescharacteristic
144#41—1482no—
145#41—1482no—
146C2×Q8—741no—
147C2×D4—371no—
148C2×D4—741no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4—741no—
152C2×D4C4×D3711yescharacteristic
153C22×C4—21no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—741no—
158M16—744no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—741no—
162C2×C8—741no—
163C4⋊C4—371no—
164C4⋊C4—741no—
165C4⋊C4C4×D3711yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C42—371no—
171C42—371no—
172C42—371no—
173C42C22×D3711yescharacteristic
174C23—21no—
175C23—371no—
176C23—741no—
177Q8—1482no—
178D4—21no—
179D4—21no—
180D4—741no—
181D4—741no—
182D4—1482no—
183D4—1482no—
184D4—1482no—
185D4—1482no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—371no—
192C2×C4—742no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—741no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—1481no—
199C2×C4—1481no—
200C2×C4C2×C4×D3711yescharacteristic
201C2×C4D4×D3711yescharacteristic
202C2×C4D4×D3711yescharacteristic
203C8—22no—
204C8—41no—
205C8—742no—
206C8—1481no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—741no—
211C22—741no—
212C22—741no—
213C22—1481no—
214C22—1481no—
215C22—1481no—
216C22C22⋊C4×D3711yescharacteristic
217C4—21no—
218C4—41no—
219C4—372no—
220C4—741no—
221C4—741no—
222C4—1481no—
223C4#1192454211yescharacteristic
224C4#1192454411yescharacteristic
225C4#1192456011yescharacteristic
226C4#1192456311yescharacteristic
227C2—81no—
228C2—2961no—
229C2—1481no—
230C2#1455749811yescharacteristic
231C2#1455753611yescharacteristic
232C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC42×C37C23
hypercenterD4⋊C8D37
hypocenterC37#1484
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557585C2semidirect
3. C4×#10596929C2semidirect
4. #14557262C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×D4⋊C8C2semidirect
123. D4⋊C8D37semidirect
124. C37#1484semidirect

Maximal subgroups

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

subgroupindex
#145580802
#145575852
C4×#105969292
#145572622
D4⋊#644362
#145572602
C37×D4⋊C82
#148437