Finite Group Databasebeta

← #17993063

Subgroups — #17993063

Order 4736.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#14557589C211yesmaximal, characteristic, complemented
3#14557584C211yesmaximal, characteristic, complemented
4#14557262C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596962—21no—
9#11924535C411yescharacteristic
10#11924532C411yescharacteristic
11#11924522—21no—
12#11924511C411yescharacteristic
13#11924509—21no—
14#11924507C411yescharacteristic
15C4×D148C2211yescharacteristic
16C4×C22⋊D37—21no—
17C42×D37C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924448—21no—
22#11924446—21no—
23C4×#64436C2211yescharacteristic
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—
56C23×C37—21no—
57C22×D37—21no—
58C22×D37C22⋊C411yescharacteristic
59D4×C37—21no—
60D4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37C22×C411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C22⋊D37—42no—
68C22⋊D37—42no—
69C22⋊D37—42no—
70C2×Dic37—21no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74D148—21no—
75D148—21no—
76D148—42no—
77C4×D37—21no—
78C4×D37—21no—
79C4×D37—21no—
80C4×D37—21no—
81C4×D37—41no—
82C4×D37—41no—
83C4×D37—41no—
84Dic74—42no—
85C8×C37—41no—
86C8×C37—41no—
87#64436—41no—
88#64436—41no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37C2×C22⋊C411yescharacteristic
93C2×D37—21no—
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—41no—
99C4×C37—21no—
100C4×C37—41no—
101C4×C37#13111yescharacteristic
102C4×C37#13111yescharacteristic
103C4×C37AGL(1,ℤ/8)11yescharacteristic
104C4×C37AGL(1,ℤ/8)11yescharacteristic
105Dic37—21no—
106Dic37—21no—
107Dic37—21no—
108Dic37—41no—
109#1496—371nomaximal, Sylow
110C2×C37—81no—
111C2×C37#40811yescharacteristic
112C2×C37#41811yescharacteristic
113C2×C37#42111yescharacteristic
114D37—41no—
115D37—81no—
116#532—371no—
117#432—371no—
118#431—371no—
119D4⋊C8—371no—
120D4⋊C8—371no—
121D4⋊C8—371no—
122D4⋊C8D3711yescharacteristic, complemented
123C37#149611yescharacteristic, complemented, Sylow
124C2×#41—741no—
125C4⋊Q8—371no—
126#127—371no—
127#124—741no—
128#121—371no—
129#121—371no—
130#121—741no—
131C4×D4—371no—
132C4×D4—741no—
133C4×D4C2×D3711yescharacteristic
134C2×C42—371no—
135C4⋊C8—371no—
136C4⋊C8—741no—
137C4⋊C8C2×D3711yescharacteristic
138C22⋊C8—741no—
139C22⋊C8—741no—
140#97—741no—
141C4×C8—371no—
142C4×C8C2×D3711yescharacteristic
143#41—1482no—
144#41—1482no—
145C2×Q8—741no—
146C2×D4—371no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4C4×D3711yescharacteristic
152C22×C4—21no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—741no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—741no—
160C2×C8—741no—
161C4⋊C4—371no—
162C4⋊C4—741no—
163C4⋊C4C4×D3711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C42—371no—
169C42—371no—
170C42—371no—
171C42C22×D3711yescharacteristic
172C23—21no—
173C23—371no—
174C23—741no—
175Q8—1482no—
176D4—21no—
177D4—21no—
178D4—741no—
179D4—741no—
180D4—1482no—
181D4—1482no—
182D4—1482no—
183D4—1482no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4—1481no—
198C2×C4C2×C4×D3711yescharacteristic
199C2×C4D4×D3711yescharacteristic
200C2×C4D4×D3711yescharacteristic
201C8—41no—
202C8—41no—
203C8—1481no—
204C8—1481no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—741no—
209C22—741no—
210C22—741no—
211C22—1481no—
212C22—1481no—
213C22—1481no—
214C22C22⋊C4×D3711yescharacteristic
215C4—21no—
216C4—41no—
217C4—741no—
218C4—741no—
219C4—741no—
220C4—1481no—
221C4#1192454211yescharacteristic
222C4#1192454411yescharacteristic
223C4#1192456011yescharacteristic
224C4#1192456311yescharacteristic
225C2—81no—
226C2—2961no—
227C2—1481no—
228C2#1455749811yescharacteristic
229C2#1455753611yescharacteristic
230C2#1455754811yescharacteristic
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#1496
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. #14557589C2semidirect
3. #14557584C2semidirect
4. #14557262C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×D4⋊C8C2semidirect
122. D4⋊C8D37semidirect
123. C37#1496semidirect

Maximal subgroups

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

subgroupindex
#145580802
#145575892
#145575842
#145572622
D4⋊#644362
#145572602
C37×D4⋊C82
#149637