Finite Group Databasebeta

← #17993019

Subgroups — #17993019

Order 4736.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×D4×D37C211yesmaximal, characteristic
2#14557584C211yesmaximal, characteristic, complemented
3#14557555C211yesmaximal, characteristic, complemented
4#14557262C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D37C411yescharacteristic
9C22×C4×D37—21no—
10C2×#10596929—21no—
11C4×D148C2211yescharacteristic
12D4×Dic37C411yescharacteristic
13#11924498C411yescharacteristic
14C4×C22⋊D37—21no—
15#11924496—21no—
16C4⋊C4×D37C411yescharacteristic
17C22⋊C4×D37—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic, complemented
20#11924465—21no—
21#11924465—21no—
22#11924448—21no—
23C4×#64436C2211yescharacteristic, complemented
24C4×D4×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic, complemented
26C4×C8×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32D4×D37—22no—
33D4×D37—22no—
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—42no—
39C2×C4×D37—42no—
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C8×C37—21no—
44C2×C8×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C22⋊C4×C37—21no—
47C42×C37C2311yescharacteristic
48C22⋊Dic37—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37C2×C411yescharacteristic
52#10596936—21no—
53C4×Dic37C2×C411yescharacteristic
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C2×#64436—21no—
57C2×#64436—21no—
58#10596929—42no—
59C23×C37—21no—
60C22×D37—24no—
61C22×D37—21no—
62C22×D37—42no—
63C22×D37—42no—
64C22×D37C22⋊C411yescharacteristic
65D4×C37—21no—
66D4×C37M1612yescomplemented
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37C22×C411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C22⋊D37—24no—
74C2×Dic37—21no—
75C2×Dic37—42no—
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C22⋊C411yescharacteristic
78C2×Dic37C22⋊C411yescharacteristic
79D148—21no—
80D148M1612yescomplemented
81C4×D37—21no—
82C4×D37—21no—
83C4×D37—41no—
84C4×D37—42no—
85C4×D37—41no—
86C4×D37—41no—
87C4×D37—42no—
88C4×D37D812yes—
89C4×D37SD1612yes—
90C8×C37—41no—
91C8×C37—41no—
92#64436—41no—
93#64436—41no—
94C22×C37—22no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37C2×C22⋊C411yescharacteristic
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—22no—
101C2×D37—48no—
102C2×D37—41no—
103C2×D37—41no—
104C2×D37#10212yes—
105C4×C37—21no—
106C4×C37—41no—
107C4×C37C2×M1611yescharacteristic
108C4×C37C2×M1611yescharacteristic
109C4×C37C2×D811yescharacteristic
110C4×C37C2×SD1611yescharacteristic
111Dic37—21no—
112Dic37—21no—
113Dic37—41no—
114Dic37#10212yes—
115#1486—371nomaximal, Sylow
116C2×C37—42no—
117C2×C37#40711yescharacteristic
118C2×C37C2×#10211yescharacteristic
119C2×C37#42111yescharacteristic
120D37—22no—
121D37—42no—
122C2×C4×D4—371no—
123#431—371no—
124#423—371no—
125D4⋊C8—371no—
126D4⋊C8—371no—
127D4⋊C8—371no—
128D4⋊C8D3711yescharacteristic, complemented
129C37#148611yescharacteristic, complemented, Sylow
130C22×D4—371no—
131C23×C4—741no—
132C2×M16—741no—
133C4×D4—371no—
134C4×D4—371no—
135C4×D4—371no—
136C4×D4—741no—
137C4×D4—741no—
138C4×D4C2×D3711yescharacteristic
139C2×C4⋊C4—371no—
140C2×C22⋊C4—741no—
141C2×C42—371no—
142C4⋊C8—371no—
143C4⋊C8—741no—
144C4⋊C8—741no—
145C4⋊C8C2×D3711yescharacteristic, complemented
146C22⋊C8—741no—
147C4×C8—371no—
148C4×C8C2×D3711yescharacteristic, complemented
149C24—741no—
150C2×D4—371no—
151C2×D4—741no—
152C2×D4—742no—
153C2×D4—742no—
154C2×D4C4×D3711yescharacteristic
155C22×C4—21no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—1482no—
164C22×C4—1482no—
165M16—1482no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—741no—
169C2×C8—741no—
170C4⋊C4—371no—
171C4⋊C4—741no—
172C4⋊C4C4×D3711yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—741no—
175C22⋊C4—741no—
176C22⋊C4—741no—
177C42—371no—
178C42—371no—
179C42—371no—
180C42C22×D3711yescharacteristic
181C23—21no—
182C23—371no—
183C23—744no—
184C23—741no—
185C23—1482no—
186C23—1482no—
187D4—21no—
188D4—372no—
189D4—744no—
190D4—741no—
191D4#1059692912yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—371no—
196C2×C4—372no—
197C2×C4—372no—
198C2×C4—371no—
199C2×C4—371no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—1481no—
204C2×C4—1482no—
205C2×C4—1482no—
206C2×C4—1482no—
207C2×C4—1481no—
208C2×C4—1481no—
209C2×C4C2×C4×D3711yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4D4×D3711yescharacteristic
212C8—41no—
213C8—41no—
214C8—1481no—
215C8—1481no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—372no—
220C22—741no—
221C22—741no—
222C22—742no—
223C22—1488no—
224C22—1481no—
225C22—1481no—
226C22C22⋊C4×D3711yescharacteristic
227C4—21no—
228C4—41no—
229C4—372no—
230C4—741no—
231C4—741no—
232C4—1481no—
233C4M16×D3711yescharacteristic
234C4C2×#1059692911yescharacteristic
235C4D8×D3711yescharacteristic
236C4SD16×D3711yescharacteristic
237C2—42no—
238C2—742no—
239C2—1482no—
240C2#1455749511yescharacteristic
241C2#102×D3711yescharacteristic
242C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC42×C37C23
hypercenterD4⋊C8D37
hypocenterC37#1486
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. #14557584C2semidirect
3. #14557555C2semidirect
4. #14557262C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×D4⋊C8C2semidirect
19. C4⋊#64436C22semidirect
23. C4×#64436C22semidirect
25. C4⋊C8×C37C22semidirect
26. C4×C8×C37C22semidirect
66. D4×C37M16semidirect
80. D148M16semidirect
128. D4⋊C8D37semidirect
129. C37#1486semidirect
145. C4⋊C8C2×D37semidirect
148. C4×C8C2×D37semidirect
191. D4#10596929semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D372
#145575842
#145575552
#145572622
D4⋊#644362
#145572602
C37×D4⋊C82
#148637