Subgroups — C₂²×#10620272 #14581095

Order 2624.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#10620272	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#66491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₄₁	C₄	1	1	yes	characteristic
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄₁	C₄	1	6	yes	—
9	C₂×C₄×D₄₁	C₂²	1	6	yes	—
10	C₂×C₈×C₄₁	C₂²	1	6	yes	complemented
11	C₂×#66491	C₂²	1	6	yes	complemented
12	#10620272	C₂²	1	16	yes	direct product factor
13	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₄₁	—	2	4	no	—
15	C₂²×D₄₁	C₂×C₄	1	6	yes	—
16	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
17	C₂×C₄×C₄₁	C₂³	1	3	yes	—
18	C₂×Dic₄₁	C₂×C₄	1	6	yes	—
19	C₄×D₄₁	C₂×C₄	1	12	yes	—
20	C₄×D₄₁	C₂³	1	4	yes	—
21	C₈×C₄₁	C₂³	1	4	yes	complemented
22	#66491	C₂³	1	4	yes	complemented
23	C₂²×C₄₁	M₁₆	1	4	yes	complemented
24	C₂²×C₄₁	C₂²×C₄	1	3	yes	—
25	C₂×D₄₁	—	2	12	no	—
26	C₂×D₄₁	C₂²×C₄	1	4	yes	—
27	C₄×C₄₁	C₂²×C₄	1	3	yes	—
28	C₄×C₄₁	C₂⁴	1	1	yes	characteristic
29	Dic₄₁	C₂²×C₄	1	4	yes	—
30	C₂×C₄₁	C₂×M₁₆	1	6	yes	complemented
31	C₂×C₄₁	C₂³×C₄	1	1	yes	characteristic
32	D₄₁	—	2	4	no	—
33	C₂²×M₁₆	—	41	1	no	maximal, Sylow
34	C₄₁	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂³×C₄	—	41	1	no	—
36	C₂×M₁₆	—	41	12	no	—
37	C₂²×C₈	—	41	1	no	—
38	C₂²×C₈	D₄₁	1	1	yes	characteristic, complemented
39	C₂⁴	—	41	1	no	—
40	C₂²×C₄	—	41	1	no	—
41	C₂²×C₄	—	41	6	no	—
42	C₂²×C₄	—	41	6	no	—
43	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
44	M₁₆	—	41	16	no	—
45	C₂×C₈	—	41	6	no	—
46	C₂×C₈	C₂×D₄₁	1	6	yes	complemented
47	C₂³	—	41	6	no	—
48	C₂³	—	82	4	no	—
49	C₂³	C₄×D₄₁	1	1	yes	characteristic
50	C₂×C₄	—	41	6	no	—
51	C₂×C₄	—	41	12	no	—
52	C₂×C₄	—	41	4	no	—
53	C₂×C₄	C₄×D₄₁	1	3	yes	—
54	C₂×C₄	C₂²×D₄₁	1	3	yes	—
55	C₈	—	41	4	no	—
56	C₈	C₂²×D₄₁	1	4	yes	complemented
57	C₂²	—	41	4	no	—
58	C₂²	—	82	12	no	—
59	C₂²	#10620272	1	4	yes	direct product factor
60	C₂²	C₂×C₄×D₄₁	1	3	yes	—
61	C₄	—	41	4	no	—
62	C₄	C₂×C₄×D₄₁	1	3	yes	—
63	C₄	C₂³×D₄₁	1	1	yes	characteristic
64	C₂	—	82	4	no	—
65	C₂	C₂×#10620272	1	6	yes	direct product factor
66	C₂	C₂²×C₄×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₁
commutator	C₂×C₄₁	C₂³×C₄
Frattini	C₄	C₂³×D₄₁
Fitting	C₂²×C₈×C₄₁	C₂
socle	C₂³×C₄₁	C₂×C₄
prime radical	C₂³×D₄₁	C₄
cosocle	C₄×C₄₁	C₂⁴
hypercenter	C₂²×C₈	D₄₁
hypocenter	C₄₁	C₂²×M₁₆
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#10620272	C₂	direct (N × H)
3. C₂²×#66491	C₂	semidirect
4. C₂²×C₈×C₄₁	C₂	semidirect
10. C₂×C₈×C₄₁	C₂²	semidirect
11. C₂×#66491	C₂²	semidirect
12. #10620272	C₂²	direct (N × H)
21. C₈×C₄₁	C₂³	semidirect
22. #66491	C₂³	semidirect
23. C₂²×C₄₁	M₁₆	semidirect
30. C₂×C₄₁	C₂×M₁₆	semidirect
34. C₄₁	C₂²×M₁₆	semidirect
38. C₂²×C₈	D₄₁	semidirect
46. C₂×C₈	C₂×D₄₁	semidirect
56. C₈	C₂²×D₄₁	semidirect
59. C₂²	#10620272	direct (N × H)
65. C₂	C₂×#10620272	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄₁	2
C₂×#10620272	2
C₂²×#66491	2
C₂²×C₈×C₄₁	2
C₂²×M₁₆	41

Subgroups — C22×#10620272 #14581095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10620272 #14581095