Subgroups — C₄×#10620272 #14580286

Order 2624.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620272	C₂	1	2	yes	maximal
2	C₄²×D₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050074	C₂	1	2	yes	maximal, complemented
4	C₄×#66491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₁	C₄	1	2	yes	—
7	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁	C₂²	1	2	yes	—
9	C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₄×Dic₄₁	C₄	1	2	yes	—
11	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
12	C₂×#66491	C₂²	1	2	yes	—
13	#10620272	C₄	1	8	yes	direct product factor
14	C₂²×D₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₄₁	—	2	4	no	—
20	C₄×D₄₁	C₂×C₄	1	4	yes	—
21	C₈×C₄₁	C₂×C₄	1	4	yes	complemented
22	#66491	C₂×C₄	1	4	yes	complemented
23	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₄₁	—	2	2	no	—
25	C₂×D₄₁	C₄²	1	2	yes	—
26	C₄×C₄₁	M₁₆	1	4	yes	complemented
27	C₄×C₄₁	C₂²×C₄	1	2	yes	—
28	Dic₄₁	—	2	2	no	—
29	Dic₄₁	C₄²	1	2	yes	—
30	C₂×C₄₁	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄₁	C₂×M₁₆	1	2	yes	—
32	D₄₁	—	2	2	no	—
33	C₄×M₁₆	—	41	1	no	maximal, Sylow
34	C₄₁	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂×M₁₆	—	41	2	no	—
36	C₂×C₄²	—	41	1	no	—
37	#97	—	41	2	no	—
38	C₄×C₈	—	41	1	no	—
39	C₄×C₈	D₄₁	1	1	yes	characteristic, complemented
40	C₂²×C₄	—	41	1	no	—
41	C₂²×C₄	—	41	2	no	—
42	M₁₆	—	41	8	no	—
43	C₂×C₈	—	41	2	no	—
44	C₂×C₈	C₂×D₄₁	1	2	yes	—
45	C₄²	—	41	2	no	—
46	C₄²	—	41	1	no	—
47	C₄²	C₂×D₄₁	1	1	yes	characteristic
48	C₂³	—	41	1	no	—
49	C₂×C₄	—	41	1	no	—
50	C₂×C₄	—	41	4	no	—
51	C₂×C₄	—	41	2	no	—
52	C₂×C₄	—	82	4	no	—
53	C₂×C₄	C₄×D₄₁	1	2	yes	—
54	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
55	C₈	—	41	4	no	—
56	C₈	C₄×D₄₁	1	4	yes	complemented
57	C₂²	—	41	2	no	—
58	C₂²	—	82	2	no	—
59	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
60	C₄	—	41	2	no	—
61	C₄	—	82	2	no	—
62	C₄	#10620272	1	4	yes	direct product factor
63	C₄	C₂×C₄×D₄₁	1	2	yes	—
64	C₂	—	82	2	no	—
65	C₂	C₄²×D₄₁	1	1	yes	characteristic
66	C₂	C₂×#10620272	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₄₁
commutator	C₂×C₄₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₄×C₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂²×C₄
prime radical	C₂²×D₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄×C₈	D₄₁
hypocenter	C₄₁	C₄×M₁₆
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #13050074	C₂	semidirect
4. C₄×#66491	C₂	semidirect
5. C₄×C₈×C₄₁	C₂	semidirect
13. #10620272	C₄	direct (N × H)
21. C₈×C₄₁	C₂×C₄	semidirect
22. #66491	C₂×C₄	semidirect
26. C₄×C₄₁	M₁₆	semidirect
34. C₄₁	C₄×M₁₆	semidirect
39. C₄×C₈	D₄₁	semidirect
56. C₈	C₄×D₄₁	semidirect
62. C₄	#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
C₂×#10620272	2
C₄²×D₄₁	2
#13050074	2
C₄×#66491	2
C₄×C₈×C₄₁	2
C₄×M₁₆	41

Subgroups — C4×#10620272 #14580286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10620272 #14580286