Subgroups — #14581204

Order 2624.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050243	C₂	1	2	yes	maximal
2	C₂×#10620272	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
4	C₂²⋊#4223	—	2	2	no	—
5	C₄⋊#4223	—	2	2	no	—
6	C₄×#4223	C₄	1	4	yes	complemented
7	C₂×C₈×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂×#66491	C₄	1	1	yes	characteristic, complemented
9	#10620272	—	2	2	no	—
10	C₂²×D₄₁	D₄	1	1	yes	characteristic
11	C₂×#4223	—	2	4	no	—
12	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₄₁	Q₈	1	1	yes	characteristic
14	C₄×D₄₁	C₂×C₄	1	2	yes	—
15	C₄×D₄₁	D₄	1	2	yes	—
16	C₈×C₄₁	—	2	1	no	—
17	#66491	—	2	1	no	—
18	C₂²×C₄₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₄₁	—	4	1	no	—
20	C₂×D₄₁	C₂²⋊C₄	1	2	yes	—
21	#4223	—	4	4	no	—
22	C₄×C₄₁	C₄²	1	1	yes	characteristic
23	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₄₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄₁	—	2	1	no	—
26	C₂×C₄₁	#95	1	1	yes	characteristic
27	D₄₁	—	2	2	no	—
28	H(3,ℤ/4)	—	41	1	no	maximal, Sylow
29	C₄₁	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
30	C₂×M₁₆	—	41	1	no	—
31	#117	—	41	2	no	—
32	C₂²×C₄	—	41	1	no	—
33	M₁₆	—	82	2	no	—
34	C₂×C₈	—	41	1	no	—
35	C₂×C₈	#4223	1	1	yes	characteristic, complemented
36	C₄⋊C₄	—	82	2	no	—
37	C₂²⋊C₄	—	82	2	no	—
38	C₄²	—	41	4	no	—
39	C₂³	—	41	1	no	—
40	C₂×C₄	—	41	1	no	—
41	C₂×C₄	—	41	2	no	—
42	C₂×C₄	—	41	2	no	—
43	C₂×C₄	—	82	4	no	—
44	C₂×C₄	C₂×#4223	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	82	1	no	—
47	C₂²	—	41	2	no	—
48	C₂²	—	164	1	no	—
49	C₂²	C₄⋊#4223	1	1	yes	characteristic
50	C₄	—	41	2	no	—
51	C₄	—	164	4	no	—
52	C₄	C₄×#4223	1	1	yes	characteristic
53	C₄	C₂²⋊#4223	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	82	2	no	—
56	C₂	(C₂×#4223)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#4223
commutator	C₄×C₄₁	C₄²
Frattini	C₂×C₄	C₂×#4223
Fitting	C₂×C₈×C₄₁	C₄
socle	C₂×C₄₁	#95
prime radical	C₂²×D₄₁	D₄
cosocle	C₂×C₄×D₄₁	C₂²
hypercenter	C₂×C₈	#4223
hypocenter	C₄₁	H(3,ℤ/4)
LCS	G ▷ C₄×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₄×#4223	C₄	semidirect
7. C₂×C₈×C₄₁	C₄	semidirect
8. C₂×#66491	C₄	semidirect
29. C₄₁	H(3,ℤ/4)	semidirect
35. C₂×C₈	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050243	2
C₂×#10620272	2
H(3,ℤ/4)	41