Subgroups — C₂×#13050075 #14580285

Order 2624.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	2	yes	maximal
2	#13050075	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₁	C₄	1	2	yes	—
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₄²×C₄₁	C₄	1	2	yes	—
7	C₄²×C₄₁	C₂²	1	2	yes	—
8	C₂×#66491	C₄	1	8	yes	complemented
9	C₂×#66491	C₂²	1	4	yes	—
10	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₄₁	—	2	4	no	—
12	C₂×C₄×C₄₁	C₂×C₄	1	4	yes	—
13	C₂×C₄×C₄₁	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
16	#66491	C₂×C₄	1	8	yes	complemented
17	C₂²×C₄₁	C₄²	1	2	yes	—
18	C₂²×C₄₁	M₁₆	1	4	yes	—
19	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₄₁	—	2	4	no	—
21	C₄×C₄₁	C₄²	1	2	yes	—
22	C₄×C₄₁	C₂²×C₄	1	2	yes	—
23	C₂×C₄₁	#97	1	4	yes	complemented
24	C₂×C₄₁	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₄₁	C₂×M₁₆	1	2	yes	—
26	C₂×#97	—	41	1	no	maximal, Sylow
27	C₄₁	C₂×#97	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₈	—	41	2	no	—
29	C₂×C₄²	D₄₁	1	1	yes	characteristic
30	#97	—	41	4	no	—
31	C₂²×C₄	Dic₄₁	1	2	yes	—
32	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
33	C₂×C₈	—	41	8	no	—
34	C₂×C₈	—	41	4	no	—
35	C₄²	Dic₄₁	1	2	yes	—
36	C₄²	C₂×D₄₁	1	2	yes	—
37	C₂³	C₂×Dic₄₁	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₄×D₄₁	1	4	yes	—
40	C₂×C₄	C₂×Dic₄₁	1	4	yes	—
41	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
42	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
43	C₈	—	41	8	no	—
44	C₂²	#10620277	1	4	yes	—
45	C₂²	C₄×Dic₄₁	1	2	yes	—
46	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₄₁	1	2	yes	—
49	C₄	C₂×C₄×D₄₁	1	2	yes	—
50	C₂	#13050075	1	4	yes	direct product factor
51	C₂	C₂×C₄×Dic₄₁	1	1	yes	characteristic
52	C₂	C₂×#10620277	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₁
commutator	C₂×C₄₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂×C₄²×C₄₁	C₂
socle, prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂×C₄²	D₄₁
hypocenter	C₄₁	C₂×#97
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #13050075	C₂	direct (N × H)
8. C₂×#66491	C₄	semidirect
16. #66491	C₂×C₄	semidirect
23. C₂×C₄₁	#97	semidirect
27. C₄₁	C₂×#97	semidirect
50. C₂	#13050075	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×#66491	2
#13050075	2
C₂×C₄²×C₄₁	2
C₂×#97	41

Subgroups — C2×#13050075 #14580285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050075 #14580285