Subgroups — C₂×#376×C₂₆₉ #46807374

Order 34432.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₂₆₉	C₂	1	3	yes	maximal
2	#376×C₂₆₉	C₂	1	8	yes	maximal, direct product factor
3	C₂×#95×C₂₆₉	C₂	1	4	yes	maximal
4	C₂³×C₄×C₂₆₉	C₂²	1	6	yes	—
5	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₂₆₉	C₄	1	24	yes	complemented
7	C₂×C₄²×C₂₆₉	C₂²	1	12	yes	—
8	#95×C₂₆₉	C₂²	1	16	yes	—
9	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₂₆₉	—	2	24	no	—
11	C₂²×C₄×C₂₆₉	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₂₆₉	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₂₆₉	C₂³	1	12	yes	—
14	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
15	C₄²×C₂₆₉	C₂×C₄	1	48	yes	complemented
16	C₂³×C₂₆₉	C₂²×C₄	1	6	yes	—
17	C₂³×C₂₆₉	#41	1	8	yes	—
18	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₂₆₉	—	2	48	no	—
20	C₂×C₄×C₂₆₉	—	2	24	no	—
21	C₂×C₄×C₂₆₉	C₄²	1	16	yes	—
22	C₂×C₄×C₂₆₉	C₂²×C₄	1	24	yes	—
23	C₂×C₄×C₂₆₉	C₂²×C₄	1	12	yes	—
24	C₂²×C₂₆₉	C₂×C₄²	1	4	yes	—
25	C₂²×C₂₆₉	#117	1	24	yes	—
26	C₂²×C₂₆₉	C₂³×C₄	1	3	yes	—
27	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
28	C₄×C₂₆₉	—	2	24	no	—
29	C₄×C₂₆₉	C₂×C₄²	1	8	yes	—
30	C₂×C₂₆₉	#376	1	8	yes	direct product factor
31	C₂×C₂₆₉	C₂²×C₄²	1	1	yes	characteristic
32	C₂×C₂₆₉	C₂×#117	1	6	yes	—
33	C₂₆₉	C₂×#376	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×#376	C₂₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄²	C₂×C₂₆₉	1	3	yes	—
36	#376	C₂×C₂₆₉	1	8	yes	direct product factor
37	C₂×#95	C₂×C₂₆₉	1	4	yes	—
38	C₂³×C₄	C₂²×C₂₆₉	1	6	yes	—
39	C₂³×C₄	C₂²×C₂₆₉	1	1	yes	characteristic
40	C₂×C₄²	C₄×C₂₆₉	1	24	yes	complemented
41	C₂×C₄²	C₂²×C₂₆₉	1	12	yes	—
42	#95	C₂²×C₂₆₉	1	16	yes	—
43	C₂⁴	C₂³×C₂₆₉	1	1	yes	characteristic
44	C₂²×C₄	—	2	24	no	—
45	C₂²×C₄	C₂×C₄×C₂₆₉	1	24	yes	—
46	C₂²×C₄	C₂×C₄×C₂₆₉	1	12	yes	—
47	C₂²×C₄	C₂³×C₂₆₉	1	12	yes	—
48	C₂²×C₄	C₂³×C₂₆₉	1	2	yes	—
49	C₄²	C₂×C₄×C₂₆₉	1	48	yes	complemented
50	C₂³	C₂²×C₄×C₂₆₉	1	6	yes	—
51	C₂³	#41×C₂₆₉	1	8	yes	—
52	C₂³	C₂⁴×C₂₆₉	1	1	yes	characteristic
53	C₂×C₄	—	2	48	no	—
54	C₂×C₄	—	2	24	no	—
55	C₂×C₄	C₄²×C₂₆₉	1	16	yes	—
56	C₂×C₄	C₂²×C₄×C₂₆₉	1	24	yes	—
57	C₂×C₄	C₂²×C₄×C₂₆₉	1	12	yes	—
58	C₂²	C₂×C₄²×C₂₆₉	1	4	yes	—
59	C₂²	#117×C₂₆₉	1	24	yes	—
60	C₂²	C₂³×C₄×C₂₆₉	1	3	yes	—
61	C₂²	C₂×#41×C₂₆₉	1	4	yes	—
62	C₄	—	2	24	no	—
63	C₄	C₂×C₄²×C₂₆₉	1	8	yes	—
64	C₂	#376×C₂₆₉	1	8	yes	direct product factor
65	C₂	C₂²×C₄²×C₂₆₉	1	1	yes	characteristic
66	C₂	C₂×#117×C₂₆₉	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄×C₂₆₉	C₂²
commutator	C₂	C₂²×C₄²×C₂₆₉
Frattini, cosocle	C₂³	C₂⁴×C₂₆₉
socle, prime radical	C₂⁴×C₂₆₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₆₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #376×C₂₆₉	C₂	direct (N × H)
6. C₂×C₄²×C₂₆₉	C₄	semidirect
15. C₄²×C₂₆₉	C₂×C₄	semidirect
30. C₂×C₂₆₉	#376	direct (N × H)
33. C₂₆₉	C₂×#376	direct (N × H)
34. C₂×#376	C₂₆₉	direct (N × H)
36. #376	C₂×C₂₆₉	direct (N × H)
40. C₂×C₄²	C₄×C₂₆₉	semidirect
49. C₄²	C₂×C₄×C₂₆₉	semidirect
64. C₂	#376×C₂₆₉	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×C₄²×C₂₆₉	2
#376×C₂₆₉	2
C₂×#95×C₂₆₉	2
C₂×#376	269

Subgroups — C2×#376×C269 #46807374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#376×C₂₆₉ #46807374