Subgroups — C₂²×#92474 #14521809

Order 1984.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#92474	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃₁⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂⁴×C₃₁	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₃₁	C₄	1	6	yes	—
6	C₂²×C₄×C₃₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₁	C₂²	1	6	yes	—
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	#92474	C₂²	1	16	yes	direct product factor
10	C₂×C₃₁⋊C₈	C₂²	1	12	yes	complemented
11	C₂³×C₃₁	—	2	4	no	—
12	C₂³×C₃₁	C₂×C₄	1	6	yes	—
13	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₁	C₂×C₄	1	12	yes	—
15	C₂×C₄×C₃₁	C₂×C₄	1	6	yes	—
16	C₂×C₄×C₃₁	C₂×C₄	1	3	yes	—
17	C₂×C₄×C₃₁	C₂³	1	3	yes	—
18	C₂×C₄×C₃₁	C₂³	1	4	yes	—
19	C₃₁⋊C₈	C₂³	1	8	yes	complemented
20	C₂²×C₃₁	—	2	12	no	—
21	C₂²×C₃₁	M₁₆	1	4	yes	complemented
22	C₂²×C₃₁	C₂²×C₄	1	4	yes	—
23	C₂²×C₃₁	C₂²×C₄	1	3	yes	—
24	C₄×C₃₁	C₂²×C₄	1	3	yes	—
25	C₄×C₃₁	C₂²×C₄	1	4	yes	—
26	C₄×C₃₁	C₂⁴	1	1	yes	characteristic
27	C₂²×M₁₆	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	—	2	4	no	—
29	C₂×C₃₁	C₂×M₁₆	1	6	yes	complemented
30	C₂×C₃₁	C₂³×C₄	1	1	yes	characteristic
31	C₂³×C₄	D₃₁	1	1	yes	characteristic
32	C₂×M₁₆	—	31	12	no	—
33	C₂²×C₈	—	31	2	no	—
34	C₃₁	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	Dic₃₁	1	1	yes	characteristic
36	C₂²×C₄	Dic₃₁	1	1	yes	characteristic
37	C₂²×C₄	Dic₃₁	1	6	yes	—
38	C₂²×C₄	C₂×D₃₁	1	6	yes	—
39	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
40	M₁₆	—	31	16	no	—
41	C₂×C₈	—	31	12	no	—
42	C₂³	—	2	4	no	—
43	C₂³	C₂×Dic₃₁	1	6	yes	—
44	C₂³	C₂×Dic₃₁	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₃₁	1	12	yes	—
46	C₂×C₄	C₂×Dic₃₁	1	6	yes	—
47	C₂×C₄	C₂×Dic₃₁	1	3	yes	—
48	C₂×C₄	C₂²×D₃₁	1	3	yes	—
49	C₂×C₄	C₂²×D₃₁	1	4	yes	—
50	C₈	—	31	8	no	—
51	C₂²	—	2	12	no	—
52	C₂²	#92474	1	4	yes	direct product factor
53	C₂²	C₂²×Dic₃₁	1	4	yes	—
54	C₂²	C₂²×Dic₃₁	1	3	yes	—
55	C₄	C₂²×Dic₃₁	1	4	yes	—
56	C₄	C₂²×Dic₃₁	1	3	yes	—
57	C₄	C₂³×D₃₁	1	1	yes	characteristic
58	C₂	—	2	4	no	—
59	C₂	C₂×#92474	1	6	yes	direct product factor
60	C₂	C₂³×Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₁
commutator	C₂×C₃₁	C₂³×C₄
Frattini	C₄	C₂³×D₃₁
Fitting	C₂³×C₄×C₃₁	C₂
socle	C₂³×C₃₁	C₂×C₄
prime radical	C₂⁴×C₃₁	C₄
cosocle	C₄×C₃₁	C₂⁴
hypercenter	C₂³×C₄	D₃₁
hypocenter	C₃₁	C₂²×M₁₆
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#92474	C₂	direct (N × H)
3. C₂²×C₃₁⋊C₈	C₂	semidirect
9. #92474	C₂²	direct (N × H)
10. C₂×C₃₁⋊C₈	C₂²	semidirect
19. C₃₁⋊C₈	C₂³	semidirect
21. C₂²×C₃₁	M₁₆	semidirect
29. C₂×C₃₁	C₂×M₁₆	semidirect
34. C₃₁	C₂²×M₁₆	semidirect
52. C₂²	#92474	direct (N × H)
59. C₂	C₂×#92474	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₃₁	2
C₂×#92474	2
C₂²×C₃₁⋊C₈	2
C₂²×M₁₆	31

Subgroups — C22×#92474 #14521809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#92474 #14521809