Subgroups — C₂²×#10621873 #14583673

Order 2752.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#10621873	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₄₃	—	2	1	no	—
6	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₃	—	2	1	no	—
8	C₂×D₁₇₂	—	2	3	no	—
9	C₂×D₁₇₂	C₂²	1	6	yes	—
10	C₂×Dic₈₆	—	2	3	no	—
11	C₂×Dic₈₆	C₂²	1	6	yes	complemented
12	C₂×C₈×C₄₃	C₂²	1	6	yes	complemented
13	#10621873	C₂²	1	16	yes	direct product factor
14	C₂³×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×D₄₃	—	2	6	no	—
16	C₂²×D₄₃	—	4	4	no	—
17	C₂×C₄×C₄₃	D₄	1	3	yes	—
18	C₂×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂×Dic₄₃	—	2	6	no	—
20	D₁₇₂	—	2	6	no	—
21	D₁₇₂	C₂³	1	4	yes	—
22	Dic₈₆	—	2	6	no	—
23	Dic₈₆	C₂³	1	4	yes	complemented
24	C₈×C₄₃	C₂³	1	4	yes	complemented
25	C₂²×C₄₃	SD₁₆	1	4	yes	complemented
26	C₂²×C₄₃	C₂×D₄	1	3	yes	—
27	C₂×D₄₃	—	2	4	no	—
28	C₂×D₄₃	—	4	12	no	—
29	C₄×C₄₃	C₂×D₄	1	3	yes	—
30	C₄×C₄₃	C₂⁴	1	1	yes	characteristic
31	Dic₄₃	—	2	4	no	—
32	C₂×C₄₃	C₂×SD₁₆	1	6	yes	complemented
33	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
34	D₄₃	—	4	4	no	—
35	C₂²×SD₁₆	—	43	1	no	maximal, Sylow
36	C₄₃	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₂²×Q₈	—	43	1	no	—
38	C₂²×D₄	—	43	1	no	—
39	C₂×SD₁₆	—	43	12	no	—
40	C₂²×C₈	D₄₃	1	1	yes	characteristic, complemented
41	C₂⁴	—	86	1	no	—
42	C₂×Q₈	—	43	6	no	—
43	C₂×Q₈	—	86	3	no	—
44	C₂×D₄	—	43	6	no	—
45	C₂×D₄	—	86	3	no	—
46	C₂²×C₄	—	86	1	no	—
47	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
48	SD₁₆	—	43	16	no	—
49	C₂×C₈	C₂×D₄₃	1	6	yes	complemented
50	C₂³	—	86	6	no	—
51	C₂³	—	172	4	no	—
52	C₂³	D₁₇₂	1	1	yes	characteristic
53	Q₈	—	43	4	no	—
54	Q₈	—	86	6	no	—
55	D₄	—	43	4	no	—
56	D₄	—	86	6	no	—
57	C₂×C₄	—	86	6	no	—
58	C₂×C₄	D₁₇₂	1	3	yes	—
59	C₂×C₄	C₂²×D₄₃	1	3	yes	—
60	C₈	C₂²×D₄₃	1	4	yes	complemented
61	C₂²	—	86	4	no	—
62	C₂²	—	172	12	no	—
63	C₂²	#10621873	1	4	yes	direct product factor
64	C₂²	C₂×D₁₇₂	1	3	yes	—
65	C₄	—	86	4	no	—
66	C₄	C₂×D₁₇₂	1	3	yes	—
67	C₄	C₂³×D₄₃	1	1	yes	characteristic
68	C₂	—	172	4	no	—
69	C₂	C₂×#10621873	1	6	yes	direct product factor
70	C₂	C₂²×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₇₂
commutator, cosocle	C₄×C₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₃
Fitting	C₂²×C₈×C₄₃	C₂
socle	C₂³×C₄₃	D₄
prime radical	C₂²×D₁₇₂	C₂
hypercenter	C₂²×C₈	D₄₃
hypocenter	C₄₃	C₂²×SD₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₈₆	C₂	semidirect
3. C₂×#10621873	C₂	direct (N × H)
4. C₂²×C₈×C₄₃	C₂	semidirect
11. C₂×Dic₈₆	C₂²	semidirect
12. C₂×C₈×C₄₃	C₂²	semidirect
13. #10621873	C₂²	direct (N × H)
23. Dic₈₆	C₂³	semidirect
24. C₈×C₄₃	C₂³	semidirect
25. C₂²×C₄₃	SD₁₆	semidirect
32. C₂×C₄₃	C₂×SD₁₆	semidirect
36. C₄₃	C₂²×SD₁₆	semidirect
40. C₂²×C₈	D₄₃	semidirect
49. C₂×C₈	C₂×D₄₃	semidirect
60. C₈	C₂²×D₄₃	semidirect
63. C₂²	#10621873	direct (N × H)
69. C₂	C₂×#10621873	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×Dic₈₆	2
C₂²×D₁₇₂	2
C₂×#10621873	2
C₂²×C₈×C₄₃	2
C₂²×SD₁₆	43

Subgroups — C22×#10621873 #14583673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10621873 #14583673