Subgroups — #14582810

Order 2752.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂×D₄₃)⋊C₄	C₂	1	3	yes	maximal
2	C₄₃⋊#95	C₂	1	3	yes	maximal, complemented
3	C₂²×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄₃	C₂²	1	1	yes	characteristic
5	C₂×Q₈×C₄₃	—	2	6	no	—
6	C₂²×C₄×C₄₃	C₂²	1	3	yes	—
7	C₂²×Dic₄₃	C₂²	1	3	yes	—
8	(C₂×D₄₃)⋊C₄	—	2	6	no	—
9	C₂³×C₄₃	C₂³	1	1	yes	characteristic
10	C₂²×D₄₃	—	2	3	no	—
11	C₂²×D₄₃	—	2	3	no	—
12	C₂²×D₄₃	Q₈	1	2	yes	complemented
13	Q₈×C₄₃	—	2	8	no	—
14	C₂×C₄×C₄₃	—	2	6	no	—
15	C₂×C₄×C₄₃	D₄	1	6	yes	—
16	C₂×Dic₄₃	—	2	3	no	—
17	C₂×Dic₄₃	—	2	6	no	—
18	C₂²×C₄₃	C₂×D₄	1	3	yes	—
19	C₂²×C₄₃	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₄₃	#41	1	3	yes	—
21	C₂×D₄₃	—	2	6	no	—
22	C₂×D₄₃	—	4	1	no	—
23	C₂×D₄₃	—	4	3	no	—
24	C₄×C₄₃	—	2	6	no	—
25	Dic₄₃	—	4	3	no	—
26	C₂×C₄₃	#120	1	1	yes	characteristic
27	C₂×C₄₃	C₂²⋊Q₈	1	3	yes	—
28	C₂×C₄₃	#124	1	3	yes	—
29	D₄₃	—	4	2	no	—
30	#393	—	43	1	no	maximal, Sylow
31	C₄₃	#393	1	1	yes	characteristic, complemented, Sylow
32	C₂²×Q₈	D₄₃	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊C₄	—	43	3	no	—
34	#95	—	43	3	no	—
35	C₂⁴	—	43	1	no	—
36	C₂×Q₈	—	2	6	no	—
37	C₂²×C₄	—	43	3	no	—
38	C₂²×C₄	C₂×D₄₃	1	3	yes	—
39	C₂²⋊C₄	—	86	6	no	—
40	C₂³	—	43	2	no	—
41	C₂³	—	86	3	no	—
42	C₂³	—	86	3	no	—
43	C₂³	C₂²×D₄₃	1	1	yes	characteristic
44	Q₈	—	2	8	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	86	6	no	—
47	C₂×C₄	—	86	3	no	—
48	C₂×C₄	C₂²⋊D₄₃	1	6	yes	—
49	C₂²	—	86	6	no	—
50	C₂²	—	172	1	no	—
51	C₂²	—	172	3	no	—
52	C₂²	Q₈×D₄₃	1	1	yes	characteristic
53	C₂²	#10621902	1	3	yes	—
54	C₂²	C₂×C₂²⋊D₄₃	1	3	yes	—
55	C₄	—	2	6	no	—
56	C₄	—	172	3	no	—
57	C₂	—	172	2	no	—
58	C₂	#13063294	1	1	yes	characteristic
59	C₂	#13063301	1	3	yes	—
60	C₂	#13063314	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₃
commutator, socle, cosocle	C₂³×C₄₃	C₂³
Fitting	C₂²×Q₈×C₄₃	C₂
prime radical	C₂³×D₄₃	C₂²
hypercenter	C₂²×Q₈	D₄₃
hypocenter	C₄₃	#393
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#95	C₂	semidirect
3. C₂²×Q₈×C₄₃	C₂	semidirect
12. C₂²×D₄₃	Q₈	semidirect
31. C₄₃	#393	semidirect
32. C₂²×Q₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂×D₄₃)⋊C₄	2
C₄₃⋊#95	2
C₂²×Q₈×C₄₃	2
#393	43