Subgroups — #14583185

Order 2752.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063325	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#13063257	C₂	1	2	yes	maximal
4	#13063250	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₆	—	2	1	no	—
7	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₃	C₂²	1	2	yes	—
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₃	—	2	1	no	—
11	C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	Dic₄₃⋊C₄	—	2	1	no	—
14	C₄×Dic₄₃	—	2	1	no	—
15	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₃	—	2	1	no	—
19	C₂×Dic₄₃	—	2	1	no	—
20	C₂×Dic₄₃	—	2	2	no	—
21	Dic₈₆	—	2	1	no	—
22	Dic₈₆	—	4	2	no	—
23	Dic₈₆	Q₈	1	2	yes	complemented
24	C₈×C₄₃	—	2	2	no	—
25	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₄₃	—	2	1	no	—
27	C₄×C₄₃	SD₁₆	1	2	yes	—
28	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₄₃	#41	1	1	yes	characteristic
30	Dic₄₃	—	2	2	no	—
31	Dic₄₃	—	4	2	no	—
32	Dic₄₃	—	4	1	no	—
33	C₂×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
34	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
35	C₂×C₄₃	#137	1	1	yes	characteristic
36	#475	—	43	1	no	maximal, Sylow
37	C₄₃	#475	1	1	yes	characteristic, complemented, Sylow
38	C₄⋊Q₈	—	43	1	no	—
39	C₄×Q₈	—	43	1	no	—
40	#106	—	43	2	no	—
41	C₄⋊C₈	D₄₃	1	1	yes	characteristic
42	#103	—	43	2	no	—
43	C₂×Q₈	—	43	1	no	—
44	C₂×Q₈	—	86	1	no	—
45	C₂×C₈	C₂×D₄₃	1	2	yes	—
46	C₄⋊C₄	—	43	2	no	—
47	C₄⋊C₄	—	43	1	no	—
48	C₄⋊C₄	—	86	1	no	—
49	C₄⋊C₄	—	86	1	no	—
50	C₄²	—	86	1	no	—
51	C₄²	C₂×D₄₃	1	1	yes	characteristic
52	Q₈	—	43	2	no	—
53	Q₈	—	86	1	no	—
54	Q₈	—	172	2	no	—
55	C₂×C₄	—	86	1	no	—
56	C₂×C₄	—	86	1	no	—
57	C₂×C₄	—	86	2	no	—
58	C₂×C₄	D₁₇₂	1	1	yes	characteristic
59	C₂×C₄	D₁₇₂	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	86	2	no	—
65	C₄	—	172	2	no	—
66	C₄	—	172	1	no	—
67	C₄	#10621873	1	2	yes	—
68	C₄	#10621900	1	1	yes	characteristic
69	C₄	Q₈×D₄₃	1	1	yes	characteristic
70	C₂	#13063305	1	1	yes	characteristic
71	C₂	C₂×#10621873	1	1	yes	characteristic
72	C₂	#13063358	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊C₈×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#475
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
23. Dic₈₆	Q₈	semidirect
37. C₄₃	#475	semidirect

Maximal subgroups

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

subgroup	index
#13063325	2
C₄×Dic₈₆	2
#13063257	2
#13063250	2
C₄⋊C₈×C₄₃	2
#475	43