Subgroups — #14583207

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063317	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#13063259	C₂	1	1	yes	maximal, characteristic
4	#13063257	C₂	1	1	yes	maximal, characteristic
5	#13063250	C₂	1	1	yes	maximal, characteristic
6	#13063250	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₄	—	2	1	no	—
16	Dic₄₃⋊C₄	—	2	1	no	—
17	Dic₄₃⋊C₄	—	2	1	no	—
18	C₄×Dic₄₃	—	2	1	no	—
19	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₃	—	2	1	no	—
23	C₂×Dic₄₃	—	2	1	no	—
24	C₂×Dic₄₃	—	2	1	no	—
25	C₂×Dic₄₃	—	2	1	no	—
26	Dic₈₆	—	2	1	no	—
27	Dic₈₆	Q₈	1	2	yes	—
28	C₈×C₄₃	—	2	1	no	—
29	C₈×C₄₃	—	2	1	no	—
30	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₃	—	2	1	no	—
32	C₄×C₄₃	—	2	1	no	—
33	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₄₃	#41	1	1	yes	characteristic
35	Dic₄₃	—	2	2	no	—
36	Dic₄₃	—	4	1	no	—
37	Dic₄₃	—	4	1	no	—
38	Dic₄₃	—	4	1	no	—
39	C₂×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₄₃	#135	1	1	yes	characteristic
41	C₂×C₄₃	#137	1	1	yes	characteristic
42	#479	—	43	1	no	maximal, Sylow
43	C₄₃	#479	1	1	yes	characteristic, complemented, Sylow
44	#125	—	43	1	no	—
45	C₄×Q₈	—	43	1	no	—
46	#107	—	43	1	no	—
47	#106	—	43	1	no	—
48	C₄⋊C₈	D₄₃	1	1	yes	characteristic
49	#103	—	43	1	no	—
50	#103	—	43	1	no	—
51	C₂×Q₈	—	43	1	no	—
52	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
53	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
54	C₄⋊C₄	—	43	1	no	—
55	C₄⋊C₄	—	43	1	no	—
56	C₄⋊C₄	—	43	1	no	—
57	C₄⋊C₄	—	86	1	no	—
58	C₄⋊C₄	—	86	1	no	—
59	C₄⋊C₄	—	86	1	no	—
60	C₄²	—	86	1	no	—
61	C₄²	C₂×D₄₃	1	1	yes	characteristic
62	Q₈	—	43	2	no	—
63	Q₈	—	86	1	no	—
64	C₂×C₄	—	86	1	no	—
65	C₂×C₄	—	86	1	no	—
66	C₂×C₄	—	86	1	no	—
67	C₂×C₄	—	86	1	no	—
68	C₂×C₄	D₁₇₂	1	1	yes	characteristic
69	C₂×C₄	D₁₇₂	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	86	2	no	—
77	C₄	—	172	1	no	—
78	C₄	—	172	1	no	—
79	C₄	—	172	1	no	—
80	C₄	#10621900	1	1	yes	characteristic
81	C₄	Q₈×D₄₃	1	1	yes	characteristic
82	C₂	#13063305	1	1	yes	characteristic
83	C₂	#13063347	1	1	yes	characteristic
84	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	#479
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
43. C₄₃	#479	semidirect

Maximal subgroups

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

subgroup	index
#13063317	2
C₄×Dic₈₆	2
#13063259	2
#13063257	2
#13063250	2
C₄⋊C₈×C₄₃	2
#479	43