Subgroups — #14582839

Order 2752.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊#95	C₂	1	2	yes	maximal
4	C₄₃⋊#95	C₂	1	2	yes	maximal
5	#95×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₃	C₂²	1	2	yes	—
7	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₃	C₂²	1	2	yes	—
10	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₃	—	2	2	no	—
12	Dic₄₃⋊C₄	—	2	2	no	—
13	C₂³×C₄₃	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₄₃	—	2	2	no	—
15	C₂×C₄×C₄₃	—	2	2	no	—
16	C₂×C₄×C₄₃	—	2	2	no	—
17	C₂×C₄×C₄₃	—	2	2	no	—
18	C₂×C₄×C₄₃	D₄	1	2	yes	—
19	C₂×Dic₄₃	—	2	1	no	—
20	C₂×Dic₄₃	—	2	1	no	—
21	C₂×Dic₄₃	—	2	1	no	—
22	C₂×Dic₄₃	—	2	2	no	—
23	C₂×Dic₄₃	—	2	4	no	—
24	C₂×Dic₄₃	—	2	2	no	—
25	C₂×Dic₄₃	Q₈	1	2	yes	—
26	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄₃	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₄₃	#41	1	2	yes	—
29	C₂²×C₄₃	#41	1	1	yes	characteristic
30	C₂²×C₄₃	#41	1	2	yes	—
31	C₄×C₄₃	—	2	2	no	—
32	C₄×C₄₃	—	4	2	no	—
33	Dic₄₃	—	2	2	no	—
34	Dic₄₃	—	4	1	no	—
35	Dic₄₃	—	4	2	no	—
36	C₂×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
37	C₂×C₄₃	#123	1	1	yes	characteristic
38	C₂×C₄₃	#124	1	1	yes	characteristic
39	C₂×C₄₃	#125	1	2	yes	—
40	C₂×C₄₃	#126	1	2	yes	—
41	#400	—	43	1	no	maximal, Sylow
42	C₄₃	#400	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄⋊C₄	—	43	1	no	—
44	C₂×C₄⋊C₄	—	43	1	no	—
45	#95	—	43	2	no	—
46	#95	—	43	2	no	—
47	#95	D₄₃	1	1	yes	characteristic
48	C₂²×C₄	—	43	1	no	—
49	C₂²×C₄	—	43	2	no	—
50	C₂²×C₄	—	43	1	no	—
51	C₂²×C₄	C₂×D₄₃	1	2	yes	—
52	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
53	C₄⋊C₄	—	86	2	no	—
54	C₄⋊C₄	—	86	2	no	—
55	C₂³	C₂²×D₄₃	1	1	yes	characteristic
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	43	2	no	—
61	C₂×C₄	—	86	1	no	—
62	C₂×C₄	—	86	1	no	—
63	C₂×C₄	—	86	1	no	—
64	C₂×C₄	—	86	2	no	—
65	C₂×C₄	—	86	4	no	—
66	C₂×C₄	—	86	2	no	—
67	C₂×C₄	D₁₇₂	1	2	yes	—
68	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
69	C₂²	#10621898	1	2	yes	—
70	C₂²	#10621900	1	1	yes	characteristic
71	C₂²	#10621900	1	2	yes	—
72	C₂²	Q₈×D₄₃	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	4	2	no	—
75	C₄	—	86	2	no	—
76	C₄	—	172	1	no	—
77	C₄	—	172	2	no	—
78	C₂	#13063305	1	1	yes	characteristic
79	C₂	#13063309	1	1	yes	characteristic
80	C₂	#13063313	1	1	yes	characteristic
81	C₂	#13063315	1	2	yes	—
82	C₂	#13063318	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₃
commutator, socle, prime radical, cosocle	C₂³×C₄₃	C₂³
Fitting	#95×C₄₃	C₂
hypercenter	#95	D₄₃
hypocenter	C₄₃	#400
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
42. C₄₃	#400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₄₃	2
C₂×Dic₄₃⋊C₄	2
C₄₃⋊#95	2
#95×C₄₃	2
#400	43