Subgroups — #14583288

Order 2752.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621873	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₄₄	C₂	1	2	yes	maximal, complemented
3	#13063322	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063313	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₂	—	2	2	no	—
7	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
8	C₂×D₁₇₂	C₂²	1	2	yes	—
9	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	2	yes	—
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	(C₂×D₄₃)⋊C₄	—	2	2	no	—
13	D₃₄₄	—	2	4	no	—
14	#10621873	—	2	4	no	—
15	C₂²×D₄₃	—	2	1	no	—
16	C₂²×D₄₃	—	2	2	no	—
17	C₂×C₄×C₄₃	D₄	1	2	yes	—
18	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₃	—	2	1	no	—
20	D₁₇₂	—	2	2	no	—
21	D₁₇₂	—	2	2	no	—
22	D₁₇₂	—	2	2	no	—
23	D₁₇₂	—	4	4	no	—
24	Dic₈₆	—	2	2	no	—
25	C₈×C₄₃	D₄	1	4	yes	complemented
26	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄₃	—	4	1	no	—
28	C₂×D₄₃	—	4	2	no	—
29	C₂×D₄₃	—	4	2	no	—
30	C₂×D₄₃	—	4	4	no	—
31	C₄×C₄₃	—	2	2	no	—
32	C₄×C₄₃	C₂×D₄	1	2	yes	—
33	Dic₄₃	—	4	1	no	—
34	C₂×C₄₃	#127	1	1	yes	characteristic
35	C₂×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
36	D₄₃	—	8	1	no	—
37	D₄₃	—	8	2	no	—
38	#496	—	43	1	no	maximal, Sylow
39	C₄₃	#496	1	1	yes	characteristic, complemented, Sylow
40	C₂×SD₁₆	—	43	2	no	—
41	C₂×D₈	—	43	2	no	—
42	#127	—	43	1	no	—
43	#124	—	43	1	no	—
44	#97	D₄₃	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	43	1	no	—
46	C₂×D₄	—	43	1	no	—
47	C₂×D₄	—	43	2	no	—
48	C₂×D₄	—	86	2	no	—
49	SD₁₆	—	86	4	no	—
50	D₈	—	86	4	no	—
51	C₂×C₈	C₂×D₄₃	1	2	yes	—
52	C₂²⋊C₄	—	86	2	no	—
53	C₄²	C₂×D₄₃	1	1	yes	characteristic
54	C₂³	—	86	1	no	—
55	C₂³	—	86	2	no	—
56	Q₈	—	86	2	no	—
57	D₄	—	86	2	no	—
58	D₄	—	86	2	no	—
59	D₄	—	86	2	no	—
60	D₄	—	172	4	no	—
61	C₂×C₄	—	86	1	no	—
62	C₂×C₄	D₁₇₂	1	2	yes	—
63	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
64	C₈	D₁₇₂	1	4	yes	complemented
65	C₂²	—	172	1	no	—
66	C₂²	—	172	2	no	—
67	C₂²	—	172	4	no	—
68	C₂²	—	172	2	no	—
69	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	172	1	no	—
72	C₄	C₂×D₁₇₂	1	2	yes	—
73	C₂	—	344	2	no	—
74	C₂	—	344	1	no	—
75	C₂	#13063322	1	1	yes	characteristic
76	C₂	#13063353	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#97×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
hypercenter	#97	D₄₃
hypocenter	C₄₃	#496
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×#10621873	C₂	semidirect
2. C₂×D₃₄₄	C₂	semidirect
3. #13063322	C₂	semidirect
4. #13063313	C₂	semidirect
5. #97×C₄₃	C₂	semidirect
25. C₈×C₄₃	D₄	semidirect
39. C₄₃	#496	semidirect
44. #97	D₄₃	semidirect
64. C₈	D₁₇₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10621873	2
C₂×D₃₄₄	2
#13063322	2
#13063313	2
#97×C₄₃	2
#496	43