Subgroups — #14583291

Order 2752.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621885	C₂	1	2	yes	maximal, complemented
2	C₂×#10621884	C₂	1	2	yes	maximal
3	#13063313	C₂	1	1	yes	maximal, characteristic
4	#13063236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₃	C₂²	1	2	yes	—
7	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
8	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₄₃	—	2	2	no	—
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	#10621885	—	2	4	no	—
12	#10621884	—	2	4	no	—
13	(C₂×D₄₃)⋊C₄	—	2	2	no	—
14	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×D₄₃	—	2	1	no	—
16	Q₈×C₄₃	—	2	2	no	—
17	Q₈×C₄₃	—	2	2	no	—
18	C₂×C₄×C₄₃	—	2	2	no	—
19	C₂×C₄×C₄₃	D₄	1	2	yes	—
20	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₃	—	2	1	no	—
22	D₁₇₂	—	2	2	no	—
23	Dic₈₆	—	2	2	no	—
24	C₄₃⋊C₈	D₄	1	4	yes	—
25	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₂×D₄₃	—	4	1	no	—
27	C₂×D₄₃	—	4	2	no	—
28	C₄×C₄₃	—	2	2	no	—
29	C₄×C₄₃	—	4	2	no	—
30	C₄×C₄₃	C₂×D₄	1	2	yes	—
31	Dic₄₃	—	4	1	no	—
32	C₂×C₄₃	#127	1	1	yes	characteristic
33	C₂×C₄₃	#137	1	2	yes	—
34	D₄₃	—	8	1	no	—
35	#497	—	43	1	no	maximal, Sylow
36	C₄₃	#497	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	43	2	no	—
38	C₂×SD₁₆	—	43	2	no	—
39	C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
40	#124	—	43	1	no	—
41	#97	—	43	1	no	—
42	C₂×Q₈	—	43	1	no	—
43	C₂×Q₈	C₂×D₄₃	1	2	yes	—
44	C₂×D₄	—	43	1	no	—
45	Q₁₆	—	86	4	no	—
46	SD₁₆	—	86	4	no	—
47	C₂×C₈	—	43	2	no	—
48	C₄⋊C₄	—	2	2	no	—
49	C₂²⋊C₄	—	86	2	no	—
50	C₄²	C₂×D₄₃	1	1	yes	characteristic
51	C₂³	—	86	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	—	86	2	no	—
55	D₄	—	86	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	86	1	no	—
58	C₂×C₄	C₂²⋊D₄₃	1	2	yes	—
59	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
60	C₈	—	43	4	no	—
61	C₂²	—	172	1	no	—
62	C₂²	—	172	2	no	—
63	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	—	172	1	no	—
67	C₄	D₄×D₄₃	1	2	yes	—
68	C₂	—	344	1	no	—
69	C₂	#13063321	1	1	yes	characteristic
70	C₂	#13063356	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊Q₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂×D₁₇₂	C₂²
hypercenter	C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#497
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10621885	C₂	semidirect
4. #13063236	C₂	semidirect
5. C₄⋊Q₈×C₄₃	C₂	semidirect
36. C₄₃	#497	semidirect
39. C₄⋊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×#10621885	2
C₂×#10621884	2
#13063313	2
#13063236	2
C₄⋊Q₈×C₄₃	2
#497	43