Subgroups — #14583283

Order 2752.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10621873	C₂	1	2	yes	maximal, complemented
3	C₂×D₃₄₄	C₂	1	1	yes	maximal, characteristic
4	#13063313	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₂	C₂²	1	2	yes	—
7	C₂×Dic₈₆	C₂²	1	2	yes	—
8	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	(C₂×D₄₃)⋊C₄	—	2	4	no	—
12	Dic₁₇₂	—	2	2	no	—
13	D₃₄₄	—	2	2	no	—
14	#10621873	—	2	4	no	—
15	C₂²×D₄₃	—	2	2	no	—
16	C₂×C₄×C₄₃	D₄	1	2	yes	—
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₃	—	2	2	no	—
19	D₁₇₂	—	2	2	no	—
20	D₁₇₂	—	2	2	no	—
21	Dic₈₆	—	2	2	no	—
22	Dic₈₆	—	2	2	no	—
23	C₈×C₄₃	D₄	1	2	yes	—
24	C₈×C₄₃	D₄	1	2	yes	—
25	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₂×D₄₃	—	4	2	no	—
27	C₂×D₄₃	—	4	4	no	—
28	C₄×C₄₃	—	2	2	no	—
29	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	Dic₄₃	—	4	2	no	—
32	C₂×C₄₃	#127	1	1	yes	characteristic
33	C₂×C₄₃	#135	1	2	yes	—
34	D₄₃	—	8	2	no	—
35	#495	—	43	1	no	maximal, Sylow
36	C₄₃	#495	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	43	1	no	—
38	C₂×SD₁₆	—	43	2	no	—
39	C₂×D₈	—	43	1	no	—
40	#124	—	43	2	no	—
41	C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	43	2	no	—
43	C₂×D₄	—	43	2	no	—
44	Q₁₆	—	86	2	no	—
45	SD₁₆	—	86	4	no	—
46	D₈	—	86	2	no	—
47	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₂²⋊C₄	—	86	4	no	—
50	C₄²	C₂×D₄₃	1	1	yes	characteristic
51	C₂³	—	86	2	no	—
52	Q₈	—	86	2	no	—
53	Q₈	—	86	2	no	—
54	D₄	—	86	2	no	—
55	D₄	—	86	2	no	—
56	C₂×C₄	—	86	2	no	—
57	C₂×C₄	D₁₇₂	1	2	yes	—
58	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
59	C₈	D₁₇₂	1	2	yes	—
60	C₈	D₁₇₂	1	2	yes	—
61	C₂²	—	172	2	no	—
62	C₂²	—	172	4	no	—
63	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	172	2	no	—
66	C₄	C₂×D₁₇₂	1	1	yes	characteristic
67	C₄	C₂×D₁₇₂	1	1	yes	characteristic
68	C₂	—	344	2	no	—
69	C₂	#13063322	1	1	yes	characteristic
70	C₂	#13063347	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂×D₃₄₄	C₂
hypercenter	C₄×C₈	D₄₃
hypocenter	C₄₃	#495
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
1. C₂×Dic₁₇₂	C₂	semidirect
2. C₂×#10621873	C₂	semidirect
4. #13063313	C₂	semidirect
5. C₄×C₈×C₄₃	C₂	semidirect
36. C₄₃	#495	semidirect
41. C₄×C₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₂	2
C₂×#10621873	2
C₂×D₃₄₄	2
#13063313	2
C₄×C₈×C₄₃	2
#495	43