Subgroups — #14582691

Order 2752.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063321	C₂	1	1	yes	maximal, characteristic
2	#13063240	C₂	1	1	yes	maximal, characteristic, complemented
3	#99×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₄₃	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊D₄₃	—	2	1	no	—
6	C₂×C₂²⋊D₄₃	—	2	1	no	—
7	C₂×D₁₇₂	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊C₄×C₄₃	—	2	1	no	—
9	C₂²⋊Dic₄₃	—	2	1	no	—
10	C₄×Dic₄₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₄₃	D₄	1	1	yes	characteristic
12	C₂³×C₄₃	D₄	1	1	yes	characteristic
13	C₂²×D₄₃	—	2	1	no	—
14	D₄×C₄₃	—	4	1	no	—
15	C₂×C₄×C₄₃	—	4	1	no	—
16	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊D₄₃	—	4	2	no	—
18	C₂²⋊D₄₃	—	4	2	no	—
19	C₂×Dic₄₃	—	2	1	no	—
20	C₂×Dic₄₃	—	4	1	no	—
21	D₁₇₂	—	4	1	no	—
22	C₂²×C₄₃	—	2	1	no	—
23	C₂²×C₄₃	—	2	1	no	—
24	C₂²×C₄₃	—	4	1	no	—
25	C₂²×C₄₃	—	4	1	no	—
26	C₂²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₄₃	—	4	1	no	—
28	C₂×D₄₃	—	4	1	no	—
29	C₂×D₄₃	—	4	1	no	—
30	C₄×C₄₃	—	2	1	no	—
31	C₄×C₄₃	—	8	1	no	—
32	Dic₄₃	—	2	2	no	—
33	Dic₄₃	—	8	1	no	—
34	C₂×C₄₃	—	2	1	no	—
35	C₂×C₄₃	—	4	1	no	—
36	C₂×C₄₃	—	4	1	no	—
37	C₂×C₄₃	#99	1	1	yes	characteristic
38	D₄₃	—	8	1	no	—
39	#353	—	43	1	no	maximal, Sylow
40	C₄₃	#353	1	1	yes	characteristic, complemented, Sylow
41	#127	—	43	1	no	—
42	#99	—	43	1	no	—
43	#99	D₄₃	1	1	yes	characteristic, complemented
44	C₂×D₄	—	43	1	no	—
45	C₂×D₄	—	86	1	no	—
46	C₂×D₄	—	86	1	no	—
47	C₂×D₄	C₂×D₄₃	1	1	yes	characteristic
48	C₂²⋊C₄	—	2	1	no	—
49	C₂²⋊C₄	—	86	1	no	—
50	C₄²	—	43	1	no	—
51	C₂³	—	86	1	no	—
52	C₂³	D₁₇₂	1	1	yes	characteristic
53	C₂³	C₂²⋊D₄₃	1	1	yes	characteristic
54	D₄	—	4	1	no	—
55	D₄	—	172	1	no	—
56	D₄	—	172	2	no	—
57	D₄	—	172	2	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	86	1	no	—
60	C₂×C₄	—	172	1	no	—
61	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
62	C₂²	—	2	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	4	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	172	1	no	—
67	C₂²	—	172	1	no	—
68	C₂²	—	172	1	no	—
69	C₂²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	8	1	no	—
72	C₄	—	86	2	no	—
73	C₄	—	344	1	no	—
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	—	4	1	no	—
77	C₂	—	344	1	no	—
78	C₂	#13063239	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13063239
commutator	C₂×C₄×C₄₃	C₂×C₄
Frattini	C₂×D₄	C₂×D₄₃
Fitting	#99×C₄₃	C₂
socle	C₂×C₄₃	#99
prime radical	#13063321	C₂
cosocle	C₂×D₄×C₄₃	C₂²
hypercenter	#99	D₄₃
hypocenter	C₄₃	#353
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #99

Complements

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

N	H ≅ G/N	type
2. #13063240	C₂	semidirect
3. #99×C₄₃	C₂	semidirect
7. C₂×D₁₇₂	C₄	semidirect
10. C₄×Dic₄₃	C₄	semidirect
40. C₄₃	#353	semidirect
43. #99	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063321	2
#13063240	2
#99×C₄₃	2
#353	43