Subgroups — #14582696

Order 2752.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063244	C₂	1	2	yes	maximal, complemented
2	#124×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
4	C₂×D₄×C₄₃	C₄	1	1	yes	characteristic
5	C₂²⋊C₄×C₄₃	—	2	2	no	—
6	C₄²×C₄₃	C₄	1	1	yes	characteristic
7	#10621877	—	2	2	no	—
8	C₂³×C₄₃	—	2	1	no	—
9	Q₈×C₄₃	—	4	1	no	—
10	D₄×C₄₃	—	4	1	no	—
11	C₂×C₄×C₄₃	—	2	1	no	—
12	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₃	D₄	1	2	yes	—
14	C₄₃⋊C₈	—	4	2	no	—
15	C₂²×C₄₃	—	4	2	no	—
16	C₂²×C₄₃	—	4	1	no	—
17	C₂²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₄₃	—	2	2	no	—
19	C₄×C₄₃	—	2	1	no	—
20	C₄×C₄₃	—	4	1	no	—
21	C₂×C₄₃	—	2	1	no	—
22	C₂×C₄₃	—	8	1	no	—
23	C₂×C₄₃	#99	1	1	yes	characteristic
24	#355	—	43	1	no	maximal, Sylow
25	C₄₃	#355	1	1	yes	characteristic, complemented, Sylow
26	#124	D₄₃	1	1	yes	characteristic
27	#101	—	43	2	no	—
28	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
29	C₂×D₄	Dic₄₃	1	1	yes	characteristic
30	M₁₆	—	86	2	no	—
31	C₂²⋊C₄	—	2	2	no	—
32	C₄²	Dic₄₃	1	1	yes	characteristic
33	C₂³	—	2	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×Dic₄₃	1	1	yes	characteristic
38	C₂×C₄	C₂²⋊D₄₃	1	2	yes	—
39	C₈	—	172	2	no	—
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊Dic₄₃	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#13063240	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #13063244	C₂	semidirect
25. C₄₃	#355	semidirect

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