Subgroups — #16811003

Order 3392.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₁₂	C₂	1	4	yes	maximal
2	#13133217	C₂	1	2	yes	maximal
3	C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₆	C₂²	1	4	yes	—
5	C₂×C₈×C₅₃	C₂²	1	2	yes	—
6	C₄²×C₅₃	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₅₃	—	2	4	no	—
8	Dic₂₁₂	—	2	8	no	—
9	C₂×C₄×C₅₃	D₄	1	2	yes	—
10	C₂×C₄×C₅₃	C₂³	1	1	yes	characteristic
11	C₂×Dic₅₃	—	2	4	no	—
12	Dic₁₀₆	—	2	8	no	—
13	C₈×C₅₃	D₄	1	4	yes	—
14	C₂²×C₅₃	C₂×D₄	1	1	yes	characteristic
15	C₄×C₅₃	Q₁₆	1	4	yes	complemented
16	C₄×C₅₃	C₂×D₄	1	2	yes	—
17	Dic₅₃	—	4	4	no	—
18	C₂×C₅₃	#127	1	1	yes	characteristic
19	C₂×C₅₃	C₂×Q₁₆	1	2	yes	—
20	#494	—	53	1	no	maximal, Sylow
21	C₅₃	#494	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₁₆	—	53	4	no	—
23	C₄⋊Q₈	—	53	2	no	—
24	C₄×C₈	D₅₃	1	1	yes	characteristic
25	C₂×Q₈	—	53	4	no	—
26	Q₁₆	—	106	8	no	—
27	C₂×C₈	C₂×D₅₃	1	2	yes	—
28	C₄⋊C₄	—	106	4	no	—
29	C₄²	C₂×D₅₃	1	1	yes	characteristic
30	Q₈	—	106	8	no	—
31	C₂×C₄	—	106	4	no	—
32	C₂×C₄	D₂₁₂	1	2	yes	—
33	C₂×C₄	C₂²×D₅₃	1	1	yes	characteristic
34	C₈	D₂₁₂	1	4	yes	—
35	C₂²	C₂×D₂₁₂	1	1	yes	characteristic
36	C₄	—	212	4	no	—
37	C₄	Dic₂₁₂	1	4	yes	complemented
38	C₄	C₂×D₂₁₂	1	2	yes	—
39	C₂	#13133214	1	1	yes	characteristic
40	C₂	C₂×Dic₂₁₂	1	2	yes	—

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

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