Subgroups — C₂×#11719949 #13133261

Order 1696.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719949	C₂	1	8	yes	maximal, direct product factor
3	C₂×D₂₁₂	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×D₅₃	C₂	1	3	yes	maximal, complemented
5	C₂²×D₅₃	C₂²	1	3	yes	—
6	Q₈×C₅₃	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅₃	C₂²	1	3	yes	—
8	C₂×Dic₅₃	C₂²	1	1	yes	characteristic
9	D₂₁₂	C₂²	1	12	yes	complemented
10	C₄×D₅₃	C₂²	1	12	yes	complemented
11	C₂²×C₅₃	C₂³	1	1	yes	characteristic
12	C₂×D₅₃	—	2	6	no	—
13	C₂×D₅₃	C₂³	1	6	yes	—
14	C₄×C₅₃	C₂³	1	6	yes	—
15	Dic₅₃	C₂³	1	2	yes	—
16	C₂×C₅₃	#41	1	2	yes	complemented
17	C₂×C₅₃	C₂⁴	1	1	yes	characteristic
18	D₅₃	—	2	6	no	—
19	C₅₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
20	C₂×#41	—	53	1	no	maximal, Sylow
21	#41	—	53	8	no	—
22	C₂×Q₈	D₅₃	1	1	yes	characteristic, complemented
23	C₂×D₄	—	53	3	no	—
24	C₂²×C₄	—	53	3	no	—
25	C₂³	—	53	3	no	—
26	Q₈	C₂×D₅₃	1	4	yes	complemented
27	D₄	—	53	12	no	—
28	C₂×C₄	—	53	1	no	—
29	C₂×C₄	—	53	12	no	—
30	C₂×C₄	C₂×D₅₃	1	3	yes	—
31	C₂²	—	53	6	no	—
32	C₂²	—	106	6	no	—
33	C₂²	C₂²×D₅₃	1	1	yes	characteristic
34	C₄	—	53	2	no	—
35	C₄	C₂²×D₅₃	1	6	yes	—
36	C₂	—	106	6	no	—
37	C₂	#11719949	1	2	yes	direct product factor
38	C₂	C₂³×D₅₃	1	1	yes	characteristic

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.