Subgroups — C₂×#27211956 #41001601

Order 26848.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27211956	C₂	1	8	yes	maximal, direct product factor
2	C₂×D₃₃₅₆	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×D₈₃₉	C₂	1	3	yes	maximal, complemented
4	C₂×Q₈×C₈₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₈₃₉	C₂²	1	3	yes	—
6	D₃₃₅₆	C₂²	1	12	yes	complemented
7	C₂×Dic₈₃₉	C₂²	1	1	yes	characteristic
8	C₄×D₈₃₉	C₂²	1	12	yes	complemented
9	Q₈×C₈₃₉	C₂²	1	4	yes	complemented
10	C₂×C₄×C₈₃₉	C₂²	1	3	yes	—
11	C₂²×C₈₃₉	C₂³	1	1	yes	characteristic
12	C₂×D₈₃₉	—	2	6	no	—
13	C₂×D₈₃₉	C₂³	1	6	yes	—
14	C₄×C₈₃₉	C₂³	1	6	yes	—
15	Dic₈₃₉	C₂³	1	2	yes	—
16	C₂×C₈₃₉	#41	1	2	yes	complemented
17	C₂×C₈₃₉	C₂⁴	1	1	yes	characteristic
18	D₈₃₉	—	2	6	no	—
19	C₈₃₉	C₂×#41	1	1	yes	characteristic, complemented, Sylow
20	C₂×#41	—	839	1	no	maximal, Sylow
21	#41	—	839	8	no	—
22	C₂×Q₈	D₈₃₉	1	1	yes	characteristic, complemented
23	C₂×D₄	—	839	3	no	—
24	C₂²×C₄	—	839	3	no	—
25	C₂³	—	839	3	no	—
26	Q₈	C₂×D₈₃₉	1	4	yes	complemented
27	D₄	—	839	12	no	—
28	C₂×C₄	—	839	1	no	—
29	C₂×C₄	—	839	12	no	—
30	C₂×C₄	C₂×D₈₃₉	1	3	yes	—
31	C₂²	—	839	6	no	—
32	C₂²	—	1678	6	no	—
33	C₂²	C₂²×D₈₃₉	1	1	yes	characteristic
34	C₄	—	839	2	no	—
35	C₄	C₂²×D₈₃₉	1	6	yes	—
36	C₂	—	1678	6	no	—
37	C₂	#27211956	1	2	yes	direct product factor
38	C₂	C₂³×D₈₃₉	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.