Subgroups — C₂×#27211945 #41001574

Order 26848.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₇₈	C₂	1	1	yes	maximal, characteristic
2	#27211945	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₈₃₉	C₂	1	1	yes	maximal, characteristic
5	Dic₁₆₇₈	—	2	1	no	—
6	Dic₁₆₇₈	C₂²	1	2	yes	—
7	C₂×Dic₈₃₉	—	2	1	no	—
8	C₈₃₉⋊C₈	C₂²	1	2	yes	—
9	Q₈×C₈₃₉	—	2	1	no	—
10	Q₈×C₈₃₉	C₂²	1	2	yes	—
11	C₂×C₄×C₈₃₉	—	2	1	no	—
12	C₂×C₄×C₈₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈₃₉	D₄	1	1	yes	characteristic
14	C₄×C₈₃₉	—	2	2	no	—
15	C₄×C₈₃₉	D₄	1	1	yes	characteristic
16	C₄×C₈₃₉	C₂³	1	1	yes	characteristic
17	Dic₈₃₉	—	2	2	no	—
18	C₂×C₈₃₉	Q₁₆	1	2	yes	complemented
19	C₂×C₈₃₉	C₂×D₄	1	1	yes	characteristic
20	C₈₃₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	839	1	no	maximal, Sylow
22	C₂×Q₈	—	839	1	no	—
23	C₂×Q₈	D₈₃₉	1	1	yes	characteristic
24	Q₁₆	—	839	4	no	—
25	C₂×C₈	—	839	1	no	—
26	Q₈	—	2	1	no	—
27	Q₈	—	839	2	no	—
28	Q₈	—	1678	1	no	—
29	Q₈	C₂×D₈₃₉	1	2	yes	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	1678	1	no	—
32	C₂×C₄	C₂×D₈₃₉	1	1	yes	characteristic
33	C₈	—	839	2	no	—
34	C₂²	C₂²⋊D₈₃₉	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	1678	2	no	—
37	C₄	C₂²⋊D₈₃₉	1	1	yes	characteristic
38	C₄	C₂²×D₈₃₉	1	1	yes	characteristic
39	C₂	#27211945	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊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.