Subgroups — #27211643

Order 13408.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₃₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₄₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
4	Dic₈₃₈	—	2	1	no	—
5	Dic₈₃₈	C₄	1	2	yes	complemented
6	C₂×Dic₄₁₉	—	2	1	no	—
7	C₂×Dic₄₁₉	—	2	1	no	—
8	C₂×C₄×C₄₁₉	C₂²	1	1	yes	characteristic
9	C₈×C₄₁₉	—	2	1	no	—
10	C₂²×C₄₁₉	D₄	1	1	yes	characteristic
11	C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₄₁₉	D₄	1	1	yes	characteristic
13	Dic₄₁₉	—	2	2	no	—
14	Dic₄₁₉	—	4	1	no	—
15	C₂×C₄₁₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₄₁₉	SD₁₆	1	1	yes	characteristic
17	C₂×C₄₁₉	Q₁₆	1	1	yes	characteristic
18	C₄₁₉	#103	1	1	yes	characteristic, complemented, Sylow
19	#103	—	419	1	no	maximal, Sylow
20	C₂×Q₈	—	419	1	no	—
21	C₂×C₈	D₄₁₉	1	1	yes	characteristic
22	C₄⋊C₄	—	419	1	no	—
23	Q₈	—	838	1	no	—
24	Q₈	—	419	2	no	—
25	C₂×C₄	—	838	1	no	—
26	C₂×C₄	—	838	1	no	—
27	C₂×C₄	C₂×D₄₁₉	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₂²	D₁₆₇₆	1	1	yes	characteristic
30	C₄	—	838	2	no	—
31	C₄	—	1676	1	no	—
32	C₄	C₄×D₄₁₉	1	1	yes	characteristic
33	C₄	C₂²⋊D₄₁₉	1	1	yes	characteristic
34	C₂	(C₂×D₄₁₉)⋊C₄	1	1	yes	characteristic
35	C₂	#20269400	1	1	yes	characteristic
36	C₂	Dic₁₆₇₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. Dic₈₃₈	C₄	semidirect
18. C₄₁₉	#103	semidirect

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