Subgroups — #41000189

Order 26816.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27211652	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₄₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₄₁₉	—	2	2	no	—
4	C₂×C₈×C₄₁₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₄₁₉	C₄	1	2	yes	complemented
6	C₂×Dic₄₁₉	—	4	2	no	—
7	C₂×C₄×C₄₁₉	D₄	1	1	yes	characteristic
8	C₈×C₄₁₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₄₁₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄₁₉	D₈	1	1	yes	characteristic
11	C₄×C₄₁₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₄₁₉	Q₁₆	1	1	yes	characteristic
13	Dic₄₁₉	—	8	2	no	—
14	C₂×C₄₁₉	#107	1	1	yes	characteristic
15	C₂×C₄₁₉	SD₃₂	1	2	yes	—
16	C₄₁₉	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	419	1	no	maximal, Sylow
18	C₂×C₁₆	D₄₁₉	1	1	yes	characteristic
19	#107	—	419	2	no	—
20	C₂×C₈	C₂×D₄₁₉	1	1	yes	characteristic
21	C₄⋊C₄	—	838	2	no	—
22	C₁₆	Dic₄₁₉	1	2	yes	complemented
23	C₂×C₄	—	1676	2	no	—
24	C₂×C₄	D₁₆₇₆	1	1	yes	characteristic
25	C₈	C₂×Dic₄₁₉	1	1	yes	characteristic
26	C₈	Dic₈₃₈	1	1	yes	characteristic
27	C₂²	D₃₃₅₂	1	1	yes	characteristic
28	C₄	—	3352	2	no	—
29	C₄	C₄⋊Dic₄₁₉	1	1	yes	characteristic
30	C₄	Dic₁₆₇₆	1	1	yes	characteristic
31	C₂	#27211652	1	1	yes	characteristic
32	C₂	#27211663	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.