Subgroups — C₄⋊(C₇₃₉⋊C₈) #37556590

Order 23648.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₃₉⋊C₈	C₂	1	2	yes	maximal
2	C₄²×C₇₃₉	C₂	1	1	yes	maximal, characteristic
3	C₇₃₉⋊C₈	—	2	2	no	—
4	C₂×C₄×C₇₃₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇₃₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
7	C₂²×C₇₃₉	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇₃₉	—	2	1	no	—
9	C₄×C₇₃₉	C₈	1	2	yes	complemented
10	C₄×C₇₃₉	D₄	1	1	yes	characteristic
11	C₄×C₇₃₉	Q₈	1	1	yes	characteristic
12	C₂×C₇₃₉	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₇₃₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₇₃₉	M₁₆	1	1	yes	characteristic
15	C₇₃₉	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	739	1	no	maximal, Sylow
17	C₂×C₈	—	739	2	no	—
18	C₄²	D₇₃₉	1	1	yes	characteristic
19	C₂×C₄	Dic₇₃₉	1	1	yes	characteristic
20	C₂×C₄	Dic₇₃₉	1	1	yes	characteristic
21	C₂×C₄	C₂×D₇₃₉	1	1	yes	characteristic
22	C₈	—	1478	2	no	—
23	C₂²	C₂×Dic₇₃₉	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	C₇₃₉⋊C₈	1	2	yes	complemented
26	C₄	D₂₉₅₆	1	1	yes	characteristic
27	C₄	Dic₁₄₇₈	1	1	yes	characteristic
28	C₂	C₄⋊Dic₇₃₉	1	1	yes	characteristic
29	C₂	C₂×C₇₃₉⋊C₈	1	1	yes	characteristic
30	C₂	#26044765	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.