Subgroups — C₂²⋊(C₇₃₉⋊C₈) #37556573

Order 23648.

50 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, complemented
2	C₂²×C₄×C₇₃₉	C₂	1	1	yes	maximal, characteristic
3	C₇₃₉⋊C₈	—	2	2	no	—
4	C₂³×C₇₃₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇₃₉	—	2	2	no	—
6	C₂×C₄×C₇₃₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
8	C₂²×C₇₃₉	—	2	1	no	—
9	C₂²×C₇₃₉	—	2	1	no	—
10	C₂²×C₇₃₉	C₈	1	2	yes	complemented
11	C₂²×C₇₃₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₇₃₉	—	2	1	no	—
13	C₄×C₇₃₉	D₄	1	2	yes	—
14	C₂×C₇₃₉	—	2	2	no	—
15	C₂×C₇₃₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₇₃₉	C₂×C₈	1	1	yes	characteristic
17	C₂×C₇₃₉	M₁₆	1	1	yes	characteristic
18	C₇₃₉	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	739	1	no	maximal, Sylow
20	C₂²×C₄	D₇₃₉	1	1	yes	characteristic
21	C₂×C₈	—	739	2	no	—
22	C₂³	Dic₇₃₉	1	1	yes	characteristic
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	Dic₇₃₉	1	1	yes	characteristic
25	C₂×C₄	C₂×D₇₃₉	1	1	yes	characteristic
26	C₈	—	1478	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	C₇₃₉⋊C₈	1	2	yes	complemented
30	C₂²	C₂×Dic₇₃₉	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	C₂²⋊D₇₃₉	1	2	yes	—
33	C₂	—	2	2	no	—
34	C₂	C₂²⋊Dic₇₃₉	1	1	yes	characteristic
35	C₂	C₂×C₇₃₉⋊C₈	1	1	yes	characteristic
36	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.