Subgroups — C₂²⋊C₈×C₆₇ #14523902

Order 2144.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂³×C₆₇	C₄	1	1	yes	characteristic
4	C₂×C₄×C₆₇	—	2	2	no	—
5	C₂×C₄×C₆₇	C₄	1	1	yes	characteristic
6	C₂×C₄×C₆₇	C₂²	1	1	yes	characteristic
7	C₈×C₆₇	—	2	2	no	—
8	C₂²×C₆₇	—	2	1	no	—
9	C₂²×C₆₇	—	2	1	no	—
10	C₂²×C₆₇	C₈	1	2	yes	complemented
11	C₂²×C₆₇	C₂×C₄	1	1	yes	characteristic
12	C₄×C₆₇	—	2	1	no	—
13	C₄×C₆₇	D₄	1	2	yes	—
14	C₂×C₆₇	—	2	2	no	—
15	C₂×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₆₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₆₇	M₁₆	1	1	yes	characteristic
18	C₆₇	C₂²⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²⋊C₈	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₄	C₂×C₆₇	1	1	yes	characteristic
21	C₂×C₈	C₂×C₆₇	1	2	yes	complemented
22	C₂³	C₄×C₆₇	1	1	yes	characteristic
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	C₄×C₆₇	1	1	yes	characteristic
25	C₂×C₄	C₂²×C₆₇	1	1	yes	characteristic
26	C₈	—	2	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	C₈×C₆₇	1	2	yes	complemented
30	C₂²	C₂×C₄×C₆₇	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	D₄×C₆₇	1	2	yes	—
33	C₂	—	2	2	no	—
34	C₂	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
35	C₂	C₂×C₈×C₆₇	1	1	yes	characteristic
36	C₂	M₁₆×C₆₇	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.