Subgroups — C₂²⋊(C₇⋊C₈) #6404

Order 224.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂³×C₇	C₄	1	1	yes	characteristic
4	C₂×C₄×C₇	—	2	2	no	—
5	C₂×C₄×C₇	C₄	1	1	yes	characteristic
6	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₇⋊C₈	—	2	2	no	—
8	C₂²⋊C₈	—	7	1	no	maximal, Sylow
9	C₂²×C₇	—	2	1	no	—
10	C₂²×C₇	—	2	1	no	—
11	C₂²×C₇	C₈	1	2	yes	complemented
12	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₇	—	2	1	no	—
14	C₄×C₇	D₄	1	2	yes	—
15	C₂²×C₄	D₇	1	1	yes	characteristic
16	C₂×C₈	—	7	2	no	—
17	C₂×C₇	—	2	2	no	—
18	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₇	C₂×C₈	1	1	yes	characteristic
20	C₂×C₇	M₁₆	1	1	yes	characteristic
21	C₂³	Dic₇	1	1	yes	characteristic
22	C₂×C₄	—	2	2	no	—
23	C₂×C₄	Dic₇	1	1	yes	characteristic
24	C₂×C₄	C₂×D₇	1	1	yes	characteristic
25	C₈	—	14	2	no	—
26	C₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	C₇⋊C₈	1	2	yes	complemented
30	C₂²	C₂×Dic₇	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	C₂²⋊D₇	1	2	yes	—
33	C₂	—	2	2	no	—
34	C₂	C₂×C₇⋊C₈	1	1	yes	characteristic
35	C₂	#1136	1	1	yes	characteristic
36	C₂	C₂²⋊Dic₇	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.