Subgroups — Q₈×Dic₇ #6508

Order 224.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₇	C₂	1	3	yes	maximal
3	C₄×Dic₇	C₂	1	3	yes	maximal
4	C₇×Q₈	C₄	1	4	yes	complemented
5	C₂×C₄×C₇	C₂²	1	3	yes	—
6	C₂×Dic₇	C₂²	1	3	yes	—
7	C₂×Dic₇	C₂²	1	1	yes	characteristic
8	C₄×Q₈	—	7	1	no	maximal, Sylow
9	C₂²×C₇	C₂³	1	1	yes	characteristic
10	C₄×C₇	C₂×C₄	1	6	yes	—
11	Dic₇	—	2	3	no	—
12	Dic₇	Q₈	1	2	yes	direct product factor
13	C₂×Q₈	D₇	1	1	yes	characteristic
14	C₄⋊C₄	—	7	3	no	—
15	C₄²	—	7	3	no	—
16	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₇	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₇	#41	1	1	yes	characteristic
19	Q₈	Dic₇	1	4	yes	direct product factor
20	C₂×C₄	—	7	1	no	—
21	C₂×C₄	—	7	3	no	—
22	C₂×C₄	C₂×D₇	1	3	yes	—
23	C₇	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₂²	C₂²×D₇	1	1	yes	characteristic
25	C₄	—	7	2	no	—
26	C₄	—	14	3	no	—
27	C₄	C₂×Dic₇	1	6	yes	—
28	C₂	Q₈×D₇	1	1	yes	characteristic
29	C₂	#1161	1	1	yes	characteristic
30	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.