Subgroups — #6409

Order 224.

42 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	1	yes	maximal, characteristic
3	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₈	—	2	1	no	—
5	C₇×Q₈	C₄	1	2	yes	complemented
6	C₂×C₄×C₇	—	2	1	no	—
7	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₇	—	2	1	no	—
9	C₇⋊C₈	—	2	1	no	—
10	#103	—	7	1	no	maximal, Sylow
11	C₂²×C₇	D₄	1	1	yes	characteristic
12	C₄×C₇	—	2	2	no	—
13	C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₄×C₇	D₄	1	1	yes	characteristic
15	Dic₇	—	4	1	no	—
16	C₂×Q₈	D₇	1	1	yes	characteristic
17	C₂×C₈	—	7	1	no	—
18	C₄⋊C₄	—	7	1	no	—
19	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₇	SD₁₆	1	1	yes	characteristic
21	C₂×C₇	Q₁₆	1	1	yes	characteristic
22	Q₈	—	2	1	no	—
23	Q₈	Dic₇	1	2	yes	complemented
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	—	14	1	no	—
26	C₂×C₄	C₂×D₇	1	1	yes	characteristic
27	C₈	—	14	1	no	—
28	C₇	#103	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₂²⋊D₇	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	28	1	no	—
32	C₄	C₂×Dic₇	1	1	yes	characteristic
33	C₄	C₂²⋊D₇	1	1	yes	characteristic
34	C₂	#1143	1	1	yes	characteristic
35	C₂	#1144	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.