Subgroups — C₂×#1143 #6504

Order 224.

68 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, complemented
2	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic
3	#1143	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇	—	2	1	no	—
6	C₇×Q₈	—	2	1	no	—
7	C₇×Q₈	C₂²	1	2	yes	complemented
8	C₂×C₄×C₇	—	2	1	no	—
9	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
10	D₂₈	—	2	1	no	—
11	D₂₈	C₂²	1	2	yes	—
12	C₇⋊C₈	C₂²	1	2	yes	complemented
13	C₂×SD₁₆	—	7	1	no	maximal, Sylow
14	C₂²×C₇	D₄	1	1	yes	characteristic
15	C₂×D₇	—	2	2	no	—
16	C₂×D₇	—	4	2	no	—
17	C₄×C₇	—	2	2	no	—
18	C₄×C₇	D₄	1	1	yes	characteristic
19	C₄×C₇	C₂³	1	1	yes	characteristic
20	C₂×Q₈	D₇	1	1	yes	characteristic, complemented
21	C₂×D₄	—	7	1	no	—
22	SD₁₆	—	7	4	no	—
23	C₂×C₈	—	7	1	no	—
24	C₂×C₇	SD₁₆	1	2	yes	complemented
25	C₂×C₇	C₂×D₄	1	1	yes	characteristic
26	D₇	—	4	2	no	—
27	C₂³	—	14	1	no	—
28	Q₈	—	2	1	no	—
29	Q₈	C₂×D₇	1	2	yes	complemented
30	D₄	—	7	2	no	—
31	D₄	—	14	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	C₂×D₇	1	1	yes	characteristic
34	C₈	—	7	2	no	—
35	C₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	14	2	no	—
37	C₂²	—	28	2	no	—
38	C₂²	C₂²⋊D₇	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	C₂²⋊D₇	1	1	yes	characteristic
41	C₄	C₂²×D₇	1	1	yes	characteristic
42	C₂	—	28	2	no	—
43	C₂	#1143	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₇	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.