Subgroups — C₂×#1144 #6506

Order 224.

60 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	C₂×Dic₁₄	C₂	1	1	yes	maximal, characteristic
3	#1144	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₇×Q₈	—	2	1	no	—
6	C₇×Q₈	C₂²	1	2	yes	—
7	C₂×C₄×C₇	—	2	1	no	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇	—	2	1	no	—
10	Dic₁₄	—	2	1	no	—
11	Dic₁₄	C₂²	1	2	yes	—
12	C₇⋊C₈	C₂²	1	2	yes	—
13	C₂×Q₁₆	—	7	1	no	maximal, Sylow
14	C₂²×C₇	D₄	1	1	yes	characteristic
15	C₄×C₇	—	2	2	no	—
16	C₄×C₇	D₄	1	1	yes	characteristic
17	C₄×C₇	C₂³	1	1	yes	characteristic
18	Dic₇	—	2	2	no	—
19	C₂×Q₈	—	7	1	no	—
20	C₂×Q₈	D₇	1	1	yes	characteristic
21	Q₁₆	—	7	4	no	—
22	C₂×C₈	—	7	1	no	—
23	C₂×C₇	Q₁₆	1	2	yes	complemented
24	C₂×C₇	C₂×D₄	1	1	yes	characteristic
25	Q₈	—	2	1	no	—
26	Q₈	—	7	2	no	—
27	Q₈	—	14	1	no	—
28	Q₈	C₂×D₇	1	2	yes	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	—	14	1	no	—
31	C₂×C₄	C₂×D₇	1	1	yes	characteristic
32	C₈	—	7	2	no	—
33	C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂²	C₂²⋊D₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	14	2	no	—
37	C₄	C₂²⋊D₇	1	1	yes	characteristic
38	C₄	C₂²×D₇	1	1	yes	characteristic
39	C₂	#1144	1	2	yes	direct product factor
40	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.