Subgroups — C₂×#87640 #11716111

Order 784.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#87640	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇²	C₂²	1	1	yes	characteristic
5	C₂×C₇×D₇	—	2	4	no	—
6	C₂×C₇×D₇	C₂²	1	4	yes	complemented
7	C₇⋊Dic₇	C₂²	1	2	yes	complemented
8	C₂×C₂²⋊D₇	—	7	2	no	maximal
9	C₂×C₇²	D₄	1	2	yes	complemented
10	C₂×C₇²	C₂³	1	1	yes	characteristic
11	C₇×D₇	—	2	4	no	—
12	C₂³×C₇	—	7	2	no	—
13	C₂²×D₇	D₇	1	2	yes	complemented
14	C₂²⋊D₇	—	7	8	no	—
15	C₂×Dic₇	—	7	2	no	—
16	C₂×Dic₇	—	14	3	no	—
17	C₇²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₇	—	2	3	no	—
19	C₂²×C₇	—	7	4	no	—
20	C₂²×C₇	—	14	4	no	—
21	C₂²×C₇	C₂×D₇	1	2	yes	—
22	C₂×D₇	—	2	4	no	—
23	C₂×D₇	C₂×D₇	1	4	yes	complemented
24	Dic₇	—	7	4	no	—
25	Dic₇	—	14	6	no	—
26	C₂×D₄	—	49	1	no	Sylow
27	C₂×C₇	—	2	6	no	—
28	C₂×C₇	—	2	3	no	—
29	C₂×C₇	—	14	4	no	—
30	C₂×C₇	C₂²⋊D₇	1	4	yes	complemented
31	C₂×C₇	C₂²×D₇	1	2	yes	—
32	D₇	—	2	4	no	—
33	C₂³	—	7	2	no	—
34	D₄	—	49	4	no	—
35	C₂×C₄	—	49	1	no	—
36	C₇	—	2	3	no	—
37	C₇	C₂×C₂²⋊D₇	1	2	yes	complemented
38	C₂²	—	7	4	no	—
39	C₂²	—	14	4	no	—
40	C₂²	D₇²	1	1	yes	characteristic
41	C₄	—	49	2	no	—
42	C₂	—	14	4	no	—
43	C₂	#87640	1	2	yes	direct product factor
44	C₂	C₂×D₇²	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.