Subgroups — C₇×#117 #6520

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₇×C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₄²×C₇	C₂	1	2	yes	maximal, complemented
5	C₂³×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₇	C₄	1	4	yes	complemented
7	C₂×C₄×C₇	C₂²	1	4	yes	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
10	#117	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₇	—	2	2	no	—
12	C₂²×C₇	C₂×C₄	1	2	yes	—
13	C₂²×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₇	—	2	4	no	—
15	C₄×C₇	C₂×C₄	1	2	yes	—
16	C₄×C₇	C₂×C₄	1	2	yes	—
17	C₂²×C₄	C₂×C₇	1	1	yes	characteristic
18	C₄⋊C₄	C₂×C₇	1	2	yes	complemented
19	C₂²⋊C₄	C₂×C₇	1	2	yes	—
20	C₄²	C₂×C₇	1	2	yes	complemented
21	C₂×C₇	—	2	2	no	—
22	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₇	#41	1	2	yes	—
24	C₂³	C₂²×C₇	1	1	yes	characteristic
25	C₂×C₄	C₄×C₇	1	4	yes	complemented
26	C₂×C₄	C₂²×C₇	1	4	yes	—
27	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
28	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
29	C₇	#117	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	—	2	2	no	—
31	C₂²	C₂×C₄×C₇	1	2	yes	—
32	C₂²	C₂³×C₇	1	1	yes	characteristic
33	C₄	—	2	4	no	—
34	C₄	C₂×C₄×C₇	1	2	yes	—
35	C₄	C₂×C₄×C₇	1	2	yes	—
36	C₂	—	2	2	no	—
37	C₂	C₂²×C₄×C₇	1	1	yes	characteristic
38	C₂	C₇×#41	1	2	yes	—

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.