Subgroups — C₇×#104 #6421

Order 224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×Q₈	C₄	1	1	yes	characteristic, complemented
5	C₇×D₄	—	2	1	no	—
6	C₇×D₄	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×C₇	—	2	1	no	—
8	C₂×C₄×C₇	—	2	1	no	—
9	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
10	C₇×C₈	—	2	1	no	—
11	#104	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₇	—	2	1	no	—
13	C₂²×C₇	D₄	1	1	yes	characteristic
14	C₄×C₇	—	2	2	no	—
15	C₄×C₇	—	2	1	no	—
16	C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₇	D₄	1	1	yes	characteristic
18	#41	C₂×C₇	1	1	yes	characteristic
19	M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
20	C₄²	C₂×C₇	1	1	yes	characteristic, complemented
21	C₂×C₇	—	2	1	no	—
22	C₂×C₇	—	4	1	no	—
23	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	Q₈	C₄×C₇	1	1	yes	characteristic, complemented
25	D₄	—	2	1	no	—
26	D₄	C₄×C₇	1	1	yes	characteristic, complemented
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	C₂²×C₇	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₇	#104	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	—	2	1	no	—
33	C₂²	C₇×D₄	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	2	1	no	—
36	C₄	C₂×C₄×C₇	1	1	yes	characteristic
37	C₄	C₇×D₄	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	4	1	no	—
40	C₂	C₇×C₂²⋊C₄	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.