Subgroups — C₇×#504 #90150

Order 448.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#131	C₂	1	1	yes	maximal, characteristic
2	C₇×M₃₂	C₂	1	3	yes	maximal, complemented
3	C₂×C₇×C₁₆	C₂	1	3	yes	maximal, complemented
4	C₇×#41	C₄	1	1	yes	characteristic
5	C₇×M₁₆	C₄	1	3	yes	—
6	C₂×C₇×C₈	C₂²	1	3	yes	—
7	C₇×C₁₆	C₂²	1	3	yes	—
8	C₇×C₁₆	C₂²	1	1	yes	characteristic
9	#504	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₇×Q₈	C₈	1	1	yes	characteristic
11	C₇×D₄	C₈	1	3	yes	—
12	C₂×C₄×C₇	C₂×C₄	1	3	yes	—
13	C₇×C₈	C₂×C₄	1	3	yes	—
14	C₇×C₈	C₂³	1	1	yes	characteristic
15	#131	C₂×C₇	1	1	yes	characteristic
16	M₃₂	C₂×C₇	1	3	yes	complemented
17	C₂×C₁₆	C₂×C₇	1	3	yes	complemented
18	C₂²×C₇	C₂×C₈	1	3	yes	—
19	C₄×C₇	C₂×C₈	1	3	yes	—
20	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
21	#41	C₄×C₇	1	1	yes	characteristic
22	M₁₆	C₄×C₇	1	3	yes	—
23	C₂×C₈	C₂²×C₇	1	3	yes	—
24	C₁₆	C₂²×C₇	1	3	yes	—
25	C₁₆	C₂²×C₇	1	1	yes	characteristic
26	C₂×C₇	—	2	3	no	—
27	C₂×C₇	C₂²×C₈	1	1	yes	characteristic
28	Q₈	C₇×C₈	1	1	yes	characteristic
29	D₄	C₇×C₈	1	3	yes	—
30	C₂×C₄	C₂×C₄×C₇	1	3	yes	—
31	C₈	C₂×C₄×C₇	1	3	yes	—
32	C₈	C₂³×C₇	1	1	yes	characteristic
33	C₇	#504	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	C₂×C₇×C₈	1	3	yes	—
35	C₄	C₂×C₇×C₈	1	3	yes	—
36	C₄	C₂²×C₄×C₇	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×C₇×C₈	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.