Subgroups — C₇×#366 #89408

Order 448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×#107	C₂	1	2	yes	maximal
3	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
4	C₇×C₄⋊C₄	—	2	2	no	—
5	C₇×C₁₆	C₄	1	2	yes	complemented
6	#366	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₄×C₇	—	4	2	no	—
8	C₂×C₄×C₇	D₄	1	1	yes	characteristic
9	C₇×C₈	C₂×C₄	1	1	yes	characteristic
10	C₇×C₈	Q₈	1	1	yes	characteristic
11	C₂×C₁₆	C₂×C₇	1	1	yes	characteristic
12	#107	C₂×C₇	1	2	yes	—
13	C₂²×C₇	D₈	1	1	yes	characteristic
14	C₄×C₇	—	8	2	no	—
15	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₇	Q₁₆	1	1	yes	characteristic
17	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
18	C₄⋊C₄	—	2	2	no	—
19	C₁₆	C₄×C₇	1	2	yes	complemented
20	C₂×C₇	#107	1	1	yes	characteristic
21	C₂×C₇	D₁₆	1	1	yes	characteristic
22	C₂×C₇	Q₃₂	1	1	yes	characteristic
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	C₇×D₄	1	1	yes	characteristic
25	C₈	C₂×C₄×C₇	1	1	yes	characteristic
26	C₈	C₇×Q₈	1	1	yes	characteristic
27	C₇	#366	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	C₇×D₈	1	1	yes	characteristic
29	C₄	—	8	2	no	—
30	C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
31	C₄	C₇×Q₁₆	1	1	yes	characteristic
32	C₂	C₇×#107	1	1	yes	characteristic
33	C₂	C₇×D₁₆	1	1	yes	characteristic
34	C₂	C₇×Q₃₂	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.