Subgroups — C₇×#365 #89407

Order 448.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₇×#108	C₂	1	1	yes	maximal, characteristic
3	C₇×#106	C₂	1	1	yes	maximal, characteristic
4	C₇×M₁₆	—	2	1	no	—
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₇×C₄⋊C₄	—	2	1	no	—
7	C₇×C₁₆	C₄	1	2	yes	complemented
8	#365	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂×C₄×C₇	—	4	1	no	—
10	C₂×C₄×C₇	D₄	1	1	yes	characteristic
11	C₇×C₈	—	4	1	no	—
12	C₇×C₈	C₂×C₄	1	1	yes	characteristic
13	C₇×C₈	Q₈	1	1	yes	characteristic
14	M₃₂	C₂×C₇	1	1	yes	characteristic
15	#108	C₂×C₇	1	1	yes	characteristic
16	#106	C₂×C₇	1	1	yes	characteristic
17	C₂²×C₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₇	—	8	1	no	—
19	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₇	SD₁₆	1	1	yes	characteristic
21	M₁₆	—	2	1	no	—
22	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
23	C₄⋊C₄	—	2	1	no	—
24	C₁₆	C₄×C₇	1	2	yes	complemented
25	C₂×C₇	—	2	1	no	—
26	C₂×C₇	#106	1	1	yes	characteristic
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	C₇×D₄	1	1	yes	characteristic
29	C₈	—	4	1	no	—
30	C₈	C₂×C₄×C₇	1	1	yes	characteristic
31	C₈	C₇×Q₈	1	1	yes	characteristic
32	C₇	#365	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	C₇×SD₁₆	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
36	C₄	C₇×SD₁₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	C₇×#106	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.