Subgroups — C₂³×C₇⋊C₈ #90471

Order 448.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇⋊C₈	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₇	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₇	C₄	1	7	yes	—
5	C₂²×C₄×C₇	C₂²	1	7	yes	—
6	C₂×C₇⋊C₈	C₂²	1	28	yes	direct product factor
7	C₂³×C₈	—	7	1	no	maximal, Sylow
8	C₂³×C₇	C₈	1	8	yes	complemented
9	C₂³×C₇	C₂×C₄	1	7	yes	—
10	C₂×C₄×C₇	C₂×C₄	1	21	yes	—
11	C₂×C₄×C₇	C₂³	1	7	yes	—
12	C₇⋊C₈	C₂³	1	8	yes	direct product factor
13	C₂³×C₄	D₇	1	1	yes	characteristic
14	C₂²×C₈	—	7	14	no	—
15	C₂²×C₇	C₂×C₈	1	28	yes	complemented
16	C₂²×C₇	C₂²×C₄	1	7	yes	—
17	C₄×C₇	C₂²×C₄	1	7	yes	—
18	C₄×C₇	C₂⁴	1	1	yes	characteristic
19	C₂⁴	Dic₇	1	1	yes	characteristic
20	C₂²×C₄	Dic₇	1	7	yes	—
21	C₂²×C₄	C₂×D₇	1	7	yes	—
22	C₂×C₈	—	7	28	no	—
23	C₂×C₇	C₂²×C₈	1	14	yes	complemented
24	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
25	C₂³	C₇⋊C₈	1	8	yes	direct product factor
26	C₂³	C₂×Dic₇	1	7	yes	—
27	C₂×C₄	C₂×Dic₇	1	21	yes	—
28	C₂×C₄	C₂²×D₇	1	7	yes	—
29	C₈	—	7	8	no	—
30	C₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²	C₂×C₇⋊C₈	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₇	1	7	yes	—
33	C₄	C₂²×Dic₇	1	7	yes	—
34	C₄	C₂³×D₇	1	1	yes	characteristic
35	C₂	C₂²×C₇⋊C₈	1	14	yes	direct product factor
36	C₂	C₂³×Dic₇	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.