Subgroups — C₂²×C₇⋊C₁₆ #89868

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇⋊C₁₆	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₇	C₄	1	1	yes	characteristic
4	C₂×C₇×C₈	C₄	1	3	yes	—
5	C₂×C₇×C₈	C₂²	1	3	yes	—
6	C₇⋊C₁₆	C₂²	1	4	yes	direct product factor
7	C₂²×C₁₆	—	7	1	no	maximal, Sylow
8	C₂³×C₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₇	C₈	1	3	yes	—
10	C₂×C₄×C₇	C₂×C₄	1	3	yes	—
11	C₇×C₈	C₂×C₄	1	3	yes	—
12	C₇×C₈	C₂³	1	1	yes	characteristic
13	C₂²×C₈	D₇	1	1	yes	characteristic
14	C₂×C₁₆	—	7	6	no	—
15	C₂²×C₇	C₁₆	1	4	yes	complemented
16	C₂²×C₇	C₂×C₈	1	3	yes	—
17	C₄×C₇	C₂×C₈	1	3	yes	—
18	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄	Dic₇	1	1	yes	characteristic
20	C₂×C₈	Dic₇	1	3	yes	—
21	C₂×C₈	C₂×D₇	1	3	yes	—
22	C₁₆	—	7	4	no	—
23	C₂×C₇	C₂×C₁₆	1	6	yes	complemented
24	C₂×C₇	C₂²×C₈	1	1	yes	characteristic
25	C₂³	C₇⋊C₈	1	1	yes	characteristic
26	C₂×C₄	C₇⋊C₈	1	3	yes	—
27	C₂×C₄	C₂×Dic₇	1	3	yes	—
28	C₈	C₂×Dic₇	1	3	yes	—
29	C₈	C₂²×D₇	1	1	yes	characteristic
30	C₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²	C₇⋊C₁₆	1	4	yes	direct product factor
32	C₂²	C₂×C₇⋊C₈	1	3	yes	—
33	C₄	C₂×C₇⋊C₈	1	3	yes	—
34	C₄	C₂²×Dic₇	1	1	yes	characteristic
35	C₂	C₂×C₇⋊C₁₆	1	6	yes	direct product factor
36	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.