Subgroups — C₇×#322 #89364

Order 448.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₈	C₂	1	2	yes	maximal
2	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₈	C₄	1	4	yes	—
4	C₂×C₇×C₈	C₄	1	2	yes	—
5	C₄²×C₇	C₂²	1	1	yes	characteristic
6	#322	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
9	C₇×C₈	—	2	4	no	—
10	C₇×C₈	C₈	1	4	yes	complemented
11	C₄×C₈	C₂×C₇	1	2	yes	—
12	C₄×C₈	C₂×C₇	1	1	yes	characteristic
13	C₂²×C₇	C₄²	1	1	yes	characteristic
14	C₄×C₇	C₂×C₈	1	2	yes	—
15	C₄×C₇	M₁₆	1	4	yes	—
16	C₂×C₈	C₄×C₇	1	4	yes	—
17	C₂×C₈	C₄×C₇	1	2	yes	—
18	C₄²	C₂²×C₇	1	1	yes	characteristic
19	C₂×C₇	C₄×C₈	1	1	yes	characteristic
20	C₂×C₇	#97	1	2	yes	—
21	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
22	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
23	C₈	—	2	4	no	—
24	C₈	C₇×C₈	1	4	yes	complemented
25	C₇	#322	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	C₄²×C₇	1	1	yes	characteristic
27	C₄	C₂×C₇×C₈	1	2	yes	—
28	C₄	C₇×M₁₆	1	4	yes	—
29	C₂	C₄×C₇×C₈	1	1	yes	characteristic
30	C₂	C₇×#97	1	2	yes	—

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.

subgroup	index
C₄×C₇×C₈	2
#322	7