Subgroups — #89250

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	1	yes	maximal, characteristic
2	C₄×C₇⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₇×C₈	C₄	1	2	yes	—
4	C₄²×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₇⋊C₈	C₄	1	4	yes	—
6	#322	—	7	1	no	maximal, Sylow
7	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
9	C₇×C₈	C₈	1	4	yes	complemented
10	C₇⋊C₈	—	2	4	no	—
11	C₄×C₈	—	7	2	no	—
12	C₄×C₈	D₇	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	—	7	4	no	—
17	C₂×C₈	Dic₇	1	2	yes	—
18	C₄²	C₂×D₇	1	1	yes	characteristic
19	C₂×C₇	C₄×C₈	1	1	yes	characteristic
20	C₂×C₇	#97	1	2	yes	—
21	C₂×C₄	C₄×D₇	1	2	yes	—
22	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
23	C₈	—	14	4	no	—
24	C₈	C₇⋊C₈	1	4	yes	complemented
25	C₇	#322	1	1	yes	characteristic, complemented, Sylow
26	C₂²	C₄×Dic₇	1	1	yes	characteristic
27	C₄	#1131	1	4	yes	—
28	C₄	C₂×C₇⋊C₈	1	2	yes	—
29	C₂	C₄×C₇⋊C₈	1	1	yes	characteristic
30	C₂	#6389	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.