Subgroups — #90503

Order 448.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₇	C₂	1	8	yes	maximal, complemented
3	#6489	C₂	1	6	yes	maximal
4	C₂×C₇×Q₈	C₄	1	8	yes	complemented
5	C₂×C₇×Q₈	C₂²	1	4	yes	—
6	C₂²×C₄×C₇	C₂²	1	3	yes	—
7	C₂²⋊Dic₇	C₂²	1	4	yes	—
8	C₄⋊Dic₇	C₂²	1	12	yes	—
9	C₄×Dic₇	C₂²	1	12	yes	—
10	#519	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₂³	1	1	yes	characteristic
12	C₇×Q₈	C₂×C₄	1	16	yes	—
13	C₂×C₄×C₇	C₂×C₄	1	12	yes	—
14	C₂×C₄×C₇	C₂³	1	6	yes	—
15	C₂×Dic₇	C₂³	1	8	yes	—
16	C₂²×Q₈	D₇	1	1	yes	characteristic
17	C₄×Q₈	—	7	8	no	—
18	#117	—	7	6	no	—
19	C₂²×C₇	—	2	2	no	—
20	C₂²×C₇	C₂²×C₄	1	2	yes	—
21	C₂²×C₇	C₂⁴	1	1	yes	characteristic
22	C₄×C₇	C₂²×C₄	1	12	yes	—
23	Dic₇	—	2	8	no	—
24	C₂×Q₈	Dic₇	1	8	yes	complemented
25	C₂×Q₈	C₂×D₇	1	4	yes	—
26	C₂²×C₄	C₂×D₇	1	3	yes	—
27	C₄⋊C₄	—	7	12	no	—
28	C₂²⋊C₄	—	7	4	no	—
29	C₄²	—	7	12	no	—
30	C₂×C₇	—	2	2	no	—
31	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
32	C₂×C₇	2₋¹⁺⁴	1	2	yes	—
33	C₂³	C₂²×D₇	1	1	yes	characteristic
34	Q₈	C₂×Dic₇	1	16	yes	—
35	C₂×C₄	—	7	8	no	—
36	C₂×C₄	C₂×Dic₇	1	12	yes	—
37	C₂×C₄	C₂²×D₇	1	6	yes	—
38	C₇	#519	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	2	2	no	—
40	C₂²	C₂²×Dic₇	1	2	yes	—
41	C₂²	C₂³×D₇	1	1	yes	characteristic
42	C₄	—	14	8	no	—
43	C₄	C₂²×Dic₇	1	12	yes	—
44	C₂	—	2	2	no	—
45	C₂	#6551	1	2	yes	—
46	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.