Subgroups — #89454

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6432	C₂	1	2	yes	maximal
2	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	#6392	C₂	1	4	yes	maximal
4	C₂×Dic₁₄	—	2	2	no	—
5	C₂×C₇×C₈	C₂²	1	2	yes	—
6	C₄²×C₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₇	—	2	2	no	—
8	C₄⋊Dic₇	C₂²	1	4	yes	—
9	#500	—	7	1	no	maximal, Sylow
10	C₂×C₄×C₇	D₄	1	1	yes	characteristic
11	C₂×C₄×C₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
13	C₂×Dic₇	—	2	4	no	—
14	Dic₁₄	—	4	4	no	—
15	C₇×C₈	Q₈	1	4	yes	complemented
16	C₄⋊Q₈	—	7	2	no	—
17	#107	—	7	4	no	—
18	C₄×C₈	D₇	1	1	yes	characteristic
19	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
20	C₄×C₇	D₈	1	2	yes	—
21	C₄×C₇	Q₁₆	1	2	yes	—
22	C₄×C₇	C₂×Q₈	1	2	yes	—
23	Dic₇	—	4	4	no	—
24	C₂×Q₈	—	14	2	no	—
25	C₂×C₈	C₂×D₇	1	2	yes	—
26	C₄⋊C₄	—	7	4	no	—
27	C₄⋊C₄	—	14	2	no	—
28	C₄²	C₂×D₇	1	1	yes	characteristic
29	C₂×C₇	C₄⋊Q₈	1	1	yes	characteristic
30	C₂×C₇	C₂×D₈	1	1	yes	characteristic
31	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
32	Q₈	—	28	4	no	—
33	C₂×C₄	—	14	4	no	—
34	C₂×C₄	D₂₈	1	1	yes	characteristic
35	C₂×C₄	D₂₈	1	1	yes	characteristic
36	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
37	C₈	Dic₁₄	1	4	yes	complemented
38	C₇	#500	1	1	yes	characteristic, complemented, Sylow
39	C₂²	C₂×D₂₈	1	1	yes	characteristic
40	C₄	—	28	4	no	—
41	C₄	D₅₆	1	2	yes	—
42	C₄	Dic₂₈	1	2	yes	—
43	C₄	C₂×Dic₁₄	1	2	yes	—
44	C₂	#6432	1	1	yes	characteristic
45	C₂	C₂×D₅₆	1	1	yes	characteristic
46	C₂	C₂×Dic₂₈	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.