Subgroups — #89455

Order 448.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6433	C₂	1	2	yes	maximal
2	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	#6392	C₂	1	2	yes	maximal
4	#6391	C₂	1	2	yes	maximal
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₄²×C₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₇	C₂²	1	4	yes	—
9	Dic₇⋊C₄	—	2	4	no	—
10	#499	—	7	1	no	maximal, Sylow
11	C₂×C₄×C₇	D₄	1	2	yes	—
12	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
13	C₂×Dic₇	—	2	4	no	—
14	C₇×C₈	Q₈	1	2	yes	—
15	C₇×C₈	Q₈	1	2	yes	—
16	#125	—	7	2	no	—
17	#107	—	7	2	no	—
18	#106	—	7	2	no	—
19	C₄×C₈	D₇	1	1	yes	characteristic
20	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₇	—	2	2	no	—
22	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₇	—	4	4	no	—
25	C₂×C₈	C₂×D₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₇	1	1	yes	characteristic
27	C₄⋊C₄	—	7	4	no	—
28	C₄⋊C₄	—	14	4	no	—
29	C₄²	C₂×D₇	1	1	yes	characteristic
30	C₂×C₇	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₇	#135	1	2	yes	—
32	C₂×C₄	—	14	4	no	—
33	C₂×C₄	D₂₈	1	2	yes	—
34	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
35	C₈	Dic₁₄	1	2	yes	—
36	C₈	Dic₁₄	1	2	yes	—
37	C₇	#499	1	1	yes	characteristic, complemented, Sylow
38	C₂²	C₂×D₂₈	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	28	4	no	—
41	C₄	C₂×Dic₁₄	1	1	yes	characteristic
42	C₄	C₂×Dic₁₄	1	1	yes	characteristic
43	C₂	#6432	1	1	yes	characteristic
44	C₂	#6467	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
37. C₇	#499	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.