Subgroups — #89289

Order 448.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#108	C₂	1	1	yes	maximal, characteristic
2	#6391	C₂	1	1	yes	maximal, characteristic
3	#6386	C₂	1	1	yes	maximal, characteristic
4	C₇×M₁₆	—	2	1	no	—
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₇	—	2	1	no	—
7	C₇⋊C₁₆	C₄	1	2	yes	complemented
8	#365	—	7	1	no	maximal, Sylow
9	C₂×C₄×C₇	D₄	1	1	yes	characteristic
10	C₂×Dic₇	—	4	1	no	—
11	C₇×C₈	—	4	1	no	—
12	C₇×C₈	C₂×C₄	1	1	yes	characteristic
13	C₇×C₈	Q₈	1	1	yes	characteristic
14	M₃₂	—	7	1	no	—
15	#108	D₇	1	1	yes	characteristic
16	#106	—	7	1	no	—
17	C₂²×C₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₇	SD₁₆	1	1	yes	characteristic
20	Dic₇	—	8	1	no	—
21	M₁₆	—	2	1	no	—
22	C₂×C₈	C₂×D₇	1	1	yes	characteristic
23	C₄⋊C₄	—	14	1	no	—
24	C₁₆	—	7	2	no	—
25	C₂×C₇	—	2	1	no	—
26	C₂×C₇	#106	1	1	yes	characteristic
27	C₂×C₄	—	28	1	no	—
28	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
29	C₈	—	4	1	no	—
30	C₈	Dic₁₄	1	1	yes	characteristic
31	C₈	C₄×D₇	1	1	yes	characteristic
32	C₇	#365	1	1	yes	characteristic, complemented, Sylow
33	C₂²	#1143	1	1	yes	characteristic
34	C₄	—	56	1	no	—
35	C₄	Dic₇⋊C₄	1	1	yes	characteristic
36	C₄	#1142	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#6382	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₇⋊C₁₆	C₄	semidirect
32. C₇	#365	semidirect

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