Subgroups — #89360

Order 448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#6393	C₂	1	1	yes	maximal, characteristic
3	#6386	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×Q₈	—	2	1	no	—
5	C₇×Q₁₆	—	2	1	no	—
6	C₇×Q₁₆	C₄	1	2	yes	—
7	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
8	#1136	—	2	1	no	—
9	C₇⋊C₁₆	—	2	1	no	—
10	#362	—	7	1	no	maximal, Sylow
11	C₇×Q₈	—	2	2	no	—
12	C₇×Q₈	—	4	1	no	—
13	C₂×C₄×C₇	—	4	1	no	—
14	C₂×C₄×C₇	D₄	1	1	yes	characteristic
15	C₇×C₈	C₂×C₄	1	1	yes	characteristic
16	C₇×C₈	D₄	1	1	yes	characteristic
17	C₇⋊C₈	—	4	1	no	—
18	C₂×Q₁₆	D₇	1	1	yes	characteristic
19	M₃₂	—	7	1	no	—
20	#108	—	7	1	no	—
21	C₂²×C₇	SD₁₆	1	1	yes	characteristic
22	C₄×C₇	—	4	2	no	—
23	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₇	D₈	1	1	yes	characteristic
25	C₂×Q₈	—	2	1	no	—
26	Q₁₆	—	2	1	no	—
27	Q₁₆	Dic₇	1	2	yes	—
28	M₁₆	—	14	1	no	—
29	C₂×C₈	C₂×D₇	1	1	yes	characteristic
30	C₁₆	—	14	1	no	—
31	C₂×C₇	—	2	1	no	—
32	C₂×C₇	#102	1	1	yes	characteristic
33	Q₈	—	2	2	no	—
34	Q₈	—	4	1	no	—
35	C₂×C₄	—	4	1	no	—
36	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
37	C₈	—	28	1	no	—
38	C₈	C₂×Dic₇	1	1	yes	characteristic
39	C₈	C₂²⋊D₇	1	1	yes	characteristic
40	C₇	#362	1	1	yes	characteristic, complemented, Sylow
41	C₂²	#1142	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	#1141	1	1	yes	characteristic
44	C₄	C₂²⋊Dic₇	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#6406	1	1	yes	characteristic

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

N	H ≅ G/N	type
40. C₇	#362	semidirect

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