Subgroups — #89341

Order 448.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇⋊C₈)	C₂	1	2	yes	maximal
3	C₂×C₇×Q₈	C₄	1	2	yes	—
4	C₇×C₄⋊C₄	—	2	2	no	—
5	C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇⋊C₈	—	2	2	no	—
7	#333	—	7	1	no	maximal, Sylow
8	C₇×Q₈	—	4	2	no	—
9	C₂×C₄×C₇	—	2	2	no	—
10	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₇	D₄	1	2	yes	—
12	C₇⋊C₈	—	4	2	no	—
13	C₄⋊Q₈	D₇	1	1	yes	characteristic
14	C₄⋊C₈	—	7	2	no	—
15	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₇	—	2	1	no	—
17	C₄×C₇	—	4	2	no	—
18	C₄×C₇	SD₁₆	1	2	yes	—
19	C₄×C₇	Q₁₆	1	2	yes	—
20	C₂×Q₈	Dic₇	1	2	yes	—
21	C₂×C₈	—	14	2	no	—
22	C₄⋊C₄	—	2	2	no	—
23	C₄²	C₂×D₇	1	1	yes	characteristic
24	C₂×C₇	#100	1	1	yes	characteristic
25	C₂×C₇	#103	1	2	yes	—
26	Q₈	—	4	2	no	—
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
29	C₂×C₄	C₂²⋊D₇	1	2	yes	—
30	C₈	—	28	2	no	—
31	C₇	#333	1	1	yes	characteristic, complemented, Sylow
32	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#1143	1	2	yes	—
36	C₄	#1144	1	2	yes	—
37	C₂	#6407	1	1	yes	characteristic
38	C₂	#6409	1	2	yes	—

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

N	H ≅ G/N	type
31. C₇	#333	semidirect

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