Subgroups — #89307

Order 448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#6389	C₂	1	1	yes	maximal, characteristic
3	#6386	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₄×Dic₇	C₄	1	1	yes	characteristic
6	C₂×C₇⋊C₈	C₄	1	1	yes	characteristic
7	C₇×C₁₆	C₄	1	2	yes	complemented
8	C₇⋊C₁₆	C₄	1	2	yes	complemented
9	#347	—	7	1	no	maximal, Sylow
10	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₇	—	2	1	no	—
12	C₇×C₈	C₂×C₄	1	1	yes	characteristic
13	C₇×C₈	C₂×C₄	1	1	yes	characteristic
14	C₇⋊C₈	—	2	1	no	—
15	M₃₂	—	7	1	no	—
16	M₃₂	D₇	1	1	yes	characteristic
17	#97	—	7	1	no	—
18	C₂²×C₇	M₁₆	1	1	yes	characteristic
19	C₄×C₇	C₄²	1	1	yes	characteristic
20	C₄×C₇	M₁₆	1	1	yes	characteristic
21	Dic₇	—	4	1	no	—
22	C₂×C₈	—	7	1	no	—
23	C₂×C₈	C₂×D₇	1	1	yes	characteristic
24	C₄²	—	7	1	no	—
25	C₁₆	—	7	2	no	—
26	C₁₆	Dic₇	1	2	yes	complemented
27	C₂×C₇	—	2	1	no	—
28	C₂×C₇	#97	1	1	yes	characteristic
29	C₂×C₄	—	14	1	no	—
30	C₂×C₄	C₄×D₇	1	1	yes	characteristic
31	C₈	—	14	1	no	—
32	C₈	C₄×D₇	1	1	yes	characteristic
33	C₈	C₂×Dic₇	1	1	yes	characteristic
34	C₇	#347	1	1	yes	characteristic, complemented, Sylow
35	C₂²	#1131	1	1	yes	characteristic
36	C₄	—	28	1	no	—
37	C₄	#1131	1	1	yes	characteristic
38	C₄	C₄×Dic₇	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#6389	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.