Subgroups — #13096144

Order 1568.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11716063	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊(C₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×D₄	—	2	1	no	—
5	C₄⋊(C₇⋊D₇)	—	2	1	no	—
6	C₇²×C₈	C₂²	1	1	yes	characteristic
7	#6400	—	7	8	no	maximal
8	C₂²×C₇²	—	4	1	no	—
9	C₂×C₇⋊D₇	—	4	1	no	—
10	C₄×C₇²	D₄	1	1	yes	characteristic
11	C₇×D₈	D₇	1	8	yes	complemented
12	D₅₆	—	7	8	no	—
13	C₇⋊C₁₆	—	7	8	no	—
14	C₂×C₇²	—	8	1	no	—
15	C₂×C₇²	D₈	1	1	yes	characteristic
16	C₇⋊D₇	—	8	1	no	—
17	C₇×D₄	—	2	8	no	—
18	D₂₈	—	14	8	no	—
19	C₇×C₈	C₂×D₇	1	8	yes	—
20	C₇²	D₁₆	1	1	yes	characteristic, complemented, Sylow
21	D₁₆	—	49	1	no	Sylow
22	C₂²×C₇	—	4	8	no	—
23	C₂×D₇	—	28	8	no	—
24	C₄×C₇	C₂²⋊D₇	1	8	yes	—
25	D₈	—	49	1	no	—
26	D₈	C₇⋊D₇	1	1	yes	characteristic, complemented
27	C₁₆	—	49	1	no	—
28	C₂×C₇	—	8	8	no	—
29	C₂×C₇	#1141	1	8	yes	—
30	D₇	—	56	8	no	—
31	D₄	—	2	1	no	—
32	D₄	—	98	1	no	—
33	C₈	C₂×C₇⋊D₇	1	1	yes	characteristic
34	C₇	#6400	1	8	yes	complemented
35	C₂²	—	4	1	no	—
36	C₂²	—	196	1	no	—
37	C₄	C₂²⋊(C₇⋊D₇)	1	1	yes	characteristic
38	C₂	—	8	1	no	—
39	C₂	—	392	1	no	—
40	C₂	#11716071	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.