Subgroups — #34089618

Order 19744.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄₆₈	C₂	1	1	yes	maximal, characteristic
2	#23754584	C₂	1	1	yes	maximal, characteristic, complemented
3	M₁₆×C₆₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₆₁₇	C₄	1	2	yes	—
5	D₂₄₆₈	—	2	1	no	—
6	D₂₄₆₈	—	2	1	no	—
7	#19096921	—	2	1	no	—
8	C₂×C₄×C₆₁₇	C₂²	1	1	yes	characteristic
9	C₈×C₆₁₇	—	2	1	no	—
10	C₂²×C₆₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₆₁₇	—	2	2	no	—
12	C₂×D₆₁₇	—	4	2	no	—
13	C₄×C₆₁₇	D₄	1	1	yes	characteristic
14	C₄×C₆₁₇	D₄	1	1	yes	characteristic
15	C₂×C₆₁₇	—	2	1	no	—
16	C₂×C₆₁₇	C₂²⋊C₄	1	1	yes	characteristic
17	D₆₁₇	—	4	2	no	—
18	C₆₁₇	#100	1	1	yes	characteristic, complemented, Sylow
19	#100	—	617	1	no	maximal, Sylow
20	C₂×D₄	—	617	1	no	—
21	M₁₆	—	617	1	no	—
22	M₁₆	D₆₁₇	1	1	yes	characteristic, complemented
23	C₂³	—	617	2	no	—
24	D₄	—	1234	1	no	—
25	D₄	—	1234	1	no	—
26	C₂×C₄	C₂×D₆₁₇	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	1234	1	no	—
29	C₂²	—	2468	2	no	—
30	C₂²	—	1234	2	no	—
31	C₂²	C₄×D₆₁₇	1	1	yes	characteristic
32	C₄	C₂²⋊D₆₁₇	1	1	yes	characteristic
33	C₄	D₂₄₆₈	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	—	2468	2	no	—
36	C₂	#23754577	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.