Subgroups — #34089691

Order 19744.

76 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	#23754577	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₆₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₆₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₁₇	C₂²	1	2	yes	—
6	D₂₄₆₈	—	2	2	no	—
7	C₂×Dic₆₁₇	C₂²	1	2	yes	—
8	Q₈×C₆₁₇	—	2	2	no	—
9	C₂×C₄×C₆₁₇	C₂²	1	2	yes	—
10	C₂×C₄×C₆₁₇	C₂²	1	1	yes	characteristic
11	C₂²×C₆₁₇	C₂³	1	1	yes	characteristic
12	C₂×D₆₁₇	—	2	2	no	—
13	C₂×D₆₁₇	—	2	4	no	—
14	C₄×C₆₁₇	—	2	2	no	—
15	C₄×C₆₁₇	D₄	1	2	yes	—
16	Dic₆₁₇	—	2	2	no	—
17	C₂×C₆₁₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₆₁₇	#41	1	2	yes	—
19	D₆₁₇	—	4	2	no	—
20	C₆₁₇	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	617	1	no	maximal, Sylow
22	C₂×Q₈	D₆₁₇	1	1	yes	characteristic, complemented
23	C₂×D₄	—	617	1	no	—
24	C₂²⋊C₄	—	617	4	no	—
25	C₄²	—	617	1	no	—
26	C₂³	—	617	2	no	—
27	Q₈	—	2	2	no	—
28	D₄	—	1234	2	no	—
29	C₂×C₄	—	617	2	no	—
30	C₂×C₄	C₂×D₆₁₇	1	2	yes	—
31	C₂×C₄	C₂×D₆₁₇	1	1	yes	characteristic
32	C₂²	—	1234	2	no	—
33	C₂²	—	1234	4	no	—
34	C₂²	C₂²×D₆₁₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	1234	2	no	—
37	C₄	C₂²⋊D₆₁₇	1	2	yes	—
38	C₂	—	2468	2	no	—
39	C₂	C₂×C₂²⋊D₆₁₇	1	1	yes	characteristic
40	C₂	#23754601	1	2	yes	—

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.