Subgroups — #31780404

Order 17536.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22577780	C₂	1	6	yes	maximal, complemented
2	C₈²×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₀₉₆	—	2	12	no	—
4	#17984085	C₂²	1	4	yes	—
5	C₄×C₈×C₁₃₇	C₂²	1	3	yes	—
6	C₂×D₅₄₈	—	2	12	no	—
7	D₁₀₉₆	—	4	24	no	—
8	C₂×C₈×C₁₃₇	D₄	1	6	yes	—
9	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
10	C₂²×D₁₃₇	—	4	4	no	—
11	D₅₄₈	—	4	24	no	—
12	C₂×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
13	C₈×C₁₃₇	D₈	1	12	yes	complemented
14	C₂²×C₁₃₇	#127	1	1	yes	characteristic
15	C₂×D₁₃₇	—	8	12	no	—
16	C₄×C₁₃₇	C₂×D₈	1	6	yes	—
17	C₂×C₁₃₇	#493	1	3	yes	—
18	D₁₃₇	—	16	4	no	—
19	C₁₃₇	#1712	1	1	yes	characteristic, complemented, Sylow
20	#1712	—	137	1	no	maximal, Sylow
21	#493	—	137	6	no	—
22	C₈²	D₁₃₇	1	1	yes	characteristic, complemented
23	C₂×D₈	—	274	12	no	—
24	#127	—	137	4	no	—
25	C₄×C₈	C₂×D₁₃₇	1	3	yes	—
26	C₂×D₄	—	274	12	no	—
27	D₈	—	548	24	no	—
28	C₂×C₈	D₅₄₈	1	6	yes	—
29	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
30	C₂³	—	548	4	no	—
31	D₄	—	548	24	no	—
32	C₂×C₄	C₂×D₅₄₈	1	3	yes	—
33	C₈	D₁₀₉₆	1	12	yes	complemented
34	C₂²	—	1096	12	no	—
35	C₂²	#17984085	1	1	yes	characteristic
36	C₄	C₂×D₁₀₉₆	1	6	yes	—
37	C₂	—	2192	4	no	—
38	C₂	#22577780	1	3	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.