Subgroups — #333×C₁₃₇ #22576868

Order 8768.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×Q₈×C₁₃₇	C₄	1	2	yes	—
4	C₂×C₈×C₁₃₇	—	2	2	no	—
5	C₄⋊C₄×C₁₃₇	—	2	2	no	—
6	C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
7	Q₈×C₁₃₇	—	4	2	no	—
8	C₂×C₄×C₁₃₇	—	2	2	no	—
9	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₃₇	D₄	1	2	yes	—
11	C₈×C₁₃₇	—	4	2	no	—
12	C₂²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₁₃₇	—	2	1	no	—
14	C₄×C₁₃₇	—	4	2	no	—
15	C₄×C₁₃₇	SD₁₆	1	2	yes	—
16	C₄×C₁₃₇	Q₁₆	1	2	yes	—
17	C₂×C₁₃₇	#100	1	1	yes	characteristic
18	C₂×C₁₃₇	#103	1	2	yes	—
19	C₁₃₇	#333	1	1	yes	characteristic, direct product factor, Sylow
20	#333	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₄⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic
22	C₄⋊C₈	C₂×C₁₃₇	1	2	yes	—
23	C₂×Q₈	C₄×C₁₃₇	1	2	yes	—
24	C₂×C₈	—	2	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
30	C₂×C₄	D₄×C₁₃₇	1	2	yes	—
31	C₈	—	4	2	no	—
32	C₂²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	SD₁₆×C₁₃₇	1	2	yes	—
36	C₄	Q₁₆×C₁₃₇	1	2	yes	—
37	C₂	#100×C₁₃₇	1	1	yes	characteristic
38	C₂	#103×C₁₃₇	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
19. C₁₃₇	#333	direct (N × H)
20. #333	C₁₃₇	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.