Subgroups — #17984145

Order 4384.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11764047	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#11764047	—	2	2	no	—
4	C₂²×D₁₃₇	C₄	1	1	yes	characteristic
5	C₂×Dic₁₃₇	C₂²	1	1	yes	characteristic
6	C₄×D₁₃₇	—	2	2	no	—
7	C₂×C₄×C₁₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×D₁₃₇	—	2	1	no	—
10	C₂×D₁₃₇	—	2	1	no	—
11	C₂×D₁₃₇	C₈	1	2	yes	complemented
12	C₄×C₁₃₇	—	2	1	no	—
13	Dic₁₃₇	D₄	1	2	yes	—
14	C₂×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×C₁₃₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₃₇	M₁₆	1	1	yes	characteristic
17	D₁₃₇	—	2	2	no	—
18	C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	137	1	no	maximal, Sylow
20	C₂²×C₄	—	137	1	no	—
21	C₂×C₈	—	137	2	no	—
22	C₂³	—	137	1	no	—
23	C₂×C₄	—	274	2	no	—
24	C₂×C₄	—	137	1	no	—
25	C₂×C₄	#10587739	1	1	yes	characteristic
26	C₈	—	274	2	no	—
27	C₂²	—	274	1	no	—
28	C₂²	—	274	1	no	—
29	C₂²	—	137	2	no	—
30	C₂²	C₂×#10587739	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	137	2	no	—
33	C₂	—	274	2	no	—
34	C₂	C₂²⋊#10587739	1	1	yes	characteristic
35	C₂	#14555518	1	1	yes	characteristic
36	C₂	#14555520	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.