Subgroups — #17984151

Order 4384.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14555518	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#10587739	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587739	—	2	1	no	—
5	#11764047	—	2	1	no	—
6	Dic₂₇₄	—	2	1	no	—
7	Dic₂₇₄	C₄	1	1	yes	characteristic, complemented
8	C₄×D₁₃₇	—	2	1	no	—
9	C₄×D₁₃₇	C₂²	1	1	yes	characteristic
10	Q₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂×D₁₃₇	D₄	1	1	yes	characteristic
12	#10587739	—	4	1	no	—
13	C₄×C₁₃₇	—	2	1	no	—
14	C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	Dic₁₃₇	—	2	1	no	—
16	Dic₁₃₇	D₄	1	1	yes	characteristic
17	C₂×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₃₇	SD₁₆	1	1	yes	characteristic
19	D₁₃₇	Q₁₆	1	1	yes	characteristic
20	C₁₃₇	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	137	1	no	maximal, Sylow
22	C₂×Q₈	—	137	1	no	—
23	C₂×C₈	—	137	1	no	—
24	C₄⋊C₄	—	137	1	no	—
25	Q₈	—	274	1	no	—
26	Q₈	—	137	1	no	—
27	Q₈	#10587739	1	1	yes	characteristic, complemented
28	C₂×C₄	—	274	1	no	—
29	C₂×C₄	—	274	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₈	—	274	1	no	—
32	C₂²	—	137	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	274	1	no	—
35	C₄	—	548	1	no	—
36	C₄	—	137	1	no	—
37	C₄	C₂×#10587739	1	1	yes	characteristic
38	C₂	—	137	1	no	—
39	C₂	—	137	1	no	—
40	C₂	C₂²⋊#10587739	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.