Subgroups — #36375031

Order 22336.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#13063703	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₃₄₉	C₂	1	1	yes	maximal, characteristic
4	D₃₄₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#13063703	C₄	1	1	yes	characteristic
6	#19150236	C₄	1	2	yes	complemented
7	C₈×D₃₄₉	C₂²	1	1	yes	characteristic
8	#19150208	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₄₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#13063703	C₈	1	2	yes	—
11	#14584102	C₈	1	2	yes	—
12	C₄×D₃₄₉	C₂×C₄	1	1	yes	characteristic
13	#14584095	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₄₉	C₂×C₈	1	1	yes	characteristic
16	#13063703	—	2	2	no	—
17	C₄×C₃₄₉	C₄²	1	1	yes	characteristic
18	Dic₃₄₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃₄₉	C₄×C₈	1	1	yes	characteristic
20	D₃₄₉	M₃₂	1	2	yes	—
21	C₃₄₉	#346	1	1	yes	characteristic, complemented, Sylow
22	#346	—	349	1	no	maximal, Sylow
23	C₂×C₁₆	—	349	1	no	—
24	C₂×C₁₆	—	349	1	no	—
25	C₄×C₈	—	349	1	no	—
26	C₂×C₈	—	349	1	no	—
27	C₂×C₈	—	349	1	no	—
28	C₄²	—	349	1	no	—
29	C₁₆	—	349	2	no	—
30	C₁₆	—	349	1	no	—
31	C₁₆	#13063703	1	1	yes	characteristic, complemented
32	C₂×C₄	—	349	1	no	—
33	C₂×C₄	—	349	2	no	—
34	C₈	—	349	2	no	—
35	C₈	—	349	1	no	—
36	C₈	C₂×#13063703	1	1	yes	characteristic
37	C₂²	—	349	1	no	—
38	C₄	—	349	1	no	—
39	C₄	—	698	2	no	—
40	C₄	C₄×#13063703	1	1	yes	characteristic
41	C₂	—	349	2	no	—
42	C₂	C₈×#13063703	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.