Subgroups — #16812786

Order 3488.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13182039	C₂	1	1	yes	maximal, characteristic, complemented
2	#13182038	C₂	1	2	yes	maximal, complemented
3	D₁₀₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11724786	C₂	1	2	yes	maximal, complemented
5	#13182028	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂²⋊D₁₀₉	C₄	1	2	yes	—
8	C₂×Dic₁₀₉	C₂²	1	2	yes	—
9	C₄×D₁₀₉	C₂²	1	1	yes	characteristic
10	Dic₂₁₈	C₄	1	1	yes	characteristic
11	#11724786	C₂²	1	1	yes	characteristic
12	#11724786	C₂²	1	2	yes	—
13	#11724786	C₂²	1	1	yes	characteristic
14	C₂²×C₁₀₉	C₂×C₄	1	2	yes	—
15	C₂×D₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	Dic₁₀₉	C₂×C₄	1	2	yes	—
18	Dic₁₀₉	C₂³	1	1	yes	characteristic
19	C₂×C₁₀₉	—	2	2	no	—
20	C₂×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
21	D₁₀₉	—	2	1	no	—
22	C₁₀₉	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	109	1	no	maximal, Sylow
24	#41	—	109	1	no	—
25	M₁₆	—	109	2	no	—
26	M₁₆	—	109	1	no	—
27	C₂×C₈	—	109	2	no	—
28	C₂×C₈	—	109	1	no	—
29	Q₈	—	109	1	no	—
30	D₄	—	109	2	no	—
31	D₄	#89137	1	1	yes	characteristic
32	C₂×C₄	—	109	2	no	—
33	C₂×C₄	—	109	1	no	—
34	C₈	—	109	1	no	—
35	C₈	—	109	2	no	—
36	C₈	—	109	1	no	—
37	C₂²	—	109	1	no	—
38	C₂²	C₂×#89137	1	2	yes	—
39	C₄	—	109	1	no	—
40	C₄	—	109	2	no	—
41	C₄	C₂×#89137	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	218	1	no	—
44	C₂	C₂²×#89137	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.