Subgroups — #20295887

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724786	C₂	1	2	yes	maximal
2	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724786	—	2	2	no	—
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
9	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
10	#11724786	—	4	2	no	—
11	C₈×C₁₀₉	C₈	1	2	yes	complemented
12	#11724784	—	2	1	no	—
13	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
16	Dic₁₀₉	—	2	1	no	—
17	Dic₁₀₉	SD₁₆	1	2	yes	—
18	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	#106	1	1	yes	characteristic
20	C₂×C₁₀₉	#108	1	1	yes	characteristic
21	C₁₀₉	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	109	1	no	maximal, Sylow
23	C₄⋊C₈	—	109	2	no	—
24	C₄×C₈	—	109	1	no	—
25	C₂×C₈	—	109	1	no	—
26	C₂×C₈	—	218	2	no	—
27	C₂×C₈	#89137	1	1	yes	characteristic
28	C₄²	—	109	1	no	—
29	C₂×C₄	—	109	1	no	—
30	C₂×C₄	—	109	1	no	—
31	C₂×C₄	C₂×#89137	1	1	yes	characteristic
32	C₈	—	436	2	no	—
33	C₈	—	218	1	no	—
34	C₈	#11724786	1	2	yes	complemented
35	C₂²	C₄⋊#89137	1	1	yes	characteristic
36	C₄	—	109	2	no	—
37	C₄	—	218	1	no	—
38	C₄	C₂×#11724786	1	1	yes	characteristic
39	C₄	#13182039	1	1	yes	characteristic
40	C₂	C₄⋊#11724786	1	1	yes	characteristic
41	C₂	#16812767	1	1	yes	characteristic
42	C₂	#16812769	1	1	yes	characteristic

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