Subgroups — #20293007

Order 6848.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₂₈	C₂	1	4	yes	maximal
2	#16812109	C₂	1	2	yes	maximal
3	C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₄	C₂²	1	4	yes	—
5	Dic₄₂₈	—	2	8	no	—
6	C₄⋊Dic₁₀₇	—	2	4	no	—
7	C₂×C₈×C₁₀₇	C₂²	1	2	yes	—
8	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₀₇	D₄	1	2	yes	—
10	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
11	C₂×Dic₁₀₇	—	2	4	no	—
12	Dic₂₁₄	—	2	8	no	—
13	C₈×C₁₀₇	D₄	1	4	yes	—
14	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₀₇	Q₁₆	1	4	yes	complemented
16	C₄×C₁₀₇	C₂×D₄	1	2	yes	—
17	Dic₁₀₇	—	4	4	no	—
18	C₂×C₁₀₇	#127	1	1	yes	characteristic
19	C₂×C₁₀₇	C₂×Q₁₆	1	2	yes	—
20	C₁₀₇	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	107	1	no	maximal, Sylow
22	C₂×Q₁₆	—	107	4	no	—
23	C₄⋊Q₈	—	107	2	no	—
24	C₄×C₈	D₁₀₇	1	1	yes	characteristic
25	C₂×Q₈	—	107	4	no	—
26	Q₁₆	—	214	8	no	—
27	C₂×C₈	C₂×D₁₀₇	1	2	yes	—
28	C₄⋊C₄	—	214	4	no	—
29	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
30	Q₈	—	214	8	no	—
31	C₂×C₄	—	214	4	no	—
32	C₂×C₄	D₄₂₈	1	2	yes	—
33	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
34	C₈	D₄₂₈	1	4	yes	—
35	C₂²	C₂×D₄₂₈	1	1	yes	characteristic
36	C₄	—	428	4	no	—
37	C₄	Dic₄₂₈	1	4	yes	complemented
38	C₄	C₂×D₄₂₈	1	2	yes	—
39	C₂	#16812106	1	1	yes	characteristic
40	C₂	C₂×Dic₄₂₈	1	2	yes	—

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