Subgroups — #20294747

Order 6976.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11724784	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724784	C₄	1	4	yes	—
4	C₂×C₈×C₁₀₉	C₄	1	2	yes	—
5	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
7	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	C₈×C₁₀₉	C₈	1	4	yes	complemented
9	#11724784	—	2	4	no	—
10	C₂²×C₁₀₉	C₄²	1	1	yes	characteristic
11	C₄×C₁₀₉	C₂×C₈	1	2	yes	—
12	C₄×C₁₀₉	M₁₆	1	4	yes	—
13	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
14	C₂×C₁₀₉	#97	1	2	yes	—
15	C₁₀₉	#322	1	1	yes	characteristic, complemented, Sylow
16	#322	—	109	1	no	maximal, Sylow
17	C₄×C₈	—	109	2	no	—
18	C₄×C₈	D₁₀₉	1	1	yes	characteristic
19	C₂×C₈	—	109	4	no	—
20	C₂×C₈	Dic₁₀₉	1	2	yes	—
21	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
22	C₂×C₄	C₄×D₁₀₉	1	2	yes	—
23	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
24	C₈	—	218	4	no	—
25	C₈	#11724784	1	4	yes	complemented
26	C₂²	C₄×Dic₁₀₉	1	1	yes	characteristic
27	C₄	C₂×#11724784	1	2	yes	—
28	C₄	#13182012	1	4	yes	—
29	C₂	C₄×#11724784	1	1	yes	characteristic
30	C₂	#16812609	1	2	yes	—

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