Subgroups — #19151978

Order 5696.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₅₆	C₂	1	4	yes	maximal
2	#15668012	C₂	1	2	yes	maximal
3	C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₈	C₂²	1	4	yes	—
5	Dic₃₅₆	—	2	8	no	—
6	C₄⋊Dic₈₉	—	2	4	no	—
7	C₂×C₈×C₈₉	C₂²	1	2	yes	—
8	C₄²×C₈₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈₉	D₄	1	2	yes	—
10	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
11	C₂×Dic₈₉	—	2	4	no	—
12	Dic₁₇₈	—	2	8	no	—
13	C₈×C₈₉	D₄	1	4	yes	—
14	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
15	C₄×C₈₉	Q₁₆	1	4	yes	complemented
16	C₄×C₈₉	C₂×D₄	1	2	yes	—
17	Dic₈₉	—	4	4	no	—
18	C₂×C₈₉	#127	1	1	yes	characteristic
19	C₂×C₈₉	C₂×Q₁₆	1	2	yes	—
20	C₈₉	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	89	1	no	maximal, Sylow
22	C₂×Q₁₆	—	89	4	no	—
23	C₄⋊Q₈	—	89	2	no	—
24	C₄×C₈	D₈₉	1	1	yes	characteristic
25	C₂×Q₈	—	89	4	no	—
26	Q₁₆	—	178	8	no	—
27	C₂×C₈	C₂×D₈₉	1	2	yes	—
28	C₄⋊C₄	—	178	4	no	—
29	C₄²	C₂×D₈₉	1	1	yes	characteristic
30	Q₈	—	178	8	no	—
31	C₂×C₄	—	178	4	no	—
32	C₂×C₄	D₃₅₆	1	2	yes	—
33	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
34	C₈	D₃₅₆	1	4	yes	—
35	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
36	C₄	—	356	4	no	—
37	C₄	Dic₃₅₆	1	4	yes	complemented
38	C₄	C₂×D₃₅₆	1	2	yes	—
39	C₂	#15668009	1	1	yes	characteristic
40	C₂	C₂×Dic₃₅₆	1	2	yes	—

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