Subgroups — #19151968

Order 5696.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668012	C₂	1	1	yes	maximal, characteristic
2	#15667935	C₂	1	4	yes	maximal
3	#15667923	C₂	1	1	yes	maximal, characteristic
4	#125×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₇₈	C₂²	1	2	yes	—
6	C₂×#10623494	C₂²	1	2	yes	—
7	C₄⋊Dic₈₉	—	2	2	no	—
8	C₄⋊C₄×C₈₉	—	2	2	no	—
9	C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
10	C₄²×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈₉	—	2	2	no	—
12	C₂×C₄×C₈₉	D₄	1	2	yes	—
13	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
14	C₂×Dic₈₉	—	2	2	no	—
15	Dic₁₇₈	—	2	4	no	—
16	#10623494	—	2	2	no	—
17	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
18	C₄×C₈₉	—	2	2	no	—
19	C₄×C₈₉	—	4	2	no	—
20	C₄×C₈₉	#41	1	2	yes	—
21	Dic₈₉	—	4	2	no	—
22	C₂×C₈₉	#124	1	1	yes	characteristic
23	C₂×C₈₉	#137	1	2	yes	—
24	C₈₉	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	89	1	no	maximal, Sylow
26	C₄⋊Q₈	—	89	1	no	—
27	#125	D₈₉	1	1	yes	characteristic
28	#103	—	89	4	no	—
29	#97	—	89	1	no	—
30	C₂×Q₈	—	89	2	no	—
31	C₂×C₈	—	89	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	178	2	no	—
34	C₄⋊C₄	C₂×D₈₉	1	2	yes	—
35	C₄²	C₂×D₈₉	1	1	yes	characteristic
36	Q₈	—	178	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	178	2	no	—
39	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
40	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
41	C₈	—	178	2	no	—
42	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	356	2	no	—
46	C₄	#13083575	1	2	yes	—
47	C₂	#15668001	1	1	yes	characteristic
48	C₂	#15668042	1	2	yes	—

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

N	H ≅ G/N	type
24. C₈₉	#491	semidirect