Subgroups — D₄×#6898 #14517813

Order 1944.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6898	C₂	1	2	yes	maximal, complemented
2	C₄×#6898	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
4	D₄×C₃²⋊C₉	C₃	1	4	yes	maximal
5	D₄×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×#6898	—	2	2	no	—
7	C₂×#6898	C₂²	1	1	yes	characteristic
8	C₂²×C₉⋊C₉	C₂×C₃	1	16	yes	complemented
9	C₂²×C₃²⋊C₉	C₂×C₃	1	8	yes	—
10	C₂²×C₉²	C₂×C₃	1	2	yes	complemented
11	C₄×C₉⋊C₉	C₂×C₃	1	8	yes	complemented
12	C₄×C₃²⋊C₉	C₂×C₃	1	4	yes	—
13	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
14	#6898	D₄	1	1	yes	characteristic, direct product factor, Sylow
15	C₃³×D₄	C₃²	1	1	yes	characteristic
16	C₃×D₄×C₉	C₃²	1	4	yes	—
17	C₃×D₄×C₉	C₃²	1	8	yes	—
18	C₂×C₉⋊C₉	—	2	16	no	—
19	C₂×C₉⋊C₉	C₂²×C₃	1	8	yes	—
20	C₂×C₃²⋊C₉	—	2	8	no	—
21	C₂×C₃²⋊C₉	C₂²×C₃	1	4	yes	—
22	C₂×C₉²	—	2	2	no	—
23	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
24	C₂²×C₃³	C₂×C₃²	1	2	yes	—
25	C₃³×C₄	C₂×C₃²	1	1	yes	characteristic
26	C₂²×C₃×C₉	C₂×C₃²	1	8	yes	—
27	C₂²×C₃×C₉	C₂×C₃²	1	16	yes	—
28	C₃×C₄×C₉	C₂×C₃²	1	4	yes	—
29	C₃×C₄×C₉	C₂×C₃²	1	8	yes	—
30	C₉⋊C₉	C₃×D₄	1	8	yes	complemented
31	C₃²⋊C₉	C₃×D₄	1	4	yes	—
32	C₉²	C₃×D₄	1	1	yes	characteristic, complemented
33	C₃²×D₄	—	3	4	no	—
34	C₃²×D₄	C₃³	1	1	yes	characteristic
35	D₄×C₉	—	3	4	no	—
36	D₄×C₉	—	3	8	no	—
37	C₂×C₃³	—	2	2	no	—
38	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
39	C₂×C₃×C₉	—	2	8	no	—
40	C₂×C₃×C₉	—	2	16	no	—
41	C₂×C₃×C₉	C₂²×C₃²	1	4	yes	—
42	C₂×C₃×C₉	C₂²×C₃²	1	8	yes	—
43	C₂²×C₃²	—	3	8	no	—
44	C₂²×C₃²	C₂×C₃³	1	2	yes	—
45	C₃²×C₄	—	3	4	no	—
46	C₃²×C₄	C₂×C₃³	1	1	yes	characteristic
47	C₂²×C₉	—	3	8	no	—
48	C₂²×C₉	—	3	16	no	—
49	C₄×C₉	—	3	4	no	—
50	C₄×C₉	—	3	8	no	—
51	C₃³	C₃²×D₄	1	1	yes	characteristic
52	C₃×C₉	C₃²×D₄	1	4	yes	—
53	C₃×C₉	C₃²×D₄	1	8	yes	—
54	C₃×D₄	—	9	1	no	—
55	C₃×D₄	#737	1	4	yes	—
56	C₂×C₃²	—	2	2	no	—
57	C₂×C₃²	—	3	4	no	—
58	C₂×C₃²	—	6	8	no	—
59	C₂×C₃²	C₂²×C₃³	1	1	yes	characteristic
60	C₂×C₉	—	3	4	no	—
61	C₂×C₉	—	3	8	no	—
62	C₂×C₉	—	6	8	no	—
63	C₂×C₉	—	6	16	no	—
64	C₂²×C₃	—	9	2	no	—
65	C₂²×C₃	C₂×#737	1	8	yes	—
66	C₃×C₄	—	9	1	no	—
67	C₃×C₄	C₂×#737	1	4	yes	—
68	C₃²	—	3	4	no	—
69	C₃²	C₃³×D₄	1	1	yes	characteristic
70	C₉	—	3	4	no	—
71	C₉	—	3	8	no	—
72	D₄	#6898	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₃	—	2	8	no	—
74	C₂×C₃	—	9	1	no	—
75	C₂×C₃	—	18	2	no	—
76	C₂×C₃	C₂²×#737	1	4	yes	—
77	C₂²	C₂×#6898	1	2	yes	complemented
78	C₄	C₂×#6898	1	1	yes	characteristic, complemented
79	C₃	—	9	1	no	—
80	C₃	D₄×#737	1	4	yes	—
81	C₂	—	2	2	no	—
82	C₂	C₂²×#6898	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂×C₃²	C₂²×C₃³
prime radical	C₃³×D₄	C₃²
LCS	G ▷ C₂×C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#6898	C₂	semidirect
2. C₄×#6898	C₂	semidirect
3. D₄×C₉⋊C₉	C₃	semidirect
5. D₄×C₉²	C₃	semidirect
8. C₂²×C₉⋊C₉	C₂×C₃	semidirect
10. C₂²×C₉²	C₂×C₃	semidirect
11. C₄×C₉⋊C₉	C₂×C₃	semidirect
13. C₄×C₉²	C₂×C₃	semidirect
14. #6898	D₄	direct (N × H)
30. C₉⋊C₉	C₃×D₄	semidirect
32. C₉²	C₃×D₄	semidirect
72. D₄	#6898	direct (N × H)
77. C₂²	C₂×#6898	semidirect
78. C₄	C₂×#6898	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#6898	2
C₄×#6898	2
D₄×C₉⋊C₉	3
D₄×C₃²⋊C₉	3
D₄×C₉²	3

Subgroups — D4×#6898 #14517813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#6898 #14517813