Subgroups — #11782417

Order 1152.

321 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588375	C₂	1	3	yes	maximal
2	#10588360	C₂	1	3	yes	maximal, complemented
3	C₈²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#68057	—	3	1	no	maximal
5	C₂×#3664	—	2	6	no	—
6	#63436	C₂²	1	1	yes	characteristic
7	#63431	C₂²	1	3	yes	—
8	C₄×C₈×C₉	C₂²	1	3	yes	—
9	#63377	—	2	6	no	—
10	#4693	—	3	3	no	—
11	#4680	—	3	3	no	—
12	C₃×C₈²	D₃	1	1	yes	characteristic
13	C₂×D₃₆	—	2	3	no	—
14	C₂×Dic₁₈	—	2	3	no	—
15	C₂×C₈×C₉	D₄	1	6	yes	—
16	C₄²×C₉	C₂³	1	1	yes	characteristic
17	C₄⋊Dic₉	—	2	6	no	—
18	#3664	—	4	12	no	—
19	#1705	—	9	1	no	Sylow
20	C₂×#204	—	6	6	no	—
21	#874	—	3	1	no	—
22	#869	—	3	3	no	—
23	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
24	#817	—	6	6	no	—
25	C₂²×D₉	—	4	1	no	—
26	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
27	C₂×Dic₉	—	4	3	no	—
28	D₃₆	—	4	6	no	—
29	Dic₁₈	—	4	6	no	—
30	C₈×C₉	SD₁₆	1	12	yes	complemented
31	#498	—	9	3	no	—
32	#492	—	9	3	no	—
33	C₈²	D₉	1	1	yes	characteristic, complemented
34	C₂×D₁₂	—	6	3	no	—
35	C₂×Dic₆	—	6	3	no	—
36	C₂×C₃×C₈	D₁₂	1	6	yes	—
37	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
38	C₄⋊Dic₃	—	6	6	no	—
39	#204	—	12	12	no	—
40	C₂²×C₉	#127	1	1	yes	characteristic
41	C₂×D₉	—	8	3	no	—
42	C₄×C₉	C₂×SD₁₆	1	6	yes	—
43	Dic₉	—	8	3	no	—
44	C₂×SD₁₆	—	18	6	no	—
45	C₄⋊Q₈	—	9	3	no	—
46	#127	—	9	1	no	—
47	#106	—	18	6	no	—
48	C₄×C₈	C₂×D₉	1	3	yes	—
49	C₂²×D₃	—	12	1	no	—
50	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
51	C₂×Dic₃	—	12	3	no	—
52	D₁₂	—	12	6	no	—
53	Dic₆	—	12	6	no	—
54	C₃×C₈	#204	1	12	yes	—
55	C₂×C₉	#492	1	3	yes	—
56	D₉	—	16	1	no	—
57	C₂×Q₈	—	18	3	no	—
58	C₂×D₄	—	18	3	no	—
59	SD₁₆	—	36	12	no	—
60	C₂×C₈	D₃₆	1	6	yes	—
61	C₄⋊C₄	—	18	6	no	—
62	C₄²	C₂²×D₉	1	1	yes	characteristic
63	C₂²×C₃	#874	1	1	yes	characteristic
64	C₂×D₃	—	24	3	no	—
65	C₃×C₄	C₂×#204	1	6	yes	—
66	Dic₃	—	24	3	no	—
67	C₉	#1705	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	36	1	no	—
69	Q₈	—	36	6	no	—
70	D₄	—	36	6	no	—
71	C₂×C₄	—	36	3	no	—
72	C₂×C₄	C₂×D₃₆	1	3	yes	—
73	C₈	#3664	1	12	yes	complemented
74	C₂×C₃	#4693	1	3	yes	—
75	D₃	—	48	1	no	—
76	C₂²	—	72	3	no	—
77	C₂²	#63436	1	1	yes	characteristic
78	C₄	—	72	3	no	—
79	C₄	C₂×#3664	1	6	yes	—
80	C₃	#68057	1	1	yes	characteristic
81	C₂	—	144	1	no	—
82	C₂	#10588375	1	3	yes	—

	subgroup	G/H
center	C₂²	#63436
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₈²×C₉	C₂
socle	C₂²×C₃	#874
prime radical	#63436	C₂²
hypercenter	C₈²	D₉
hypocenter	C₉	#1705
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #10588360	C₂	semidirect
3. C₈²×C₉	C₂	semidirect
30. C₈×C₉	SD₁₆	semidirect
33. C₈²	D₉	semidirect
67. C₉	#1705	semidirect
73. C₈	#3664	semidirect

Maximal subgroups

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

subgroup	index
#10588375	2
#10588360	2
C₈²×C₉	2
#68057	3