Subgroups — #11857082

Order 1152.

972 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63431	C₂	1	6	yes	maximal
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
3	#10588615	C₂	1	8	yes	maximal
4	#73311	—	3	1	no	maximal
5	C₂²×Dic₁₈	C₂²	1	4	yes	—
6	C₂×C₄²×C₉	C₂²	1	3	yes	—
7	C₂×C₄²×C₉	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₉	C₂²	1	24	yes	—
9	#63431	—	2	24	no	—
10	C₂×#869	—	3	6	no	—
11	C₃×C₄³	D₃	1	1	yes	characteristic
12	#4935	—	3	8	no	—
13	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₉	C₂³	1	6	yes	—
15	C₂²×Dic₉	C₂³	1	8	yes	—
16	C₂×Dic₁₈	—	2	24	no	—
17	C₄²×C₉	D₄	1	12	yes	—
18	C₄²×C₉	Q₈	1	16	yes	complemented
19	C₄⋊Dic₉	—	2	48	no	—
20	#2868	—	9	1	no	Sylow
21	C₂²×Dic₆	—	3	4	no	—
22	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
24	C₂×C₄⋊Dic₃	—	3	24	no	—
25	#869	—	6	24	no	—
26	C₂³×C₉	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
28	C₂×C₄×C₉	C₂×D₄	1	12	yes	—
29	C₂×C₄×C₉	C₂×Q₈	1	24	yes	—
30	C₂×Dic₉	—	2	24	no	—
31	Dic₁₈	—	4	16	no	—
32	C₂×C₄⋊Q₈	—	9	6	no	—
33	#384	—	9	8	no	—
34	C₄³	D₉	1	1	yes	characteristic
35	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
36	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
37	C₂²×Dic₃	—	3	8	no	—
38	C₂×Dic₆	—	6	24	no	—
39	C₃×C₄²	Dic₆	1	16	yes	—
40	C₃×C₄²	D₁₂	1	12	yes	—
41	C₄⋊Dic₃	—	6	48	no	—
42	C₂²×C₉	C₂²×D₄	1	3	yes	—
43	C₂²×C₉	C₂²×Q₈	1	4	yes	—
44	C₄×C₉	#127	1	4	yes	—
45	C₄×C₉	C₄⋊Q₈	1	24	yes	complemented
46	Dic₉	—	4	8	no	—
47	C₂²×Q₈	—	9	4	no	—
48	C₄⋊Q₈	—	18	24	no	—
49	C₂×C₄⋊C₄	—	9	24	no	—
50	C₂×C₄²	C₂×D₉	1	4	yes	—
51	C₂×C₄²	C₂×D₉	1	3	yes	—
52	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
53	C₂×C₃×C₄	C₂×Dic₆	1	24	yes	—
54	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	—
55	C₂×C₃×C₄	C₂×D₁₂	1	6	yes	—
56	C₂×Dic₃	—	6	24	no	—
57	Dic₆	—	12	16	no	—
58	C₂×C₉	C₂×#127	1	1	yes	characteristic
59	C₂×C₉	C₂×C₄⋊Q₈	1	6	yes	—
60	C₂×Q₈	—	18	24	no	—
61	C₂²×C₄	—	9	8	no	—
62	C₂²×C₄	C₂²×D₉	1	6	yes	—
63	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
64	C₄⋊C₄	—	18	48	no	—
65	C₄²	Dic₁₈	1	16	yes	complemented
66	C₄²	D₃₆	1	12	yes	—
67	C₂²×C₃	C₂²×Dic₆	1	4	yes	—
68	C₂²×C₃	C₂²×D₁₂	1	3	yes	—
69	C₃×C₄	#869	1	24	yes	—
70	C₃×C₄	#874	1	4	yes	—
71	Dic₃	—	12	8	no	—
72	C₉	#2868	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂³×D₉	1	1	yes	characteristic
74	Q₈	—	36	16	no	—
75	C₂×C₄	—	18	24	no	—
76	C₂×C₄	C₂×Dic₁₈	1	24	yes	—
77	C₂×C₄	C₂×D₃₆	1	12	yes	—
78	C₂×C₄	C₂×D₃₆	1	6	yes	—
79	C₂×C₃	C₂×#869	1	6	yes	—
80	C₂×C₃	C₂×#874	1	1	yes	characteristic
81	C₂²	C₂²×Dic₁₈	1	4	yes	—
82	C₂²	C₂²×D₃₆	1	3	yes	—
83	C₄	—	36	8	no	—
84	C₄	#63431	1	24	yes	complemented
85	C₄	#63436	1	4	yes	—
86	C₃	#73311	1	1	yes	characteristic
87	C₂	C₂×#63431	1	6	yes	—
88	C₂	C₂×#63436	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂³×C₉	C₂⁴
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₄³×C₉	C₂
hypercenter	C₄³	D₉
hypocenter	C₉	#2868
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
18. C₄²×C₉	Q₈	semidirect
45. C₄×C₉	C₄⋊Q₈	semidirect
65. C₄²	Dic₁₈	semidirect
72. C₉	#2868	semidirect
84. C₄	#63431	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63431	2
C₄³×C₉	2
#10588615	2
#73311	3