Subgroups — #11857083

Order 1152.

1944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64078	C₂	1	6	yes	maximal
2	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic
3	#10592634	C₂	1	8	yes	maximal
4	#73311	—	3	4	no	maximal
5	C₂²×#634	C₂²	1	4	yes	—
6	C₂×C₃²×C₄²	C₂²	1	3	yes	—
7	C₂×C₃²×C₄²	C₂²	1	4	yes	—
8	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	24	yes	—
9	#64078	—	2	24	no	—
10	C₂×#869	—	3	24	no	—
11	C₃×C₄³	D₃	1	4	yes	—
12	#4935	—	3	32	no	—
13	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
14	C₂²×C₃²×C₄	C₂³	1	6	yes	—
15	C₂²×C₃⋊Dic₃	C₂³	1	8	yes	—
16	C₂×#634	—	2	24	no	—
17	C₃²×C₄²	D₄	1	12	yes	—
18	C₃²×C₄²	Q₈	1	16	yes	complemented
19	C₄⋊(C₃⋊Dic₃)	—	2	48	no	—
20	#2868	—	9	1	no	Sylow
21	C₂²×Dic₆	—	3	16	no	—
22	C₂×C₃×C₄²	C₂×D₃	1	16	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	12	yes	—
24	C₂×C₄⋊Dic₃	—	3	96	no	—
25	#869	—	6	96	no	—
26	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
27	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
28	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
29	C₂×C₃²×C₄	C₂×Q₈	1	24	yes	—
30	C₂×C₃⋊Dic₃	—	2	24	no	—
31	#634	—	4	16	no	—
32	C₂×C₄⋊Q₈	—	9	6	no	—
33	#384	—	9	8	no	—
34	C₄³	C₃⋊D₃	1	1	yes	characteristic
35	C₂²×C₃×C₄	C₂²×D₃	1	24	yes	—
36	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
37	C₂²×Dic₃	—	3	32	no	—
38	C₂×Dic₆	—	6	96	no	—
39	C₃×C₄²	Dic₆	1	64	yes	complemented
40	C₃×C₄²	D₁₂	1	48	yes	—
41	C₄⋊Dic₃	—	6	192	no	—
42	C₂²×C₃²	C₂²×D₄	1	3	yes	—
43	C₂²×C₃²	C₂²×Q₈	1	4	yes	—
44	C₃²×C₄	#127	1	4	yes	—
45	C₃²×C₄	C₄⋊Q₈	1	24	yes	complemented
46	C₃⋊Dic₃	—	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×C₃⋊D₃	1	4	yes	—
51	C₂×C₄²	C₂×C₃⋊D₃	1	3	yes	—
52	C₂³×C₃	C₂³×D₃	1	4	yes	—
53	C₂×C₃×C₄	C₂×Dic₆	1	96	yes	—
54	C₂×C₃×C₄	C₂×D₁₂	1	48	yes	—
55	C₂×C₃×C₄	C₂×D₁₂	1	24	yes	—
56	C₂×Dic₃	—	6	96	no	—
57	Dic₆	—	12	64	no	—
58	C₂×C₃²	C₂×#127	1	1	yes	characteristic
59	C₂×C₃²	C₂×C₄⋊Q₈	1	6	yes	—
60	C₂×Q₈	—	18	24	no	—
61	C₂²×C₄	—	9	8	no	—
62	C₂²×C₄	C₂²×C₃⋊D₃	1	6	yes	—
63	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
64	C₄⋊C₄	—	18	48	no	—
65	C₄²	#634	1	16	yes	complemented
66	C₄²	C₄⋊(C₃⋊D₃)	1	12	yes	—
67	C₂²×C₃	C₂²×Dic₆	1	16	yes	—
68	C₂²×C₃	C₂²×D₁₂	1	12	yes	—
69	C₃×C₄	#869	1	96	yes	complemented
70	C₃×C₄	#874	1	16	yes	—
71	Dic₃	—	12	32	no	—
72	C₃²	#2868	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂³×C₃⋊D₃	1	1	yes	characteristic
74	Q₈	—	36	16	no	—
75	C₂×C₄	—	18	24	no	—
76	C₂×C₄	C₂×#634	1	24	yes	—
77	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	12	yes	—
78	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	6	yes	—
79	C₂×C₃	C₂×#869	1	24	yes	—
80	C₂×C₃	C₂×#874	1	4	yes	—
81	C₂²	C₂²×#634	1	4	yes	—
82	C₂²	C₂²×C₄⋊(C₃⋊D₃)	1	3	yes	—
83	C₄	—	36	8	no	—
84	C₄	#64078	1	24	yes	complemented
85	C₄	#64083	1	4	yes	—
86	C₃	#73311	1	4	yes	complemented
87	C₂	C₂×#64078	1	6	yes	—
88	C₂	C₂×#64083	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×C₃⋊D₃
commutator, socle, prime radical, cosocle	C₂³×C₃²	C₂⁴
Fitting	C₃²×C₄³	C₂
hypercenter	C₄³	C₃⋊D₃
hypocenter	C₃²	#2868
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
18. C₃²×C₄²	Q₈	semidirect
39. C₃×C₄²	Dic₆	semidirect
45. C₃²×C₄	C₄⋊Q₈	semidirect
65. C₄²	#634	semidirect
69. C₃×C₄	#869	semidirect
72. C₃²	#2868	semidirect
84. C₄	#64078	semidirect
86. C₃	#73311	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64078	2
C₃²×C₄³	2
#10592634	2
#73311	3