Subgroups — #26132700

Order 12032.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245154	C₂	1	3	yes	maximal
2	#20245147	C₂	1	3	yes	maximal
3	C₄₇×#1747	C₂	1	1	yes	maximal, characteristic
4	C₂×#13093964	C₂²	1	3	yes	—
5	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
6	#15688944	—	2	6	no	—
7	C₄⋊(C₄₇⋊C₁₆)	—	2	6	no	—
8	C₄₇×#405	C₂²	1	3	yes	—
9	C₄₇×#338	C₄	1	1	yes	characteristic
10	C₄₇×H(3,ℤ/4)	C₄	1	3	yes	—
11	#13093964	—	2	6	no	—
12	C₂×C₄₇⋊C₁₆	—	2	3	no	—
13	C₂×C₄₇⋊C₁₆	—	2	3	no	—
14	C₂×M₁₆×C₄₇	C₂×C₄	1	3	yes	—
15	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
16	#117×C₄₇	C₂×C₄	1	3	yes	—
17	#97×C₄₇	Q₈	1	6	yes	—
18	C₄×C₈×C₄₇	D₄	1	6	yes	—
19	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
20	M₁₆×C₄₇	—	2	6	no	—
21	C₂×C₈×C₄₇	C₄⋊C₄	1	6	yes	—
22	C₂×C₈×C₄₇	C₂×D₄	1	3	yes	—
23	C₂×C₈×C₄₇	C₂×Q₈	1	3	yes	—
24	C₄⋊C₄×C₄₇	—	2	3	no	—
25	C₂²⋊C₄×C₄₇	—	2	3	no	—
26	C₄²×C₄₇	C₄⋊C₄	1	6	yes	—
27	C₄₇⋊C₁₆	—	4	1	no	—
28	C₄₇⋊C₁₆	—	4	3	no	—
29	C₂³×C₄₇	#131	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	2	6	no	—
31	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₄₇	#131	1	3	yes	—
33	C₈×C₄₇	—	2	6	no	—
34	C₈×C₄₇	#127	1	1	yes	characteristic
35	C₈×C₄₇	C₄⋊Q₈	1	3	yes	—
36	#12902	—	47	1	no	maximal, Sylow
37	C₂²×C₄₇	—	4	1	no	—
38	C₂²×C₄₇	#424	1	3	yes	—
39	C₄×C₄₇	—	4	6	no	—
40	C₄×C₄₇	#384	1	1	yes	characteristic
41	C₄×C₄₇	#424	1	3	yes	—
42	#2153	—	47	3	no	—
43	#2151	—	47	3	no	—
44	#1747	D₄₇	1	1	yes	characteristic
45	C₂×C₄₇	—	2	3	no	—
46	C₂×C₄₇	#1843	1	1	yes	characteristic
47	C₂×M₃₂	—	47	3	no	—
48	C₂²×C₁₆	—	47	1	no	—
49	#405	C₂×D₄₇	1	3	yes	—
50	#364	—	94	6	no	—
51	C₄⋊C₁₆	—	94	6	no	—
52	#338	Dic₄₇	1	1	yes	characteristic
53	H(3,ℤ/4)	Dic₄₇	1	3	yes	—
54	C₄₇	#12902	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₁₆	C₂×Dic₄₇	1	3	yes	—
56	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
57	#117	C₂×Dic₄₇	1	3	yes	—
58	M₃₂	—	94	6	no	—
59	C₂×C₁₆	—	94	3	no	—
60	C₂×C₁₆	—	94	3	no	—
61	#97	Dic₉₄	1	6	yes	—
62	C₄×C₈	D₁₈₈	1	6	yes	—
63	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
64	M₁₆	—	2	6	no	—
65	C₂×C₈	C₄⋊Dic₄₇	1	6	yes	—
66	C₂×C₈	C₂×Dic₉₄	1	3	yes	—
67	C₂×C₈	C₂×D₁₈₈	1	3	yes	—
68	C₄⋊C₄	—	2	3	no	—
69	C₂²⋊C₄	—	2	3	no	—
70	C₄²	C₄⋊Dic₄₇	1	6	yes	—
71	C₁₆	—	188	1	no	—
72	C₁₆	—	188	3	no	—
73	C₂³	#13094031	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	C₂×C₄⋊Dic₄₇	1	3	yes	—
76	C₂×C₄	#13094031	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	#13094021	1	1	yes	characteristic
79	C₈	#13094024	1	3	yes	—
80	C₂²	—	4	1	no	—
81	C₂²	#15689150	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	#15688993	1	1	yes	characteristic
84	C₄	#15689150	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	#20243542	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13094021
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1747	C₂
socle	C₂×C₄₇	#1843
prime radical	C₂³×C₄₇	#131
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1747	D₄₇
hypocenter	C₄₇	#12902
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1747

Complements

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

N	H ≅ G/N	type
54. C₄₇	#12902	semidirect

Maximal subgroups

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

subgroup	index
#20245154	2
#20245147	2
C₄₇×#1747	2
#12902	47