Subgroups — #20241470

Order 6016.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093964	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093964	—	2	2	no	—
4	#13093964	C₄	1	4	yes	complemented
5	C₂×C₄₇⋊C₁₆	—	2	2	no	—
6	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₄₇	C₄	1	1	yes	characteristic
9	C₄×C₈×C₄₇	—	2	2	no	—
10	C₂²×C₄×C₄₇	—	2	1	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	—	2	1	no	—
14	C₂×C₈×C₄₇	C₈	1	2	yes	—
15	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	D₄	1	2	yes	—
18	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
19	C₄²×C₄₇	—	2	1	no	—
20	C₄²×C₄₇	C₈	1	2	yes	—
21	C₄₇⋊C₁₆	—	2	4	no	—
22	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₄₇	—	2	4	no	—
24	C₂×C₄×C₄₇	—	2	2	no	—
25	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
31	C₈×C₄₇	—	2	2	no	—
32	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
33	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
34	C₂²×C₄₇	—	2	2	no	—
35	C₂²×C₄₇	#97	1	1	yes	characteristic
36	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₄₇	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₄₇	—	2	4	no	—
39	C₄×C₄₇	#95	1	1	yes	characteristic
40	C₄×C₄₇	C₄×C₈	1	1	yes	characteristic
41	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
43	#1376	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	—	2	1	no	—
45	C₂×C₄₇	—	2	1	no	—
46	C₂×C₄₇	#336	1	1	yes	characteristic
47	C₂×C₄₇	#364	1	2	yes	—
48	C₂×M₃₂	—	47	2	no	—
49	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
50	C₄₇	#1376	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
53	C₂×C₄²	Dic₄₇	1	1	yes	characteristic
54	M₃₂	—	47	4	no	—
55	M₃₂	—	94	2	no	—
56	C₂×C₁₆	—	94	2	no	—
57	C₄×C₈	—	2	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₄₇⋊C₈	1	2	yes	—
63	C₂×C₈	Dic₉₄	1	1	yes	characteristic
64	C₂×C₈	C₄×D₄₇	1	2	yes	—
65	C₂×C₈	D₁₈₈	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
67	C₄²	—	2	1	no	—
68	C₄²	C₄₇⋊C₈	1	2	yes	—
69	C₁₆	—	94	4	no	—
70	C₂³	#10625329	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
75	C₂×C₄	#10625329	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
77	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	Dic₄₇⋊C₄	1	2	yes	—
81	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#13093935	1	1	yes	characteristic
84	C₂²	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
85	C₂²	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄₇⋊#95	1	1	yes	characteristic
88	C₄	C₄×C₄₇⋊C₈	1	1	yes	characteristic
89	C₄	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
90	C₄	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#15688878	1	1	yes	characteristic
94	C₂	#15688944	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₁₈₈
commutator	C₄×C₄₇	C₄×C₈
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₄⋊C₈
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1376
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #13093964	C₄	semidirect
50. C₄₇	#1376	semidirect