Subgroups — #20243294

Order 6016.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093960	C₂	1	2	yes	maximal
2	C₄×#10625329	C₂	1	2	yes	maximal
3	#15688888	C₂	1	2	yes	maximal
4	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625329	C₂²	1	4	yes	—
6	#13093960	C₄	1	8	yes	complemented
7	#13093935	—	2	2	no	—
8	C₄×C₄₇⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	#97×C₄₇	C₄	1	4	yes	—
13	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
14	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₄₇	—	2	2	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
19	C₄²×C₄₇	C₂×C₄	1	2	yes	—
20	C₄²×C₄₇	D₄	1	2	yes	—
21	#10625329	—	2	4	no	—
22	#10625329	C₂×C₄	1	8	yes	—
23	C₂×C₄₇⋊C₈	—	2	4	no	—
24	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	#41	1	2	yes	—
31	C₈×C₄₇	—	2	2	no	—
32	C₈×C₄₇	C₄²	1	4	yes	—
33	C₄₇⋊C₈	—	2	8	no	—
34	C₂²×C₄₇	—	2	2	no	—
35	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄₇	C₄×Q₈	1	2	yes	—
37	C₄×C₄₇	—	2	4	no	—
38	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₄₇	#117	1	1	yes	characteristic
40	C₄×C₄₇	C₄×D₄	1	2	yes	—
41	#1778	—	47	1	no	maximal, Sylow
42	C₂×C₄₇	—	2	2	no	—
43	C₂×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄₇	#430	1	2	yes	—
45	C₂×#108	—	47	2	no	—
46	C₄×M₁₆	—	47	2	no	—
47	C₂×#97	D₄₇	1	1	yes	characteristic
48	#341	—	47	2	no	—
49	C₄₇	#1778	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	47	4	no	—
51	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
53	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
54	#108	—	47	8	no	—
55	#97	—	94	2	no	—
56	#97	Dic₄₇	1	4	yes	—
57	C₄×C₈	—	94	2	no	—
58	C₂²×C₄	Dic₉₄	1	2	yes	—
59	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
60	M₁₆	—	47	8	no	—
61	M₁₆	—	94	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	94	4	no	—
64	C₂×C₈	C₄×D₄₇	1	4	yes	—
65	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
66	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
67	C₄²	D₁₈₈	1	2	yes	—
68	C₄²	C₂×Dic₄₇	1	2	yes	—
69	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₄₇	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
73	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
74	C₂×C₄	#10625350	1	2	yes	—
75	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	94	8	no	—
78	C₈	C₄×Dic₄₇	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
81	C₂²	C₄×Dic₉₄	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
84	C₄	#13093983	1	1	yes	characteristic
85	C₄	C₄×D₁₈₈	1	2	yes	—
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
88	C₂	#15689172	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	#1778
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #13093960	C₄	semidirect
49. C₄₇	#1778	semidirect