Subgroups — #20241548

Order 6016.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688920	C₂	1	1	yes	maximal, characteristic
2	#15688918	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#497	C₂	1	1	yes	maximal, characteristic
4	#13093943	—	2	1	no	—
5	#13093939	—	2	1	no	—
6	C₂×Q₁₆×C₄₇	—	2	1	no	—
7	C₂×SD₁₆×C₄₇	—	2	1	no	—
8	C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
9	#124×C₄₇	C₂²	1	1	yes	characteristic
10	#97×C₄₇	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₄₇	—	2	1	no	—
12	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
13	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
14	Q₁₆×C₄₇	—	4	2	no	—
15	SD₁₆×C₄₇	—	4	2	no	—
16	C₂×C₈×C₄₇	—	2	1	no	—
17	C₄⋊C₄×C₄₇	—	4	1	no	—
18	C₂²⋊C₄×C₄₇	—	4	1	no	—
19	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊Dic₄₇	—	4	1	no	—
21	#10625329	—	4	1	no	—
22	C₂³×C₄₇	—	2	1	no	—
23	Q₈×C₄₇	—	4	1	no	—
24	Q₈×C₄₇	—	4	1	no	—
25	Q₈×C₄₇	—	4	1	no	—
26	D₄×C₄₇	—	4	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₄₇	—	8	1	no	—
32	C₈×C₄₇	—	2	2	no	—
33	C₄₇⋊C₈	—	8	1	no	—
34	C₂²×C₄₇	—	4	1	no	—
35	C₂²×C₄₇	—	8	1	no	—
36	C₂²×C₄₇	#99	1	1	yes	characteristic
37	C₄×C₄₇	—	2	1	no	—
38	C₄×C₄₇	—	4	1	no	—
39	C₄×C₄₇	—	4	1	no	—
40	C₄×C₄₇	—	8	1	no	—
41	Dic₄₇	—	16	1	no	—
42	#1407	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	—	2	1	no	—
44	C₂×C₄₇	—	8	1	no	—
45	C₂×C₄₇	#353	1	1	yes	characteristic
46	#497	D₄₇	1	1	yes	characteristic
47	#355	—	47	1	no	—
48	#354	—	47	1	no	—
49	C₄₇	#1407	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×SD₁₆	—	2	1	no	—
52	C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
53	#124	C₂×D₄₇	1	1	yes	characteristic
54	#101	—	94	1	no	—
55	#99	—	94	1	no	—
56	#97	Dic₄₇	1	1	yes	characteristic, complemented
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
60	Q₁₆	—	4	2	no	—
61	SD₁₆	—	4	2	no	—
62	M₁₆	—	188	1	no	—
63	C₂×C₈	—	2	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	188	1	no	—
67	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	4	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	376	1	no	—
77	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₈	—	376	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#13093939	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	752	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#15688916	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688916
commutator	C₄²×C₄₇	C₂×C₄
Frattini	#124	C₂×D₄₇
Fitting	C₄₇×#497	C₂
socle	C₂×C₄₇	#353
hypercenter	#497	D₄₇
hypocenter	C₄₇	#1407
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #497

Complements

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

N	H ≅ G/N	type
8. C₄⋊Q₈×C₄₇	C₄	semidirect
10. #97×C₄₇	C₄	semidirect
49. C₄₇	#1407	semidirect
52. C₄⋊Q₈	Dic₄₇	semidirect
56. #97	Dic₄₇	semidirect