Subgroups — #20244493

Order 6016.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689923	C₂	1	3	yes	maximal, complemented
2	#15689091	C₂	1	3	yes	maximal, complemented
3	C₄₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625350	C₂²	1	3	yes	—
5	#13094057	—	2	6	no	—
6	#13094052	—	2	6	no	—
7	#13094046	—	2	6	no	—
8	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	(C₂×D₄₇)⋊C₈	—	2	6	no	—
10	C₂×M₁₆×C₄₇	C₂²	1	3	yes	—
11	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₇	—	2	3	no	—
13	#10625350	—	2	6	no	—
14	#10625350	—	2	6	no	—
15	C₂×D₁₈₈	D₄	1	3	yes	—
16	C₂×C₄×D₄₇	—	2	3	no	—
17	C₂×Dic₉₄	D₄	1	3	yes	—
18	M₁₆×C₄₇	—	2	6	no	—
19	C₂×C₈×C₄₇	D₄	1	6	yes	—
20	C₂×C₄₇⋊C₈	—	2	3	no	—
21	Dic₁₈₈	—	2	6	no	—
22	D₃₇₆	—	2	6	no	—
23	#10625325	—	2	12	no	—
24	C₂³×C₄₇	#41	1	1	yes	characteristic
25	C₂²×D₄₇	—	2	3	no	—
26	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
28	C₂²⋊D₄₇	—	4	6	no	—
29	C₂×Dic₄₇	—	2	3	no	—
30	D₁₈₈	—	2	6	no	—
31	C₄×D₄₇	—	4	3	no	—
32	C₄×D₄₇	—	4	3	no	—
33	Dic₉₄	—	2	6	no	—
34	C₈×C₄₇	—	2	6	no	—
35	C₄₇⋊C₈	—	4	1	no	—
36	C₂²×C₄₇	—	4	1	no	—
37	C₂²×C₄₇	#121	1	3	yes	—
38	C₂×D₄₇	—	4	6	no	—
39	C₂×D₄₇	—	4	3	no	—
40	C₄×C₄₇	#120	1	3	yes	—
41	C₄×C₄₇	#127	1	1	yes	characteristic
42	Dic₄₇	—	4	3	no	—
43	#2017	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	—	2	3	no	—
45	C₂×C₄₇	#392	1	1	yes	characteristic
46	D₄₇	—	8	3	no	—
47	#575	—	47	3	no	—
48	#408	—	47	3	no	—
49	#338	D₄₇	1	1	yes	characteristic, complemented
50	C₄₇	#2017	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	47	3	no	—
52	#137	—	94	6	no	—
53	AGL(1,ℤ/8)	—	94	6	no	—
54	#135	—	94	6	no	—
55	C₂×M₁₆	C₂×D₄₇	1	3	yes	—
56	C₂²×C₈	—	47	1	no	—
57	C₂²⋊C₈	—	94	6	no	—
58	#41	—	94	6	no	—
59	#41	—	94	6	no	—
60	C₂×Q₈	—	47	3	no	—
61	C₂×D₄	—	47	3	no	—
62	C₂×D₄	—	94	3	no	—
63	C₂²×C₄	—	94	3	no	—
64	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
65	Q₁₆	—	94	6	no	—
66	SD₁₆	—	94	12	no	—
67	D₈	—	94	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	94	3	no	—
70	C₂×C₈	D₁₈₈	1	6	yes	—
71	C₂³	—	94	3	no	—
72	C₂³	#10625354	1	1	yes	characteristic
73	Q₈	—	94	6	no	—
74	D₄	—	94	6	no	—
75	D₄	—	188	6	no	—
76	C₂×C₄	—	94	3	no	—
77	C₂×C₄	—	188	3	no	—
78	C₂×C₄	—	188	3	no	—
79	C₂×C₄	C₂×D₁₈₈	1	3	yes	—
80	C₂×C₄	D₄×D₄₇	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	188	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	188	6	no	—
85	C₂²	—	188	3	no	—
86	C₂²	#13093999	1	3	yes	—
87	C₄	—	188	3	no	—
88	C₄	#13093994	1	3	yes	—
89	C₄	#13094021	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	376	3	no	—
92	C₂	#15689033	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13094021
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#338	C₂
socle	C₂×C₄₇	#392
hypercenter	#338	D₄₇
hypocenter	C₄₇	#2017
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #15689923	C₂	semidirect
2. #15689091	C₂	semidirect
3. C₄₇×#338	C₂	semidirect
49. #338	D₄₇	semidirect
50. C₄₇	#2017	semidirect