Subgroups — #20243528

Order 6016.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093935	C₂	1	1	yes	maximal, characteristic
3	#15688887	C₂	1	4	yes	maximal
4	C₄₇×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625329	C₂²	1	2	yes	—
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
8	#13093935	C₄	1	4	yes	—
9	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₄₇	—	2	2	no	—
12	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
13	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
14	M₁₆×C₄₇	—	2	4	no	—
15	C₂×C₈×C₄₇	—	2	2	no	—
16	C₄²×C₄₇	C₂×C₄	1	2	yes	—
17	C₄²×C₄₇	D₄	1	2	yes	—
18	#10625329	—	2	4	no	—
19	C₂×C₄₇⋊C₈	—	2	2	no	—
20	C₂×C₄₇⋊C₈	—	2	2	no	—
21	C₂×C₄₇⋊C₈	—	2	2	no	—
22	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
23	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₄₇	—	4	2	no	—
25	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	#41	1	2	yes	—
29	C₂×C₄×C₄₇	#41	1	2	yes	—
30	C₈×C₄₇	—	4	2	no	—
31	C₄₇⋊C₈	—	2	4	no	—
32	C₄₇⋊C₈	—	4	2	no	—
33	C₂²×C₄₇	—	2	2	no	—
34	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄₇	#125	1	2	yes	—
36	C₄×C₄₇	—	2	4	no	—
37	C₄×C₄₇	#117	1	2	yes	—
38	C₄×C₄₇	#124	1	1	yes	characteristic
39	C₄×C₄₇	#124	1	1	yes	characteristic
40	#1838	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	—	2	2	no	—
42	C₂×C₄₇	#382	1	1	yes	characteristic
43	C₂×C₄₇	#430	1	2	yes	—
44	#423	—	47	1	no	—
45	#423	D₄₇	1	1	yes	characteristic
46	C₂×#97	—	47	1	no	—
47	#341	—	47	4	no	—
48	C₄₇	#1838	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	47	2	no	—
50	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
51	C₂²×C₈	—	47	2	no	—
52	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	94	2	no	—
55	#97	—	47	4	no	—
56	C₂²×C₄	Dic₉₄	1	2	yes	—
57	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	94	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	47	4	no	—
62	C₂×C₈	—	94	2	no	—
63	C₂×C₈	—	94	2	no	—
64	C₂×C₈	—	94	2	no	—
65	C₄²	C₄×D₄₇	1	2	yes	—
66	C₄²	C₂²⋊D₄₇	1	2	yes	—
67	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	Dic₄₇⋊C₄	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
71	C₂×C₄	#10625352	1	2	yes	—
72	C₂×C₄	#10625354	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	94	4	no	—
76	C₈	—	188	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
79	C₂²	#13094015	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#13093982	1	2	yes	—
82	C₄	#13094011	1	1	yes	characteristic
83	C₄	#13094013	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#15688988	1	1	yes	characteristic
86	C₂	#15689171	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#423	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	#423	D₄₇
hypocenter	C₄₇	#1838
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
48. C₄₇	#1838	semidirect