Subgroups — #20243022

Order 6016.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689519	C₂	1	2	yes	maximal
2	#15689503	C₂	1	1	yes	maximal, characteristic
3	#15689473	C₂	1	2	yes	maximal
4	#15688844	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#498	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	—	2	2	no	—
7	#13094024	C₂²	1	1	yes	characteristic
8	#13094024	C₂²	1	1	yes	characteristic
9	#13093955	—	2	4	no	—
10	#13093948	—	2	4	no	—
11	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
13	#106×C₄₇	—	2	2	no	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	2	2	no	—
16	C₂×Dic₉₄	—	2	1	no	—
17	C₂×Dic₉₄	—	2	1	no	—
18	C₂×C₈×C₄₇	D₄	1	2	yes	—
19	C₄⋊C₄×C₄₇	—	2	2	no	—
20	C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₄²×C₄₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₄₇	—	2	2	no	—
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
25	Dic₁₈₈	—	4	4	no	—
26	Q₈×C₄₇	—	4	4	no	—
27	C₂×C₄×C₄₇	—	4	2	no	—
28	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₄₇	—	4	1	no	—
31	C₂×Dic₄₇	—	4	1	no	—
32	Dic₉₄	—	4	2	no	—
33	Dic₉₄	—	4	2	no	—
34	C₈×C₄₇	SD₁₆	1	4	yes	—
35	C₄₇⋊C₈	—	2	4	no	—
36	C₂²×C₄₇	#127	1	1	yes	characteristic
37	C₄×C₄₇	—	8	2	no	—
38	C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
39	C₄×C₄₇	#137	1	4	yes	—
40	Dic₄₇	—	8	1	no	—
41	Dic₄₇	—	8	1	no	—
42	#1716	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	#492	1	1	yes	characteristic
44	C₂×C₄₇	#497	1	2	yes	—
45	#498	—	47	2	no	—
46	#498	D₄₇	1	1	yes	characteristic
47	#494	—	47	1	no	—
48	#487	—	47	2	no	—
49	#322	—	47	1	no	—
50	C₄₇	#1716	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₁₆	—	94	2	no	—
52	C₄⋊Q₈	—	47	1	no	—
53	C₄⋊Q₈	—	47	1	no	—
54	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
55	#106	—	2	2	no	—
56	#106	—	94	4	no	—
57	#103	—	94	4	no	—
58	C₄×C₈	—	47	2	no	—
59	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	94	1	no	—
62	C₂×Q₈	—	94	1	no	—
63	Q₁₆	—	188	4	no	—
64	C₂×C₈	—	47	4	no	—
65	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	94	2	no	—
69	C₄⋊C₄	—	94	2	no	—
70	C₄²	C₂²×D₄₇	1	1	yes	characteristic
71	Q₈	—	4	4	no	—
72	Q₈	—	188	2	no	—
73	Q₈	—	188	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	188	1	no	—
76	C₂×C₄	—	188	1	no	—
77	C₂×C₄	D₄×D₄₇	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
79	C₈	—	94	4	no	—
80	C₈	#10625336	1	4	yes	—
81	C₂²	#13094020	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	376	1	no	—
84	C₄	—	376	1	no	—
85	C₄	C₂×#10625336	1	2	yes	—
86	C₄	#13094053	1	4	yes	—
87	C₂	#15689497	1	1	yes	characteristic
88	C₂	#15689514	1	2	yes	—

	subgroup	G/H
center	C₂²	#13094020
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#498	C₂
socle	C₂²×C₄₇	#127
hypercenter	#498	D₄₇
hypocenter	C₄₇	#1716
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
50. C₄₇	#1716	semidirect