Subgroups — #20242987

Order 6016.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689521	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689475	C₂	1	2	yes	maximal, complemented
3	#15689469	C₂	1	2	yes	maximal
4	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#492	C₂	1	1	yes	maximal, characteristic
6	#13094024	C₂²	1	2	yes	—
7	#13093956	—	2	2	no	—
8	#13093947	—	2	4	no	—
9	#13093945	—	2	4	no	—
10	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₄₇	—	2	2	no	—
12	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	#127×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	2	1	no	—
16	C₂×D₄×C₄₇	—	2	1	no	—
17	C₂×D₄×C₄₇	—	2	2	no	—
18	C₂×Dic₉₄	—	2	2	no	—
19	SD₁₆×C₄₇	—	4	4	no	—
20	C₂×C₈×C₄₇	D₄	1	2	yes	—
21	C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄²×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
26	C₂³×C₄₇	—	4	1	no	—
27	Q₈×C₄₇	—	4	2	no	—
28	D₄×C₄₇	—	4	2	no	—
29	D₄×C₄₇	—	4	4	no	—
30	C₂×C₄×C₄₇	—	4	1	no	—
31	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₇	—	4	2	no	—
34	Dic₉₄	—	4	4	no	—
35	C₈×C₄₇	SD₁₆	1	4	yes	—
36	C₄₇⋊C₈	—	2	4	no	—
37	C₂²×C₄₇	—	8	1	no	—
38	C₂²×C₄₇	—	8	2	no	—
39	C₂²×C₄₇	#127	1	1	yes	characteristic
40	C₄×C₄₇	—	8	1	no	—
41	C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
42	C₄×C₄₇	#135	1	4	yes	—
43	Dic₄₇	—	8	2	no	—
44	#1708	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	—	16	1	no	—
46	C₂×C₄₇	#492	1	1	yes	characteristic
47	C₂×C₄₇	#495	1	2	yes	—
48	#498	—	47	1	no	—
49	#492	D₄₇	1	1	yes	characteristic
50	#487	—	47	2	no	—
51	#486	—	47	2	no	—
52	C₈²	—	47	1	no	—
53	C₄₇	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	2	2	no	—
55	C₄⋊Q₈	—	47	2	no	—
56	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
57	#127	C₂×D₄₇	1	1	yes	characteristic
58	#106	—	94	2	no	—
59	#103	—	94	4	no	—
60	#102	—	94	4	no	—
61	C₄×C₈	—	47	2	no	—
62	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	94	2	no	—
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	2	1	no	—
67	SD₁₆	—	4	4	no	—
68	C₂×C₈	—	47	4	no	—
69	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	94	2	no	—
72	C₄⋊C₄	—	94	2	no	—
73	C₄²	C₂²×D₄₇	1	1	yes	characteristic
74	C₂³	—	4	1	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	188	4	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	4	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	188	2	no	—
81	C₂×C₄	D₄×D₄₇	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
83	C₈	—	94	4	no	—
84	C₈	#10625335	1	4	yes	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	#13094020	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	376	2	no	—
90	C₄	C₂×#10625335	1	2	yes	—
91	C₄	#13094045	1	4	yes	—
92	C₂	—	16	1	no	—
93	C₂	#15689495	1	1	yes	characteristic
94	C₂	#15689504	1	2	yes	—

	subgroup	G/H
center	C₂²	#13094020
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#492	C₂
socle	C₂²×C₄₇	#127
hypercenter	#492	D₄₇
hypocenter	C₄₇	#1708
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #15689521	C₂	semidirect
2. #15689475	C₂	semidirect
4. C₈×C₄₇⋊C₈	C₂	semidirect
53. C₄₇	#1708	semidirect