Subgroups — #20243518

Order 6016.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#15688989	C₂	1	1	yes	maximal, characteristic
3	#15688885	C₂	1	4	yes	maximal
4	C₄₇×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
8	C₄₇⋊#95	—	2	2	no	—
9	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	#95×C₄₇	—	2	2	no	—
12	C₂²×C₄×C₄₇	—	2	2	no	—
13	C₂²×C₄×C₄₇	D₄	1	2	yes	—
14	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₄₇	—	2	2	no	—
16	C₄⋊C₄×C₄₇	—	2	4	no	—
17	C₄²×C₄₇	C₂×C₄	1	2	yes	—
18	C₄²×C₄₇	Q₈	1	2	yes	—
19	C₄⋊Dic₄₇	—	2	4	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×D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	—	2	4	no	—
25	C₂×C₄×C₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	—	4	4	no	—
27	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	#41	1	2	yes	—
31	C₂×C₄×C₄₇	#41	1	2	yes	—
32	C₂×Dic₄₇	—	4	2	no	—
33	C₂×Dic₄₇	—	4	4	no	—
34	C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄₇	#124	1	1	yes	characteristic
37	C₂²×C₄₇	#124	1	1	yes	characteristic
38	C₂²×C₄₇	#135	1	4	yes	—
39	C₄×C₄₇	—	2	4	no	—
40	C₄×C₄₇	—	8	2	no	—
41	C₄×C₄₇	#117	1	2	yes	—
42	C₄×C₄₇	#125	1	2	yes	—
43	Dic₄₇	—	8	2	no	—
44	#1835	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	#382	1	1	yes	characteristic
46	C₂×C₄₇	#427	1	2	yes	—
47	C₂×C₄₇	#488	1	2	yes	—
48	C₂×C₄₇	#488	1	2	yes	—
49	C₂×C₄×C₈	—	47	1	no	—
50	#382	—	47	1	no	—
51	#382	D₄₇	1	1	yes	characteristic
52	#340	—	47	4	no	—
53	C₄₇	#1835	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	47	2	no	—
55	C₂×C₄⋊C₄	—	47	2	no	—
56	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
57	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
58	C₄×C₈	—	47	4	no	—
59	#95	—	2	2	no	—
60	#95	—	94	2	no	—
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	94	2	no	—
63	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
64	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
65	C₂×C₈	—	47	4	no	—
66	C₂×C₈	—	94	2	no	—
67	C₂×C₈	—	94	2	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	94	4	no	—
70	C₄²	Dic₉₄	1	2	yes	—
71	C₄²	C₄×D₄₇	1	2	yes	—
72	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	188	2	no	—
77	C₂×C₄	—	188	4	no	—
78	C₂×C₄	Dic₄₇⋊C₄	1	4	yes	—
79	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
81	C₂×C₄	#10625352	1	2	yes	—
82	C₂×C₄	#10625354	1	2	yes	—
83	C₈	—	94	4	no	—
84	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
85	C₂²	#13094011	1	1	yes	characteristic
86	C₂²	#13094013	1	1	yes	characteristic
87	C₂²	#13094044	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	376	2	no	—
91	C₄	#13093982	1	2	yes	—
92	C₄	#13094015	1	2	yes	—
93	C₂	#15688988	1	1	yes	characteristic
94	C₂	#15689159	1	2	yes	—
95	C₂	#15689477	1	2	yes	—
96	C₂	#15689480	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#382	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#382	D₄₇
hypocenter	C₄₇	#1835
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
7. C₄×C₄₇⋊C₈	C₄	semidirect
53. C₄₇	#1835	semidirect