Subgroups — #26103928

Order 12032.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245663	C₂	1	1	yes	maximal, characteristic
2	#20241460	C₂	1	1	yes	maximal, characteristic
3	C₄₇×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	#15689528	—	2	1	no	—
5	#15688949	—	2	1	no	—
6	#15688949	C₄	1	2	yes	—
7	#15688876	—	2	1	no	—
8	C₂×C₃₂×C₄₇	—	2	1	no	—
9	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	#13094024	—	4	1	no	—
11	#13093958	—	2	2	no	—
12	#13093958	—	4	1	no	—
13	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
14	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
16	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₃₂×C₄₇	—	4	1	no	—
18	C₂×Dic₉₄	—	8	1	no	—
19	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	SD₁₆	1	1	yes	characteristic
21	C₄²×C₄₇	D₈	1	1	yes	characteristic
22	C₄⋊Dic₄₇	—	4	2	no	—
23	C₄⋊Dic₄₇	—	8	1	no	—
24	C₂×C₄₇⋊C₈	—	8	1	no	—
25	C₁₆×C₄₇	—	2	1	no	—
26	C₁₆×C₄₇	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₄₇	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
29	C₂×C₄×C₄₇	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₄₇	SD₃₂	1	1	yes	characteristic
31	C₂×Dic₄₇	—	8	2	no	—
32	Dic₉₄	—	16	1	no	—
33	Dic₉₄	—	16	1	no	—
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	#101	1	1	yes	characteristic
36	C₈×C₄₇	#103	1	1	yes	characteristic
37	C₄₇⋊C₈	—	16	1	no	—
38	#7450	—	47	1	no	maximal, Sylow
39	C₂²×C₄₇	#357	1	1	yes	characteristic
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	#332	1	1	yes	characteristic
42	C₄×C₄₇	#362	1	1	yes	characteristic
43	C₄×C₄₇	D₃₂	1	1	yes	characteristic
44	C₄×C₄₇	SD₆₄	1	1	yes	characteristic
45	Dic₄₇	—	16	2	no	—
46	#2252	—	47	1	no	—
47	C₄⋊C₃₂	D₄₇	1	1	yes	characteristic
48	#1371	—	47	1	no	—
49	C₂×C₄₇	#1364	1	1	yes	characteristic
50	C₂×C₄₇	#1415	1	1	yes	characteristic
51	C₂×C₄₇	#1420	1	1	yes	characteristic
52	#500	—	94	1	no	—
53	C₂×C₃₂	—	2	1	no	—
54	#366	—	47	2	no	—
55	#366	—	94	1	no	—
56	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic
57	#335	—	94	1	no	—
58	C₄₇	#7450	1	1	yes	characteristic, complemented, Sylow
59	C₄⋊Q₈	—	188	1	no	—
60	C₂×C₁₆	C₄×D₄₇	1	1	yes	characteristic
61	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
62	#107	—	94	2	no	—
63	#107	—	188	1	no	—
64	C₄⋊C₈	—	188	1	no	—
65	C₄×C₈	D₁₈₈	1	1	yes	characteristic
66	C₃₂	—	4	1	no	—
67	C₂×Q₈	—	376	1	no	—
68	C₂×C₈	—	376	1	no	—
69	C₂×C₈	#10625325	1	1	yes	characteristic
70	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
71	C₄⋊C₄	—	376	1	no	—
72	C₄⋊C₄	—	188	2	no	—
73	C₄²	D₃₇₆	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	#10625335	1	1	yes	characteristic
76	C₁₆	#10625337	1	1	yes	characteristic
77	Q₈	—	752	1	no	—
78	Q₈	—	752	1	no	—
79	C₂×C₄	—	376	2	no	—
80	C₂×C₄	#13093946	1	1	yes	characteristic
81	C₂×C₄	D₇₅₂	1	1	yes	characteristic
82	C₂×C₄	#13093969	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	752	1	no	—
85	C₈	#13093942	1	1	yes	characteristic
86	C₈	#13093947	1	1	yes	characteristic
87	C₂²	#15688925	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	752	2	no	—
90	C₄	#15688868	1	1	yes	characteristic
91	C₄	#15688940	1	1	yes	characteristic
92	C₄	D₁₅₀₄	1	1	yes	characteristic
93	C₄	#15688962	1	1	yes	characteristic
94	C₂	#20241442	1	1	yes	characteristic
95	C₂	#20241567	1	1	yes	characteristic
96	C₂	#20241582	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15688925
commutator	C₂×C₁₆×C₄₇	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₄₇
Fitting	C₄₇×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₄₇	#357
cosocle	C₄×C₁₆×C₄₇	C₂²
hypercenter	C₄⋊C₃₂	D₄₇
hypocenter	C₄₇	#7450
LCS	G ▷ C₂×C₁₆×C₄₇ ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
58. C₄₇	#7450	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20245663	2
#20241460	2
C₄₇×C₄⋊C₃₂	2
#7450	47