Subgroups — #26130992

Order 12032.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245640	C₂	1	4	yes	maximal
2	#20243006	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1713	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093970	—	2	8	no	—
6	#15689528	—	2	2	no	—
7	#15689503	C₂²	1	2	yes	—
8	C₄×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	C₄₇×#500	—	2	2	no	—
10	C₄₇×#494	C₂²	1	2	yes	—
11	C₈²×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₈₈	—	2	4	no	—
13	#13094024	—	2	2	no	—
14	#13093970	—	4	16	no	—
15	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	—
16	#13093958	—	4	4	no	—
17	C₂×Q₁₆×C₄₇	—	2	4	no	—
18	C₄⋊Q₈×C₄₇	—	2	2	no	—
19	#107×C₄₇	—	4	4	no	—
20	C₄×C₈×C₄₇	D₄	1	2	yes	—
21	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₄₇	—	4	2	no	—
23	C₂×Dic₉₄	—	4	2	no	—
24	Q₁₆×C₄₇	—	4	8	no	—
25	C₂×C₈×C₄₇	D₈	1	4	yes	—
26	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
27	C₄⋊C₄×C₄₇	—	4	4	no	—
28	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₄⋊Dic₄₇	—	4	4	no	—
30	Dic₁₈₈	—	4	8	no	—
31	C₄₇⋊C₁₆	D₈	1	8	yes	—
32	Q₈×C₄₇	—	8	4	no	—
33	C₂×C₄×C₄₇	—	8	2	no	—
34	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
36	C₂×Dic₄₇	—	8	2	no	—
37	Dic₉₄	—	8	4	no	—
38	C₈×C₄₇	Q₃₂	1	8	yes	complemented
39	C₈×C₄₇	C₂×D₈	1	4	yes	—
40	#12516	—	47	1	no	maximal, Sylow
41	C₂²×C₄₇	#493	1	1	yes	characteristic
42	C₄×C₄₇	—	16	2	no	—
43	C₄×C₄₇	#493	1	2	yes	—
44	C₄×C₄₇	C₂×Q₃₂	1	4	yes	—
45	Dic₄₇	—	16	2	no	—
46	#2247	—	47	4	no	—
47	#1713	—	47	1	no	—
48	#1713	D₄₇	1	1	yes	characteristic
49	C₈×C₁₆	—	47	1	no	—
50	C₂×C₄₇	#1712	1	1	yes	characteristic
51	C₂×C₄₇	#2247	1	2	yes	—
52	C₂×Q₃₂	—	94	8	no	—
53	#500	—	2	2	no	—
54	#500	—	94	2	no	—
55	#494	—	47	2	no	—
56	#494	C₂×D₄₇	1	2	yes	—
57	C₄×C₁₆	—	47	2	no	—
58	C₈²	C₂×D₄₇	1	1	yes	characteristic
59	C₄₇	#12516	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₁₆	—	2	4	no	—
61	C₂×Q₁₆	—	94	4	no	—
62	C₄⋊Q₈	—	2	2	no	—
63	C₄⋊Q₈	—	94	2	no	—
64	Q₃₂	—	188	16	no	—
65	C₂×C₁₆	—	47	4	no	—
66	#107	—	4	4	no	—
67	#107	—	188	4	no	—
68	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
69	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
70	C₂×Q₈	—	4	2	no	—
71	C₂×Q₈	—	188	2	no	—
72	Q₁₆	—	4	8	no	—
73	Q₁₆	—	188	8	no	—
74	C₂×C₈	#10625334	1	4	yes	—
75	C₂×C₈	D₄×D₄₇	1	2	yes	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	188	4	no	—
78	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
79	C₁₆	—	47	8	no	—
80	Q₈	—	8	4	no	—
81	Q₈	—	376	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	376	2	no	—
84	C₂×C₄	#13094020	1	1	yes	characteristic
85	C₂×C₄	C₂×#10625334	1	2	yes	—
86	C₈	#13093970	1	8	yes	complemented
87	C₈	D₈×D₄₇	1	4	yes	—
88	C₂²	#15689499	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	752	2	no	—
91	C₄	#15689498	1	2	yes	—
92	C₄	C₂×#13093970	1	4	yes	—
93	C₂	#20243002	1	1	yes	characteristic
94	C₂	#20245640	1	2	yes	—

	subgroup	G/H
center	C₂²	#15689499
commutator, cosocle	C₄×C₈×C₄₇	C₂³
Frattini	C₄×C₈	C₂²×D₄₇
Fitting	C₄₇×#1713	C₂
socle, prime radical	C₂²×C₄₇	#493
hypercenter	#1713	D₄₇
hypocenter	C₄₇	#12516
LCS	G ▷ C₄×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
38. C₈×C₄₇	Q₃₂	semidirect
59. C₄₇	#12516	semidirect
86. C₈	#13093970	semidirect

Maximal subgroups

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

subgroup	index
#20245640	2
#20243006	2
C₈×C₄₇⋊C₁₆	2
C₄₇×#1713	2
#12516	47