Subgroups — #26103014

Order 12032.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20241458	C₂	1	2	yes	maximal
2	C₄₇×#1713	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₇⋊C₁₆)	—	2	2	no	—
4	C₄₇×#500	—	2	2	no	—
5	C₄₇×#494	C₄	1	2	yes	—
6	C₈²×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄₇⋊C₁₆	—	4	2	no	—
8	C₂×Q₁₆×C₄₇	—	4	2	no	—
9	C₄⋊Q₈×C₄₇	—	2	2	no	—
10	#107×C₄₇	—	4	2	no	—
11	#107×C₄₇	—	4	2	no	—
12	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈×C₄₇	D₄	1	2	yes	—
14	C₂×Q₈×C₄₇	—	4	2	no	—
15	Q₁₆×C₄₇	—	8	4	no	—
16	C₂×C₈×C₄₇	—	2	1	no	—
17	C₂×C₈×C₄₇	D₈	1	2	yes	—
18	C₂×C₈×C₄₇	SD₁₆	1	2	yes	—
19	C₄⋊C₄×C₄₇	—	4	4	no	—
20	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄₇⋊C₁₆	—	8	2	no	—
22	Q₈×C₄₇	—	8	4	no	—
23	C₂×C₄×C₄₇	—	8	2	no	—
24	C₂×C₄×C₄₇	#100	1	1	yes	characteristic
25	C₂×C₄×C₄₇	#102	1	2	yes	—
26	C₈×C₄₇	—	2	2	no	—
27	C₈×C₄₇	—	2	2	no	—
28	C₈×C₄₇	SD₃₂	1	2	yes	—
29	C₈×C₄₇	Q₃₂	1	2	yes	—
30	#7098	—	47	1	no	maximal, Sylow
31	C₂²×C₄₇	#331	1	1	yes	characteristic
32	C₄×C₄₇	—	2	1	no	—
33	C₄×C₄₇	—	16	2	no	—
34	C₄×C₄₇	#358	1	2	yes	—
35	C₄×C₄₇	#362	1	2	yes	—
36	#1713	D₄₇	1	1	yes	characteristic
37	#1370	—	47	2	no	—
38	C₂×C₄₇	#1357	1	1	yes	characteristic
39	C₂×C₄₇	#1362	1	2	yes	—
40	#500	—	2	2	no	—
41	#494	Dic₄₇	1	2	yes	—
42	C₄⋊C₁₆	—	94	2	no	—
43	C₈²	C₂×D₄₇	1	1	yes	characteristic
44	C₄₇	#7098	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	4	2	no	—
46	C₄⋊Q₈	—	2	2	no	—
47	C₂×C₁₆	—	188	2	no	—
48	#107	—	4	2	no	—
49	#107	—	4	2	no	—
50	C₄×C₈	C₂×Dic₄₇	1	1	yes	characteristic
51	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
52	C₂×Q₈	—	4	2	no	—
53	Q₁₆	—	8	4	no	—
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	#10625334	1	2	yes	—
56	C₂×C₈	#10625335	1	2	yes	—
57	C₄⋊C₄	—	4	4	no	—
58	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
59	C₁₆	—	376	2	no	—
60	Q₈	—	8	4	no	—
61	C₂×C₄	—	8	2	no	—
62	C₂×C₄	#13093941	1	1	yes	characteristic
63	C₂×C₄	#13093945	1	2	yes	—
64	C₈	—	2	2	no	—
65	C₈	—	2	2	no	—
66	C₈	#13093967	1	2	yes	—
67	C₈	#13093970	1	2	yes	—
68	C₂²	#15688867	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	16	2	no	—
71	C₄	#15688927	1	2	yes	—
72	C₄	#15688939	1	2	yes	—
73	C₂	#20241425	1	1	yes	characteristic
74	C₂	#20241437	1	2	yes	—

	subgroup	G/H
center	C₂²	#15688867
commutator	C₄×C₈×C₄₇	C₂×C₄
Frattini	C₈²	C₂×D₄₇
Fitting	C₄₇×#1713	C₂
socle, prime radical	C₂²×C₄₇	#331
cosocle	C₈²×C₄₇	C₂²
hypercenter	#1713	D₄₇
hypocenter	C₄₇	#7098
LCS	G ▷ C₄×C₈×C₄₇ ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
44. C₄₇	#7098	semidirect

Maximal subgroups

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

subgroup	index
#20241458	2
C₄₇×#1713	2
#7098	47