Subgroups — C₄₇×#1413 #20239023

Order 6016.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#491	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#356	C₂	1	2	yes	maximal
3	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
4	#125×C₄₇	C₄	1	1	yes	characteristic
5	#103×C₄₇	—	2	2	no	—
6	#101×C₄₇	—	2	2	no	—
7	#97×C₄₇	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₄₇	D₄	1	2	yes	—
9	M₁₆×C₄₇	—	4	2	no	—
10	C₂×C₈×C₄₇	—	2	1	no	—
11	C₄⋊C₄×C₄₇	—	2	1	no	—
12	C₄⋊C₄×C₄₇	—	4	1	no	—
13	C₄⋊C₄×C₄₇	—	4	1	no	—
14	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₄₇	—	4	2	no	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	4	1	no	—
19	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₄₇	—	4	1	no	—
21	C₈×C₄₇	—	8	2	no	—
22	C₂²×C₄₇	#99	1	1	yes	characteristic
23	C₄×C₄₇	—	2	1	no	—
24	C₄×C₄₇	—	4	1	no	—
25	C₄×C₄₇	—	4	2	no	—
26	C₄×C₄₇	—	8	1	no	—
27	#1413	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₄₇	—	2	1	no	—
29	C₂×C₄₇	#354	1	1	yes	characteristic
30	#491	C₂×C₄₇	1	1	yes	characteristic
31	#356	C₂×C₄₇	1	2	yes	—
32	C₄₇	#1413	1	1	yes	characteristic, direct product factor, Sylow
33	C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
34	#125	C₄×C₄₇	1	1	yes	characteristic
35	#103	—	2	2	no	—
36	#101	—	2	2	no	—
37	#97	C₄×C₄₇	1	1	yes	characteristic
38	C₂×Q₈	D₄×C₄₇	1	2	yes	—
39	M₁₆	—	4	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄⋊C₄	—	4	1	no	—
44	C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	8	2	no	—
52	C₂²	#99×C₄₇	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	4	2	no	—
56	C₄	—	8	1	no	—
57	C₂	—	2	1	no	—
58	C₂	C₄₇×#354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₇	#354
commutator	C₄²	C₂×C₄×C₄₇
Frattini, cosocle	C₄⋊Q₈	C₂²×C₄₇
prime radical	C₂²×C₄₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₇ ◁ C₂²×C₄₇ ◁ C₂×C₄×C₄₇ ◁ C₄⋊Q₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
27. #1413	C₄₇	direct (N × H)
32. C₄₇	#1413	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#491	2
C₄₇×#356	2
#1413	47

Subgroups — C47×#1413 #20239023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1413 #20239023