Subgroups — #43252962

Order 28544.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28383379	C₂	1	2	yes	maximal
2	#494×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	#20297223	—	2	2	no	—
4	C₂×Q₁₆×C₂₂₃	—	2	2	no	—
5	C₄⋊Q₈×C₂₂₃	C₄	1	1	yes	characteristic
6	C₄⋊Q₈×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₂₃	C₄	1	1	yes	characteristic
8	#16813154	—	4	2	no	—
9	C₂×Q₈×C₂₂₃	—	2	1	no	—
10	C₂×Q₈×C₂₂₃	D₄	1	2	yes	—
11	Q₁₆×C₂₂₃	—	4	4	no	—
12	C₂×C₈×C₂₂₃	—	2	1	no	—
13	C₄⋊C₄×C₂₂₃	—	4	1	no	—
14	C₄⋊C₄×C₂₂₃	—	4	1	no	—
15	C₄²×C₂₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂₂₃⋊C₈	—	8	2	no	—
17	Q₈×C₂₂₃	—	4	2	no	—
18	Q₈×C₂₂₃	—	4	2	no	—
19	C₂×C₄×C₂₂₃	—	2	1	no	—
20	C₂×C₄×C₂₂₃	—	2	2	no	—
21	C₂×C₄×C₂₂₃	—	4	1	no	—
22	C₂×C₄×C₂₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₂₃	—	2	2	no	—
24	C₂²×C₂₂₃	#99	1	1	yes	characteristic
25	C₄×C₂₂₃	—	2	2	no	—
26	C₄×C₂₂₃	—	2	1	no	—
27	C₄×C₂₂₃	—	4	2	no	—
28	C₄×C₂₂₃	—	8	1	no	—
29	C₂×C₂₂₃	—	2	1	no	—
30	C₂×C₂₂₃	#353	1	1	yes	characteristic
31	C₂₂₃	#1411	1	1	yes	characteristic, complemented, Sylow
32	#1411	—	223	1	no	maximal, Sylow
33	#494	D₂₂₃	1	1	yes	characteristic
34	#356	—	223	2	no	—
35	C₂×Q₁₆	—	2	2	no	—
36	C₄⋊Q₈	Dic₂₂₃	1	1	yes	characteristic
37	C₄⋊Q₈	C₂×D₂₂₃	1	1	yes	characteristic
38	#101	—	446	2	no	—
39	C₄×C₈	Dic₂₂₃	1	1	yes	characteristic
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	C₂²⋊D₂₂₃	1	2	yes	—
42	Q₁₆	—	4	4	no	—
43	M₁₆	—	892	2	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄²	C₂×Dic₂₂₃	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	C₂²⋊Dic₂₂₃	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	1784	2	no	—
56	C₂²	#20297219	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	2	no	—
60	C₄	—	8	1	no	—
61	C₂	—	2	1	no	—
62	C₂	#28383373	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28383373
commutator	C₄²×C₂₂₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₂₃
Fitting	#494×C₂₂₃	C₂
socle	C₂×C₂₂₃	#353
prime radical	C₂²×C₂₂₃	#99
cosocle	C₄⋊Q₈×C₂₂₃	C₂²
hypercenter	#494	D₂₂₃
hypocenter	C₂₂₃	#1411
LCS	G ▷ C₄²×C₂₂₃ ▷ C₂×C₄×C₂₂₃ ▷ C₂²×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #494

Complements

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

N	H ≅ G/N	type
31. C₂₂₃	#1411	semidirect

Maximal subgroups

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

subgroup	index
#28383379	2
#494×C₂₂₃	2
#1411	223