Subgroups — #1411×C₂₂₃ #43250426

Order 28544.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	#356×C₂₂₃	C₂	1	2	yes	maximal
3	C₂×Q₁₆×C₂₂₃	—	2	2	no	—
4	C₄⋊Q₈×C₂₂₃	C₄	1	1	yes	characteristic
5	C₄⋊Q₈×C₂₂₃	C₂²	1	1	yes	characteristic
6	#101×C₂₂₃	—	2	2	no	—
7	C₄×C₈×C₂₂₃	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₂₂₃	—	2	1	no	—
9	C₂×Q₈×C₂₂₃	D₄	1	2	yes	—
10	Q₁₆×C₂₂₃	—	4	4	no	—
11	M₁₆×C₂₂₃	—	4	2	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	Q₈×C₂₂₃	—	4	2	no	—
17	Q₈×C₂₂₃	—	4	2	no	—
18	C₂×C₄×C₂₂₃	—	2	1	no	—
19	C₂×C₄×C₂₂₃	—	2	2	no	—
20	C₂×C₄×C₂₂₃	—	4	1	no	—
21	C₂×C₄×C₂₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₂₃	—	2	2	no	—
23	C₈×C₂₂₃	—	8	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, direct product factor, Sylow
32	#1411	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	#494	C₂×C₂₂₃	1	1	yes	characteristic
34	#356	C₂×C₂₂₃	1	2	yes	—
35	C₂×Q₁₆	—	2	2	no	—
36	C₄⋊Q₈	C₄×C₂₂₃	1	1	yes	characteristic
37	C₄⋊Q₈	C₂²×C₂₂₃	1	1	yes	characteristic
38	#101	—	2	2	no	—
39	C₄×C₈	C₄×C₂₂₃	1	1	yes	characteristic
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	D₄×C₂₂₃	1	2	yes	—
42	Q₁₆	—	4	4	no	—
43	M₁₆	—	4	2	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄²	C₂×C₄×C₂₂₃	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⋊C₄×C₂₂₃	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	8	2	no	—
56	C₂²	#99×C₂₂₃	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	#353×C₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₂₃	#353
commutator	C₄²	C₂×C₄×C₂₂₃
Frattini, cosocle	C₄⋊Q₈	C₂²×C₂₂₃
prime radical	C₂²×C₂₂₃	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₂₃ ◁ C₂²×C₂₂₃ ◁ C₂×C₄×C₂₂₃ ◁ C₄⋊Q₈×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
31. C₂₂₃	#1411	direct (N × H)
32. #1411	C₂₂₃	direct (N × H)

Maximal subgroups

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

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

Subgroups — #1411×C223 #43250426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1411×C₂₂₃ #43250426