Subgroups — C₂₃×#1837 #15669456

Order 2944.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#341	C₂	1	4	yes	maximal
4	C₂×M₁₆×C₂₃	C₂²	1	4	yes	—
5	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃×C₄⋊C₈	—	2	4	no	—
8	C₄×C₈×C₂₃	C₄	1	2	yes	—
9	C₄×C₈×C₂₃	C₄	1	2	yes	—
10	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	M₁₆×C₂₃	—	2	8	no	—
13	C₂×C₈×C₂₃	—	2	4	no	—
14	C₂×C₈×C₂₃	—	2	4	no	—
15	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
16	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₂₃	D₄	1	2	yes	—
19	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	4	no	—
21	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	#41	1	4	yes	—
26	C₈×C₂₃	—	2	4	no	—
27	C₈×C₂₃	—	4	4	no	—
28	#1837	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₂₃	—	2	2	no	—
30	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₃	#125	1	2	yes	—
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	#108	1	4	yes	—
34	C₄×C₂₃	#117	1	2	yes	—
35	C₄×C₂₃	#124	1	2	yes	—
36	#423	C₂×C₂₃	1	2	yes	—
37	C₂×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
38	#341	C₂×C₂₃	1	4	yes	—
39	C₂×C₂₃	—	2	2	no	—
40	C₂×C₂₃	#382	1	1	yes	characteristic
41	C₂×C₂₃	C₂×#108	1	2	yes	—
42	C₂×M₁₆	C₂²×C₂₃	1	4	yes	—
43	C₂²×C₈	C₂²×C₂₃	1	2	yes	—
44	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
45	C₄⋊C₈	—	2	4	no	—
46	C₄×C₈	C₄×C₂₃	1	2	yes	—
47	C₄×C₈	C₄×C₂₃	1	2	yes	—
48	C₂₃	#1837	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₄	Q₈×C₂₃	1	2	yes	—
50	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
51	M₁₆	—	2	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	2	4	no	—
54	C₂×C₈	C₂×C₄×C₂₃	1	4	yes	—
55	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
56	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
57	C₄²	D₄×C₂₃	1	2	yes	—
58	C₂³	C₂×Q₈×C₂₃	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
61	C₂×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
62	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
63	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
64	C₂×C₄	#41×C₂₃	1	4	yes	—
65	C₈	—	2	4	no	—
66	C₈	—	4	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
69	C₂²	C₂₃×#125	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	C₂₃×#108	1	4	yes	—
72	C₄	C₂₃×#117	1	2	yes	—
73	C₄	C₂₃×#124	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂₃×#382	1	1	yes	characteristic
76	C₂	C₂×C₂₃×#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
28. #1837	C₂₃	direct (N × H)
48. C₂₃	#1837	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#423	2
C₂×C₄×C₈×C₂₃	2
C₂₃×#341	2
#1837	23

Subgroups — C23×#1837 #15669456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1837 #15669456