Subgroups — C₂₃×#1835 #15669454

Order 2944.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#382	C₂	1	2	yes	maximal
3	C₂₃×#340	C₂	1	4	yes	maximal
4	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₃	C₄	1	4	yes	complemented
8	C₂₃×#95	—	2	4	no	—
9	C₂²×C₄×C₂₃	—	2	4	no	—
10	C₂²×C₄×C₂₃	D₄	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	4	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
14	C₄⋊C₄×C₂₃	—	2	8	no	—
15	C₄²×C₂₃	C₂×C₄	1	2	yes	—
16	C₄²×C₂₃	Q₈	1	2	yes	—
17	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	4	no	—
19	C₂×C₄×C₂₃	—	4	4	no	—
20	C₂×C₄×C₂₃	—	4	8	no	—
21	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₃	#41	1	4	yes	—
25	C₈×C₂₃	—	2	4	no	—
26	#1835	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₃	#124	1	2	yes	—
29	C₂²×C₂₃	#135	1	4	yes	—
30	C₄×C₂₃	—	2	4	no	—
31	C₄×C₂₃	—	8	4	no	—
32	C₄×C₂₃	#117	1	2	yes	—
33	C₄×C₂₃	#125	1	2	yes	—
34	C₂×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
35	#382	C₂×C₂₃	1	2	yes	—
36	#340	C₂×C₂₃	1	4	yes	—
37	C₂×C₂₃	#382	1	1	yes	characteristic
38	C₂×C₂₃	#427	1	2	yes	—
39	C₂×C₂₃	#488	1	4	yes	—
40	C₂²×C₈	C₂²×C₂₃	1	2	yes	—
41	C₂×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
42	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
43	C₄×C₈	C₄×C₂₃	1	4	yes	complemented
44	#95	—	2	4	no	—
45	C₂₃	#1835	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₄	—	2	4	no	—
47	C₂²×C₄	D₄×C₂₃	1	2	yes	—
48	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	C₂×C₄×C₂₃	1	4	yes	—
51	C₄⋊C₄	—	2	8	no	—
52	C₄²	C₂×C₄×C₂₃	1	2	yes	—
53	C₄²	Q₈×C₂₃	1	2	yes	—
54	C₂³	C₂×D₄×C₂₃	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	4	4	no	—
57	C₂×C₄	—	4	8	no	—
58	C₂×C₄	C₄⋊C₄×C₂₃	1	4	yes	—
59	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
60	C₂×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
61	C₂×C₄	#41×C₂₃	1	4	yes	—
62	C₈	—	2	4	no	—
63	C₂²	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
64	C₂²	C₂₃×#124	1	2	yes	—
65	C₂²	C₂₃×#135	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	8	4	no	—
68	C₄	C₂₃×#117	1	2	yes	—
69	C₄	C₂₃×#125	1	2	yes	—
70	C₂	C₂₃×#382	1	1	yes	characteristic
71	C₂	C₂₃×#427	1	2	yes	—
72	C₂	C₂₃×#488	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
7. C₄×C₈×C₂₃	C₄	semidirect
26. #1835	C₂₃	direct (N × H)
43. C₄×C₈	C₄×C₂₃	semidirect
45. C₂₃	#1835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₂₃	2
C₂₃×#382	2
C₂₃×#340	2
#1835	23

Subgroups — C23×#1835 #15669454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1835 #15669454