Subgroups — #15673538

Order 2944.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092441	C₂	1	2	yes	maximal
2	#13092182	C₂	1	4	yes	maximal
3	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×#67267	C₂²	1	4	yes	—
7	C₂₃×#97	C₄	1	4	yes	—
8	C₄⋊(C₂₃⋊C₈)	—	2	4	no	—
9	C₂²×C₄×C₂₃	Q₈	1	2	yes	—
10	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
11	C₂×C₈×C₂₃	—	2	4	no	—
12	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
13	C₄²×C₂₃	C₂×C₄	1	2	yes	—
14	C₄²×C₂₃	D₄	1	2	yes	—
15	#67267	—	2	8	no	—
16	C₂×C₂₃⋊C₈	—	2	4	no	—
17	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	4	2	no	—
19	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃	#41	1	4	yes	—
23	C₈×C₂₃	—	2	4	no	—
24	C₂₃⋊C₈	—	4	4	no	—
25	#1838	—	23	1	no	maximal, Sylow
26	C₂²×C₂₃	—	2	2	no	—
27	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₃	#125	1	2	yes	—
29	C₄×C₂₃	—	2	4	no	—
30	C₄×C₂₃	#117	1	2	yes	—
31	C₄×C₂₃	#124	1	2	yes	—
32	#423	—	23	2	no	—
33	C₂×#97	D₂₃	1	1	yes	characteristic
34	#341	—	23	4	no	—
35	C₂×C₂₃	—	2	2	no	—
36	C₂×C₂₃	#382	1	1	yes	characteristic
37	C₂×C₂₃	#430	1	2	yes	—
38	C₂×M₁₆	—	23	4	no	—
39	C₂²×C₈	C₂×D₂₃	1	2	yes	—
40	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
41	C₄⋊C₈	—	46	4	no	—
42	#97	Dic₂₃	1	4	yes	—
43	C₂₃	#1838	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	Dic₄₆	1	2	yes	—
45	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
46	M₁₆	—	46	8	no	—
47	C₂×C₈	—	2	4	no	—
48	C₂×C₈	—	46	4	no	—
49	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
50	C₄²	D₉₂	1	2	yes	—
51	C₄²	C₂×Dic₂₃	1	2	yes	—
52	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₄⋊Dic₂₃	1	4	yes	—
55	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
56	C₂×C₄	#67288	1	4	yes	—
57	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
58	C₈	—	2	4	no	—
59	C₈	—	92	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	#10625041	1	2	yes	—
62	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
63	C₄	—	2	4	no	—
64	C₄	#10625046	1	2	yes	—
65	C₄	#10625097	1	2	yes	—
66	C₂	—	2	2	no	—
67	C₂	#13092283	1	1	yes	characteristic
68	C₂	#13092466	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂×C₂₃×#97	C₂
socle	C₂²×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	#1838
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
43. C₂₃	#1838	semidirect

Maximal subgroups

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

subgroup	index
#13092441	2
#13092182	2
C₂×C₂₃×#97	2
#1838	23