Subgroups — #15673542

Order 2944.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092172	C₂	1	6	yes	maximal
2	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₃	C₂²	1	3	yes	—
4	C₂²×C₂₃⋊C₈	C₂²	1	4	yes	—
5	C₂₃×#95	C₄	1	4	yes	—
6	C₂²×C₄×C₂₃	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
8	C₄²×C₂₃	—	2	6	no	—
9	C₂×C₂₃⋊C₈	—	2	12	no	—
10	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₃	—	2	6	no	—
12	C₂×C₄×C₂₃	—	2	12	no	—
13	C₂×C₄×C₂₃	#41	1	6	yes	—
14	C₂₃⋊C₈	—	4	4	no	—
15	#1840	—	23	1	no	maximal, Sylow
16	C₂²×C₂₃	#117	1	3	yes	—
17	C₂²×C₂₃	#131	1	4	yes	—
18	C₄×C₂₃	—	4	6	no	—
19	C₄×C₂₃	#126	1	4	yes	—
20	#376	D₂₃	1	1	yes	characteristic
21	#336	—	23	6	no	—
22	C₂×C₂₃	#383	1	1	yes	characteristic
23	C₂×C₂₃	#433	1	6	yes	—
24	C₂²×C₈	—	23	4	no	—
25	C₂×C₄²	C₂×D₂₃	1	3	yes	—
26	#95	Dic₂₃	1	4	yes	—
27	C₂₃	#1840	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₄	C₂×Dic₂₃	1	6	yes	—
29	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
30	C₂×C₈	—	46	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#67288	1	6	yes	—
36	C₈	—	92	4	no	—
37	C₂²	#10625097	1	3	yes	—
38	C₂²	#10625119	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#10625047	1	4	yes	—
41	C₂	#13092285	1	1	yes	characteristic
42	C₂	#13092478	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator, socle, prime radical	C₂³×C₂₃	C₂²×C₄
Fitting	C₂₃×#376	C₂
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#376	D₂₃
hypocenter	C₂₃	#1840
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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

N	H ≅ G/N	type
27. C₂₃	#1840	semidirect

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