Subgroups — #1840×C₂₂₃ #43250855

Order 28544.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#376×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	#336×C₂₂₃	C₂	1	6	yes	maximal
3	C₂²×C₈×C₂₂₃	C₂²	1	4	yes	—
4	C₂×C₄²×C₂₂₃	C₂²	1	3	yes	—
5	#95×C₂₂₃	C₄	1	4	yes	—
6	C₂²×C₄×C₂₂₃	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₂₂₃	C₂³	1	1	yes	characteristic
8	C₂×C₈×C₂₂₃	—	2	12	no	—
9	C₄²×C₂₂₃	—	2	6	no	—
10	C₂³×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₂₃	—	2	6	no	—
12	C₂×C₄×C₂₂₃	—	2	12	no	—
13	C₂×C₄×C₂₂₃	#41	1	6	yes	—
14	C₈×C₂₂₃	—	4	4	no	—
15	C₂²×C₂₂₃	#117	1	3	yes	—
16	C₂²×C₂₂₃	#131	1	4	yes	—
17	C₄×C₂₂₃	—	4	6	no	—
18	C₄×C₂₂₃	#126	1	4	yes	—
19	C₂×C₂₂₃	#383	1	1	yes	characteristic
20	C₂×C₂₂₃	#433	1	6	yes	—
21	C₂₂₃	#1840	1	1	yes	characteristic, direct product factor, Sylow
22	#1840	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	#376	C₂×C₂₂₃	1	1	yes	characteristic
24	#336	C₂×C₂₂₃	1	6	yes	—
25	C₂²×C₈	C₂²×C₂₂₃	1	4	yes	—
26	C₂×C₄²	C₂²×C₂₂₃	1	3	yes	—
27	#95	C₄×C₂₂₃	1	4	yes	—
28	C₂²×C₄	C₂×C₄×C₂₂₃	1	6	yes	—
29	C₂²×C₄	C₂³×C₂₂₃	1	1	yes	characteristic
30	C₂×C₈	—	2	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×C₄×C₂₂₃	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#41×C₂₂₃	1	6	yes	—
36	C₈	—	4	4	no	—
37	C₂²	#117×C₂₂₃	1	3	yes	—
38	C₂²	#131×C₂₂₃	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#126×C₂₂₃	1	4	yes	—
41	C₂	#383×C₂₂₃	1	1	yes	characteristic
42	C₂	#433×C₂₂₃	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₂₃	C₂³
commutator	C₂³	C₂²×C₄×C₂₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₂₃
socle, prime radical	C₂³×C₂₂₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
21. C₂₂₃	#1840	direct (N × H)
22. #1840	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
#376×C₂₂₃	2
#336×C₂₂₃	2
#1840	223

Subgroups — #1840×C223 #43250855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1840×C₂₂₃ #43250855