Subgroups — C₂³×#14583829 #36370522

Order 22144.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14583829	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#13063436	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583829	C₂²	1	28	yes	direct product factor
4	C₂²×#13063436	C₄	1	7	yes	—
5	C₂²×#13063436	C₂²	1	7	yes	—
6	C₂³×C₄×C₁₇₃	C₄	1	1	yes	characteristic
7	#14583829	C₂³	1	8	yes	direct product factor
8	C₂×#13063436	C₂×C₄	1	21	yes	—
9	C₂×#13063436	C₂³	1	7	yes	—
10	C₂⁴×C₁₇₃	C₈	1	1	yes	characteristic
11	C₂²×C₄×C₁₇₃	C₈	1	7	yes	—
12	C₂²×C₄×C₁₇₃	C₂×C₄	1	7	yes	—
13	#13063436	C₂²×C₄	1	7	yes	—
14	#13063436	C₂⁴	1	1	yes	characteristic
15	C₂³×C₁₇₃	C₁₆	1	8	yes	complemented
16	C₂³×C₁₇₃	C₂×C₈	1	7	yes	—
17	C₂×C₄×C₁₇₃	C₂×C₈	1	21	yes	—
18	C₂×C₄×C₁₇₃	C₂²×C₄	1	7	yes	—
19	C₂²×C₁₇₃	C₂×C₁₆	1	28	yes	complemented
20	C₂²×C₁₇₃	C₂²×C₈	1	7	yes	—
21	C₄×C₁₇₃	C₂²×C₈	1	7	yes	—
22	C₄×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
23	C₂×C₁₇₃	C₂²×C₁₆	1	14	yes	complemented
24	C₂×C₁₇₃	C₂³×C₈	1	1	yes	characteristic
25	C₁₇₃	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂³×C₁₆	—	173	1	no	maximal, Sylow
27	C₂³×C₈	—	173	1	no	—
28	C₂²×C₁₆	—	173	14	no	—
29	C₂³×C₄	#10621924	1	1	yes	characteristic
30	C₂²×C₈	—	173	7	no	—
31	C₂²×C₈	—	173	7	no	—
32	C₂×C₁₆	—	173	28	no	—
33	C₂⁴	#13063443	1	1	yes	characteristic
34	C₂²×C₄	#13063443	1	7	yes	—
35	C₂²×C₄	C₂×#10621924	1	7	yes	—
36	C₂×C₈	—	173	21	no	—
37	C₂×C₈	—	173	7	no	—
38	C₁₆	—	173	8	no	—
39	C₂³	#14583829	1	8	yes	direct product factor
40	C₂³	C₂×#13063443	1	7	yes	—
41	C₂×C₄	C₂×#13063443	1	21	yes	—
42	C₂×C₄	C₂²×#10621924	1	7	yes	—
43	C₈	—	173	7	no	—
44	C₈	—	173	1	no	—
45	C₂²	C₂×#14583829	1	28	yes	direct product factor
46	C₂²	C₂²×#13063443	1	7	yes	—
47	C₄	C₂²×#13063443	1	7	yes	—
48	C₄	C₂³×#10621924	1	1	yes	characteristic
49	C₂	C₂²×#14583829	1	14	yes	direct product factor
50	C₂	C₂³×#13063443	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#10621924
commutator, hypocenter	C₁₇₃	C₂³×C₁₆
Frattini	C₄	C₂³×#10621924
Fitting	C₂³×C₄×C₁₇₃	C₄
socle, prime radical	C₂⁴×C₁₇₃	C₈
cosocle	#13063436	C₂⁴
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14583829	C₂	direct (N × H)
3. C₂×#14583829	C₂²	direct (N × H)
7. #14583829	C₂³	direct (N × H)
15. C₂³×C₁₇₃	C₁₆	semidirect
19. C₂²×C₁₇₃	C₂×C₁₆	semidirect
23. C₂×C₁₇₃	C₂²×C₁₆	semidirect
25. C₁₇₃	C₂³×C₁₆	semidirect
39. C₂³	#14583829	direct (N × H)
45. C₂²	C₂×#14583829	direct (N × H)
49. C₂	C₂²×#14583829	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14583829	2
C₂³×#13063436	2
C₂³×C₁₆	173

Subgroups — C23×#14583829 #36370522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#14583829 #36370522