Subgroups — #36368475

Order 22144.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14583829	C₂	1	2	yes	maximal
2	C₈×#13063436	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583829	C₄	1	4	yes	—
4	C₄×#13063436	C₄	1	1	yes	characteristic
5	C₄×#13063436	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₇₃	C₄	1	1	yes	characteristic
7	#14583829	C₈	1	8	yes	complemented
8	C₂×#13063436	C₈	1	2	yes	—
9	C₂×#13063436	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₇₃	C₈	1	2	yes	—
11	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
12	#13063436	—	2	2	no	—
13	#13063436	C₂×C₈	1	4	yes	—
14	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₇₃	—	2	2	no	—
18	C₂²×C₁₇₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₇₃	C₄×C₈	1	2	yes	—
20	C₄×C₁₇₃	M₃₂	1	2	yes	—
21	C₄×C₁₇₃	M₃₂	1	2	yes	—
22	C₂×C₁₇₃	C₈²	1	1	yes	characteristic
23	C₂×C₁₇₃	#346	1	1	yes	characteristic
24	C₂×C₁₇₃	#346	1	1	yes	characteristic
25	C₁₇₃	#1311	1	1	yes	characteristic, complemented, Sylow
26	#1311	—	173	1	no	maximal, Sylow
27	C₄×C₁₆	—	173	2	no	—
28	C₈²	—	173	1	no	—
29	C₂×C₁₆	—	173	4	no	—
30	C₄×C₈	—	173	1	no	—
31	C₄×C₈	—	173	1	no	—
32	C₄×C₈	#10621924	1	1	yes	characteristic
33	C₂×C₈	—	173	2	no	—
34	C₂×C₈	—	173	2	no	—
35	C₂×C₈	#13063443	1	2	yes	—
36	C₄²	C₂×#10621924	1	1	yes	characteristic
37	C₁₆	—	173	8	no	—
38	C₂×C₄	C₄×#10621924	1	1	yes	characteristic
39	C₂×C₄	C₂×#13063443	1	1	yes	characteristic
40	C₂×C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	—	346	2	no	—
43	C₈	—	173	4	no	—
44	C₂²	C₄×#13063443	1	1	yes	characteristic
45	C₄	C₈×#10621924	1	2	yes	—
46	C₄	#19149753	1	2	yes	—
47	C₄	#19149754	1	2	yes	—
48	C₂	C₈×#13063443	1	1	yes	characteristic
49	C₂	#26012379	1	1	yes	characteristic
50	C₂	#26012380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#10621924
commutator	C₂×C₁₇₃	C₈²
Fitting	C₄×C₈×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	C₄×C₈
cosocle	C₄×#13063436	C₂²
hypercenter	C₄×C₈	#10621924
hypocenter	C₁₇₃	#1311
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #14583829	C₈	semidirect
25. C₁₇₃	#1311	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14583829	2
C₈×#13063436	2
#1311	173