Subgroups — C₈×#14583801 #36351478

Order 22144.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14583801	C₂	1	2	yes	maximal
2	C₈²×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583801	C₄	1	4	yes	—
4	C₄×C₈×C₁₇₃	C₄	1	2	yes	—
5	C₄×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
6	#14583801	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₁₇₃	C₈	1	4	yes	—
8	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
9	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₇₃	C₂×C₈	1	2	yes	—
12	C₈×C₁₇₃	C₁₆	1	8	yes	complemented
13	C₈×C₁₇₃	C₂×C₈	1	4	yes	—
14	C₂²×C₁₇₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₇₃	C₄×C₈	1	2	yes	—
16	C₄×C₁₇₃	C₂×C₁₆	1	4	yes	—
17	C₂×C₁₇₃	C₈²	1	1	yes	characteristic
18	C₂×C₁₇₃	C₄×C₁₆	1	2	yes	—
19	C₁₇₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₈×C₁₆	—	173	1	no	maximal, Sylow
21	C₄×C₁₆	—	173	2	no	—
22	C₈²	D₁₇₃	1	1	yes	characteristic
23	C₂×C₁₆	—	173	4	no	—
24	C₄×C₈	Dic₁₇₃	1	2	yes	—
25	C₄×C₈	C₂×D₁₇₃	1	1	yes	characteristic
26	C₂×C₈	#13063436	1	4	yes	—
27	C₂×C₈	C₄×D₁₇₃	1	2	yes	—
28	C₄²	C₂×Dic₁₇₃	1	1	yes	characteristic
29	C₁₆	—	173	8	no	—
30	C₂×C₄	C₄×Dic₁₇₃	1	1	yes	characteristic
31	C₂×C₄	C₂×#13063436	1	2	yes	—
32	C₈	#14583801	1	8	yes	direct product factor
33	C₈	C₈×D₁₇₃	1	4	yes	—
34	C₂²	C₄×#13063436	1	1	yes	characteristic
35	C₄	C₈×Dic₁₇₃	1	2	yes	—
36	C₄	C₂×#14583801	1	4	yes	—
37	C₂	C₈×#13063436	1	1	yes	characteristic
38	C₂	C₄×#14583801	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₁₇₃
commutator, hypocenter	C₁₇₃	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₁₇₃
Fitting	C₈²×C₁₇₃	C₂
socle, prime radical	C₂²×C₁₇₃	C₄×C₈
cosocle	C₄×C₈×C₁₇₃	C₂²
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. #14583801	C₈	direct (N × H)
12. C₈×C₁₇₃	C₁₆	semidirect
19. C₁₇₃	C₈×C₁₆	semidirect
32. C₈	#14583801	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#14583801	2
C₈²×C₁₇₃	2
C₈×C₁₆	173

Subgroups — C8×#14583801 #36351478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14583801 #36351478