Subgroups — Q₈×#14583829 #36369976

Order 22144.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14583829	C₂	1	3	yes	maximal
2	C₄×#14583829	C₂	1	3	yes	maximal
3	Q₈×#13063436	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583829	C₂²	1	3	yes	—
5	C₂×#14583829	C₂²	1	1	yes	characteristic
6	C₄⋊#13063436	C₄	1	3	yes	—
7	C₄×#13063436	C₂²	1	3	yes	—
8	C₄×Q₈×C₁₇₃	C₄	1	1	yes	characteristic
9	#14583829	—	2	3	no	—
10	#14583829	Q₈	1	2	yes	direct product factor
11	C₂×#13063436	C₂×C₄	1	3	yes	—
12	C₂×#13063436	C₂³	1	1	yes	characteristic
13	C₂×Q₈×C₁₇₃	C₈	1	1	yes	characteristic
14	C₄⋊C₄×C₁₇₃	C₈	1	3	yes	—
15	C₄²×C₁₇₃	C₂×C₄	1	3	yes	—
16	#13063436	—	2	3	no	—
17	#13063436	C₂×Q₈	1	1	yes	characteristic
18	#13063436	#41	1	1	yes	characteristic
19	Q₈×C₁₇₃	C₁₆	1	4	yes	complemented
20	C₂×C₄×C₁₇₃	C₂×C₈	1	3	yes	—
21	C₂×C₄×C₁₇₃	C₂×C₈	1	3	yes	—
22	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₁₇₃	—	2	3	no	—
25	C₄×C₁₇₃	C₂×C₁₆	1	6	yes	—
26	C₄×C₁₇₃	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₁₇₃	#131	1	1	yes	characteristic
28	C₂×C₁₇₃	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₁₇₃	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₁₇₃	#504	1	1	yes	characteristic
31	C₁₇₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
32	Q₈×C₁₆	—	173	1	no	maximal, Sylow
33	C₈×Q₈	—	173	1	no	—
34	C₄⋊C₁₆	—	173	3	no	—
35	C₄×C₁₆	—	173	3	no	—
36	C₄×Q₈	#10621924	1	1	yes	characteristic
37	C₂×C₁₆	—	173	3	no	—
38	C₂×C₁₆	—	173	1	no	—
39	C₄⋊C₈	—	173	3	no	—
40	C₄×C₈	—	173	3	no	—
41	C₂×Q₈	#13063443	1	1	yes	characteristic
42	C₂×C₈	—	173	3	no	—
43	C₂×C₈	—	173	1	no	—
44	C₄⋊C₄	#13063443	1	3	yes	—
45	C₄²	C₂×#10621924	1	3	yes	—
46	C₁₆	—	346	3	no	—
47	C₁₆	—	173	2	no	—
48	Q₈	#14583829	1	4	yes	direct product factor
49	C₂×C₄	C₂×#13063443	1	3	yes	—
50	C₂×C₄	C₂×#13063443	1	3	yes	—
51	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
52	C₈	—	346	3	no	—
53	C₈	—	173	1	no	—
54	C₈	—	173	1	no	—
55	C₂²	C₂²×#13063443	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#14583829	1	6	yes	—
58	C₄	Q₈×#10621924	1	1	yes	characteristic
59	C₄	#19149767	1	1	yes	characteristic
60	C₂	Q₈×#13063443	1	1	yes	characteristic
61	C₂	C₂²×#14583829	1	1	yes	characteristic
62	C₂	#26012549	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10621924
commutator	C₂×C₁₇₃	C₂²×C₁₆
Fitting	C₄×Q₈×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	C₂²×C₈
cosocle	C₂×#13063436	C₂³
hypercenter	C₄×Q₈	#10621924
hypocenter	C₁₇₃	Q₈×C₁₆
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. #14583829	Q₈	direct (N × H)
19. Q₈×C₁₇₃	C₁₆	semidirect
31. C₁₇₃	Q₈×C₁₆	semidirect
48. Q₈	#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
C₄⋊#14583829	2
C₄×#14583829	2
Q₈×#13063436	2
Q₈×C₁₆	173

Subgroups — Q8×#14583829 #36369976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#14583829 #36369976