Subgroups — #13063443⋊C₁₆ #36368477

Order 22144.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012377	C₂	1	1	yes	maximal, characteristic
2	C₈×#13063443	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583829	C₄	1	2	yes	—
5	C₄×#13063443	C₄	1	1	yes	characteristic
6	C₄×#13063443	C₄	1	1	yes	characteristic
7	C₂×#14583801	C₄	1	1	yes	characteristic
8	C₈×Dic₁₇₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₇₃	C₄	1	1	yes	characteristic
10	C₂×#13063443	C₈	1	2	yes	—
11	C₂×#13063443	C₈	1	2	yes	—
12	#14583829	—	2	2	no	—
13	C₂×#13063436	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
15	#14583801	—	2	1	no	—
16	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₇₃	—	2	1	no	—
18	#13063443	—	2	2	no	—
19	#13063443	C₁₆	1	4	yes	complemented
20	C₂×Dic₁₇₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₁₇₃	C₂×C₈	1	1	yes	characteristic
22	#13063436	M₁₆	1	2	yes	—
23	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
24	C₈×C₁₇₃	M₁₆	1	1	yes	characteristic
25	C₈×C₁₇₃	M₁₆	1	1	yes	characteristic
26	C₂²×C₁₇₃	C₄×C₈	1	1	yes	characteristic
27	C₄×C₁₇₃	#97	1	1	yes	characteristic
28	C₄×C₁₇₃	#97	1	1	yes	characteristic
29	Dic₁₇₃	C₂×C₁₆	1	2	yes	—
30	Dic₁₇₃	M₃₂	1	2	yes	—
31	C₂×C₁₇₃	#322	1	1	yes	characteristic
32	C₂×C₁₇₃	C₄×C₁₆	1	1	yes	characteristic
33	C₂×C₁₇₃	#346	1	1	yes	characteristic
34	C₁₇₃	#1312	1	1	yes	characteristic, complemented, Sylow
35	#1312	—	173	1	no	maximal, Sylow
36	C₄×C₁₆	—	173	1	no	—
37	C₄×C₁₆	—	173	1	no	—
38	C₈²	—	173	1	no	—
39	C₂×C₁₆	—	173	2	no	—
40	C₂×C₁₆	—	173	1	no	—
41	C₂×C₁₆	#10621924	1	1	yes	characteristic
42	C₄×C₈	—	173	1	no	—
43	C₄×C₈	—	173	1	no	—
44	C₄×C₈	—	173	1	no	—
45	C₂×C₈	—	173	2	no	—
46	C₂×C₈	—	173	2	no	—
47	C₂×C₈	—	173	1	no	—
48	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
49	C₄²	—	173	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	346	2	no	—
52	C₁₆	—	346	1	no	—
53	C₂×C₄	—	173	1	no	—
54	C₂×C₄	—	173	1	no	—
55	C₂×C₄	C₄×#10621924	1	1	yes	characteristic
56	C₈	—	346	2	no	—
57	C₈	—	173	4	no	—
58	C₈	—	173	2	no	—
59	C₈	#14583835	1	1	yes	characteristic
60	C₈	#14583836	1	1	yes	characteristic
61	C₂²	C₈×#10621924	1	1	yes	characteristic
62	C₄	—	173	2	no	—
63	C₄	—	173	2	no	—
64	C₄	#19149733	1	1	yes	characteristic
65	C₄	#19149734	1	1	yes	characteristic
66	C₂	#13063443⋊C₈	1	1	yes	characteristic
67	C₂	C₁₆×#10621924	1	1	yes	characteristic
68	C₂	#26012378	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10621924
commutator	C₂×C₁₇₃	C₄×C₁₆
Fitting	C₂×C₁₆×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	C₄×C₈
cosocle	C₈×Dic₁₇₃	C₂²
hypercenter	C₂×C₁₆	#10621924
hypocenter	C₁₇₃	#1312
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. #13063443	C₁₆	semidirect
34. C₁₇₃	#1312	semidirect

Maximal subgroups

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

subgroup	index
#26012377	2
C₈×#13063443	2
C₁₆×Dic₁₇₃	2
#1312	173

Subgroups — #13063443⋊C16 #36368477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #13063443⋊C₁₆ #36368477