Subgroups — D₁₇₃⋊M₆₄ #36369984

Order 22144.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012424	C₂	1	2	yes	maximal, complemented
2	#26012423	C₂	1	2	yes	maximal, complemented
3	D₁₇₃⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₆×D₁₇₃	C₂	1	1	yes	maximal, characteristic
5	#19149729	C₂²	1	4	yes	complemented
6	C₂×C₈×D₁₇₃	C₄	1	1	yes	characteristic
7	C₂×#14583801	C₂²	1	1	yes	characteristic
8	C₁₆×D₁₇₃	C₄	1	1	yes	characteristic
9	C₁₆×D₁₇₃	C₄	1	1	yes	characteristic
10	C₁₆×D₁₇₃	C₂²	1	1	yes	characteristic
11	C₁₆×D₁₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₇₃	C₄	1	1	yes	characteristic
13	C₂×C₄×D₁₇₃	C₈	1	1	yes	characteristic
14	C₂×#13063436	C₈	1	1	yes	characteristic
15	C₈×D₁₇₃	C₈	1	1	yes	characteristic
16	C₈×D₁₇₃	C₈	1	1	yes	characteristic
17	C₈×D₁₇₃	C₂×C₄	1	1	yes	characteristic
18	C₈×D₁₇₃	C₂×C₄	1	1	yes	characteristic
19	#14583801	C₂×C₄	1	1	yes	characteristic
20	#14583801	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₁₇₃	C₁₆	1	1	yes	characteristic
25	C₂×Dic₁₇₃	C₁₆	1	1	yes	characteristic
26	C₄×D₁₇₃	C₁₆	1	1	yes	characteristic
27	C₄×D₁₇₃	C₁₆	1	1	yes	characteristic
28	C₄×D₁₇₃	C₂×C₈	1	1	yes	characteristic
29	C₄×D₁₇₃	C₂×C₈	1	1	yes	characteristic
30	#13063436	C₂×C₈	1	1	yes	characteristic
31	#13063436	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
34	C₈×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₁₇₃	C₂×C₁₆	1	1	yes	characteristic
36	C₂×D₁₇₃	—	2	2	no	—
37	C₂×D₁₇₃	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₁₇₃	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₁₇₃	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
41	Dic₁₇₃	C₂×C₁₆	1	1	yes	characteristic
42	Dic₁₇₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₁₇₃	—	2	1	no	—
44	C₂×C₁₇₃	C₂²×C₁₆	1	1	yes	characteristic
45	D₁₇₃	—	2	1	no	—
46	D₁₇₃	M₆₄	1	2	yes	complemented
47	C₁₇₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₆₄	—	173	1	no	maximal, Sylow
49	C₂²×C₁₆	—	173	1	no	—
50	M₆₄	—	173	2	no	—
51	M₆₄	—	173	2	no	—
52	C₂×C₃₂	—	173	2	no	—
53	C₂²×C₈	—	173	1	no	—
54	C₂×C₁₆	—	173	1	no	—
55	C₂×C₁₆	—	173	1	no	—
56	C₂×C₁₆	—	173	1	no	—
57	C₂×C₁₆	—	173	1	no	—
58	C₂×C₁₆	—	173	1	no	—
59	C₂×C₁₆	#10621924	1	1	yes	characteristic
60	C₃₂	—	173	4	no	—
61	C₂²×C₄	—	173	1	no	—
62	C₂×C₈	—	173	1	no	—
63	C₂×C₈	—	173	1	no	—
64	C₂×C₈	—	173	1	no	—
65	C₂×C₈	—	173	1	no	—
66	C₂×C₈	—	173	1	no	—
67	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
68	C₁₆	—	173	1	no	—
69	C₁₆	—	173	1	no	—
70	C₁₆	C₂×#10621924	1	1	yes	characteristic
71	C₁₆	C₂×#10621924	1	1	yes	characteristic
72	C₂³	—	173	1	no	—
73	C₂×C₄	—	173	1	no	—
74	C₂×C₄	—	173	1	no	—
75	C₂×C₄	—	173	1	no	—
76	C₂×C₄	—	173	1	no	—
77	C₂×C₄	—	173	1	no	—
78	C₂×C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
79	C₈	—	173	1	no	—
80	C₈	—	173	1	no	—
81	C₈	D₁₇₃⋊C₈	1	1	yes	characteristic
82	C₈	C₂²×#10621924	1	1	yes	characteristic
83	C₂²	—	346	2	no	—
84	C₂²	—	173	1	no	—
85	C₂²	—	173	1	no	—
86	C₂²	D₁₇₃⋊C₁₆	1	1	yes	characteristic
87	C₄	—	173	1	no	—
88	C₄	—	173	1	no	—
89	C₄	D₁₇₃⋊C₁₆	1	1	yes	characteristic
90	C₄	C₂×D₁₇₃⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	346	1	no	—
93	C₂	—	173	2	no	—
94	C₂	C₂×D₁₇₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×#10621924
commutator, socle	C₂×C₁₇₃	C₂²×C₁₆
Frattini	C₈	C₂²×#10621924
Fitting	C₂×C₁₆×C₁₇₃	C₄
prime radical	C₂²×D₁₇₃	C₁₆
cosocle	#14583801	C₂³
hypercenter	C₂×C₁₆	#10621924
hypocenter	C₁₇₃	C₂×M₆₄
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #26012424	C₂	semidirect
2. #26012423	C₂	semidirect
3. D₁₇₃⋊C₃₂	C₂	semidirect
5. #19149729	C₂²	semidirect
46. D₁₇₃	M₆₄	semidirect
47. C₁₇₃	C₂×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
#26012424	2
#26012423	2
D₁₇₃⋊C₃₂	2
C₂×C₁₆×D₁₇₃	2
C₂×M₆₄	173

Subgroups — D173⋊M64 #36369984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇₃⋊M₆₄ #36369984