Subgroups — C₂×#22625099 #34014561

Order 18688.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625099	C₂	1	4	yes	maximal, direct product factor
2	C₂×#17989426	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#17989426	C₂²	1	4	yes	complemented
5	C₂×C₁₆×D₇₃	C₄	1	1	yes	characteristic
6	C₂×#14556497	C₂²	1	1	yes	characteristic
7	C₃₂×D₇₃	C₄	1	2	yes	—
8	C₃₂×D₇₃	C₂²	1	2	yes	—
9	C₂×C₃₂×C₇₃	C₄	1	1	yes	characteristic
10	C₂×C₈×D₇₃	C₈	1	1	yes	characteristic
11	C₂×#11924003	C₈	1	1	yes	characteristic
12	C₁₆×D₇₃	C₈	1	2	yes	—
13	C₁₆×D₇₃	C₂×C₄	1	2	yes	—
14	#14556497	C₂×C₄	1	1	yes	characteristic
15	#14556497	C₂³	1	1	yes	characteristic
16	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₇₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×D₇₃	C₁₆	1	1	yes	characteristic
19	C₂×#10596831	C₁₆	1	1	yes	characteristic
20	C₈×D₇₃	C₁₆	1	2	yes	—
21	C₈×D₇₃	C₂×C₈	1	2	yes	—
22	#11924003	C₂×C₈	1	2	yes	—
23	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×D₇₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
29	C₄×D₇₃	C₃₂	1	2	yes	—
30	C₄×D₇₃	C₂×C₁₆	1	2	yes	—
31	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
33	#10596831	C₂×C₁₆	1	2	yes	—
34	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
35	C₂×D₇₃	C₆₄	1	4	yes	complemented
36	C₂×D₇₃	C₂×C₃₂	1	2	yes	—
37	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
39	Dic₇₃	C₂×C₃₂	1	2	yes	—
40	C₂²×C₆₄	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	C₂×C₆₄	1	2	yes	complemented
42	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
43	D₇₃	C₂×C₆₄	1	4	yes	complemented
44	C₂²×C₃₂	—	73	1	no	—
45	C₂×C₆₄	—	73	2	no	—
46	C₂×C₆₄	—	73	4	no	—
47	C₇₃	C₂²×C₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₁₆	—	73	1	no	—
49	C₂×C₃₂	—	73	1	no	—
50	C₂×C₃₂	—	73	2	no	—
51	C₂×C₃₂	—	73	2	no	—
52	C₂×C₃₂	#64408	1	1	yes	characteristic
53	C₆₄	—	73	4	no	—
54	C₂²×C₈	—	73	1	no	—
55	C₂×C₁₆	—	73	1	no	—
56	C₂×C₁₆	—	73	2	no	—
57	C₂×C₁₆	—	73	2	no	—
58	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
59	C₃₂	—	73	1	no	—
60	C₃₂	—	73	1	no	—
61	C₃₂	C₂×#64408	1	2	yes	—
62	C₂²×C₄	—	73	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	2	no	—
66	C₂×C₈	#11924036	1	1	yes	characteristic
67	C₁₆	—	73	2	no	—
68	C₁₆	#11924036	1	1	yes	characteristic
69	C₁₆	C₂²×#64408	1	1	yes	characteristic
70	C₂³	—	73	1	no	—
71	C₂×C₄	—	73	1	no	—
72	C₂×C₄	—	73	2	no	—
73	C₂×C₄	—	73	2	no	—
74	C₂×C₄	#14556664	1	1	yes	characteristic
75	C₈	—	73	2	no	—
76	C₈	#14556664	1	1	yes	characteristic
77	C₈	C₂×#11924036	1	1	yes	characteristic
78	C₂²	—	73	2	no	—
79	C₂²	—	73	4	no	—
80	C₂²	#17989518	1	1	yes	characteristic
81	C₄	—	73	2	no	—
82	C₄	#17989518	1	1	yes	characteristic
83	C₄	C₂×#14556664	1	1	yes	characteristic
84	C₂	—	73	4	no	—
85	C₂	#22625099	1	2	yes	direct product factor
86	C₂	C₂×#17989518	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	#64408
commutator, hypocenter	C₇₃	C₂²×C₆₄
Frattini	C₁₆	C₂²×#64408
Fitting	C₂×C₃₂×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₃₂
prime radical	C₂²×D₇₃	C₃₂
cosocle	#14556497	C₂³
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #22625099	C₂	direct (N × H)
2. C₂×#17989426	C₂	semidirect
4. #17989426	C₂²	semidirect
35. C₂×D₇₃	C₆₄	semidirect
41. C₂×C₇₃	C₂×C₆₄	semidirect
43. D₇₃	C₂×C₆₄	semidirect
47. C₇₃	C₂²×C₆₄	semidirect
85. C₂	#22625099	direct (N × H)

Maximal subgroups

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

subgroup	index
#22625099	2
C₂×#17989426	2
C₂×C₃₂×D₇₃	2
C₂²×C₆₄	73

Subgroups — C2×#22625099 #34014561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625099 #34014561