Subgroups — C₂×#22627036 #34034482

Order 18688.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627036	C₂	1	4	yes	maximal, direct product factor
2	C₂×#17989669	C₂	1	2	yes	maximal, complemented
3	C₂×#17989518	C₂	1	1	yes	maximal, characteristic
4	#17989669	C₂²	1	4	yes	complemented
5	#17989518	C₄	1	2	yes	—
6	#17989518	C₂²	1	2	yes	—
7	C₂×#14556641	C₄	1	1	yes	characteristic
8	C₂×#14556641	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×D₇₃	C₄	1	1	yes	characteristic
10	#14556641	C₂×C₄	1	2	yes	—
11	#14556641	C₂×C₄	1	1	yes	characteristic
12	#14556641	C₂³	1	1	yes	characteristic
13	C₂×C₈×D₇₃	C₈	1	1	yes	characteristic
14	C₂×#11924003	C₂×C₄	1	1	yes	characteristic
15	C₁₆×D₇₃	C₈	1	2	yes	—
16	C₁₆×D₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
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	1	yes	characteristic
23	#11924003	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₇₃	C₂×C₈	1	2	yes	—
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	—	2	2	no	—
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	C₂×M₁₂₈	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	M₁₂₈	1	2	yes	complemented
42	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
43	D₇₃	—	2	2	no	—
44	C₂²×C₃₂	—	73	1	no	—
45	M₁₂₈	—	73	4	no	—
46	C₂×C₆₄	—	73	2	no	—
47	C₇₃	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₁₆	—	73	1	no	—
49	C₂×C₃₂	—	73	1	no	—
50	C₂×C₃₂	—	73	1	no	—
51	C₂×C₃₂	—	73	2	no	—
52	C₂×C₃₂	—	73	2	no	—
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	#10596842	1	1	yes	characteristic
59	C₃₂	—	73	1	no	—
60	C₃₂	—	73	2	no	—
61	C₃₂	—	73	1	no	—
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	C₂×#10596842	1	1	yes	characteristic
67	C₁₆	—	73	1	no	—
68	C₁₆	—	73	1	no	—
69	C₁₆	C₂×#10596842	1	2	yes	—
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	#14556686	1	1	yes	characteristic
75	C₈	—	73	2	no	—
76	C₈	#14556686	1	1	yes	characteristic
77	C₈	C₂²×#10596842	1	1	yes	characteristic
78	C₂²	—	73	2	no	—
79	C₂²	—	146	2	no	—
80	C₂²	#17989694	1	1	yes	characteristic
81	C₄	—	73	2	no	—
82	C₄	#17989694	1	1	yes	characteristic
83	C₄	C₂×#14556686	1	1	yes	characteristic
84	C₂	—	146	2	no	—
85	C₂	#22627036	1	2	yes	direct product factor
86	C₂	C₂×#17989694	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#10596842
commutator	C₂×C₇₃	C₂²×C₃₂
Frattini	C₈	C₂²×#10596842
Fitting	C₂×C₁₆×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₃₂
prime radical	C₂²×D₇₃	C₃₂
cosocle	#14556641	C₂³
hypercenter	C₂×C₁₆	#10596842
hypocenter	C₇₃	C₂×M₁₂₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #22627036	C₂	direct (N × H)
2. C₂×#17989669	C₂	semidirect
4. #17989669	C₂²	semidirect
41. C₂×C₇₃	M₁₂₈	semidirect
47. C₇₃	C₂×M₁₂₈	semidirect
85. C₂	#22627036	direct (N × H)

Maximal subgroups

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

subgroup	index
#22627036	2
C₂×#17989669	2
C₂×#17989518	2
C₂×M₁₂₈	73

Subgroups — C2×#22627036 #34034482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22627036 #34034482