Subgroups — C₂×#22627035 #34034480

Order 18688.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627035	C₂	1	4	yes	maximal, direct product factor
2	C₂×#17989669	C₂	1	2	yes	maximal, complemented
3	C₂²×#14556641	C₂	1	1	yes	maximal, characteristic
4	#17989669	C₂²	1	4	yes	complemented
5	C₂×#14556641	C₄	1	2	yes	—
6	C₂×#14556641	C₄	1	1	yes	characteristic
7	C₂×#14556641	C₂²	1	1	yes	characteristic
8	C₂×#14556641	C₂²	1	2	yes	—
9	C₂²×#11924003	C₄	1	1	yes	characteristic
10	#14556641	C₂×C₄	1	1	yes	characteristic
11	#14556641	C₂×C₄	1	2	yes	—
12	#14556641	C₂³	1	1	yes	characteristic
13	C₂×#11924003	C₈	1	2	yes	—
14	C₂×#11924003	C₈	1	1	yes	characteristic
15	C₂×#11924003	C₂×C₄	1	2	yes	—
16	C₂×#11924003	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₇₃	C₈	1	1	yes	characteristic
18	#11924003	C₂×C₈	1	2	yes	—
19	#11924003	C₂×C₈	1	1	yes	characteristic
20	#11924003	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₁₆	1	1	yes	characteristic
23	C₂×C₈×C₇₃	C₁₆	1	2	yes	—
24	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	—
25	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂³×C₇₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₃₂	1	2	yes	—
28	C₂×C₄×C₇₃	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂×C₁₆	1	2	yes	—
30	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₇₃	C₂×C₁₆	1	2	yes	—
32	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
34	C₂²×C₇₃	—	2	2	no	—
35	C₂²×C₇₃	C₂×C₃₂	1	2	yes	—
36	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₇₃	C₂×C₃₂	1	2	yes	—
38	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
39	C₄×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
40	C₂×M₁₂₈	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	—	2	2	no	—
42	C₂×C₇₃	M₁₂₈	1	2	yes	complemented
43	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
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	2	no	—
50	C₂×C₃₂	—	73	1	no	—
51	C₂×C₃₂	—	73	1	no	—
52	C₂×C₃₂	—	73	2	no	—
53	C₆₄	—	73	4	no	—
54	C₂²×C₈	#10596842	1	1	yes	characteristic
55	C₂×C₁₆	—	73	2	no	—
56	C₂×C₁₆	—	73	2	no	—
57	C₂×C₁₆	—	73	1	no	—
58	C₂×C₁₆	—	73	1	no	—
59	C₃₂	—	73	1	no	—
60	C₃₂	—	73	1	no	—
61	C₃₂	—	73	2	no	—
62	C₂²×C₄	#11924040	1	1	yes	characteristic
63	C₂×C₈	#11924040	1	1	yes	characteristic
64	C₂×C₈	#11924040	1	2	yes	—
65	C₂×C₈	C₂×#10596842	1	2	yes	—
66	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
67	C₁₆	—	73	2	no	—
68	C₁₆	—	73	1	no	—
69	C₁₆	—	73	1	no	—
70	C₂³	#14556681	1	1	yes	characteristic
71	C₂×C₄	#14556681	1	2	yes	—
72	C₂×C₄	#14556681	1	1	yes	characteristic
73	C₂×C₄	C₂×#11924040	1	2	yes	—
74	C₂×C₄	C₂×#11924040	1	1	yes	characteristic
75	C₈	C₂×#11924040	1	2	yes	—
76	C₈	C₂×#11924040	1	1	yes	characteristic
77	C₈	C₂²×#10596842	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#14556681	1	2	yes	—
80	C₂²	C₂×#14556681	1	1	yes	characteristic
81	C₄	C₂×#14556681	1	2	yes	—
82	C₄	C₂×#14556681	1	1	yes	characteristic
83	C₄	C₂²×#11924040	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#22627035	1	2	yes	direct product factor
86	C₂	C₂²×#14556681	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #22627035	C₂	direct (N × H)
2. C₂×#17989669	C₂	semidirect
4. #17989669	C₂²	semidirect
42. C₂×C₇₃	M₁₂₈	semidirect
47. C₇₃	C₂×M₁₂₈	semidirect
85. C₂	#22627035	direct (N × H)

Maximal subgroups

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

subgroup	index
#22627035	2
C₂×#17989669	2
C₂²×#14556641	2
C₂×M₁₂₈	73

Subgroups — C2×#22627035 #34034480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22627035 #34034480