Subgroups — C₂²⋊#17989669 #34033155

Order 18688.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989669	C₂	1	2	yes	maximal, complemented
2	C₂²×#14556641	C₂	1	1	yes	maximal, characteristic
3	#17989669	—	2	2	no	—
4	C₂×#14556641	—	2	2	no	—
5	C₂×#14556641	C₄	1	1	yes	characteristic
6	C₂×#14556641	C₂²	1	1	yes	characteristic
7	C₂²×#11924003	C₄	1	1	yes	characteristic
8	#14556641	—	2	1	no	—
9	#14556641	D₄	1	2	yes	—
10	C₂×#11924003	—	2	1	no	—
11	C₂×#11924003	—	2	1	no	—
12	C₂×#11924003	C₈	1	1	yes	characteristic
13	C₂×#11924003	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₇₃	C₈	1	1	yes	characteristic
15	#11924003	—	2	1	no	—
16	#11924003	C₂²⋊C₄	1	1	yes	characteristic
17	#11924003	M₁₆	1	1	yes	characteristic
18	C₂²×C₄×C₇₃	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₇₃	—	2	1	no	—
20	C₂×C₈×C₇₃	—	2	1	no	—
21	C₂×C₈×C₇₃	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂³×C₇₃	C₃₂	1	1	yes	characteristic
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
28	C₈×C₇₃	—	2	1	no	—
29	C₈×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₈×C₇₃	M₃₂	1	1	yes	characteristic
31	C₂²×C₇₃	—	2	1	no	—
32	C₂²×C₇₃	—	2	1	no	—
33	C₂²×C₇₃	C₆₄	1	2	yes	complemented
34	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
35	C₄×C₇₃	—	2	1	no	—
36	C₄×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
37	C₄×C₇₃	M₆₄	1	1	yes	characteristic
38	C₂²⋊C₆₄	—	73	1	no	maximal, Sylow
39	C₂×C₇₃	—	2	2	no	—
40	C₂×C₇₃	C₂²⋊C₃₂	1	1	yes	characteristic
41	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
42	C₂×C₇₃	M₁₂₈	1	1	yes	characteristic
43	C₂²×C₃₂	—	73	1	no	—
44	C₂×C₆₄	—	73	2	no	—
45	C₇₃	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₁₆	—	73	1	no	—
47	C₂×C₃₂	—	73	1	no	—
48	C₂×C₃₂	—	73	1	no	—
49	C₂×C₃₂	—	146	2	no	—
50	C₆₄	—	146	2	no	—
51	C₂²×C₈	#10596842	1	1	yes	characteristic
52	C₂×C₁₆	—	73	1	no	—
53	C₂×C₁₆	—	73	1	no	—
54	C₂×C₁₆	—	146	1	no	—
55	C₂×C₁₆	—	146	1	no	—
56	C₃₂	—	73	2	no	—
57	C₃₂	—	146	1	no	—
58	C₂²×C₄	#11924040	1	1	yes	characteristic
59	C₂×C₈	—	2	1	no	—
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	#11924040	1	1	yes	characteristic
62	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
63	C₁₆	—	73	1	no	—
64	C₁₆	—	73	1	no	—
65	C₁₆	—	146	1	no	—
66	C₂³	#14556681	1	1	yes	characteristic
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	#14556681	1	1	yes	characteristic
70	C₂×C₄	C₂×#11924040	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	C₂²⋊#10596842	1	1	yes	characteristic
73	C₈	#14556687	1	1	yes	characteristic
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	#17989669	1	2	yes	complemented
77	C₂²	C₂×#14556681	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	C₂²⋊#11924040	1	1	yes	characteristic
80	C₄	#17989695	1	1	yes	characteristic
81	C₂	—	2	2	no	—
82	C₂	C₂²⋊#14556681	1	1	yes	characteristic
83	C₂	C₂×#17989669	1	1	yes	characteristic
84	C₂	#22627035	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₆₄
Fitting	C₂²×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₃₂
prime radical	C₂³×C₇₃	C₃₂
cosocle	C₂×#14556641	C₂²
hypercenter	C₂²×C₈	#10596842
hypocenter	C₇₃	C₂²⋊C₆₄
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. C₂×#17989669	C₂	semidirect
33. C₂²×C₇₃	C₆₄	semidirect
45. C₇₃	C₂²⋊C₆₄	semidirect
76. C₂²	#17989669	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989669	2
C₂²×#14556641	2
C₂²⋊C₆₄	73

Subgroups — C22⋊#17989669 #34033155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#17989669 #34033155