Subgroups — #22627165

Order 9344.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989696	C₂	1	2	yes	maximal, complemented
2	#17989695	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989694	C₂	1	2	yes	maximal, complemented
4	C₂×#14556681	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989646	C₂	1	1	yes	maximal, characteristic
6	#14556681	C₂²	1	1	yes	characteristic
7	#14556681	C₂²	1	1	yes	characteristic
8	#14556681	C₂²	1	2	yes	—
9	#14556666	C₄	1	2	yes	—
10	#14556665	C₄	1	1	yes	characteristic
11	#14556664	C₂²	1	2	yes	—
12	C₂×#11924031	C₂²	1	1	yes	characteristic
13	#14556599	C₄	1	1	yes	characteristic
14	#11924031	C₂×C₄	1	1	yes	characteristic
15	#11924031	C₂×C₄	1	2	yes	—
16	#11924031	C₂³	1	1	yes	characteristic
17	#11924028	C₈	1	1	yes	characteristic
18	#11924011	C₈	1	2	yes	—
19	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
20	C₈×D₇₃	C₂×C₄	1	2	yes	—
21	M₁₆×C₇₃	C₈	1	1	yes	characteristic
22	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₇₃	C₁₆	1	2	yes	—
24	D₂₉₂	C₁₆	1	1	yes	characteristic
25	C₄×D₇₃	C₂×C₈	1	2	yes	—
26	Dic₁₄₆	C₁₆	1	1	yes	characteristic
27	C₈×C₇₃	C₂×C₈	1	2	yes	—
28	#10596831	C₂×C₈	1	1	yes	characteristic
29	#10596831	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₇₃	C₂×C₁₆	1	2	yes	—
32	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
34	Dic₇₃	C₂×C₁₆	1	2	yes	—
35	C₂×C₇₃	—	2	1	no	—
36	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
37	D₇₃	—	2	2	no	—
38	#2258	—	73	1	no	maximal, Sylow
39	C₇₃	#2258	1	1	yes	characteristic, complemented, Sylow
40	#504	—	73	1	no	—
41	M₆₄	—	73	1	no	—
42	M₆₄	—	73	2	no	—
43	C₂×C₃₂	—	73	1	no	—
44	C₂×C₃₂	—	73	2	no	—
45	#131	—	73	1	no	—
46	M₃₂	—	73	1	no	—
47	M₃₂	—	73	2	no	—
48	C₂×C₁₆	—	73	1	no	—
49	C₂×C₁₆	—	73	2	no	—
50	C₃₂	—	73	1	no	—
51	C₃₂	—	73	1	no	—
52	C₃₂	—	73	2	no	—
53	#41	—	73	1	no	—
54	M₁₆	—	73	2	no	—
55	M₁₆	#10596842	1	1	yes	characteristic
56	C₂×C₈	—	73	1	no	—
57	C₂×C₈	—	73	2	no	—
58	C₁₆	—	73	1	no	—
59	C₁₆	—	73	2	no	—
60	C₁₆	—	73	1	no	—
61	Q₈	—	73	1	no	—
62	D₄	—	73	2	no	—
63	D₄	—	73	1	no	—
64	C₂×C₄	—	73	2	no	—
65	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
66	C₈	—	73	1	no	—
67	C₈	—	73	1	no	—
68	C₈	C₂×#10596842	1	2	yes	—
69	C₂²	—	73	2	no	—
70	C₂²	#14556686	1	1	yes	characteristic
71	C₄	—	73	2	no	—
72	C₄	#14556686	1	1	yes	characteristic
73	C₄	C₂²×#10596842	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	146	2	no	—
76	C₂	C₂×#14556686	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₁₆
Fitting	M₁₆×C₇₃	C₈
hypercenter	M₁₆	#10596842
hypocenter	C₇₃	#2258
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #17989696	C₂	semidirect
2. #17989695	C₂	semidirect
3. #17989694	C₂	semidirect
4. C₂×#14556681	C₂	semidirect
39. C₇₃	#2258	semidirect