Subgroups — #22625046

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989519	C₂	1	2	yes	maximal, complemented
2	C₂×#14556531	C₂	1	1	yes	maximal, characteristic
3	#14556641	—	2	2	no	—
4	#14556531	—	2	2	no	—
5	C₂×#11924003	C₄	1	1	yes	characteristic
6	C₂×#11924003	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
8	#11924003	—	2	1	no	—
9	#11924003	D₄	1	2	yes	—
10	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
11	C₂×C₈×C₇₃	—	2	1	no	—
12	C₂×C₈×C₇₃	—	2	1	no	—
13	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
14	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₇₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₇₃	—	2	1	no	—
17	C₂×C₄×C₇₃	—	2	1	no	—
18	C₂×C₄×C₇₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₇₃	—	2	1	no	—
21	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₃	M₁₆	1	1	yes	characteristic
23	C₂²×C₇₃	—	2	1	no	—
24	C₂²×C₇₃	—	4	1	no	—
25	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
26	C₄×C₇₃	—	2	1	no	—
27	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₇₃	M₃₂	1	1	yes	characteristic
29	C₂×C₇₃	—	2	1	no	—
30	C₂×C₇₃	—	4	1	no	—
31	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
32	#1400	—	73	1	no	maximal, Sylow
33	C₇₃	#1400	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₃₂	—	73	1	no	—
35	M₆₄	—	73	2	no	—
36	C₂²×C₈	#64408	1	1	yes	characteristic
37	M₃₂	—	146	2	no	—
38	C₂×C₁₆	—	73	1	no	—
39	C₂×C₁₆	—	73	1	no	—
40	C₃₂	—	146	2	no	—
41	C₂²×C₄	#10596833	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	#10596833	1	1	yes	characteristic
45	C₂×C₈	C₂×#64408	1	1	yes	characteristic
46	C₁₆	—	73	2	no	—
47	C₁₆	—	146	1	no	—
48	C₂³	#11924031	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	#11924031	1	1	yes	characteristic
52	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	C₂²⋊#64408	1	1	yes	characteristic
55	C₈	#11924037	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×#11924031	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	C₂²⋊#10596833	1	1	yes	characteristic
61	C₄	#14556665	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊#11924031	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#64408
commutator	C₂²×C₇₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂×C₇₃	C₂²⋊C₁₆
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1400
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #17989519	C₂	semidirect
33. C₇₃	#1400	semidirect