Subgroups — #22624999

Order 9344.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989597	C₂	1	2	yes	maximal
2	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
3	#14556670	—	2	2	no	—
4	#14556660	—	2	2	no	—
5	#14556659	C₄	1	4	yes	complemented
6	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
7	#14556530	—	2	2	no	—
8	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
10	C₄⋊#64408	—	2	4	no	—
11	C₂²⋊#64408	—	4	2	no	—
12	C₄×#64408	—	4	2	no	—
13	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
14	C₂×#10596831	Q₈	1	1	yes	characteristic
15	C₈×D₇₃	C₂×C₄	1	2	yes	—
16	C₈×D₇₃	D₄	1	2	yes	—
17	#11924003	—	2	1	no	—
18	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₇₃	—	2	1	no	—
20	C₂²×D₇₃	D₈	1	1	yes	characteristic
21	C₂×#64408	—	4	4	no	—
22	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
23	C₂×Dic₇₃	Q₁₆	1	1	yes	characteristic
24	C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
25	C₄×D₇₃	SD₁₆	1	2	yes	—
26	C₈×C₇₃	C₄²	1	1	yes	characteristic
27	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	#10596831	C₄⋊C₄	1	2	yes	—
29	C₂²×C₇₃	#107	1	1	yes	characteristic
30	C₂×D₇₃	—	4	1	no	—
31	C₂×D₇₃	#102	1	2	yes	—
32	#64408	—	8	4	no	—
33	C₄×C₇₃	#95	1	1	yes	characteristic
34	C₄×C₇₃	#106	1	1	yes	characteristic
35	Dic₇₃	#103	1	2	yes	—
36	C₂×C₇₃	—	2	1	no	—
37	C₂×C₇₃	#340	1	1	yes	characteristic
38	D₇₃	—	2	2	no	—
39	#1384	—	73	1	no	maximal, Sylow
40	C₇₃	#1384	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₃₂	—	73	1	no	—
42	#427	—	73	2	no	—
43	C₂²×C₈	—	73	1	no	—
44	#117	—	146	2	no	—
45	M₃₂	—	146	2	no	—
46	C₂×C₁₆	—	73	1	no	—
47	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
48	#107	—	146	2	no	—
49	#106	—	73	4	no	—
50	C₂²×C₄	—	73	1	no	—
51	C₂×C₈	—	73	1	no	—
52	C₂×C₈	—	73	2	no	—
53	C₂×C₈	—	73	2	no	—
54	C₂×C₈	C₂×#64408	1	1	yes	characteristic
55	C₄⋊C₄	—	146	4	no	—
56	C₂²⋊C₄	—	292	2	no	—
57	C₄²	—	292	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	146	1	no	—
60	C₂³	—	73	1	no	—
61	C₂×C₄	—	292	4	no	—
62	C₂×C₄	—	73	1	no	—
63	C₂×C₄	—	73	2	no	—
64	C₂×C₄	—	73	2	no	—
65	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
66	C₈	—	73	2	no	—
67	C₈	C₄×#64408	1	1	yes	characteristic
68	C₈	C₂²⋊#64408	1	1	yes	characteristic
69	C₂²	—	292	1	no	—
70	C₂²	—	73	2	no	—
71	C₂²	#14556660	1	1	yes	characteristic
72	C₄	—	584	4	no	—
73	C₄	—	73	2	no	—
74	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
75	C₄	#14556659	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	146	2	no	—
78	C₂	#17989461	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556659
commutator	C₈×C₇₃	C₄²
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂×C₇₃	#340
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1384
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #14556659	C₄	semidirect
8. C₂×#11924003	C₄	semidirect
9. C₂×C₁₆×C₇₃	C₄	semidirect
40. C₇₃	#1384	semidirect
47. C₂×C₁₆	#64408	semidirect