Subgroups — #22624895

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989509	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989428	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988704	C₂	1	1	yes	maximal, characteristic
4	#14556665	—	2	1	no	—
5	C₄×#10596833	—	2	1	no	—
6	#14556598	—	2	1	no	—
7	#14556527	C₄	1	1	yes	characteristic
8	#14556518	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	#135×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	2	2	no	—
12	#11924031	—	4	1	no	—
13	#11924012	—	2	1	no	—
14	#11924012	—	4	1	no	—
15	C₂×#10596831	—	4	1	no	—
16	C₂×#10596831	D₄	1	1	yes	characteristic
17	C₄×Dic₇₃	D₄	1	1	yes	characteristic
18	#41×C₇₃	—	2	1	no	—
19	Q₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
20	SD₁₆×C₇₃	—	2	1	no	—
21	D₈×C₇₃	C₈	1	1	yes	characteristic, complemented
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	Q₈×C₇₃	—	2	1	no	—
24	D₄×C₇₃	—	2	1	no	—
25	D₄×C₇₃	—	4	1	no	—
26	C₂×C₄×C₇₃	—	4	1	no	—
27	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	—	2	1	no	—
29	#10596833	—	4	2	no	—
30	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₃	M₁₆	1	1	yes	characteristic
32	#10596831	—	4	1	no	—
33	#10596831	D₈	1	1	yes	characteristic
34	#10596831	SD₁₆	1	1	yes	characteristic
35	C₂²×C₇₃	—	4	1	no	—
36	C₂²×C₇₃	#104	1	1	yes	characteristic
37	C₄×C₇₃	—	4	1	no	—
38	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₇₃	#102	1	1	yes	characteristic
40	Dic₇₃	—	2	2	no	—
41	C₂×C₇₃	—	2	1	no	—
42	C₂×C₇₃	—	8	1	no	—
43	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
44	#1336	—	73	1	no	maximal, Sylow
45	C₇₃	#1336	1	1	yes	characteristic, complemented, Sylow
46	#443	—	73	1	no	—
47	#364	—	73	1	no	—
48	#322	—	73	1	no	—
49	#135	#64408	1	1	yes	characteristic
50	#131	—	146	1	no	—
51	M₃₂	—	146	1	no	—
52	#108	—	73	1	no	—
53	#104	—	146	1	no	—
54	C₄×C₈	—	73	1	no	—
55	C₄×C₈	—	146	1	no	—
56	#41	—	2	1	no	—
57	Q₁₆	#10596833	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#10596833	1	1	yes	characteristic, complemented
60	M₁₆	—	292	1	no	—
61	M₁₆	—	146	1	no	—
62	C₂×C₈	—	292	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	146	2	no	—
65	C₂×C₈	C₂×#64408	1	1	yes	characteristic
66	C₄²	—	73	1	no	—
67	C₁₆	—	292	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	146	1	no	—
73	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
74	C₈	—	292	2	no	—
75	C₈	—	292	1	no	—
76	C₈	—	73	1	no	—
77	C₈	—	73	1	no	—
78	C₈	C₂×#10596833	1	1	yes	characteristic
79	C₈	#11924037	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#14556655	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	146	2	no	—
84	C₄	C₂²⋊#10596833	1	1	yes	characteristic
85	C₄	#14556653	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#10596833	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556653
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	#135×C₇₃	C₄
socle	C₂×C₇₃	D₄⋊C₈
hypercenter	#135	#64408
hypocenter	C₇₃	#1336
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #17989509	C₂	semidirect
2. #17989428	C₂	semidirect
19. Q₁₆×C₇₃	C₈	semidirect
21. D₈×C₇₃	C₈	semidirect
45. C₇₃	#1336	semidirect
57. Q₁₆	#10596833	semidirect
59. D₈	#10596833	semidirect