Subgroups — #22626301

Order 9344.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989509	C₂	1	2	yes	maximal, complemented
2	#17989483	C₂	1	2	yes	maximal
3	#17989480	C₂	1	2	yes	maximal, complemented
4	M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	#14556665	C₂²	1	4	yes	—
6	C₂×#11924012	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
8	#14556501	C₄	1	1	yes	characteristic
9	#14556501	C₂²	1	1	yes	characteristic
10	C₈×Dic₇₃	C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
13	#11924031	—	2	4	no	—
14	C₂²×Dic₇₃	—	2	1	no	—
15	#11924012	—	2	2	no	—
16	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596831	C₂³	1	1	yes	characteristic
18	C₄×Dic₇₃	—	2	1	no	—
19	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	M₁₆×C₇₃	—	2	2	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	2	1	no	—
28	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	—	2	1	no	—
31	C₂×Dic₇₃	—	2	1	no	—
32	C₂×Dic₇₃	—	4	2	no	—
33	C₈×C₇₃	—	2	1	no	—
34	C₈×C₇₃	M₁₆	1	2	yes	—
35	#10596831	—	2	1	no	—
36	#10596831	#41	1	2	yes	—
37	C₂²×C₇₃	—	2	1	no	—
38	C₂²×C₇₃	—	4	1	no	—
39	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₇₃	—	2	1	no	—
41	C₄×C₇₃	#117	1	1	yes	characteristic
42	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
43	Dic₇₃	—	2	2	no	—
44	Dic₇₃	—	4	1	no	—
45	C₂×C₇₃	—	2	1	no	—
46	C₂×C₇₃	—	4	1	no	—
47	C₂×C₇₃	#432	1	1	yes	characteristic
48	#2165	—	73	1	no	maximal, Sylow
49	C₇₃	#2165	1	1	yes	characteristic, complemented, Sylow
50	C₄×M₁₆	—	73	1	no	—
51	#364	—	73	2	no	—
52	#349	—	73	2	no	—
53	#347	—	73	2	no	—
54	C₂×M₁₆	—	73	1	no	—
55	C₂×M₁₆	#64408	1	1	yes	characteristic
56	C₂×C₄²	—	73	1	no	—
57	M₃₂	—	73	4	no	—
58	#97	—	73	1	no	—
59	#97	—	73	1	no	—
60	C₄×C₈	—	73	1	no	—
61	C₄×C₈	—	73	1	no	—
62	C₂²×C₄	—	146	1	no	—
63	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	146	2	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	C₂×#64408	1	1	yes	characteristic
69	C₂×C₈	C₂×#64408	1	1	yes	characteristic
70	C₄²	—	73	1	no	—
71	C₄²	—	73	1	no	—
72	C₄²	—	146	1	no	—
73	C₁₆	—	146	4	no	—
74	C₂³	#11924038	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	292	2	no	—
78	C₂×C₄	—	146	1	no	—
79	C₂×C₄	—	146	1	no	—
80	C₂×C₄	#11924038	1	1	yes	characteristic
81	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	73	2	no	—
84	C₈	—	146	1	no	—
85	C₈	#11924037	1	2	yes	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#11924038	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	292	1	no	—
91	C₄	—	146	2	no	—
92	C₄	#14556670	1	1	yes	characteristic
93	C₄	C₂×#11924037	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#17989608	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂×C₇₃	#432
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#2165
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #17989509	C₂	semidirect
3. #17989480	C₂	semidirect
49. C₇₃	#2165	semidirect