Subgroups — #22626300

Order 9344.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989510	C₂	1	2	yes	maximal, complemented
2	#17989483	C₂	1	2	yes	maximal
3	#17989479	C₂	1	2	yes	maximal, complemented
4	C₄×#11924012	C₂	1	1	yes	maximal, characteristic
5	#14556665	C₂²	1	4	yes	—
6	C₂×#11924012	C₄	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	1	yes	characteristic
8	#14556502	C₄	1	1	yes	characteristic
9	#14556502	C₂²	1	1	yes	characteristic
10	C₄×#10596831	C₄	1	1	yes	characteristic
11	C₄×#10596831	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
13	#11924031	—	2	4	no	—
14	#11924012	—	2	2	no	—
15	#11924012	—	2	2	no	—
16	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	—	2	1	no	—
21	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₇₃	—	2	1	no	—
23	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×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	—	2	1	no	—
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	—	4	2	no	—
31	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	#10596831	—	2	1	no	—
34	#10596831	—	2	1	no	—
35	#10596831	M₁₆	1	2	yes	—
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	2	no	—
41	C₄×C₇₃	—	2	1	no	—
42	C₄×C₇₃	—	4	1	no	—
43	C₄×C₇₃	#117	1	1	yes	characteristic
44	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
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	—	73	1	no	—
56	C₂×C₄²	#64408	1	1	yes	characteristic
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	—	2	1	no	—
63	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
64	M₁₆	—	146	2	no	—
65	M₁₆	—	146	2	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	—	73	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₄²	—	2	1	no	—
71	C₄²	C₂×#64408	1	1	yes	characteristic
72	C₄²	C₂×#64408	1	1	yes	characteristic
73	C₁₆	—	146	4	no	—
74	C₂³	#11924037	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#11924037	1	1	yes	characteristic
81	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
82	C₈	—	73	2	no	—
83	C₈	—	73	2	no	—
84	C₈	—	146	1	no	—
85	C₈	—	146	1	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#11924037	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	2	1	no	—
91	C₄	—	4	1	no	—
92	C₄	#14556670	1	1	yes	characteristic
93	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#17989607	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂×C₇₃	#432
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	#2165
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #17989510	C₂	semidirect
3. #17989479	C₂	semidirect
49. C₇₃	#2165	semidirect