Subgroups — #22624975

Order 9344.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556665	C₂	1	2	yes	maximal
2	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
3	#14556665	—	2	2	no	—
4	#14556665	C₄	1	4	yes	complemented
5	C₂×#11924031	—	2	2	no	—
6	C₂²×#10596831	C₄	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₄×#10596831	—	2	2	no	—
9	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
10	#11924031	—	2	4	no	—
11	C₂×#10596831	—	2	1	no	—
12	C₂×#10596831	—	2	1	no	—
13	C₂×#10596831	C₈	1	2	yes	—
14	C₂×#10596831	C₂×C₄	1	2	yes	—
15	C₂×#10596831	D₄	1	1	yes	characteristic
16	C₂×#10596831	D₄	1	2	yes	—
17	C₂×#10596831	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₇₃	—	2	1	no	—
19	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₇₃	—	2	1	no	—
21	C₄²×C₇₃	C₈	1	2	yes	—
22	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	2	4	no	—
24	C₂×C₄×C₇₃	—	2	2	no	—
25	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
31	#10596831	—	2	2	no	—
32	#10596831	C₂²⋊C₄	1	2	yes	—
33	#10596831	C₄⋊C₄	1	2	yes	—
34	C₂²×C₇₃	—	2	2	no	—
35	C₂²×C₇₃	#97	1	1	yes	characteristic
36	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₇₃	—	2	4	no	—
39	C₄×C₇₃	#95	1	1	yes	characteristic
40	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
41	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₇₃	—	2	1	no	—
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	#336	1	1	yes	characteristic
46	C₂×C₇₃	#364	1	2	yes	—
47	#1376	—	73	1	no	maximal, Sylow
48	C₇₃	#1376	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₃₂	—	73	2	no	—
50	C₂×C₄×C₈	—	73	1	no	—
51	C₂²×C₈	—	73	1	no	—
52	C₂²×C₈	—	73	1	no	—
53	C₂×C₄²	#64408	1	1	yes	characteristic
54	M₃₂	—	73	4	no	—
55	M₃₂	—	146	2	no	—
56	C₂×C₁₆	—	146	2	no	—
57	C₄×C₈	—	146	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
60	C₂×C₈	—	73	2	no	—
61	C₂×C₈	—	73	2	no	—
62	C₂×C₈	—	73	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	146	1	no	—
66	C₂×C₈	—	146	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	#10596833	1	2	yes	—
69	C₁₆	—	146	4	no	—
70	C₂³	#11924037	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₄×#64408	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
76	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
77	C₂×C₄	#11924036	1	1	yes	characteristic
78	C₂×C₄	#11924038	1	1	yes	characteristic
79	C₈	—	73	2	no	—
80	C₈	—	73	2	no	—
81	C₈	—	146	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#14556646	1	1	yes	characteristic
84	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
85	C₂²	#14556658	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#10596833	1	1	yes	characteristic
89	C₄	#14556648	1	1	yes	characteristic
90	C₄	C₄⋊#10596833	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#17989453	1	1	yes	characteristic
94	C₂	#17989510	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#64408
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂²×C₇₃	C₄⋊C₈
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	#1376
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #14556665	C₄	semidirect
48. C₇₃	#1376	semidirect