Subgroups — #22625588

Order 9344.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556646	C₂	1	3	yes	maximal
2	C₂×C₄×#10596833	C₂	1	3	yes	maximal
3	#17988432	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596833	C₂²	1	1	yes	characteristic
5	C₂²×#10596833	C₂²	1	3	yes	—
6	#14556646	C₄	1	12	yes	complemented
7	C₄×#10596833	C₄	1	12	yes	complemented
8	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
9	#14556498	C₄	1	3	yes	—
10	#95×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	C₂×C₄	1	6	yes	—
12	C₂×#10596833	C₂×C₄	1	6	yes	—
13	C₂×#10596833	C₂×C₄	1	12	yes	—
14	C₂²×Dic₇₃	C₂×C₄	1	3	yes	—
15	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
16	C₄×Dic₇₃	C₂×C₄	1	6	yes	—
17	C₄×Dic₇₃	C₂×C₄	1	6	yes	—
18	C₂²×C₄×C₇₃	C₂×C₄	1	3	yes	—
19	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₄×C₇₃	—	2	6	no	—
21	C₂×C₄×C₇₃	C₄²	1	6	yes	—
22	C₂×Dic₇₃	—	2	3	no	—
23	C₂×Dic₇₃	—	2	3	no	—
24	C₂×Dic₇₃	C₄²	1	6	yes	—
25	C₂×Dic₇₃	C₂²×C₄	1	3	yes	—
26	C₂×Dic₇₃	C₂²×C₄	1	3	yes	—
27	#10596833	C₄²	1	4	yes	—
28	#10596833	C₄²	1	12	yes	—
29	C₂²×C₇₃	C₂×C₄²	1	3	yes	—
30	C₂²×C₇₃	#131	1	3	yes	—
31	C₂²×C₇₃	#131	1	1	yes	characteristic
32	C₄×C₇₃	—	2	6	no	—
33	Dic₇₃	—	2	6	no	—
34	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
35	Dic₇₃	C₂×C₄²	1	3	yes	—
36	C₂×C₇₃	C₄³	1	1	yes	characteristic
37	C₂×C₇₃	#405	1	3	yes	—
38	C₂×C₇₃	#405	1	3	yes	—
39	#1726	—	73	1	no	maximal, Sylow
40	C₇₃	#1726	1	1	yes	characteristic, complemented, Sylow
41	C₂×#97	—	73	3	no	—
42	C₂×C₄×C₈	—	73	3	no	—
43	#376	—	73	1	no	—
44	C₂²×C₈	—	73	1	no	—
45	C₂²×C₈	—	73	3	no	—
46	C₂×C₄²	—	73	3	no	—
47	#97	—	73	12	no	—
48	C₄×C₈	—	73	12	no	—
49	#95	—	73	3	no	—
50	#95	#64408	1	1	yes	characteristic
51	C₂²×C₄	—	73	1	no	—
52	C₂²×C₄	—	73	3	no	—
53	C₂²×C₄	C₂×#64408	1	3	yes	—
54	C₂×C₈	—	73	6	no	—
55	C₂×C₈	—	73	6	no	—
56	C₂×C₈	—	73	12	no	—
57	C₄²	—	73	6	no	—
58	C₄²	—	73	6	no	—
59	C₂³	C₂²×#64408	1	1	yes	characteristic
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	73	3	no	—
62	C₂×C₄	—	73	3	no	—
63	C₂×C₄	—	73	6	no	—
64	C₂×C₄	—	146	3	no	—
65	C₂×C₄	—	146	3	no	—
66	C₂×C₄	C₄×#64408	1	6	yes	—
67	C₈	—	73	4	no	—
68	C₈	—	73	12	no	—
69	C₂²	C₂×C₄×#64408	1	3	yes	—
70	C₂²	#14556678	1	3	yes	—
71	C₂²	#14556679	1	1	yes	characteristic
72	C₄	—	2	6	no	—
73	C₄	—	73	1	no	—
74	C₄	—	73	3	no	—
75	C₄	—	146	6	no	—
76	C₂	C₄²×#64408	1	1	yes	characteristic
77	C₂	#17989551	1	3	yes	—
78	C₂	#17989552	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator	C₂×C₇₃	C₄³
Fitting	#95×C₇₃	C₄
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	#95	#64408
hypocenter	C₇₃	#1726
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
6. #14556646	C₄	semidirect
7. C₄×#10596833	C₄	semidirect
40. C₇₃	#1726	semidirect