Subgroups — #22626971

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989686	C₂	1	2	yes	maximal
2	#17989591	C₂	1	1	yes	maximal, characteristic
3	#14556687	—	2	2	no	—
4	C₂×#11924038	C₄	1	1	yes	characteristic
5	C₂×#11924038	C₂²	1	1	yes	characteristic
6	C₄⋊#10596833	—	2	2	no	—
7	C₄²×D₇₃	C₄	1	1	yes	characteristic
8	#11924040	—	4	2	no	—
9	#11924038	—	4	1	no	—
10	#11924038	—	4	1	no	—
11	C₂×#10596833	—	2	1	no	—
12	C₂×#10596833	D₄	1	2	yes	—
13	C₂×C₄×D₇₃	—	2	1	no	—
14	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
15	C₄×Dic₇₃	—	2	1	no	—
16	C₄×Dic₇₃	C₈	1	1	yes	characteristic
17	C₄²×C₇₃	C₈	1	1	yes	characteristic
18	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₇₃	—	2	1	no	—
22	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×D₇₃	—	2	1	no	—
24	C₄×D₇₃	—	2	1	no	—
25	C₄×D₇₃	—	4	2	no	—
26	#10596833	—	2	2	no	—
27	#10596833	—	4	1	no	—
28	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×D₇₃	—	2	1	no	—
30	C₂×D₇₃	—	4	1	no	—
31	C₄×C₇₃	—	2	2	no	—
32	C₄×C₇₃	—	2	1	no	—
33	Dic₇₃	—	4	1	no	—
34	Dic₇₃	#99	1	1	yes	characteristic
35	Dic₇₃	#101	1	1	yes	characteristic
36	C₂×C₇₃	—	2	1	no	—
37	C₂×C₇₃	#324	1	1	yes	characteristic
38	D₇₃	—	4	1	no	—
39	#1327	—	73	1	no	maximal, Sylow
40	C₇₃	#1327	1	1	yes	characteristic, complemented, Sylow
41	#423	—	73	1	no	—
42	#349	—	73	2	no	—
43	C₂×M₁₆	—	73	1	no	—
44	C₂×M₁₆	—	73	1	no	—
45	C₂×C₄²	—	73	1	no	—
46	M₃₂	—	146	2	no	—
47	C₄⋊C₈	—	146	2	no	—
48	C₂²×C₄	—	73	1	no	—
49	C₂²×C₄	—	146	1	no	—
50	M₁₆	—	292	1	no	—
51	M₁₆	—	292	1	no	—
52	C₂×C₈	—	73	2	no	—
53	C₂×C₈	—	146	1	no	—
54	C₄²	—	73	1	no	—
55	C₄²	—	146	1	no	—
56	C₄²	#10596842	1	1	yes	characteristic
57	C₁₆	—	292	2	no	—
58	C₂³	—	73	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	292	2	no	—
61	C₂×C₄	—	73	1	no	—
62	C₂×C₄	—	146	1	no	—
63	C₂×C₄	—	146	1	no	—
64	C₂×C₄	—	146	1	no	—
65	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
66	C₈	—	292	1	no	—
67	C₈	—	146	2	no	—
68	C₂²	—	292	1	no	—
69	C₂²	—	146	1	no	—
70	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	292	1	no	—
74	C₄	—	73	1	no	—
75	C₄	—	73	1	no	—
76	C₂	—	2	1	no	—
77	C₂	—	292	1	no	—
78	C₂	#17989673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989673
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂×C₇₃	#324
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1327
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
40. C₇₃	#1327	semidirect