Subgroups — #22627121

Order 9344.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556688	C₂	1	2	yes	maximal
2	#17989690	C₂	1	4	yes	maximal, complemented
3	C₄×#11924036	C₂	1	1	yes	maximal, characteristic
4	#14556688	—	2	4	no	—
5	C₂×#11924040	C₂²	1	4	yes	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₄×#10596833	C₄	1	2	yes	—
9	C₄×#10596833	C₂²	1	2	yes	—
10	C₄²×D₇₃	C₄	1	1	yes	characteristic
11	#11924040	—	2	4	no	—
12	#11924036	—	2	2	no	—
13	#11924036	D₄	1	2	yes	—
14	#11924036	Q₈	1	2	yes	—
15	C₂×#10596833	C₂×C₄	1	2	yes	—
16	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596833	C₂³	1	1	yes	characteristic
18	C₂×C₄×D₇₃	C₈	1	2	yes	—
19	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₇₃	C₈	1	1	yes	characteristic
21	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
22	C₄²×C₇₃	C₈	1	1	yes	characteristic
23	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
27	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×D₇₃	—	2	4	no	—
29	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
30	C₄×D₇₃	M₁₆	1	2	yes	—
31	#10596833	—	2	2	no	—
32	#10596833	C₄⋊C₄	1	2	yes	—
33	#10596833	C₂×D₄	1	1	yes	characteristic
34	#10596833	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
36	C₂×D₇₃	—	2	2	no	—
37	C₂×D₇₃	C₄⋊C₈	1	2	yes	—
38	C₄×C₇₃	—	2	2	no	—
39	C₄×C₇₃	C₄⋊C₈	1	2	yes	—
40	Dic₇₃	M₃₂	1	4	yes	complemented
41	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
43	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
44	C₂×C₇₃	C₂×M₃₂	1	2	yes	—
45	D₇₃	—	2	2	no	—
46	#2150	—	73	1	no	maximal, Sylow
47	C₇₃	#2150	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₃₂	—	73	2	no	—
49	C₂×C₄×C₈	—	73	1	no	—
50	C₄⋊C₁₆	—	73	4	no	—
51	C₂²×C₈	—	73	1	no	—
52	C₂²×C₈	—	73	1	no	—
53	C₂×C₄²	—	73	1	no	—
54	M₃₂	—	146	4	no	—
55	C₂×C₁₆	—	73	4	no	—
56	C₄×C₈	—	73	2	no	—
57	C₄×C₈	—	73	2	no	—
58	C₂²×C₄	—	73	1	no	—
59	C₂²×C₄	—	73	2	no	—
60	C₂×C₈	—	73	1	no	—
61	C₂×C₈	—	73	1	no	—
62	C₂×C₈	—	73	2	no	—
63	C₂×C₈	—	73	2	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	146	2	no	—
66	C₄²	—	73	1	no	—
67	C₄²	—	73	2	no	—
68	C₄²	#10596842	1	1	yes	characteristic
69	C₁₆	—	146	4	no	—
70	C₂³	—	73	1	no	—
71	C₂×C₄	—	73	1	no	—
72	C₂×C₄	—	73	2	no	—
73	C₂×C₄	—	73	2	no	—
74	C₂×C₄	—	73	2	no	—
75	C₂×C₄	—	146	4	no	—
76	C₂×C₄	C₂×#10596842	1	2	yes	—
77	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
78	C₈	—	73	1	no	—
79	C₈	—	73	2	no	—
80	C₈	—	73	1	no	—
81	C₈	—	146	2	no	—
82	C₂²	—	73	2	no	—
83	C₂²	—	146	2	no	—
84	C₂²	C₂²×#10596842	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	73	1	no	—
87	C₄	—	73	1	no	—
88	C₄	—	73	4	no	—
89	C₄	C₄⋊#10596842	1	2	yes	—
90	C₂	—	146	2	no	—
91	C₂	C₂×C₄⋊#10596842	1	1	yes	characteristic
92	C₂	#17989706	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₄²×C₇₃	C₈
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#2150
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #17989690	C₂	semidirect
40. Dic₇₃	M₃₂	semidirect
47. C₇₃	#2150	semidirect