Subgroups — #22626964

Order 9344.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#11924040	C₂	1	2	yes	maximal
2	C₂×C₄⋊#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924040	—	2	2	no	—
4	C₂²×#10596833	C₄	1	1	yes	characteristic
5	C₂²×#10596833	C₂²	1	1	yes	characteristic
6	C₄⋊#10596833	—	2	2	no	—
7	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
8	#11924040	—	4	2	no	—
9	C₂×#10596833	—	2	1	no	—
10	C₂×#10596833	—	4	1	no	—
11	C₂×#10596833	—	4	1	no	—
12	C₂×#10596833	D₄	1	2	yes	—
13	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
14	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
15	C₄×Dic₇₃	—	2	1	no	—
16	C₄×Dic₇₃	—	2	1	no	—
17	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
18	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	—	2	1	no	—
21	C₂×C₄×C₇₃	C₁₆	1	2	yes	complemented
22	C₂×Dic₇₃	—	2	1	no	—
23	C₂×Dic₇₃	—	2	1	no	—
24	C₂×Dic₇₃	—	2	1	no	—
25	C₂×Dic₇₃	—	4	1	no	—
26	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
28	#10596833	—	2	2	no	—
29	#10596833	—	4	1	no	—
30	C₂²×C₇₃	—	2	1	no	—
31	C₂²×C₇₃	—	2	1	no	—
32	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
34	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
35	C₄×C₇₃	—	2	2	no	—
36	Dic₇₃	—	2	1	no	—
37	Dic₇₃	—	4	1	no	—
38	Dic₇₃	#99	1	1	yes	characteristic
39	Dic₇₃	#101	1	1	yes	characteristic
40	C₂×C₇₃	—	2	1	no	—
41	C₂×C₇₃	—	2	1	no	—
42	C₂×C₇₃	#324	1	1	yes	characteristic
43	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₂×C₇₃	#349	1	1	yes	characteristic
45	#1322	—	73	1	no	maximal, Sylow
46	C₇₃	#1322	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄⋊C₈	—	73	1	no	—
48	C₂²⋊C₁₆	—	73	2	no	—
49	C₂²×C₈	—	73	1	no	—
50	C₂²×C₈	—	73	1	no	—
51	C₂×C₄²	—	73	1	no	—
52	C₂×C₁₆	—	146	2	no	—
53	C₄⋊C₈	—	146	2	no	—
54	C₂²×C₄	—	73	1	no	—
55	C₂²×C₄	—	73	1	no	—
56	C₂²×C₄	#10596842	1	1	yes	characteristic
57	C₂×C₈	—	292	1	no	—
58	C₂×C₈	—	292	1	no	—
59	C₂×C₈	—	73	2	no	—
60	C₂×C₈	—	146	1	no	—
61	C₄²	—	146	1	no	—
62	C₄²	—	146	1	no	—
63	C₁₆	—	292	2	no	—
64	C₂³	C₂×#10596842	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	292	1	no	—
68	C₂×C₄	—	73	1	no	—
69	C₂×C₄	—	73	1	no	—
70	C₂×C₄	—	146	1	no	—
71	C₂×C₄	—	146	1	no	—
72	C₂×C₄	—	146	1	no	—
73	C₂×C₄	#11924040	1	2	yes	complemented
74	C₈	—	292	1	no	—
75	C₈	—	146	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
79	C₂²	C₂×#11924040	1	1	yes	characteristic
80	C₂²	#14556687	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	292	1	no	—
83	C₄	—	73	1	no	—
84	C₄	—	73	1	no	—
85	C₄	—	146	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#17989673	1	1	yes	characteristic
89	C₂	C₂²⋊#11924040	1	1	yes	characteristic
90	C₂	#17989686	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10596842
commutator	C₂²×C₇₃	C₂×C₁₆
Frattini	C₂³	C₂×#10596842
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#1322
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
21. C₂×C₄×C₇₃	C₁₆	semidirect
46. C₇₃	#1322	semidirect
73. C₂×C₄	#11924040	semidirect