Subgroups — #22609682

Order 9344.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556502	C₂	1	1	yes	maximal, characteristic
2	#17988433	C₂	1	1	yes	maximal, characteristic
3	#17988341	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596831	C₂²	1	2	yes	—
6	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
7	#14556502	C₄	1	4	yes	complemented
8	#14556498	C₄	1	4	yes	—
9	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
10	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₇₃	C₄	1	4	yes	complemented
12	C₂²×Dic₇₃	C₂×C₄	1	4	yes	—
13	C₂×#10596831	—	2	4	no	—
14	C₂×#10596831	C₂×C₄	1	4	yes	—
15	C₄×Dic₇₃	—	2	4	no	—
16	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₇₃	—	2	4	no	—
19	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
20	C₄²×C₇₃	C₂×C₄	1	2	yes	—
21	C₄²×C₇₃	C₂×C₄	1	2	yes	—
22	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	2	4	no	—
24	C₂×C₄×C₇₃	C₄²	1	4	yes	—
25	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	#41	1	4	yes	—
28	C₂×Dic₇₃	—	2	4	no	—
29	C₂×Dic₇₃	—	2	8	no	—
30	C₈×C₇₃	—	2	4	no	—
31	#10596831	—	2	4	no	—
32	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
33	C₂²×C₇₃	#117	1	2	yes	—
34	C₂²×C₇₃	#131	1	4	yes	—
35	C₄×C₇₃	—	2	4	no	—
36	C₄×C₇₃	#117	1	2	yes	—
37	C₄×C₇₃	#117	1	2	yes	—
38	Dic₇₃	—	4	4	no	—
39	C₂×C₇₃	#376	1	1	yes	characteristic
40	C₂×C₇₃	#405	1	2	yes	—
41	C₂×C₇₃	#433	1	4	yes	—
42	#1746	—	73	1	no	maximal, Sylow
43	C₇₃	#1746	1	1	yes	characteristic, complemented, Sylow
44	C₂×#97	—	73	1	no	—
45	C₂×C₄×C₈	D₇₃	1	1	yes	characteristic
46	#376	—	73	1	no	—
47	#336	—	73	4	no	—
48	C₂²×C₈	—	73	2	no	—
49	C₂²×C₈	C₂×D₇₃	1	2	yes	—
50	C₂×C₄²	—	73	2	no	—
51	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
52	#97	—	73	4	no	—
53	C₄×C₈	Dic₇₃	1	4	yes	complemented
54	#95	—	73	4	no	—
55	C₂²×C₄	—	73	4	no	—
56	C₂²×C₄	C₄×D₇₃	1	2	yes	—
57	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
58	C₂×C₈	—	2	4	no	—
59	C₂×C₈	—	73	4	no	—
60	C₂×C₈	—	146	4	no	—
61	C₂×C₈	C₂×Dic₇₃	1	4	yes	—
62	C₄²	—	146	4	no	—
63	C₄²	C₄×D₇₃	1	2	yes	—
64	C₄²	C₂×Dic₇₃	1	2	yes	—
65	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	146	4	no	—
68	C₂×C₄	—	146	8	no	—
69	C₂×C₄	C₄×Dic₇₃	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
72	C₂×C₄	#11924028	1	4	yes	—
73	C₈	—	2	4	no	—
74	C₈	—	146	4	no	—
75	C₂²	C₂×C₄×Dic₇₃	1	1	yes	characteristic
76	C₂²	#14556548	1	2	yes	—
77	C₂²	#14556597	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	292	4	no	—
80	C₄	#14556548	1	2	yes	—
81	C₄	#14556550	1	2	yes	—
82	C₂	#17988433	1	1	yes	characteristic
83	C₂	#17988542	1	2	yes	—
84	C₂	#17988646	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₃
commutator	C₂²×C₇₃	C₂×C₄²
Fitting	C₂×C₄×C₈×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₇₃
hypocenter	C₇₃	#1746
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #14556502	C₄	semidirect
11. C₄×C₈×C₇₃	C₄	semidirect
43. C₇₃	#1746	semidirect
53. C₄×C₈	Dic₇₃	semidirect