Subgroups — #34034214

Order 18688.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627001	C₂	1	6	yes	maximal
2	#22625588	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11924040	C₂²	1	4	yes	—
4	C₂×#14556646	C₄	1	3	yes	—
5	C₂×C₄×#10596833	C₂²	1	3	yes	—
6	#17988432	C₄	1	1	yes	characteristic
7	C₂×#11924040	—	2	12	no	—
8	C₂²×#10596833	C₂×C₄	1	3	yes	—
9	C₂²×#10596833	C₂³	1	1	yes	characteristic
10	#14556646	—	2	6	no	—
11	C₄×#10596833	—	2	6	no	—
12	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
13	#14556498	C₈	1	3	yes	—
14	#95×C₇₃	C₈	1	1	yes	characteristic
15	#11924040	—	4	4	no	—
16	C₂×#10596833	—	2	3	no	—
17	C₂×#10596833	—	2	3	no	—
18	C₂×#10596833	M₁₆	1	6	yes	—
19	C₂×#10596833	#41	1	6	yes	—
20	C₂²×Dic₇₃	C₂×C₈	1	3	yes	—
21	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	—	2	3	no	—
23	C₄×Dic₇₃	—	2	3	no	—
24	C₂²×C₄×C₇₃	C₂×C₈	1	3	yes	—
25	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	—	2	3	no	—
27	C₂×C₄×C₇₃	—	2	6	no	—
28	C₂×Dic₇₃	—	2	3	no	—
29	C₂×Dic₇₃	—	2	3	no	—
30	C₂×Dic₇₃	—	2	3	no	—
31	C₂×Dic₇₃	#117	1	3	yes	—
32	C₂×Dic₇₃	C₂×M₁₆	1	3	yes	—
33	#10596833	—	2	6	no	—
34	#10596833	#126	1	4	yes	—
35	C₂²×C₇₃	#431	1	3	yes	—
36	C₂²×C₇₃	#504	1	3	yes	—
37	C₂²×C₇₃	#504	1	1	yes	characteristic
38	C₄×C₇₃	—	4	3	no	—
39	Dic₇₃	—	4	3	no	—
40	Dic₇₃	#383	1	1	yes	characteristic
41	Dic₇₃	#432	1	3	yes	—
42	#12895	—	73	1	no	maximal, Sylow
43	C₂×C₇₃	#1839	1	1	yes	characteristic
44	C₂×C₇₃	#2164	1	3	yes	—
45	C₂×C₇₃	#2164	1	3	yes	—
46	#1726	—	73	1	no	—
47	#1374	—	73	6	no	—
48	C₇₃	#12895	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	73	4	no	—
50	C₂×#97	—	73	3	no	—
51	C₂×C₄×C₈	—	73	3	no	—
52	#376	—	73	1	no	—
53	C₂²×C₈	—	73	1	no	—
54	C₂²×C₈	—	73	3	no	—
55	C₂×C₄²	—	73	3	no	—
56	C₂×C₁₆	—	146	12	no	—
57	#97	—	146	6	no	—
58	C₄×C₈	—	146	6	no	—
59	#95	—	73	3	no	—
60	#95	#10596842	1	1	yes	characteristic
61	C₂²×C₄	—	73	1	no	—
62	C₂²×C₄	—	73	3	no	—
63	C₂²×C₄	C₂×#10596842	1	3	yes	—
64	C₂×C₈	—	73	6	no	—
65	C₂×C₈	—	73	6	no	—
66	C₂×C₈	—	146	3	no	—
67	C₂×C₈	—	146	3	no	—
68	C₄²	—	146	3	no	—
69	C₄²	—	146	3	no	—
70	C₁₆	—	292	4	no	—
71	C₂³	C₂²×#10596842	1	1	yes	characteristic
72	C₂×C₄	—	2	3	no	—
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	73	3	no	—
75	C₂×C₄	—	73	3	no	—
76	C₂×C₄	—	146	3	no	—
77	C₂×C₄	—	146	3	no	—
78	C₂×C₄	—	146	3	no	—
79	C₈	—	73	4	no	—
80	C₈	—	146	6	no	—
81	C₂²	#17989700	1	3	yes	—
82	C₂²	#17989708	1	3	yes	—
83	C₂²	#17989709	1	1	yes	characteristic
84	C₄	—	4	3	no	—
85	C₄	—	292	3	no	—
86	C₄	—	73	1	no	—
87	C₄	—	73	3	no	—
88	C₂	#22627074	1	1	yes	characteristic
89	C₂	#22627136	1	3	yes	—
90	C₂	#22627137	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10596842
commutator, socle, prime radical	C₂³×C₇₃	C₂²×C₈
Fitting	#95×C₇₃	C₈
cosocle	C₂²×#10596833	C₂³
hypercenter	#95	#10596842
hypocenter	C₇₃	#12895
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
48. C₇₃	#12895	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22627001	2
#22625588	2
#12895	73