Subgroups — #401×#64408 #34014777

Order 18688.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625118	C₂	1	7	yes	maximal
2	#95×#64408	C₂	1	7	yes	maximal
3	#401×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×#64408	C₂²	1	7	yes	—
5	C₂×(C₂×#64408)⋊C₄	C₂²	1	21	yes	—
6	C₇₃⋊#401	C₄	1	7	yes	complemented
7	#95×D₇₃	C₂²	1	7	yes	—
8	#401×C₇₃	C₄	1	1	yes	characteristic, complemented
9	C₂³×#64408	C₂³	1	7	yes	—
10	C₂³×#64408	C₂³	1	1	yes	characteristic
11	C₂×C₄×#64408	—	2	42	no	—
12	(C₂×#64408)⋊C₄	—	2	42	no	—
13	C₂²×C₄×D₇₃	C₂³	1	7	yes	—
14	#14556498	C₂×C₄	1	21	yes	—
15	#95×C₇₃	C₂×C₄	1	7	yes	—
16	C₂²×#64408	—	2	21	no	—
17	C₂²×#64408	—	2	21	no	—
18	C₂²×#64408	#41	1	14	yes	—
19	C₂²×#64408	#41	1	14	yes	—
20	C₄×#64408	—	4	28	no	—
21	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
22	C₂²×Dic₇₃	C₂²×C₄	1	7	yes	—
23	C₂×C₄×D₇₃	—	2	21	no	—
24	C₂×C₄×D₇₃	—	2	21	no	—
25	C₂²×C₄×C₇₃	C₂²×C₄	1	7	yes	—
26	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
27	C₂²×D₇₃	C₂×#41	1	7	yes	—
28	C₂²×D₇₃	C₂×#41	1	7	yes	—
29	C₂×#64408	—	2	42	no	—
30	C₂×#64408	—	4	7	no	—
31	C₂×#64408	—	4	21	no	—
32	C₂×#64408	#126	1	28	yes	—
33	C₂×C₄×C₇₃	—	2	21	no	—
34	C₂×Dic₇₃	—	2	21	no	—
35	C₄×D₇₃	—	4	7	no	—
36	C₄×D₇₃	—	4	21	no	—
37	C₂²×C₇₃	C₄×#41	1	7	yes	—
38	C₂×D₇₃	C₂×#126	1	7	yes	—
39	C₂×D₇₃	#529	1	21	yes	—
40	#64408	—	4	14	no	—
41	#64408	#401	1	8	yes	direct product factor
42	C₄×C₇₃	—	4	7	no	—
43	Dic₇₃	—	4	7	no	—
44	C₄×#401	—	73	1	no	maximal, Sylow
45	C₂×C₇₃	C₄×#126	1	7	yes	—
46	D₇₃	C₂×#401	1	1	yes	characteristic
47	D₇₃	#2401	1	7	yes	—
48	C₂×#401	—	73	1	no	—
49	#1443	—	73	7	no	—
50	C₄×#95	—	73	7	no	—
51	C₇₃	C₄×#401	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄²	—	73	7	no	—
53	#401	—	73	7	no	—
54	#401	#64408	1	1	yes	characteristic, direct product factor
55	C₂×#95	—	73	7	no	—
56	C₂×#95	—	73	21	no	—
57	C₂³×C₄	—	73	1	no	—
58	C₂³×C₄	—	73	7	no	—
59	C₂³×C₄	—	73	7	no	—
60	C₂×C₄²	—	146	42	no	—
61	#95	—	73	21	no	—
62	#95	—	146	42	no	—
63	#95	C₂×#64408	1	7	yes	—
64	C₂⁴	—	73	1	no	—
65	C₂²×C₄	—	73	14	no	—
66	C₂²×C₄	—	73	14	no	—
67	C₂²×C₄	—	73	7	no	—
68	C₂²×C₄	—	146	21	no	—
69	C₂²×C₄	—	146	21	no	—
70	C₂²×C₄	—	146	21	no	—
71	C₂²×C₄	—	146	21	no	—
72	C₂²×C₄	C₂²×#64408	1	7	yes	—
73	C₄²	—	292	28	no	—
74	C₂³	—	73	7	no	—
75	C₂³	—	73	7	no	—
76	C₂³	C₂³×#64408	1	1	yes	characteristic
77	C₂×C₄	—	2	21	no	—
78	C₂×C₄	—	292	7	no	—
79	C₂×C₄	—	292	21	no	—
80	C₂×C₄	—	292	7	no	—
81	C₂×C₄	—	292	21	no	—
82	C₂×C₄	—	73	28	no	—
83	C₂×C₄	—	146	42	no	—
84	C₂×C₄	—	146	21	no	—
85	C₂²	—	73	7	no	—
86	C₂²	—	73	21	no	—
87	C₂²	#41×#64408	1	7	yes	—
88	C₄	—	4	7	no	—
89	C₄	—	292	14	no	—
90	C₄	—	292	7	no	—
91	C₄	—	73	8	no	—
92	C₂	—	73	7	no	—
93	C₂	—	73	1	no	—
94	C₂	#126×#64408	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#64408
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	#401×C₇₃	C₄
prime radical, cosocle	C₂³×D₇₃	C₂⁴
hypercenter	#401	#64408
hypocenter	C₇₃	C₄×#401
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #401

Complements

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

N	H ≅ G/N	type
6. C₇₃⋊#401	C₄	semidirect
8. #401×C₇₃	C₄	semidirect
41. #64408	#401	direct (N × H)
51. C₇₃	C₄×#401	semidirect
54. #401	#64408	direct (N × H)

Maximal subgroups

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

subgroup	index
#22625118	2
#95×#64408	2
#401×D₇₃	2
C₄×#401	73