Subgroups — #34012083

Order 18688.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989475	C₂	1	3	yes	maximal
2	C₂×C₄×#11924031	C₂	1	3	yes	maximal
3	#22609618	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924031	C₂²	1	1	yes	characteristic
5	C₂²×#11924031	C₂²	1	3	yes	—
6	#17989475	C₄	1	12	yes	complemented
7	C₄×#11924031	C₄	1	12	yes	complemented
8	C₂×#14556502	C₄	1	3	yes	—
9	C₂×C₄×#10596831	C₂²	1	3	yes	—
10	#376×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#11924031	C₂×C₄	1	6	yes	—
12	C₂×#11924031	C₂×C₄	1	6	yes	—
13	C₂×#11924031	C₂×C₄	1	12	yes	—
14	C₂²×#10596831	C₂×C₄	1	3	yes	—
15	C₂²×#10596831	C₂³	1	1	yes	characteristic
16	#14556502	C₈	1	12	yes	—
17	C₄×#10596831	C₂×C₄	1	6	yes	—
18	C₄×#10596831	C₂×C₄	1	6	yes	—
19	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
20	#95×C₇₃	C₈	1	4	yes	—
21	#11924031	C₄²	1	4	yes	—
22	#11924031	C₄²	1	12	yes	—
23	C₂×#10596831	C₄²	1	6	yes	—
24	C₂×#10596831	C₂×C₈	1	12	yes	—
25	C₂×#10596831	C₂²×C₄	1	3	yes	—
26	C₂×#10596831	C₂²×C₄	1	3	yes	—
27	C₂²×C₄×C₇₃	C₂×C₈	1	6	yes	—
28	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₄²×C₇₃	C₄²	1	6	yes	—
30	C₄²×C₇₃	C₂×C₈	1	6	yes	—
31	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	12	no	—
33	C₂×C₄×C₇₃	C₄×C₈	1	12	yes	—
34	C₂×C₄×C₇₃	C₂×C₄²	1	3	yes	—
35	C₂×C₄×C₇₃	C₂²×C₈	1	3	yes	—
36	#10596831	C₄×C₈	1	12	yes	—
37	#10596831	C₂×C₄²	1	1	yes	characteristic
38	#10596831	C₂×C₄²	1	3	yes	—
39	C₂²×C₇₃	C₂×C₄×C₈	1	3	yes	—
40	C₂²×C₇₃	#504	1	4	yes	—
41	C₄×C₇₃	—	2	12	no	—
42	C₄×C₇₃	C₄³	1	1	yes	characteristic
43	C₄×C₇₃	C₂×C₄×C₈	1	3	yes	—
44	#12539	—	73	1	no	maximal, Sylow
45	C₂×C₇₃	C₄²×C₈	1	1	yes	characteristic
46	C₂×C₇₃	#2108	1	6	yes	—
47	C₂×#346	—	73	3	no	—
48	C₂×C₄×C₁₆	—	73	3	no	—
49	#1726	—	73	1	no	—
50	C₇₃	#12539	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₁₆	—	73	1	no	—
52	C₂²×C₁₆	—	73	3	no	—
53	C₂×#97	—	73	3	no	—
54	C₂×C₄×C₈	—	73	3	no	—
55	#376	#64408	1	1	yes	characteristic
56	#346	—	73	12	no	—
57	C₄×C₁₆	—	73	12	no	—
58	C₂²×C₈	—	73	1	no	—
59	C₂²×C₈	—	73	3	no	—
60	C₂×C₄²	C₂×#64408	1	3	yes	—
61	C₂×C₁₆	—	73	6	no	—
62	C₂×C₁₆	—	73	6	no	—
63	C₂×C₁₆	—	73	12	no	—
64	#97	—	73	12	no	—
65	C₄×C₈	—	73	6	no	—
66	C₄×C₈	—	73	6	no	—
67	#95	#10596833	1	4	yes	—
68	C₂²×C₄	C₂×#10596833	1	6	yes	—
69	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
70	C₂×C₈	—	73	12	no	—
71	C₂×C₈	—	73	6	no	—
72	C₂×C₈	—	73	3	no	—
73	C₂×C₈	—	73	3	no	—
74	C₄²	C₄×#64408	1	6	yes	—
75	C₄²	#11924036	1	6	yes	—
76	C₁₆	—	73	4	no	—
77	C₁₆	—	73	12	no	—
78	C₂³	C₂²×#10596833	1	1	yes	characteristic
79	C₂×C₄	—	2	12	no	—
80	C₂×C₄	C₄×#10596833	1	12	yes	—
81	C₂×C₄	C₂×C₄×#64408	1	3	yes	—
82	C₂×C₄	C₂×#11924036	1	3	yes	—
83	C₈	—	73	1	no	—
84	C₈	—	73	3	no	—
85	C₈	—	73	12	no	—
86	C₂²	C₂×C₄×#10596833	1	3	yes	—
87	C₂²	#17989645	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	C₄²×#64408	1	1	yes	characteristic
90	C₄	C₄×#11924036	1	3	yes	—
91	C₂	C₄²×#10596833	1	1	yes	characteristic
92	C₂	#22626140	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₄²×C₈
Fitting	#376×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₂²×C₈
cosocle	C₂²×#10596831	C₂³
hypercenter	#376	#64408
hypocenter	C₇₃	#12539
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
6. #17989475	C₄	semidirect
7. C₄×#11924031	C₄	semidirect
50. C₇₃	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989475	2
C₂×C₄×#11924031	2
#22609618	2
#12539	73