Subgroups — #32973697

Order 18688.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988417	C₂	1	2	yes	maximal
2	C₂×M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556527	—	2	2	no	—
4	#17988417	—	2	2	no	—
5	#17988417	C₄	1	4	yes	—
6	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
7	M₆₄×C₇₃	—	2	2	no	—
8	C₂×C₃₂×C₇₃	C₄	1	2	yes	—
9	C₂×#11924012	—	4	2	no	—
10	#14556527	—	2	4	no	—
11	#14556527	—	4	2	no	—
12	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
15	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
16	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
17	C₃₂×C₇₃	—	2	2	no	—
18	#11924012	—	4	4	no	—
19	#11924012	—	8	2	no	—
20	C₂×#10596831	—	8	2	no	—
21	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
23	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
25	C₂×C₈×C₇₃	Q₁₆	1	1	yes	characteristic
26	C₁₆×C₇₃	C₄²	1	1	yes	characteristic
27	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆×C₇₃	C₄⋊C₄	1	2	yes	—
29	C₂³×C₇₃	Q₃₂	1	1	yes	characteristic
30	C₂×C₄×C₇₃	#102	1	2	yes	—
31	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
32	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₇₃	SD₃₂	1	2	yes	—
34	C₈×C₇₃	#95	1	1	yes	characteristic
35	C₈×C₇₃	#103	1	2	yes	—
36	C₈×C₇₃	#106	1	1	yes	characteristic
37	#10596831	—	8	4	no	—
38	C₂²×C₇₃	—	4	1	no	—
39	C₂²×C₇₃	#358	1	2	yes	—
40	C₂²×C₇₃	#366	1	1	yes	characteristic
41	C₄×C₇₃	#340	1	1	yes	characteristic
42	C₄×C₇₃	#357	1	2	yes	—
43	C₄×C₇₃	#367	1	1	yes	characteristic
44	#7476	—	73	1	no	maximal, Sylow
45	C₂×C₇₃	—	2	2	no	—
46	C₂×C₇₃	—	2	1	no	—
47	C₂×C₇₃	#1380	1	1	yes	characteristic
48	C₂×M₆₄	D₇₃	1	1	yes	characteristic
49	C₂×#368	—	73	2	no	—
50	C₇₃	#7476	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
52	C₂×#108	—	146	2	no	—
53	M₆₄	—	2	2	no	—
54	C₂×C₃₂	Dic₇₃	1	2	yes	—
55	#368	—	73	4	no	—
56	#368	—	146	2	no	—
57	C₂×M₁₆	—	292	2	no	—
58	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
59	C₂×C₁₆	Dic₁₄₆	1	1	yes	characteristic
60	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
61	C₂×C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
62	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
63	#108	—	292	2	no	—
64	#108	—	146	4	no	—
65	C₃₂	—	2	2	no	—
66	C₂²×C₄	D₅₈₄	1	1	yes	characteristic
67	M₁₆	—	292	4	no	—
68	M₁₆	—	584	2	no	—
69	C₂×C₈	—	584	2	no	—
70	C₂×C₈	#11924005	1	2	yes	—
71	C₂×C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
72	C₂×C₈	#11924017	1	2	yes	—
73	C₂×C₈	Dic₂₉₂	1	1	yes	characteristic
74	C₁₆	C₄×Dic₇₃	1	1	yes	characteristic
75	C₁₆	C₂²⋊Dic₇₃	1	1	yes	characteristic
76	C₁₆	#11924007	1	2	yes	—
77	C₂³	Dic₅₈₄	1	1	yes	characteristic
78	C₂×C₄	#14556513	1	2	yes	—
79	C₂×C₄	#14556525	1	1	yes	characteristic
80	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
81	C₂×C₄	#14556536	1	2	yes	—
82	C₈	—	584	4	no	—
83	C₈	#14556498	1	1	yes	characteristic
84	C₈	#14556516	1	2	yes	—
85	C₈	#14556523	1	1	yes	characteristic
86	C₂²	—	4	1	no	—
87	C₂²	#17988392	1	2	yes	—
88	C₂²	#17988413	1	1	yes	characteristic
89	C₄	#17988350	1	1	yes	characteristic
90	C₄	#17988389	1	2	yes	—
91	C₄	#17988415	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	—	2	1	no	—
94	C₂	#22608023	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17988415
commutator	C₁₆×C₇₃	C₄²
Frattini	C₂²×C₁₆	C₂×D₇₃
Fitting	C₂×M₆₄×C₇₃	C₂
socle	C₂×C₇₃	#1380
prime radical	C₂³×C₇₃	Q₃₂
cosocle	C₂²×C₁₆×C₇₃	C₂²
hypercenter	C₂×M₆₄	D₇₃
hypocenter	C₇₃	#7476
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
50. C₇₃	#7476	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988417	2
C₂×M₆₄×C₇₃	2
#7476	73