Subgroups — #34001268

Order 18688.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625099	C₂	1	1	yes	maximal, characteristic, complemented
2	#22625092	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#17989513	—	2	1	no	—
5	#17989426	—	2	1	no	—
6	D₁₆×D₇₃	—	2	1	no	—
7	D₂₃₃₆	C₄	1	1	yes	characteristic, complemented
8	#17988422	—	2	1	no	—
9	C₃₂×D₇₃	C₂²	1	1	yes	characteristic
10	D₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
11	#14556660	—	4	1	no	—
12	D₈×D₇₃	—	4	1	no	—
13	D₁₁₆₈	—	2	1	no	—
14	#14556532	—	4	1	no	—
15	C₁₆×D₇₃	D₄	1	1	yes	characteristic
16	#14556497	D₄	1	1	yes	characteristic
17	D₁₆×C₇₃	—	2	1	no	—
18	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄⋊#64408	—	8	1	no	—
20	D₄×D₇₃	—	8	1	no	—
21	D₅₈₄	—	4	1	no	—
22	#11924013	—	8	1	no	—
23	C₈×D₇₃	D₈	1	1	yes	characteristic
24	#11924003	SD₁₆	1	1	yes	characteristic
25	D₈×C₇₃	—	4	1	no	—
26	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×D₇₃	—	16	1	no	—
28	C₂×#64408	—	16	1	no	—
29	D₄×C₇₃	—	8	1	no	—
30	C₂²⋊D₇₃	—	16	1	no	—
31	D₂₉₂	—	8	1	no	—
32	C₄×D₇₃	D₁₆	1	1	yes	characteristic
33	C₈×C₇₃	#102	1	1	yes	characteristic
34	#10596831	SD₃₂	1	1	yes	characteristic
35	C₂²×C₇₃	—	16	1	no	—
36	C₂×D₇₃	—	16	1	no	—
37	C₂×D₇₃	—	32	1	no	—
38	C₂×D₇₃	—	32	1	no	—
39	C₂×D₇₃	D₃₂	1	1	yes	characteristic
40	#64408	—	32	1	no	—
41	C₄×C₇₃	#357	1	1	yes	characteristic
42	Dic₇₃	SD₆₄	1	1	yes	characteristic
43	#7537	—	73	1	no	maximal, Sylow
44	C₂×C₇₃	—	32	1	no	—
45	C₂×C₇₃	#1415	1	1	yes	characteristic
46	D₇₃	—	32	1	no	—
47	D₇₃	D₆₄	1	1	yes	characteristic
48	D₇₃	SD₁₂₈	1	1	yes	characteristic
49	C₂×D₃₂	—	73	1	no	—
50	C₂×C₆₄	—	73	1	no	—
51	#1423	—	73	1	no	—
52	C₇₃	#7537	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₁₆	—	146	1	no	—
54	D₃₂	—	73	1	no	—
55	D₃₂	—	146	1	no	—
56	D₃₂	#64408	1	1	yes	characteristic, complemented
57	C₂×C₃₂	—	73	1	no	—
58	#366	—	146	1	no	—
59	C₆₄	—	146	1	no	—
60	C₂×D₈	—	292	1	no	—
61	D₁₆	—	2	1	no	—
62	D₁₆	—	292	1	no	—
63	D₁₆	—	146	1	no	—
64	C₂×C₁₆	—	73	1	no	—
65	#107	—	292	1	no	—
66	C₃₂	—	73	1	no	—
67	C₃₂	C₂×#64408	1	1	yes	characteristic
68	C₂×D₄	—	584	1	no	—
69	D₈	—	4	1	no	—
70	D₈	—	292	1	no	—
71	D₈	—	584	1	no	—
72	C₂×C₈	—	73	1	no	—
73	C₄⋊C₄	—	584	1	no	—
74	C₁₆	—	73	1	no	—
75	C₁₆	C₂²⋊#64408	1	1	yes	characteristic
76	C₂³	—	1168	1	no	—
77	D₄	—	8	1	no	—
78	D₄	—	584	1	no	—
79	D₄	—	1168	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	1168	1	no	—
82	C₈	—	73	1	no	—
83	C₈	#14556653	1	1	yes	characteristic
84	C₂²	—	16	1	no	—
85	C₂²	—	2336	1	no	—
86	C₂²	—	2336	1	no	—
87	C₂²	—	73	1	no	—
88	C₂²	—	1168	1	no	—
89	C₄	—	2336	1	no	—
90	C₄	—	73	1	no	—
91	C₄	#17989499	1	1	yes	characteristic
92	C₂	—	32	1	no	—
93	C₂	—	2336	1	no	—
94	C₂	—	73	1	no	—
95	C₂	—	73	1	no	—
96	C₂	#22625080	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22625080
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₃₂	C₂×#64408
Fitting	D₃₂×C₇₃	C₄
socle	C₂×C₇₃	#1415
prime radical	D₃₂×D₇₃	C₂
cosocle	C₃₂×D₇₃	C₂²
hypercenter	D₃₂	#64408
hypocenter	C₇₃	#7537
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #22625099	C₂	semidirect
2. #22625092	C₂	semidirect
7. D₂₃₃₆	C₄	semidirect
10. D₃₂×C₇₃	C₄	semidirect
52. C₇₃	#7537	semidirect
56. D₃₂	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22625099	2
#22625092	2
D₃₂×D₇₃	2
#7537	73