Subgroups — #33007035

Order 18688.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22612237	C₂	1	2	yes	maximal, complemented
2	Dic₂₃₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#22608146	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989016	—	2	2	no	—
7	Dic₁₁₆₈	C₂²	1	2	yes	—
8	#17988425	—	2	2	no	—
9	C₃₂×D₇₃	C₂²	1	1	yes	characteristic
10	#17988306	C₂²	1	1	yes	characteristic
11	D₃₂×C₇₃	C₂²	1	2	yes	—
12	C₆₄×C₇₃	C₂²	1	1	yes	characteristic
13	#14556610	—	4	2	no	—
14	Dic₅₈₄	—	2	2	no	—
15	#14556535	—	4	2	no	—
16	C₁₆×D₇₃	D₄	1	1	yes	characteristic
17	#14556497	D₄	1	1	yes	characteristic
18	D₁₆×C₇₃	—	2	2	no	—
19	C₃₂×C₇₃	C₂³	1	1	yes	characteristic
20	#11924027	—	8	2	no	—
21	Dic₂₉₂	—	4	2	no	—
22	#11924016	—	8	2	no	—
23	C₈×D₇₃	D₈	1	1	yes	characteristic
24	#11924003	D₈	1	1	yes	characteristic
25	D₈×C₇₃	—	4	2	no	—
26	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
27	D₄×C₇₃	—	8	2	no	—
28	C₂²⋊D₇₃	—	16	2	no	—
29	C₂×Dic₇₃	—	16	2	no	—
30	C₄×D₇₃	D₁₆	1	1	yes	characteristic
31	Dic₁₄₆	—	8	2	no	—
32	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
33	#10596831	D₁₆	1	1	yes	characteristic
34	C₂²×C₇₃	—	16	2	no	—
35	C₂×D₇₃	D₃₂	1	1	yes	characteristic
36	C₄×C₇₃	C₂×D₁₆	1	1	yes	characteristic
37	Dic₇₃	—	16	2	no	—
38	Dic₇₃	D₃₂	1	1	yes	characteristic
39	#13741	—	73	1	no	maximal, Sylow
40	C₂×C₇₃	—	32	2	no	—
41	C₂×C₇₃	C₂×D₃₂	1	1	yes	characteristic
42	D₇₃	—	2	1	no	—
43	#2262	—	73	2	no	—
44	Q₁₂₈	—	73	1	no	—
45	SD₁₂₈	—	73	2	no	—
46	D₆₄	D₇₃	1	1	yes	characteristic, complemented
47	C₂×C₆₄	—	73	1	no	—
48	C₇₃	#13741	1	1	yes	characteristic, complemented, Sylow
49	#508	—	146	2	no	—
50	Q₆₄	—	73	2	no	—
51	SD₆₄	—	146	2	no	—
52	D₃₂	C₂×D₇₃	1	2	yes	—
53	C₂×C₃₂	—	73	1	no	—
54	C₆₄	—	73	1	no	—
55	C₆₄	C₂×D₇₃	1	1	yes	characteristic
56	#135	—	292	2	no	—
57	Q₃₂	—	146	2	no	—
58	SD₃₂	—	292	2	no	—
59	D₁₆	—	2	2	no	—
60	C₂×C₁₆	—	73	1	no	—
61	C₃₂	—	73	1	no	—
62	C₃₂	C₂²×D₇₃	1	1	yes	characteristic
63	#41	—	584	2	no	—
64	Q₁₆	—	292	2	no	—
65	SD₁₆	—	584	2	no	—
66	D₈	—	4	2	no	—
67	C₂×C₈	—	73	1	no	—
68	C₁₆	—	73	1	no	—
69	C₁₆	D₄×D₇₃	1	1	yes	characteristic
70	Q₈	—	584	2	no	—
71	D₄	—	8	2	no	—
72	D₄	—	1168	2	no	—
73	C₂×C₄	—	73	1	no	—
74	C₂×C₄	—	1168	2	no	—
75	C₈	—	73	1	no	—
76	C₈	D₈×D₇₃	1	1	yes	characteristic
77	C₂²	—	16	2	no	—
78	C₂²	—	73	1	no	—
79	C₄	—	73	1	no	—
80	C₄	—	1168	2	no	—
81	C₄	D₁₆×D₇₃	1	1	yes	characteristic
82	C₂	—	32	2	no	—
83	C₂	—	146	1	no	—
84	C₂	D₃₂×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₇₃
commutator, cosocle	C₃₂×C₇₃	C₂³
Frattini	C₃₂	C₂²×D₇₃
Fitting	C₇₃×D₆₄	C₂
socle	C₂×C₇₃	C₂×D₃₂
hypercenter	D₆₄	D₇₃
hypocenter	C₇₃	#13741
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. #22612237	C₂	semidirect
2. Dic₂₃₃₆	C₂	semidirect
3. #22608146	C₂	semidirect
4. C₆₄×D₇₃	C₂	semidirect
5. C₇₃×D₆₄	C₂	semidirect
46. D₆₄	D₇₃	semidirect
48. C₇₃	#13741	semidirect

Maximal subgroups

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

subgroup	index
#22612237	2
Dic₂₃₃₆	2
#22608146	2
C₆₄×D₇₃	2
C₇₃×D₆₄	2
#13741	73