Subgroups — #33000699

Order 18688.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22612184	C₂	1	4	yes	maximal
2	#22609549	C₂	1	2	yes	maximal
3	C₈×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₈₄	—	2	8	no	—
5	#17988992	—	2	4	no	—
6	#17988967	C₂²	1	4	yes	—
7	C₄×C₁₆×C₇₃	C₂²	1	2	yes	—
8	C₈²×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₉₂	—	2	8	no	—
10	#14556591	—	2	4	no	—
11	Dic₅₈₄	—	4	16	no	—
12	#14556525	—	4	8	no	—
13	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
14	C₄×C₈×C₇₃	D₄	1	2	yes	—
15	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₁₄₆	—	4	4	no	—
17	Dic₂₉₂	—	4	16	no	—
18	C₄⋊Dic₇₃	—	4	8	no	—
19	C₂×C₈×C₇₃	D₈	1	4	yes	—
20	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
21	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
22	C₁₆×C₇₃	D₈	1	8	yes	—
23	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
24	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
25	C₂×Dic₇₃	—	8	4	no	—
26	Dic₁₄₆	—	8	8	no	—
27	C₈×C₇₃	Q₃₂	1	8	yes	complemented
28	C₈×C₇₃	C₂×D₈	1	4	yes	—
29	C₂²×C₇₃	#493	1	1	yes	characteristic
30	C₄×C₇₃	#493	1	2	yes	—
31	C₄×C₇₃	C₂×Q₃₂	1	4	yes	—
32	Dic₇₃	—	16	4	no	—
33	#12516	—	73	1	no	maximal, Sylow
34	C₂×C₇₃	#1712	1	1	yes	characteristic
35	C₂×C₇₃	#2247	1	2	yes	—
36	#2247	—	73	4	no	—
37	#1713	—	73	2	no	—
38	C₈×C₁₆	D₇₃	1	1	yes	characteristic
39	C₇₃	#12516	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₃₂	—	146	8	no	—
41	#500	—	146	4	no	—
42	#494	—	73	4	no	—
43	C₄×C₁₆	C₂×D₇₃	1	2	yes	—
44	C₈²	C₂×D₇₃	1	1	yes	characteristic
45	C₂×Q₁₆	—	146	8	no	—
46	C₄⋊Q₈	—	146	4	no	—
47	Q₃₂	—	292	16	no	—
48	C₂×C₁₆	D₂₉₂	1	4	yes	—
49	#107	—	292	8	no	—
50	C₄×C₈	D₂₉₂	1	2	yes	—
51	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
52	C₂×Q₈	—	292	4	no	—
53	Q₁₆	—	292	16	no	—
54	C₂×C₈	D₅₈₄	1	4	yes	—
55	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
56	C₄⋊C₄	—	292	8	no	—
57	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
58	C₁₆	D₅₈₄	1	8	yes	—
59	Q₈	—	584	8	no	—
60	C₂×C₄	—	584	4	no	—
61	C₂×C₄	#14556588	1	1	yes	characteristic
62	C₂×C₄	C₂×D₅₈₄	1	2	yes	—
63	C₈	Dic₅₈₄	1	8	yes	complemented
64	C₈	C₂×D₅₈₄	1	4	yes	—
65	C₂²	#17988964	1	1	yes	characteristic
66	C₄	—	1168	4	no	—
67	C₄	#17988964	1	2	yes	—
68	C₄	C₂×Dic₅₈₄	1	4	yes	—
69	C₂	#22609546	1	1	yes	characteristic
70	C₂	#22612184	1	2	yes	—

	subgroup	G/H
center	C₂²	#17988964
commutator, cosocle	C₄×C₈×C₇₃	C₂³
Frattini	C₄×C₈	C₂²×D₇₃
Fitting	C₈×C₁₆×C₇₃	C₂
socle, prime radical	C₂²×C₇₃	#493
hypercenter	C₈×C₁₆	D₇₃
hypocenter	C₇₃	#12516
LCS	G ▷ C₄×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
27. C₈×C₇₃	Q₃₂	semidirect
39. C₇₃	#12516	semidirect
63. C₈	Dic₅₈₄	semidirect

Maximal subgroups

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

subgroup	index
#22612184	2
#22609549	2
C₈×C₁₆×C₇₃	2
#12516	73