Subgroups — #34032993

Order 18688.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627014	C₂	1	2	yes	maximal
2	C₁₆×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556681	C₄	1	4	yes	—
4	#17989473	C₂²	1	1	yes	characteristic
5	C₈×#10596833	C₄	1	1	yes	characteristic
6	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
7	#14556681	C₈	1	8	yes	complemented
8	C₂×#11924031	C₂×C₄	1	2	yes	—
9	C₄×#10596833	C₈	1	2	yes	—
10	C₂×#11924003	C₈	1	1	yes	characteristic
11	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
13	C₂×#10596833	C₁₆	1	4	yes	—
14	#11924031	C₂×C₈	1	4	yes	—
15	C₂×#10596831	C₄²	1	1	yes	characteristic
16	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
17	#11924003	C₁₆	1	2	yes	—
18	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₇₃	C₁₆	1	2	yes	—
20	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
21	C₂×Dic₇₃	C₂×C₁₆	1	2	yes	—
22	#10596833	C₃₂	1	8	yes	complemented
23	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
24	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
25	#10596831	C₄×C₈	1	2	yes	—
26	C₂²×C₇₃	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₇₃	C₈²	1	1	yes	characteristic
28	C₄×C₇₃	C₄×C₁₆	1	1	yes	characteristic
29	Dic₇₃	C₂×C₃₂	1	4	yes	—
30	C₈×C₃₂	—	73	1	no	maximal, Sylow
31	C₂×C₇₃	C₈×C₁₆	1	1	yes	characteristic
32	C₂×C₇₃	C₄×C₃₂	1	2	yes	—
33	C₄×C₃₂	—	73	2	no	—
34	C₈×C₁₆	—	73	1	no	—
35	C₇₃	C₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃₂	—	73	4	no	—
37	C₄×C₁₆	—	73	1	no	—
38	C₄×C₁₆	—	73	1	no	—
39	C₈²	—	73	1	no	—
40	C₂×C₁₆	—	73	2	no	—
41	C₂×C₁₆	—	73	1	no	—
42	C₂×C₁₆	#10596842	1	1	yes	characteristic
43	C₄×C₈	—	73	2	no	—
44	C₄×C₈	—	73	1	no	—
45	C₃₂	—	73	8	no	—
46	C₂×C₈	—	73	4	no	—
47	C₂×C₈	—	73	1	no	—
48	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
49	C₄²	—	73	1	no	—
50	C₁₆	—	73	4	no	—
51	C₁₆	—	73	2	no	—
52	C₁₆	#11924040	1	2	yes	—
53	C₂×C₄	—	73	2	no	—
54	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
55	C₈	—	73	8	no	—
56	C₈	—	73	2	no	—
57	C₈	C₂×#11924040	1	1	yes	characteristic
58	C₈	#14556686	1	1	yes	characteristic
59	C₂²	#64408⋊C₁₆	1	1	yes	characteristic
60	C₄	—	73	4	no	—
61	C₄	C₈×#10596842	1	1	yes	characteristic
62	C₄	C₄×#11924040	1	1	yes	characteristic
63	C₂	C₈×#11924040	1	1	yes	characteristic
64	C₂	#64408⋊C₃₂	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#10596842
commutator, hypocenter	C₇₃	C₈×C₃₂
Frattini	C₂×C₈	C₂×#10596842
Fitting	C₂×C₁₆×C₇₃	C₈
socle, prime radical	C₂²×C₇₃	C₄×C₁₆
cosocle	#17989473	C₂²
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
7. #14556681	C₈	semidirect
22. #10596833	C₃₂	semidirect
35. C₇₃	C₈×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#22627014	2
C₁₆×#10596833	2
C₈×C₃₂	73