Subgroups — #16792538

Order 3328.

2286 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719059	C₂	1	14	yes	maximal
2	C₄³×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊#261	C₂²	1	28	yes	—
4	C₂×C₄²×D₁₃	C₂²	1	7	yes	—
5	#11719059	—	2	56	no	—
6	C₄³×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₄²×Dic₁₃	C₄	1	7	yes	complemented
8	C₂³×#261	C₂³	1	8	yes	—
9	C₂²×C₄×D₁₃	C₂³	1	7	yes	—
10	C₂×C₄⋊#261	—	2	168	no	—
11	C₂×C₄²×C₁₃	C₂×C₄	1	7	yes	—
12	C₂×C₄×Dic₁₃	C₂×C₄	1	21	yes	—
13	C₄²×D₁₃	D₄	1	28	yes	—
14	C₄²×D₁₃	Q₈	1	28	yes	—
15	#14692	—	13	1	no	maximal, Sylow
16	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
17	C₂²×#261	—	2	56	no	—
18	C₂²×C₄×C₁₃	C₂²×C₄	1	7	yes	—
19	C₂²×Dic₁₃	C₂²×C₄	1	7	yes	—
20	C₂×C₄×D₁₃	C₂×D₄	1	42	yes	—
21	C₂×C₄×D₁₃	C₂×Q₈	1	42	yes	—
22	C₄⋊#261	—	4	112	no	—
23	C₄²×C₁₃	C₄⋊C₄	1	28	yes	complemented
24	C₄×Dic₁₃	C₄⋊C₄	1	84	yes	complemented
25	C₂×#384	—	13	14	no	—
26	C₂×C₄³	—	13	1	no	—
27	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
28	C₂²×D₁₃	C₂²×D₄	1	7	yes	—
29	C₂²×D₁₃	C₂²×Q₈	1	7	yes	—
30	C₂×#261	—	4	56	no	—
31	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	42	yes	—
32	C₂×Dic₁₃	C₂×C₄⋊C₄	1	42	yes	—
33	C₄×D₁₃	#127	1	28	yes	—
34	C₄×D₁₃	C₄⋊Q₈	1	84	yes	—
35	C₂²×C₄⋊C₄	—	13	28	no	—
36	C₂²×C₄²	—	13	7	no	—
37	#384	—	26	56	no	—
38	C₄³	—	13	7	no	—
39	C₄³	#261	1	1	yes	characteristic, complemented
40	C₂²×C₁₃	C₂²×C₄⋊C₄	1	7	yes	—
41	C₂×D₁₃	C₂×#127	1	7	yes	—
42	C₂×D₁₃	C₂×C₄⋊Q₈	1	21	yes	—
43	#261	—	8	8	no	—
44	C₄×C₁₃	#384	1	28	yes	complemented
45	Dic₁₃	#384	1	28	yes	complemented
46	C₂³×C₄	—	13	7	no	—
47	C₂³×C₄	—	13	8	no	—
48	C₂×C₄⋊C₄	—	26	168	no	—
49	C₂×C₄²	—	13	21	no	—
50	C₂×C₄²	—	13	28	no	—
51	C₂×C₄²	—	13	28	no	—
52	C₂×C₄²	C₂×#261	1	7	yes	—
53	C₂×C₁₃	C₂×#384	1	7	yes	—
54	D₁₃	#2867	1	1	yes	characteristic
55	D₁₃	#2868	1	7	yes	—
56	C₂⁴	—	13	1	no	—
57	C₂²×C₄	—	13	7	no	—
58	C₂²×C₄	—	13	42	no	—
59	C₂²×C₄	—	13	42	no	—
60	C₂²×C₄	—	26	56	no	—
61	C₂²×C₄	C₂²×#261	1	7	yes	—
62	C₄⋊C₄	—	52	112	no	—
63	C₄²	—	13	84	no	—
64	C₄²	C₄⋊#261	1	28	yes	complemented
65	C₁₃	#14692	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	13	7	no	—
67	C₂³	—	13	7	no	—
68	C₂³	C₂³×#261	1	1	yes	characteristic
69	C₂×C₄	—	13	42	no	—
70	C₂×C₄	—	13	28	no	—
71	C₂×C₄	—	13	84	no	—
72	C₂×C₄	—	52	56	no	—
73	C₂×C₄	C₂×C₄⋊#261	1	42	yes	—
74	C₂²	—	13	7	no	—
75	C₂²	—	13	21	no	—
76	C₂²	C₂²×C₄⋊#261	1	7	yes	—
77	C₄	—	13	28	no	—
78	C₄	—	104	8	no	—
79	C₄	#11719059	1	28	yes	complemented
80	C₂	—	13	1	no	—
81	C₂	—	13	7	no	—
82	C₂	C₂×#11719059	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#261
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄³×C₁₃	C₄
prime radical, cosocle	C₂³×D₁₃	C₂⁴
hypercenter	C₄³	#261
hypocenter	C₁₃	#14692
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
6. C₄³×C₁₃	C₄	semidirect
7. C₄²×Dic₁₃	C₄	semidirect
23. C₄²×C₁₃	C₄⋊C₄	semidirect
24. C₄×Dic₁₃	C₄⋊C₄	semidirect
39. C₄³	#261	semidirect
44. C₄×C₁₃	#384	semidirect
45. Dic₁₃	#384	semidirect
64. C₄²	C₄⋊#261	semidirect
65. C₁₃	#14692	semidirect
79. C₄	#11719059	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719059	2
C₄³×D₁₃	2
#14692	13