Subgroups — #16792537

Order 3328.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130012	C₂	1	14	yes	maximal
2	C₄³×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×D₁₃	C₂²	1	7	yes	—
4	C₂×(C₂×#261)⋊C₄	C₂²	1	28	yes	—
5	C₄³×C₁₃	C₄	1	1	yes	characteristic, complemented
6	C₄²×Dic₁₃	C₄	1	7	yes	complemented
7	C₂³×#261	C₂³	1	8	yes	—
8	C₂²×C₄×D₁₃	C₂³	1	7	yes	—
9	C₂×C₄²×C₁₃	C₂×C₄	1	7	yes	—
10	C₂×C₄×Dic₁₃	C₂×C₄	1	7	yes	—
11	C₂×C₄×Dic₁₃	C₂×C₄	1	14	yes	—
12	C₄²×D₁₃	—	2	28	no	—
13	(C₂×#261)⋊C₄	—	2	56	no	—
14	#14691	—	13	1	no	maximal, Sylow
15	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
16	C₂²×#261	—	2	56	no	—
17	C₂²×C₄×C₁₃	C₂²×C₄	1	7	yes	—
18	C₂²×Dic₁₃	C₂²×C₄	1	7	yes	—
19	C₂×C₄×D₁₃	—	2	28	no	—
20	C₂×C₄×D₁₃	#41	1	28	yes	—
21	C₄²×C₁₃	—	2	14	no	—
22	C₄×Dic₁₃	—	2	14	no	—
23	C₄×Dic₁₃	—	2	28	no	—
24	C₂×C₄³	—	13	1	no	—
25	#1434	—	13	14	no	—
26	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
27	C₂²×D₁₃	C₂×#41	1	14	yes	—
28	C₂×#261	—	4	56	no	—
29	C₂×C₄×C₁₃	—	2	14	no	—
30	C₂×C₄×C₁₃	#117	1	14	yes	—
31	C₂×Dic₁₃	—	2	14	no	—
32	C₂×Dic₁₃	#117	1	14	yes	—
33	C₄×D₁₃	—	2	56	no	—
34	C₂²×C₄²	—	13	7	no	—
35	C₂×#95	—	13	28	no	—
36	C₄³	—	13	7	no	—
37	C₄³	#261	1	1	yes	characteristic, complemented
38	C₂²×C₁₃	C₂×#117	1	7	yes	—
39	C₂×D₁₃	#529	1	28	yes	—
40	#261	—	8	8	no	—
41	C₄×C₁₃	—	2	14	no	—
42	Dic₁₃	—	2	14	no	—
43	C₂³×C₄	—	13	7	no	—
44	C₂³×C₄	—	13	8	no	—
45	C₂×C₄²	—	13	14	no	—
46	C₂×C₄²	—	13	7	no	—
47	C₂×C₄²	—	26	28	no	—
48	C₂×C₄²	C₂×#261	1	7	yes	—
49	#95	—	26	56	no	—
50	C₂×C₁₃	#2283	1	7	yes	—
51	D₁₃	#2866	1	8	yes	—
52	C₂⁴	—	13	1	no	—
53	C₂²×C₄	—	13	7	no	—
54	C₂²×C₄	—	13	28	no	—
55	C₂²×C₄	—	26	28	no	—
56	C₂²×C₄	—	26	56	no	—
57	C₂²×C₄	C₂²×#261	1	7	yes	—
58	C₄²	—	2	14	no	—
59	C₄²	—	26	28	no	—
60	C₄²	—	26	14	no	—
61	C₁₃	#14691	1	1	yes	characteristic, complemented, Sylow
62	C₂³	—	13	14	no	—
63	C₂³	C₂³×#261	1	1	yes	characteristic
64	C₂×C₄	—	2	14	no	—
65	C₂×C₄	—	13	14	no	—
66	C₂×C₄	—	26	56	no	—
67	C₂×C₄	—	26	14	no	—
68	C₂×C₄	—	52	56	no	—
69	C₂×C₄	#88237	1	14	yes	—
70	C₂²	—	13	28	no	—
71	C₂²	C₂×#88237	1	7	yes	—
72	C₄	—	2	14	no	—
73	C₄	—	26	14	no	—
74	C₄	—	104	8	no	—
75	C₂	—	13	8	no	—
76	C₂	#13131283	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	#14691
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
5. C₄³×C₁₃	C₄	semidirect
6. C₄²×Dic₁₃	C₄	semidirect
37. C₄³	#261	semidirect
61. C₁₃	#14691	semidirect

Maximal subgroups

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

subgroup	index
#13130012	2
C₄³×D₁₃	2
#14691	13