Subgroups — #16789018

Order 3328.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718231	C₂	1	3	yes	maximal
2	C₂×C₄×#6092	C₂	1	3	yes	maximal
3	#13114523	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6092	C₂²	1	1	yes	characteristic
5	C₂²×#6092	C₂²	1	3	yes	—
6	C₁₃×#376	C₄	1	1	yes	characteristic
7	C₂×#88043	C₄	1	3	yes	—
8	C₂×C₄×#1055	C₂²	1	3	yes	—
9	#11718231	C₄	1	12	yes	complemented
10	C₄×#6092	C₄	1	12	yes	complemented
11	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
12	C₂²×#1055	C₂×C₄	1	3	yes	—
13	C₂²×#1055	C₂³	1	1	yes	characteristic
14	C₂×#6092	C₂×C₄	1	6	yes	—
15	C₂×#6092	C₂×C₄	1	6	yes	—
16	C₂×#6092	C₂×C₄	1	12	yes	—
17	C₁₃×#95	C₈	1	4	yes	—
18	#88043	C₈	1	12	yes	—
19	C₄×#1055	C₂×C₄	1	6	yes	—
20	C₄×#1055	C₂×C₄	1	6	yes	—
21	#12539	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
23	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₄²×C₁₃	C₄²	1	6	yes	—
25	C₄²×C₁₃	C₂×C₈	1	6	yes	—
26	C₂×#1055	C₄²	1	6	yes	—
27	C₂×#1055	C₂×C₈	1	12	yes	—
28	C₂×#1055	C₂²×C₄	1	3	yes	—
29	C₂×#1055	C₂²×C₄	1	3	yes	—
30	#6092	C₄²	1	4	yes	—
31	#6092	C₄²	1	12	yes	—
32	C₂×#346	—	13	3	no	—
33	C₂×C₄×C₁₆	—	13	3	no	—
34	#1726	—	13	1	no	—
35	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₃	—	2	12	no	—
37	C₂×C₄×C₁₃	C₄×C₈	1	12	yes	—
38	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
39	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
40	#1055	C₄×C₈	1	12	yes	—
41	#1055	C₂×C₄²	1	1	yes	characteristic
42	#1055	C₂×C₄²	1	3	yes	—
43	C₂²×C₁₆	—	13	1	no	—
44	C₂²×C₁₆	—	13	3	no	—
45	C₂×#97	—	13	3	no	—
46	C₂×C₄×C₈	—	13	3	no	—
47	#376	#261	1	1	yes	characteristic
48	#346	—	13	12	no	—
49	C₄×C₁₆	—	13	12	no	—
50	C₂²×C₁₃	C₂×C₄×C₈	1	3	yes	—
51	C₂²×C₁₃	#504	1	4	yes	—
52	C₄×C₁₃	—	2	12	no	—
53	C₄×C₁₃	C₄³	1	1	yes	characteristic
54	C₄×C₁₃	C₂×C₄×C₈	1	3	yes	—
55	C₂²×C₈	—	13	3	no	—
56	C₂²×C₈	—	13	1	no	—
57	C₂×C₄²	C₂×#261	1	3	yes	—
58	C₂×C₁₆	—	13	6	no	—
59	C₂×C₁₆	—	13	6	no	—
60	C₂×C₁₆	—	13	12	no	—
61	#97	—	13	12	no	—
62	C₄×C₈	—	13	6	no	—
63	C₄×C₈	—	13	6	no	—
64	#95	#1057	1	4	yes	—
65	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
66	C₂×C₁₃	#2108	1	6	yes	—
67	C₂²×C₄	C₂×#1057	1	6	yes	—
68	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
69	C₂×C₈	—	13	12	no	—
70	C₂×C₈	—	13	3	no	—
71	C₂×C₈	—	13	3	no	—
72	C₂×C₈	—	13	6	no	—
73	C₄²	D₁₃⋊C₈	1	6	yes	—
74	C₄²	C₄×#261	1	6	yes	—
75	C₁₆	—	13	4	no	—
76	C₁₆	—	13	12	no	—
77	C₁₃	#12539	1	1	yes	characteristic, complemented, Sylow
78	C₂³	C₂²×#1057	1	1	yes	characteristic
79	C₂×C₄	—	2	12	no	—
80	C₂×C₄	C₄×#1057	1	12	yes	—
81	C₂×C₄	C₂×D₁₃⋊C₈	1	3	yes	—
82	C₂×C₄	C₂×C₄×#261	1	3	yes	—
83	C₈	—	13	12	no	—
84	C₈	—	13	1	no	—
85	C₈	—	13	3	no	—
86	C₂²	C₂×C₄×#1057	1	3	yes	—
87	C₂²	#11719162	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	C₄×D₁₃⋊C₈	1	3	yes	—
90	C₄	C₄²×#261	1	1	yes	characteristic
91	C₂	C₄²×#1057	1	1	yes	characteristic
92	C₂	#13131045	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₄²×C₈
Fitting	C₁₃×#376	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	#376	#261
hypocenter	C₁₃	#12539
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
9. #11718231	C₄	semidirect
10. C₄×#6092	C₄	semidirect
77. C₁₃	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718231	2
C₂×C₄×#6092	2
#13114523	2
#12539	13