Subgroups — #16790237

Order 3328.

342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129874	C₂	1	6	yes	maximal
2	C₄²×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6092	C₂²	1	4	yes	—
4	C₄³×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄×#1055	C₄	1	3	yes	—
6	C₂×C₄×#1055	C₂²	1	3	yes	—
7	C₂×C₄²×C₁₃	C₈	1	3	yes	—
8	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
9	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
10	C₂²×#1055	C₂×C₄	1	3	yes	—
11	C₂²×#1055	C₂³	1	1	yes	characteristic
12	C₂×#6092	—	2	12	no	—
13	C₄×#1055	—	2	6	no	—
14	C₄×#1055	—	2	6	no	—
15	#12894	—	13	1	no	maximal, Sylow
16	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
18	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₄²×C₁₃	—	2	6	no	—
20	C₄²×C₁₃	—	2	3	no	—
21	C₄²×C₁₃	—	2	3	no	—
22	C₄²×C₁₃	C₁₆	1	4	yes	complemented
23	C₂×#1055	—	2	3	no	—
24	C₂×#1055	—	2	3	no	—
25	C₂×#1055	M₁₆	1	6	yes	—
26	C₂×#1055	#41	1	6	yes	—
27	#6092	—	4	4	no	—
28	C₄²×C₈	—	13	1	no	—
29	#1374	—	13	6	no	—
30	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	3	no	—
32	C₂×C₄×C₁₃	—	2	3	no	—
33	C₂×C₄×C₁₃	—	2	3	no	—
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	C₂×C₁₆	1	6	yes	—
36	C₂×C₄×C₁₃	M₃₂	1	6	yes	—
37	C₂×C₄×C₁₃	#117	1	3	yes	—
38	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
39	#1055	—	2	6	no	—
40	#1055	#126	1	4	yes	—
41	C₂²×C₁₆	—	13	4	no	—
42	C₂×C₄×C₈	—	13	3	no	—
43	C₂×C₄×C₈	—	13	3	no	—
44	C₄³	#261	1	1	yes	characteristic
45	C₂²×C₁₃	#431	1	3	yes	—
46	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
47	C₂²×C₁₃	C₂×M₃₂	1	3	yes	—
48	C₄×C₁₃	—	2	6	no	—
49	C₄×C₁₃	—	2	6	no	—
50	C₄×C₁₃	#383	1	1	yes	characteristic
51	C₄×C₁₃	#432	1	3	yes	—
52	C₂²×C₈	—	13	1	no	—
53	C₂²×C₈	—	13	3	no	—
54	C₂×C₄²	#1057	1	3	yes	—
55	C₂×C₄²	#1057	1	1	yes	characteristic
56	C₂×C₄²	C₂×#261	1	3	yes	—
57	C₂×C₁₆	—	26	12	no	—
58	C₄×C₈	—	26	6	no	—
59	C₄×C₈	—	26	6	no	—
60	C₂×C₁₃	#1839	1	1	yes	characteristic
61	C₂×C₁₃	#2162	1	3	yes	—
62	C₂×C₁₃	#2163	1	3	yes	—
63	C₂²×C₄	C₂×#1057	1	3	yes	—
64	C₂²×C₄	C₂×#1057	1	3	yes	—
65	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
66	C₂×C₈	—	13	6	no	—
67	C₂×C₈	—	13	6	no	—
68	C₂×C₈	—	26	3	no	—
69	C₂×C₈	—	26	3	no	—
70	C₄²	—	2	6	no	—
71	C₄²	—	2	3	no	—
72	C₄²	—	2	3	no	—
73	C₄²	#6092	1	4	yes	complemented
74	C₁₆	—	52	4	no	—
75	C₁₃	#12894	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂²×#1057	1	1	yes	characteristic
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	C₂×#6092	1	6	yes	—
82	C₂×C₄	#88106	1	6	yes	—
83	C₂×C₄	D₁₃⋊M₁₆	1	3	yes	—
84	C₂×C₄	#88237	1	3	yes	—
85	C₈	—	13	4	no	—
86	C₈	—	26	6	no	—
87	C₂²	C₂²×#6092	1	1	yes	characteristic
88	C₂²	C₂×#88106	1	3	yes	—
89	C₂²	#11719119	1	3	yes	—
90	C₄	—	2	6	no	—
91	C₄	—	2	6	no	—
92	C₄	#11719055	1	3	yes	—
93	C₄	#11719061	1	1	yes	characteristic
94	C₂	#13130763	1	1	yes	characteristic
95	C₂	#13131193	1	3	yes	—
96	C₂	#13131197	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₄³×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₄³	#261
hypocenter	C₁₃	#12894
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
22. C₄²×C₁₃	C₁₆	semidirect
73. C₄²	#6092	semidirect
75. C₁₃	#12894	semidirect

Maximal subgroups

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

subgroup	index
#13129874	2
C₄²×#1055	2
#12894	13