Subgroups — #13116648

Order 1664.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#11718145	C₂	1	2	yes	maximal
3	#11718058	C₂	1	2	yes	maximal, complemented
4	#11718055	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
8	C₁₃×#97	C₄	1	1	yes	characteristic
9	C₁₃×#97	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#88052	C₂²	1	4	yes	—
13	C₂²×C₄×C₁₃	—	2	1	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₁₃×M₁₆	—	2	2	no	—
16	C₁₃×M₁₆	—	2	2	no	—
17	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₄²×C₁₃	—	2	1	no	—
22	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	#6090	—	2	4	no	—
25	#2165	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	—	2	1	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	—	4	2	no	—
32	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₃	—	2	1	no	—
35	C₈×C₁₃	—	2	1	no	—
36	C₈×C₁₃	M₁₆	1	2	yes	—
37	C₈×C₁₃	#41	1	2	yes	—
38	C₄×M₁₆	D₁₃	1	1	yes	characteristic
39	#364	—	13	2	no	—
40	#349	—	13	2	no	—
41	#347	—	13	2	no	—
42	C₂²×C₁₃	—	2	1	no	—
43	C₂²×C₁₃	—	4	1	no	—
44	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₁₃	—	2	2	no	—
46	C₄×C₁₃	—	2	1	no	—
47	C₄×C₁₃	—	4	1	no	—
48	C₄×C₁₃	#117	1	1	yes	characteristic
49	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
50	C₂×M₁₆	Dic₁₃	1	1	yes	characteristic
51	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₄²	Dic₁₃	1	1	yes	characteristic
53	M₃₂	—	13	4	no	—
54	#97	Dic₁₃	1	1	yes	characteristic
55	#97	C₂×D₁₃	1	1	yes	characteristic
56	C₄×C₈	Dic₁₃	1	1	yes	characteristic
57	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₁₃	—	2	1	no	—
59	C₂×C₁₃	—	4	1	no	—
60	C₂×C₁₃	#432	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
67	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
68	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
69	C₄²	—	2	1	no	—
70	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
71	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
72	C₁₆	—	26	4	no	—
73	C₁₃	#2165	1	1	yes	characteristic, complemented, Sylow
74	C₂³	#6099	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#6099	1	1	yes	characteristic
81	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	2	1	no	—
84	C₈	#6099	1	2	yes	—
85	C₈	#6127	1	2	yes	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#6099	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	2	1	no	—
91	C₄	—	4	1	no	—
92	C₄	C₂×#6099	1	1	yes	characteristic
93	C₄	#88180	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#11718587	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88180
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×M₁₆	C₂
socle	C₂×C₁₃	#432
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₄×M₁₆	D₁₃
hypocenter	C₁₃	#2165
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #97 ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #11718058	C₂	semidirect
4. #11718055	C₂	semidirect
73. C₁₃	#2165	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×M₁₆	2
#11718145	2
#11718058	2
#11718055	2
#2165	13