Subgroups — #15750601

Order 3328.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13112970	C₂	1	1	yes	maximal, characteristic
2	#13112910	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1372	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₃×#335	—	2	1	no	—
6	C₂×#88034	C₄	1	1	yes	characteristic
7	C₂×#88034	C₄	1	1	yes	characteristic
8	#11718050	—	2	1	no	—
9	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
11	C₁₃×C₄⋊C₈	—	4	1	no	—
12	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₄⋊#1055	—	4	1	no	—
14	#88034	—	2	1	no	—
15	#88034	C₈	1	2	yes	complemented
16	#7463	—	13	1	no	maximal, Sylow
17	C₂×C₈×C₁₃	—	8	1	no	—
18	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
20	C₄²×C₁₃	D₈	1	1	yes	characteristic
21	C₂×#1055	—	8	1	no	—
22	C₁₃×C₁₆	—	2	1	no	—
23	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
24	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
25	#1397	—	13	1	no	—
26	#1372	—	13	1	no	—
27	#1372	D₁₃	1	1	yes	characteristic
28	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
29	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
31	C₈×C₁₃	—	2	1	no	—
32	C₈×C₁₃	—	16	1	no	—
33	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
34	C₈×C₁₃	#108	1	1	yes	characteristic
35	#1055	—	16	1	no	—
36	C₂×C₃₂	—	13	1	no	—
37	C₂×C₃₂	—	13	1	no	—
38	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
39	#335	—	2	1	no	—
40	#335	—	26	1	no	—
41	C₂²×C₁₃	#367	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	2	1	no	—
44	C₄×C₁₃	#335	1	1	yes	characteristic
45	C₄×C₁₃	#368	1	1	yes	characteristic
46	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
47	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
48	C₄⋊C₈	—	4	1	no	—
49	C₄⋊C₈	—	52	1	no	—
50	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
51	C₃₂	—	13	2	no	—
52	C₃₂	—	26	1	no	—
53	C₂×C₁₃	#1372	1	1	yes	characteristic
54	C₂×C₁₃	#1426	1	1	yes	characteristic
55	C₂×C₁₃	#1426	1	1	yes	characteristic
56	C₂×C₈	—	8	1	no	—
57	C₂×C₈	—	104	1	no	—
58	C₂×C₈	#6101	1	1	yes	characteristic
59	C₂×C₈	#6107	1	1	yes	characteristic
60	C₄²	#6104	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	C₈×D₁₃	1	1	yes	characteristic
63	C₁₆	#6094	1	1	yes	characteristic
64	C₁₃	#7463	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	#88047	1	1	yes	characteristic
66	C₂×C₄	#88067	1	1	yes	characteristic
67	C₂×C₄	#88068	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	16	1	no	—
70	C₈	—	208	1	no	—
71	C₈	#88054	1	1	yes	characteristic
72	C₈	#88062	1	1	yes	characteristic
73	C₂²	#11718082	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	#11718071	1	1	yes	characteristic
77	C₄	#11718085	1	1	yes	characteristic
78	C₂	#13112909	1	1	yes	characteristic
79	C₂	#13113041	1	1	yes	characteristic
80	C₂	#13113043	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718082
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#1372	C₂
socle, prime radical	C₂²×C₁₃	#367
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#1372	D₁₃
hypocenter	C₁₃	#7463
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

Complements

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

N	H ≅ G/N	type
15. #88034	C₈	semidirect
64. C₁₃	#7463	semidirect

Maximal subgroups

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

subgroup	index
#13112970	2
#13112910	2
C₁₃×#1372	2
#7463	13