Subgroups — #13129798

Order 1664.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718857	C₂	1	1	yes	maximal, characteristic
2	#11718261	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#1057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#135	C₄	1	1	yes	characteristic
5	#88202	—	2	1	no	—
6	C₄×#1057	—	2	1	no	—
7	#88106	—	2	1	no	—
8	#88077	—	2	1	no	—
9	#88059	C₄	1	1	yes	characteristic
10	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#41	—	2	1	no	—
12	C₂×#1057	—	2	2	no	—
13	C₁₃×Q₁₆	C₈	1	1	yes	characteristic, complemented
14	C₁₃×SD₁₆	—	2	1	no	—
15	C₁₃×D₈	C₈	1	1	yes	characteristic, complemented
16	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₁₃	D₄	1	1	yes	characteristic
18	#6099	—	2	1	no	—
19	#6099	—	4	1	no	—
20	C₂×#1055	—	4	1	no	—
21	C₂×#1055	D₄	1	1	yes	characteristic
22	#6092	—	4	1	no	—
23	#1335	—	13	1	no	maximal, Sylow
24	Q₈×C₁₃	—	2	1	no	—
25	D₄×C₁₃	—	2	1	no	—
26	D₄×C₁₃	—	4	1	no	—
27	C₂×C₄×C₁₃	—	4	1	no	—
28	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	2	1	no	—
30	#1057	—	2	4	no	—
31	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₃	M₁₆	1	1	yes	characteristic
33	#1055	—	4	1	no	—
34	#1055	D₈	1	1	yes	characteristic
35	#1055	SD₁₆	1	1	yes	characteristic
36	#443	—	13	1	no	—
37	#364	—	13	1	no	—
38	C₈²	—	13	1	no	—
39	C₂²×C₁₃	—	4	1	no	—
40	C₂²×C₁₃	#104	1	1	yes	characteristic
41	C₄×C₁₃	—	4	1	no	—
42	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₃	#102	1	1	yes	characteristic
44	Dic₁₃	—	2	2	no	—
45	#135	#261	1	1	yes	characteristic
46	#131	—	26	1	no	—
47	M₃₂	—	26	1	no	—
48	#108	—	13	1	no	—
49	#104	—	26	1	no	—
50	C₄×C₈	—	13	1	no	—
51	C₄×C₈	—	26	1	no	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	8	1	no	—
54	C₂×C₁₃	D₄⋊C₈	1	1	yes	characteristic
55	#41	—	2	1	no	—
56	Q₁₆	#1057	1	1	yes	characteristic, complemented
57	SD₁₆	—	2	1	no	—
58	D₈	#1057	1	1	yes	characteristic, complemented
59	M₁₆	—	26	1	no	—
60	M₁₆	—	52	1	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	26	2	no	—
63	C₂×C₈	—	52	1	no	—
64	C₂×C₈	C₂×#261	1	1	yes	characteristic
65	C₄²	—	13	1	no	—
66	C₁₆	—	52	1	no	—
67	C₁₃	#1335	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	26	1	no	—
73	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
74	C₈	—	13	1	no	—
75	C₈	—	13	1	no	—
76	C₈	—	26	4	no	—
77	C₈	—	52	1	no	—
78	C₈	C₂×#1057	1	1	yes	characteristic
79	C₈	#6122	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#88116	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	26	2	no	—
84	C₄	#88115	1	1	yes	characteristic
85	C₄	C₂²⋊#1057	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#1057	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88115
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#261
Fitting, prime radical	C₁₃×#135	C₄
socle	C₂×C₁₃	D₄⋊C₈
cosocle	C₈×Dic₁₃	C₂²
hypercenter	#135	#261
hypocenter	C₁₃	#1335
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
2. #11718261	C₂	semidirect
3. C₈×#1057	C₂	semidirect
13. C₁₃×Q₁₆	C₈	semidirect
15. C₁₃×D₈	C₈	semidirect
56. Q₁₆	#1057	semidirect
58. D₈	#1057	semidirect
67. C₁₃	#1335	semidirect

Maximal subgroups

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

subgroup	index
#11718857	2
#11718261	2
C₈×#1057	2
#1335	13