Subgroups — #13129801

Order 1664.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718556	C₂	1	1	yes	maximal, characteristic
2	#11718261	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718251	C₂	1	1	yes	maximal, characteristic, complemented
4	#88161	—	2	1	no	—
5	#88158	C₄	1	1	yes	characteristic
6	C₄×#1057	—	2	1	no	—
7	#88106	—	2	1	no	—
8	C₁₃×#108	C₄	1	1	yes	characteristic
9	#88065	—	2	1	no	—
10	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	#6127	—	2	1	no	—
12	C₂×#1057	—	2	2	no	—
13	C₁₃×M₁₆	—	2	1	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₄×Dic₁₃	D₄	1	1	yes	characteristic
16	C₂×#1055	D₄	1	1	yes	characteristic
17	Dic₅₂	C₈	1	1	yes	characteristic, complemented
18	D₁₀₄	C₈	1	1	yes	characteristic, complemented
19	#6095	—	2	1	no	—
20	#6094	—	4	1	no	—
21	C₈×D₁₃	—	4	1	no	—
22	#6092	—	4	1	no	—
23	#1336	—	13	1	no	maximal, Sylow
24	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₁₃	—	4	1	no	—
26	C₂×Dic₁₃	—	2	1	no	—
27	D₅₂	—	2	1	no	—
28	C₄×D₁₃	—	4	1	no	—
29	Dic₂₆	—	2	1	no	—
30	#1057	—	4	2	no	—
31	C₈×C₁₃	—	4	1	no	—
32	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₃	M₁₆	1	1	yes	characteristic
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	#322	—	13	1	no	—
39	C₂²×C₁₃	#104	1	1	yes	characteristic
40	C₂×D₁₃	—	4	1	no	—
41	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₃	#102	1	1	yes	characteristic
43	Dic₁₃	—	2	2	no	—
44	Dic₁₃	—	4	1	no	—
45	#135	—	13	1	no	—
46	#131	—	26	1	no	—
47	M₃₂	—	26	1	no	—
48	#108	#261	1	1	yes	characteristic
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	D₄⋊C₈	1	1	yes	characteristic
54	D₁₃	—	8	1	no	—
55	#41	—	26	1	no	—
56	Q₁₆	—	13	1	no	—
57	SD₁₆	—	26	1	no	—
58	D₈	—	13	1	no	—
59	M₁₆	—	2	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	#1336	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	26	1	no	—
69	D₄	—	26	1	no	—
70	D₄	—	52	1	no	—
71	C₂×C₄	—	26	1	no	—
72	C₂×C₄	—	52	1	no	—
73	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
74	C₈	—	4	1	no	—
75	C₈	—	13	1	no	—
76	C₈	—	13	1	no	—
77	C₈	—	52	2	no	—
78	C₈	D₁₃⋊C₈	1	1	yes	characteristic
79	C₈	#6118	1	1	yes	characteristic
80	C₂²	—	52	1	no	—
81	C₂²	#88118	1	1	yes	characteristic
82	C₄	—	26	2	no	—
83	C₄	—	52	1	no	—
84	C₄	#88111	1	1	yes	characteristic
85	C₄	#88115	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	104	1	no	—
88	C₂	#11718243	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88115
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#108	C₄
socle	C₂×C₁₃	D₄⋊C₈
prime radical	#88158	C₄
cosocle	C₈×Dic₁₃	C₂²
hypercenter	#108	#261
hypocenter	C₁₃	#1336
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #11718261	C₂	semidirect
3. #11718251	C₂	semidirect
17. Dic₅₂	C₈	semidirect
18. D₁₀₄	C₈	semidirect
67. C₁₃	#1336	semidirect

Maximal subgroups

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

subgroup	index
#11718556	2
#11718261	2
#11718251	2
#1336	13