Subgroups — #13120946

Order 1664.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88129	C₂	1	3	yes	maximal
2	C₂×#88123	C₂	1	3	yes	maximal, complemented
3	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718338	C₂	1	8	yes	maximal, complemented
5	C₂²×D₅₂	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₆	C₂²	1	3	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₂×#6103	C₂²	1	12	yes	—
9	C₂×C₄⋊Dic₁₃	C₂²	1	12	yes	—
10	#88129	—	2	12	no	—
11	#88123	—	2	12	no	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	C₂³×D₁₃	C₂³	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂³	1	6	yes	—
17	C₂×D₅₂	—	2	6	no	—
18	C₂×Dic₂₆	—	2	12	no	—
19	C₂×Dic₂₆	—	2	6	no	—
20	C₄²×C₁₃	D₄	1	12	yes	—
21	#6103	—	2	24	no	—
22	C₄⋊Dic₁₃	—	2	24	no	—
23	#2658	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
25	C₂²×D₁₃	—	2	6	no	—
26	C₂²×D₁₃	—	2	8	no	—
27	C₂×C₄×C₁₃	—	2	12	no	—
28	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
29	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
30	C₂×Dic₁₃	—	2	12	no	—
31	C₂×Dic₁₃	—	2	6	no	—
32	D₅₂	—	4	4	no	—
33	Dic₂₆	—	4	12	no	—
34	C₂×C₄⋊Q₈	—	13	3	no	—
35	C₂×#124	—	13	3	no	—
36	#399	—	13	8	no	—
37	#376	D₁₃	1	1	yes	characteristic, complemented
38	C₂²×C₁₃	C₂²×D₄	1	3	yes	—
39	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
40	C₂×D₁₃	—	4	2	no	—
41	C₂×D₁₃	—	4	12	no	—
42	C₄×C₁₃	—	2	12	no	—
43	C₄×C₁₃	#127	1	4	yes	—
44	Dic₁₃	—	4	6	no	—
45	C₂²×Q₈	—	13	3	no	—
46	C₂²×D₄	—	13	1	no	—
47	C₄⋊Q₈	—	26	12	no	—
48	#124	—	26	12	no	—
49	C₂×C₄⋊C₄	—	13	12	no	—
50	C₂×C₂²⋊C₄	—	13	12	no	—
51	C₂×C₄²	C₂×D₁₃	1	3	yes	—
52	#95	C₂×D₁₃	1	4	yes	—
53	C₂×C₁₃	C₂×#127	1	1	yes	characteristic
54	C₂×C₁₃	#536	1	6	yes	—
55	D₁₃	—	8	2	no	—
56	C₂⁴	—	13	2	no	—
57	C₂×Q₈	—	26	6	no	—
58	C₂×Q₈	—	26	12	no	—
59	C₂×D₄	—	26	6	no	—
60	C₂²×C₄	—	13	6	no	—
61	C₂²×C₄	C₂²×D₁₃	1	6	yes	—
62	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
63	C₄⋊C₄	—	26	24	no	—
64	C₂²⋊C₄	—	26	24	no	—
65	C₄²	D₅₂	1	12	yes	—
66	C₁₃	#2658	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	26	6	no	—
68	C₂³	—	26	8	no	—
69	C₂³	C₂³×D₁₃	1	1	yes	characteristic
70	Q₈	—	52	12	no	—
71	D₄	—	52	4	no	—
72	C₂×C₄	—	2	12	no	—
73	C₂×C₄	—	26	6	no	—
74	C₂×C₄	—	26	12	no	—
75	C₂×C₄	C₂×D₅₂	1	12	yes	—
76	C₂×C₄	C₂×D₅₂	1	6	yes	—
77	C₂²	—	52	2	no	—
78	C₂²	—	52	12	no	—
79	C₂²	C₂²×D₅₂	1	3	yes	—
80	C₂²	#88257	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	52	6	no	—
83	C₄	#88128	1	4	yes	—
84	C₂	—	104	2	no	—
85	C₂	C₂×#88128	1	1	yes	characteristic
86	C₂	#11719231	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#376	C₂
prime radical	C₂²×D₅₂	C₂²
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2658
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
2. C₂×#88123	C₂	semidirect
3. C₁₃×#376	C₂	semidirect
4. #11718338	C₂	semidirect
37. #376	D₁₃	semidirect
66. C₁₃	#2658	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88129	2
C₂×#88123	2
C₁₃×#376	2
#11718338	2
#2658	13