Subgroups — #13113008

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718743	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#356	C₂	1	1	yes	maximal, characteristic
3	#11718140	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	#88124	C₄	1	1	yes	characteristic
6	C₁₃×#101	—	2	1	no	—
7	#88076	—	2	1	no	—
8	#88075	—	2	1	no	—
9	#88075	—	2	1	no	—
10	#88043	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
13	C₁₃×M₁₆	—	4	1	no	—
14	C₁₃×C₄⋊C₄	—	4	1	no	—
15	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₁₃	—	2	1	no	—
17	#6101	—	4	1	no	—
18	#6099	—	4	1	no	—
19	C₂×#1055	—	2	1	no	—
20	#1413	—	13	1	no	maximal, Sylow
21	Q₈×C₁₃	—	4	1	no	—
22	Q₈×C₁₃	—	4	1	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	2	1	no	—
25	C₂×C₄×C₁₃	—	2	1	no	—
26	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₃	—	4	1	no	—
28	C₈×C₁₃	—	8	1	no	—
29	#1055	—	4	1	no	—
30	#1055	—	8	1	no	—
31	#491	—	13	1	no	—
32	#356	—	13	1	no	—
33	#356	D₁₃	1	1	yes	characteristic
34	C₂²×C₁₃	#99	1	1	yes	characteristic
35	C₄×C₁₃	—	2	1	no	—
36	C₄×C₁₃	—	4	1	no	—
37	C₄×C₁₃	—	4	1	no	—
38	C₄×C₁₃	—	4	1	no	—
39	Dic₁₃	—	8	1	no	—
40	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
41	#125	—	13	1	no	—
42	#103	—	26	1	no	—
43	#103	—	26	1	no	—
44	#101	—	2	1	no	—
45	#101	—	26	1	no	—
46	#97	—	13	1	no	—
47	C₂×C₁₃	—	2	1	no	—
48	C₂×C₁₃	#354	1	1	yes	characteristic
49	C₂×Q₈	D₅₂	1	1	yes	characteristic
50	C₂×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
51	M₁₆	—	4	1	no	—
52	M₁₆	—	52	1	no	—
53	C₂×C₈	—	26	1	no	—
54	C₄⋊C₄	—	4	1	no	—
55	C₄⋊C₄	—	26	1	no	—
56	C₄⋊C₄	—	52	1	no	—
57	C₄²	C₄×D₁₃	1	1	yes	characteristic
58	C₁₃	#1413	1	1	yes	characteristic, complemented, Sylow
59	Q₈	—	4	1	no	—
60	Q₈	—	4	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	52	1	no	—
65	C₂×C₄	#6103	1	1	yes	characteristic
66	C₈	—	8	1	no	—
67	C₈	—	52	1	no	—
68	C₈	—	104	1	no	—
69	C₂²	#88046	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	104	1	no	—
75	C₂	—	2	1	no	—
76	C₂	#11718065	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718065
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₃
Fitting	C₁₃×#356	C₂
socle	C₂×C₁₃	#354
prime radical	C₂²×C₁₃	#99
cosocle	C₁₃×C₄⋊Q₈	C₂²
hypercenter	#356	D₁₃
hypocenter	C₁₃	#1413
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
58. C₁₃	#1413	semidirect

Maximal subgroups

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

subgroup	index
#11718743	2
C₁₃×#356	2
#11718140	2
#1413	13