Subgroups — #13129965

Order 1664.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718747	C₂	1	1	yes	maximal, characteristic
2	#11718228	C₂	1	1	yes	maximal, characteristic
3	#11718226	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
5	C₂×#6107	—	2	1	no	—
6	C₂×#6106	—	2	1	no	—
7	#88129	C₂²	1	1	yes	characteristic
8	#88113	—	2	1	no	—
9	#88107	—	2	1	no	—
10	#88043	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₃	—	2	1	no	—
12	C₂×D₅₂	D₄	1	1	yes	characteristic
13	C₂×Dic₂₆	D₄	1	1	yes	characteristic
14	C₂²⋊#261	—	4	1	no	—
15	#6122	—	4	1	no	—
16	C₁₃×C₄⋊C₄	—	4	1	no	—
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	#6107	—	4	2	no	—
19	#6106	—	4	2	no	—
20	#6103	—	4	1	no	—
21	C₂×#1055	—	2	1	no	—
22	#1407	—	13	1	no	maximal, Sylow
23	C₂²×D₁₃	—	2	1	no	—
24	C₂×#261	—	8	1	no	—
25	Q₈×C₁₃	—	4	1	no	—
26	Q₈×C₁₃	—	4	1	no	—
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	4	1	no	—
29	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₁₃	—	2	1	no	—
31	D₅₂	—	4	1	no	—
32	Dic₂₆	—	4	1	no	—
33	#1057	—	8	1	no	—
34	#1055	—	2	2	no	—
35	#497	—	13	1	no	—
36	#355	—	13	1	no	—
37	#354	—	13	1	no	—
38	C₂²×C₁₃	#99	1	1	yes	characteristic
39	C₂×D₁₃	—	4	1	no	—
40	C₂×D₁₃	—	8	1	no	—
41	#261	—	16	1	no	—
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	4	1	no	—
44	C₄×C₁₃	—	8	1	no	—
45	Dic₁₃	—	4	1	no	—
46	C₂×Q₁₆	—	26	1	no	—
47	C₂×SD₁₆	—	26	1	no	—
48	C₄⋊Q₈	#261	1	1	yes	characteristic, complemented
49	#124	—	13	1	no	—
50	#101	—	26	1	no	—
51	#99	—	26	1	no	—
52	#97	—	13	1	no	—
53	C₂×C₁₃	—	2	1	no	—
54	C₂×C₁₃	#353	1	1	yes	characteristic
55	D₁₃	—	8	1	no	—
56	C₂×Q₈	—	2	1	no	—
57	C₂×Q₈	—	13	1	no	—
58	C₂×D₄	—	13	1	no	—
59	Q₁₆	—	52	2	no	—
60	SD₁₆	—	52	2	no	—
61	M₁₆	—	52	1	no	—
62	C₂×C₈	—	26	1	no	—
63	C₄⋊C₄	—	4	1	no	—
64	C₂²⋊C₄	—	52	1	no	—
65	C₂²⋊C₄	—	52	1	no	—
66	C₄²	C₂×#261	1	1	yes	characteristic
67	C₁₃	#1407	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	26	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	52	1	no	—
72	D₄	—	52	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	26	1	no	—
76	C₂×C₄	—	104	1	no	—
77	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
78	C₈	—	26	2	no	—
79	C₈	—	104	1	no	—
80	C₂²	—	52	1	no	—
81	C₂²	—	104	1	no	—
82	C₂²	#88119	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	52	1	no	—
87	C₄	—	208	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	104	1	no	—
90	C₂	#11718294	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718294
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×C₄⋊Q₈	C₄
socle	C₂×C₁₃	#353
prime radical	C₂×D₅₂	D₄
cosocle	#88129	C₂²
hypercenter	C₄⋊Q₈	#261
hypocenter	C₁₃	#1407
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
4. C₁₃×C₄⋊Q₈	C₄	semidirect
10. #88043	C₄	semidirect
48. C₄⋊Q₈	#261	semidirect
67. C₁₃	#1407	semidirect

Maximal subgroups

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

subgroup	index
#11718747	2
#11718228	2
#11718226	2
#1407	13