Subgroups — C₂²×#88069 #13127948

Order 1664.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#88069	C₂	1	12	yes	maximal, direct product factor
4	C₂²×#6090	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₃	—	2	1	no	—
6	C₂²×Dic₂₆	—	2	1	no	—
7	C₂×C₁₃×Q₁₆	—	2	3	no	—
8	C₂×C₁₃×Q₁₆	C₂²	1	6	yes	—
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₂	—	2	3	no	—
11	C₂×Dic₅₂	C₂²	1	6	yes	—
12	#88069	C₂²	1	16	yes	direct product factor
13	C₂×#6090	C₂²	1	6	yes	—
14	C₂×Q₈×C₁₃	—	2	6	no	—
15	C₂×Q₈×C₁₃	—	4	3	no	—
16	C₂²×C₄×C₁₃	—	4	1	no	—
17	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×Dic₁₃	—	4	1	no	—
19	C₂×Dic₂₆	—	2	6	no	—
20	C₂×Dic₂₆	—	4	3	no	—
21	C₁₃×Q₁₆	—	2	6	no	—
22	C₁₃×Q₁₆	C₂³	1	4	yes	—
23	C₂×C₈×C₁₃	D₄	1	3	yes	—
24	C₂×C₈×C₁₃	C₂³	1	3	yes	—
25	Dic₅₂	—	2	6	no	—
26	Dic₅₂	C₂³	1	4	yes	—
27	#6090	C₂³	1	4	yes	—
28	C₂²×Q₃₂	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	D₈	1	1	yes	characteristic
30	Q₈×C₁₃	—	2	4	no	—
31	Q₈×C₁₃	—	4	6	no	—
32	C₂×C₄×C₁₃	—	4	6	no	—
33	C₂×C₄×C₁₃	D₈	1	3	yes	—
34	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
35	C₂×Dic₁₃	—	4	6	no	—
36	Dic₂₆	—	2	4	no	—
37	Dic₂₆	—	4	6	no	—
38	C₈×C₁₃	C₂×D₄	1	3	yes	—
39	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
40	C₂²×Q₁₆	—	13	1	no	—
41	C₂²×Q₁₆	D₁₃	1	1	yes	characteristic
42	C₂×Q₃₂	—	13	12	no	—
43	C₂²×C₁₆	—	13	1	no	—
44	C₂²×C₁₃	Q₃₂	1	4	yes	complemented
45	C₂²×C₁₃	C₂×D₈	1	3	yes	—
46	C₄×C₁₃	—	4	4	no	—
47	C₄×C₁₃	C₂×D₈	1	3	yes	—
48	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
49	Dic₁₃	—	4	4	no	—
50	C₂²×Q₈	—	2	1	no	—
51	C₂²×Q₈	—	26	1	no	—
52	C₂×Q₁₆	—	2	3	no	—
53	C₂×Q₁₆	—	13	6	no	—
54	C₂×Q₁₆	—	26	3	no	—
55	C₂×Q₁₆	C₂×D₁₃	1	6	yes	—
56	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
57	Q₃₂	—	13	16	no	—
58	C₂×C₁₆	—	13	6	no	—
59	C₂×C₁₃	C₂×Q₃₂	1	6	yes	complemented
60	C₂×C₁₃	C₂²×D₈	1	1	yes	characteristic
61	C₂×Q₈	—	2	6	no	—
62	C₂×Q₈	—	4	3	no	—
63	C₂×Q₈	—	26	6	no	—
64	C₂×Q₈	—	52	3	no	—
65	C₂²×C₄	—	4	1	no	—
66	C₂²×C₄	—	52	1	no	—
67	C₂²×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
68	Q₁₆	—	2	6	no	—
69	Q₁₆	—	13	4	no	—
70	Q₁₆	—	26	6	no	—
71	Q₁₆	C₂²×D₁₃	1	4	yes	—
72	C₂×C₈	C₂²⋊D₁₃	1	3	yes	—
73	C₂×C₈	C₂²×D₁₃	1	3	yes	—
74	C₁₆	—	13	4	no	—
75	C₁₃	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
76	C₂³	#6104	1	1	yes	characteristic
77	Q₈	—	2	4	no	—
78	Q₈	—	4	6	no	—
79	Q₈	—	26	4	no	—
80	Q₈	—	52	6	no	—
81	C₂×C₄	—	4	6	no	—
82	C₂×C₄	—	52	6	no	—
83	C₂×C₄	#6104	1	3	yes	—
84	C₂×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
85	C₈	C₂×C₂²⋊D₁₃	1	3	yes	—
86	C₈	C₂³×D₁₃	1	1	yes	characteristic
87	C₂²	#88069	1	4	yes	direct product factor
88	C₂²	C₂×#6104	1	3	yes	—
89	C₄	—	4	4	no	—
90	C₄	—	52	4	no	—
91	C₄	C₂×#6104	1	3	yes	—
92	C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
93	C₂	C₂×#88069	1	6	yes	direct product factor
94	C₂	C₂²×#6104	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#6104
commutator, cosocle	C₈×C₁₃	C₂⁴
Frattini	C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×Q₁₆	C₂
socle, prime radical	C₂³×C₁₃	D₈
hypercenter	C₂²×Q₁₆	D₁₃
hypocenter	C₁₃	C₂²×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#88069	C₂	direct (N × H)
12. #88069	C₂²	direct (N × H)
44. C₂²×C₁₃	Q₃₂	semidirect
59. C₂×C₁₃	C₂×Q₃₂	semidirect
75. C₁₃	C₂²×Q₃₂	semidirect
87. C₂²	#88069	direct (N × H)
93. C₂	C₂×#88069	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×Q₁₆	2
C₂²×Dic₅₂	2
C₂×#88069	2
C₂²×#6090	2
C₂²×Q₃₂	13

Subgroups — C22×#88069 #13127948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88069 #13127948