Subgroups — C₂²×#88038 #13127931

Order 1664.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88038	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄×D₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#1055	C₄	1	1	yes	characteristic
8	C₂×C₈×D₁₃	C₄	1	6	yes	—
9	C₂×C₈×D₁₃	C₂²	1	6	yes	—
10	C₂×C₁₃×C₁₆	C₂²	1	6	yes	complemented
11	C₂×#6090	C₂²	1	6	yes	complemented
12	#88038	C₂²	1	16	yes	direct product factor
13	C₂³×D₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₃	C₈	1	1	yes	characteristic
16	C₂×C₄×D₁₃	C₈	1	6	yes	—
17	C₂×C₄×D₁₃	C₂×C₄	1	6	yes	—
18	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₁₃	C₂³	1	3	yes	—
20	C₂×#1055	C₂×C₄	1	6	yes	—
21	C₈×D₁₃	C₂×C₄	1	12	yes	—
22	C₈×D₁₃	C₂³	1	4	yes	—
23	C₁₃×C₁₆	C₂³	1	4	yes	complemented
24	#6090	C₂³	1	4	yes	complemented
25	C₂²×M₃₂	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₂²×D₁₃	—	2	4	no	—
28	C₂²×D₁₃	C₂×C₈	1	6	yes	—
29	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
31	C₂×Dic₁₃	C₂×C₈	1	6	yes	—
32	C₄×D₁₃	C₂×C₈	1	12	yes	—
33	C₄×D₁₃	C₂²×C₄	1	4	yes	—
34	C₈×C₁₃	C₂²×C₄	1	3	yes	—
35	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
36	#1055	C₂²×C₄	1	4	yes	—
37	C₂³×C₈	—	13	1	no	—
38	C₂×M₃₂	—	13	12	no	—
39	C₂²×C₁₆	—	13	1	no	—
40	C₂²×C₁₆	D₁₃	1	1	yes	characteristic, complemented
41	C₂²×C₁₃	M₃₂	1	4	yes	complemented
42	C₂²×C₁₃	C₂²×C₈	1	3	yes	—
43	C₂×D₁₃	—	2	12	no	—
44	C₂×D₁₃	C₂²×C₈	1	4	yes	—
45	C₄×C₁₃	C₂²×C₈	1	3	yes	—
46	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
47	Dic₁₃	C₂²×C₈	1	4	yes	—
48	C₂³×C₄	—	13	1	no	—
49	C₂²×C₈	—	13	1	no	—
50	C₂²×C₈	—	13	6	no	—
51	C₂²×C₈	—	13	6	no	—
52	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
53	M₃₂	—	13	16	no	—
54	C₂×C₁₆	—	13	6	no	—
55	C₂×C₁₆	C₂×D₁₃	1	6	yes	complemented
56	C₂×C₁₃	C₂×M₃₂	1	6	yes	complemented
57	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
58	D₁₃	—	2	4	no	—
59	C₂⁴	—	13	1	no	—
60	C₂²×C₄	—	13	1	no	—
61	C₂²×C₄	—	13	6	no	—
62	C₂²×C₄	—	13	6	no	—
63	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
64	C₂×C₈	—	13	6	no	—
65	C₂×C₈	—	13	12	no	—
66	C₂×C₈	—	13	4	no	—
67	C₂×C₈	C₄×D₁₃	1	3	yes	—
68	C₂×C₈	C₂²×D₁₃	1	3	yes	—
69	C₁₆	—	13	4	no	—
70	C₁₆	C₂²×D₁₃	1	4	yes	complemented
71	C₁₃	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	13	6	no	—
73	C₂³	—	26	4	no	—
74	C₂³	C₈×D₁₃	1	1	yes	characteristic
75	C₂×C₄	—	13	6	no	—
76	C₂×C₄	—	13	12	no	—
77	C₂×C₄	—	13	4	no	—
78	C₂×C₄	C₈×D₁₃	1	3	yes	—
79	C₂×C₄	C₂×C₄×D₁₃	1	3	yes	—
80	C₈	—	13	4	no	—
81	C₈	C₂×C₄×D₁₃	1	3	yes	—
82	C₈	C₂³×D₁₃	1	1	yes	characteristic
83	C₂²	—	13	4	no	—
84	C₂²	—	26	12	no	—
85	C₂²	#88038	1	4	yes	direct product factor
86	C₂²	C₂×C₈×D₁₃	1	3	yes	—
87	C₄	—	13	4	no	—
88	C₄	C₂×C₈×D₁₃	1	3	yes	—
89	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
90	C₂	—	26	4	no	—
91	C₂	C₂×#88038	1	6	yes	direct product factor
92	C₂	C₂²×C₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	C₂×C₈
prime radical	C₂³×D₁₃	C₈
cosocle	C₈×C₁₃	C₂⁴
hypercenter	C₂²×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₁₆	C₂	semidirect
3. C₂²×#6090	C₂	semidirect
4. C₂×#88038	C₂	direct (N × H)
10. C₂×C₁₃×C₁₆	C₂²	semidirect
11. C₂×#6090	C₂²	semidirect
12. #88038	C₂²	direct (N × H)
23. C₁₃×C₁₆	C₂³	semidirect
24. #6090	C₂³	semidirect
40. C₂²×C₁₆	D₁₃	semidirect
41. C₂²×C₁₃	M₃₂	semidirect
55. C₂×C₁₆	C₂×D₁₃	semidirect
56. C₂×C₁₃	C₂×M₃₂	semidirect
70. C₁₆	C₂²×D₁₃	semidirect
71. C₁₃	C₂²×M₃₂	semidirect
85. C₂²	#88038	direct (N × H)
91. C₂	C₂×#88038	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×C₈×D₁₃	2
C₂²×C₁₃×C₁₆	2
C₂²×#6090	2
C₂×#88038	2
C₂²×M₃₂	13

Subgroups — C22×#88038 #13127931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88038 #13127931