Subgroups — C₂²×D₅₄₄ #17192440

Order 4352.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₇₂	C₂	1	2	yes	maximal, complemented
2	C₂×D₅₄₄	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₃₆	—	2	2	no	—
5	C₂×D₂₇₂	—	2	6	no	—
6	C₂×D₂₇₂	C₂²	1	12	yes	complemented
7	D₅₄₄	C₂²	1	16	yes	direct product factor
8	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₇×C₃₂	C₂²	1	6	yes	complemented
10	C₂²×D₆₈	—	4	2	no	—
11	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
12	C₂×D₁₃₆	—	2	12	no	—
13	C₂×D₁₃₆	—	4	6	no	—
14	C₂×C₁₆×C₁₇	D₄	1	3	yes	—
15	C₂×C₁₆×C₁₇	C₂³	1	3	yes	—
16	D₂₇₂	—	2	12	no	—
17	D₂₇₂	C₂³	1	8	yes	complemented
18	C₁₇×C₃₂	C₂³	1	4	yes	complemented
19	C₂³×D₁₇	—	8	2	no	—
20	C₂²×C₄×C₁₇	D₈	1	1	yes	characteristic
21	C₂×D₆₈	—	4	12	no	—
22	C₂×D₆₈	—	8	6	no	—
23	C₂×C₈×C₁₇	D₈	1	3	yes	—
24	C₂×C₈×C₁₇	C₂×D₄	1	3	yes	—
25	D₁₃₆	—	2	8	no	—
26	D₁₃₆	—	4	12	no	—
27	C₁₆×C₁₇	C₂×D₄	1	3	yes	—
28	C₁₆×C₁₇	C₂⁴	1	1	yes	characteristic
29	C₂²×D₃₂	—	17	1	no	maximal, Sylow
30	C₂³×C₁₇	D₁₆	1	1	yes	characteristic
31	C₂²×D₁₇	—	8	12	no	—
32	C₂²×D₁₇	—	16	8	no	—
33	C₂×C₄×C₁₇	D₁₆	1	3	yes	—
34	C₂×C₄×C₁₇	C₂×D₈	1	3	yes	—
35	D₆₈	—	4	8	no	—
36	D₆₈	—	8	12	no	—
37	C₈×C₁₇	C₂×D₈	1	3	yes	—
38	C₈×C₁₇	C₂²×D₄	1	1	yes	characteristic
39	C₂²×D₁₆	—	17	2	no	—
40	C₂×D₃₂	—	17	12	no	—
41	C₂²×C₃₂	D₁₇	1	1	yes	characteristic, complemented
42	C₂²×C₁₇	D₃₂	1	4	yes	complemented
43	C₂²×C₁₇	C₂×D₁₆	1	3	yes	—
44	C₂×D₁₇	—	8	8	no	—
45	C₂×D₁₇	—	16	24	no	—
46	C₄×C₁₇	C₂×D₁₆	1	3	yes	—
47	C₄×C₁₇	C₂²×D₈	1	1	yes	characteristic
48	C₂²×D₈	—	34	2	no	—
49	C₂×D₁₆	—	17	12	no	—
50	C₂×D₁₆	—	34	6	no	—
51	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
52	D₃₂	—	17	16	no	—
53	C₂×C₃₂	C₂×D₁₇	1	6	yes	complemented
54	C₂×C₁₇	C₂×D₃₂	1	6	yes	complemented
55	C₂×C₁₇	C₂²×D₁₆	1	1	yes	characteristic
56	D₁₇	—	16	8	no	—
57	C₂²×D₄	—	68	2	no	—
58	C₂×D₈	—	34	12	no	—
59	C₂×D₈	—	68	6	no	—
60	C₂²×C₈	D₆₈	1	1	yes	characteristic
61	D₁₆	—	17	8	no	—
62	D₁₆	—	34	12	no	—
63	C₂×C₁₆	D₆₈	1	3	yes	—
64	C₂×C₁₆	C₂²×D₁₇	1	3	yes	—
65	C₃₂	C₂²×D₁₇	1	4	yes	complemented
66	C₁₇	C₂²×D₃₂	1	1	yes	characteristic, complemented, Sylow
67	C₂⁴	—	136	2	no	—
68	C₂×D₄	—	68	12	no	—
69	C₂×D₄	—	136	6	no	—
70	C₂²×C₄	D₁₃₆	1	1	yes	characteristic
71	D₈	—	34	8	no	—
72	D₈	—	68	12	no	—
73	C₂×C₈	D₁₃₆	1	3	yes	—
74	C₂×C₈	C₂×D₆₈	1	3	yes	—
75	C₁₆	C₂×D₆₈	1	3	yes	—
76	C₁₆	C₂³×D₁₇	1	1	yes	characteristic
77	C₂³	—	272	8	no	—
78	C₂³	—	136	12	no	—
79	C₂³	D₂₇₂	1	1	yes	characteristic
80	D₄	—	68	8	no	—
81	D₄	—	136	12	no	—
82	C₂×C₄	D₂₇₂	1	3	yes	—
83	C₂×C₄	C₂×D₁₃₆	1	3	yes	—
84	C₈	C₂×D₁₃₆	1	3	yes	—
85	C₈	C₂²×D₆₈	1	1	yes	characteristic
86	C₂²	—	272	24	no	—
87	C₂²	—	136	8	no	—
88	C₂²	D₅₄₄	1	4	yes	direct product factor
89	C₂²	C₂×D₂₇₂	1	3	yes	—
90	C₄	C₂×D₂₇₂	1	3	yes	—
91	C₄	C₂²×D₁₃₆	1	1	yes	characteristic
92	C₂	—	272	8	no	—
93	C₂	C₂×D₅₄₄	1	6	yes	direct product factor
94	C₂	C₂²×D₂₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₇₂
commutator, cosocle	C₁₆×C₁₇	C₂⁴
Frattini	C₁₆	C₂³×D₁₇
Fitting	C₂²×C₁₇×C₃₂	C₂
socle	C₂³×C₁₇	D₁₆
hypercenter	C₂²×C₃₂	D₁₇
hypocenter	C₁₇	C₂²×D₃₂
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₇₂	C₂	semidirect
2. C₂×D₅₄₄	C₂	direct (N × H)
3. C₂²×C₁₇×C₃₂	C₂	semidirect
6. C₂×D₂₇₂	C₂²	semidirect
7. D₅₄₄	C₂²	direct (N × H)
9. C₂×C₁₇×C₃₂	C₂²	semidirect
17. D₂₇₂	C₂³	semidirect
18. C₁₇×C₃₂	C₂³	semidirect
41. C₂²×C₃₂	D₁₇	semidirect
42. C₂²×C₁₇	D₃₂	semidirect
53. C₂×C₃₂	C₂×D₁₇	semidirect
54. C₂×C₁₇	C₂×D₃₂	semidirect
65. C₃₂	C₂²×D₁₇	semidirect
66. C₁₇	C₂²×D₃₂	semidirect
88. C₂²	D₅₄₄	direct (N × H)
93. C₂	C₂×D₅₄₄	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×D₂₇₂	2
C₂×D₅₄₄	2
C₂²×C₁₇×C₃₂	2
C₂²×D₃₂	17

Subgroups — C22×D544 #17192440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₅₄₄ #17192440