Subgroups — C₂⁴×Dic₂₉₂ #33999766

Order 18688.

11166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₁₄₆	C₂	1	2	yes	maximal
2	C₂³×Dic₂₉₂	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₄₆	—	2	30	no	—
5	C₂³×Dic₁₄₆	C₂²	1	60	yes	—
6	C₂⁴×Dic₇₃	—	2	2	no	—
7	C₂²×Dic₂₉₂	C₂²	1	560	yes	direct product factor
8	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₇₃	C₂²	1	30	yes	—
10	C₂²×Dic₁₄₆	—	2	420	no	—
11	C₂²×Dic₁₄₆	C₂³	1	280	yes	—
12	C₂³×Dic₇₃	—	2	60	no	—
13	C₂×Dic₂₉₂	C₂³	1	960	yes	direct product factor
14	C₂⁵×C₇₃	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₇₃	D₄	1	15	yes	—
16	C₂³×C₄×C₇₃	C₂³	1	15	yes	—
17	C₂²×C₈×C₇₃	C₂³	1	140	yes	—
18	C₂×Dic₁₄₆	—	2	840	no	—
19	C₂×Dic₁₄₆	C₂⁴	1	240	yes	—
20	C₂²×Dic₇₃	—	2	280	no	—
21	Dic₂₉₂	C₂⁴	1	256	yes	direct product factor
22	C₂⁴×C₇₃	Q₁₆	1	16	yes	complemented
23	C₂⁴×C₇₃	C₂×D₄	1	15	yes	—
24	C₂²×C₄×C₇₃	C₂×D₄	1	105	yes	—
25	C₂²×C₄×C₇₃	C₂⁴	1	35	yes	—
26	C₂×C₈×C₇₃	C₂⁴	1	120	yes	—
27	C₂³×C₇₃	C₂×Q₁₆	1	120	yes	complemented
28	C₂³×C₇₃	C₂²×D₄	1	35	yes	—
29	C₂×C₄×C₇₃	C₂²×D₄	1	105	yes	—
30	C₂×C₄×C₇₃	C₂⁵	1	15	yes	—
31	C₂×Dic₇₃	—	2	240	no	—
32	Dic₁₄₆	—	2	240	no	—
33	Dic₁₄₆	C₂⁵	1	32	yes	—
34	C₈×C₇₃	C₂⁵	1	16	yes	—
35	C₂²×C₇₃	C₂²×Q₁₆	1	140	yes	complemented
36	C₂²×C₇₃	C₂³×D₄	1	15	yes	—
37	C₄×C₇₃	C₂³×D₄	1	15	yes	—
38	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
39	Dic₇₃	—	2	32	no	—
40	C₂⁴×Q₁₆	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	C₂³×Q₁₆	1	30	yes	complemented
42	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
43	C₂⁴×Q₈	—	73	2	no	—
44	C₂³×Q₁₆	—	73	60	no	—
45	C₂⁴×C₈	D₇₃	1	1	yes	characteristic
46	C₇₃	C₂⁴×Q₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂³×Q₈	—	73	60	no	—
48	C₂³×Q₈	—	146	30	no	—
49	C₂⁴×C₄	—	146	2	no	—
50	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
51	C₂²×Q₁₆	—	73	560	no	—
52	C₂³×C₈	C₂×D₇₃	1	30	yes	—
53	C₂⁵	D₂₉₂	1	1	yes	characteristic
54	C₂²×Q₈	—	73	280	no	—
55	C₂²×Q₈	—	146	420	no	—
56	C₂³×C₄	—	146	60	no	—
57	C₂³×C₄	D₂₉₂	1	15	yes	—
58	C₂³×C₄	C₂²×D₇₃	1	15	yes	—
59	C₂×Q₁₆	—	73	960	no	—
60	C₂²×C₈	C₂²×D₇₃	1	140	yes	—
61	C₂⁴	Dic₂₉₂	1	16	yes	direct product factor
62	C₂⁴	C₂×D₂₉₂	1	15	yes	—
63	C₂×Q₈	—	73	240	no	—
64	C₂×Q₈	—	146	840	no	—
65	C₂²×C₄	—	146	280	no	—
66	C₂²×C₄	C₂×D₂₉₂	1	105	yes	—
67	C₂²×C₄	C₂³×D₇₃	1	35	yes	—
68	Q₁₆	—	73	256	no	—
69	C₂×C₈	C₂³×D₇₃	1	120	yes	—
70	C₂³	C₂×Dic₂₉₂	1	120	yes	direct product factor
71	C₂³	C₂²×D₂₉₂	1	35	yes	—
72	Q₈	—	73	32	no	—
73	Q₈	—	146	240	no	—
74	C₂×C₄	—	146	240	no	—
75	C₂×C₄	C₂²×D₂₉₂	1	105	yes	—
76	C₂×C₄	C₂⁴×D₇₃	1	15	yes	—
77	C₈	C₂⁴×D₇₃	1	16	yes	—
78	C₂²	C₂²×Dic₂₉₂	1	140	yes	direct product factor
79	C₂²	C₂³×D₂₉₂	1	15	yes	—
80	C₄	—	146	32	no	—
81	C₄	C₂³×D₂₉₂	1	15	yes	—
82	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
83	C₂	C₂³×Dic₂₉₂	1	30	yes	direct product factor
84	C₂	C₂⁴×D₂₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	D₂₉₂
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂⁴×C₈×C₇₃	C₂
socle, prime radical	C₂⁵×C₇₃	D₄
hypercenter	C₂⁴×C₈	D₇₃
hypocenter	C₇₃	C₂⁴×Q₁₆
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
2. C₂³×Dic₂₉₂	C₂	direct (N × H)
7. C₂²×Dic₂₉₂	C₂²	direct (N × H)
13. C₂×Dic₂₉₂	C₂³	direct (N × H)
21. Dic₂₉₂	C₂⁴	direct (N × H)
22. C₂⁴×C₇₃	Q₁₆	semidirect
27. C₂³×C₇₃	C₂×Q₁₆	semidirect
35. C₂²×C₇₃	C₂²×Q₁₆	semidirect
41. C₂×C₇₃	C₂³×Q₁₆	semidirect
46. C₇₃	C₂⁴×Q₁₆	semidirect
61. C₂⁴	Dic₂₉₂	direct (N × H)
70. C₂³	C₂×Dic₂₉₂	direct (N × H)
78. C₂²	C₂²×Dic₂₉₂	direct (N × H)
83. C₂	C₂³×Dic₂₉₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₁₄₆	2
C₂³×Dic₂₉₂	2
C₂⁴×C₈×C₇₃	2
C₂⁴×Q₁₆	73

Subgroups — C24×Dic292 #33999766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×Dic₂₉₂ #33999766