Subgroups — C₂×Dic₂₃₃₆ #33007034

Order 18688.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆₈	C₂	1	2	yes	maximal
2	Dic₂₃₃₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₈₄	—	2	2	no	—
5	Dic₁₁₆₈	—	2	2	no	—
6	Dic₁₁₆₈	C₂²	1	4	yes	—
7	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
8	C₆₄×C₇₃	C₂²	1	2	yes	—
9	C₂×Dic₂₉₂	—	4	2	no	—
10	Dic₅₈₄	—	2	4	no	—
11	Dic₅₈₄	—	4	2	no	—
12	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
13	C₃₂×C₇₃	D₄	1	1	yes	characteristic
14	C₃₂×C₇₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	8	2	no	—
16	Dic₂₉₂	—	4	4	no	—
17	Dic₂₉₂	—	8	2	no	—
18	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
19	C₁₆×C₇₃	D₈	1	1	yes	characteristic
20	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
22	C₂×Dic₇₃	—	16	2	no	—
23	Dic₁₄₆	—	8	4	no	—
24	Dic₁₄₆	—	16	2	no	—
25	C₈×C₇₃	D₁₆	1	1	yes	characteristic
26	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
27	C₂²×C₇₃	D₃₂	1	1	yes	characteristic
28	C₄×C₇₃	D₃₂	1	1	yes	characteristic
29	C₄×C₇₃	C₂×D₁₆	1	1	yes	characteristic
30	Dic₇₃	—	16	4	no	—
31	C₂×Q₁₂₈	—	73	1	no	maximal, Sylow
32	C₂×C₇₃	Q₁₂₈	1	2	yes	complemented
33	C₂×C₇₃	C₂×D₃₂	1	1	yes	characteristic
34	C₂×Q₆₄	—	73	2	no	—
35	Q₁₂₈	—	73	4	no	—
36	C₂×C₆₄	D₇₃	1	1	yes	characteristic
37	C₇₃	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₃₂	—	146	2	no	—
39	Q₆₄	—	73	4	no	—
40	Q₆₄	—	146	2	no	—
41	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
42	C₆₄	C₂×D₇₃	1	2	yes	—
43	C₂×Q₁₆	—	292	2	no	—
44	Q₃₂	—	292	2	no	—
45	Q₃₂	—	146	4	no	—
46	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
47	C₃₂	D₂₉₂	1	1	yes	characteristic
48	C₃₂	C₂²×D₇₃	1	1	yes	characteristic
49	C₂×Q₈	—	584	2	no	—
50	Q₁₆	—	292	4	no	—
51	Q₁₆	—	584	2	no	—
52	C₂×C₈	D₅₈₄	1	1	yes	characteristic
53	C₁₆	D₅₈₄	1	1	yes	characteristic
54	C₁₆	C₂×D₂₉₂	1	1	yes	characteristic
55	Q₈	—	584	4	no	—
56	Q₈	—	1168	2	no	—
57	C₂×C₄	—	1168	2	no	—
58	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
59	C₈	D₁₁₆₈	1	1	yes	characteristic
60	C₈	C₂×D₅₈₄	1	1	yes	characteristic
61	C₂²	D₂₃₃₆	1	1	yes	characteristic
62	C₄	—	1168	4	no	—
63	C₄	D₂₃₃₆	1	1	yes	characteristic
64	C₄	C₂×D₁₁₆₈	1	1	yes	characteristic
65	C₂	Dic₂₃₃₆	1	2	yes	direct product factor
66	C₂	C₂×D₂₃₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₃₃₆
commutator, cosocle	C₃₂×C₇₃	C₂³
Frattini	C₃₂	C₂²×D₇₃
Fitting	C₂×C₆₄×C₇₃	C₂
socle, prime radical	C₂²×C₇₃	D₃₂
hypercenter	C₂×C₆₄	D₇₃
hypocenter	C₇₃	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₂₃₃₆	C₂	direct (N × H)
32. C₂×C₇₃	Q₁₂₈	semidirect
37. C₇₃	C₂×Q₁₂₈	semidirect
65. C₂	Dic₂₃₃₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆₈	2
Dic₂₃₃₆	2
C₂×C₆₄×C₇₃	2
C₂×Q₁₂₈	73

Subgroups — C2×Dic2336 #33007034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₃₃₆ #33007034