Subgroups — C₂×#13092254 #15675697

Order 2944.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₆₈	C₂	1	1	yes	maximal, characteristic
2	#13092254	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₂₃	—	2	1	no	—
6	C₂×D₁₈₄	—	2	1	no	—
7	C₂₃×Q₃₂	—	2	1	no	—
8	C₂₃×Q₃₂	C₂²	1	2	yes	complemented
9	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	D₃₆₈	—	2	1	no	—
11	D₃₆₈	C₂²	1	2	yes	—
12	C₂₃⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂×Q₈×C₂₃	—	4	1	no	—
14	C₂×D₉₂	—	4	1	no	—
15	Q₁₆×C₂₃	—	2	2	no	—
16	Q₁₆×C₂₃	—	4	1	no	—
17	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
18	D₁₈₄	—	2	2	no	—
19	D₁₈₄	—	4	1	no	—
20	C₁₆×C₂₃	D₄	1	1	yes	characteristic
21	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
22	C₂²×D₂₃	—	8	1	no	—
23	Q₈×C₂₃	—	4	2	no	—
24	Q₈×C₂₃	—	8	1	no	—
25	C₂×C₄×C₂₃	—	8	1	no	—
26	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
27	D₉₂	—	4	2	no	—
28	D₉₂	—	8	1	no	—
29	C₈×C₂₃	D₈	1	1	yes	characteristic
30	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂×SD₆₄	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
33	C₂×D₂₃	—	8	2	no	—
34	C₂×D₂₃	—	16	2	no	—
35	C₄×C₂₃	—	8	2	no	—
36	C₄×C₂₃	D₁₆	1	1	yes	characteristic
37	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
38	C₂×Q₃₂	D₂₃	1	1	yes	characteristic, complemented
39	C₂×D₁₆	—	23	1	no	—
40	SD₆₄	—	23	4	no	—
41	C₂×C₃₂	—	23	1	no	—
42	C₂×C₂₃	SD₆₄	1	2	yes	complemented
43	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
44	D₂₃	—	16	2	no	—
45	C₂×Q₁₆	—	2	1	no	—
46	C₂×D₈	—	46	1	no	—
47	Q₃₂	—	2	1	no	—
48	Q₃₂	C₂×D₂₃	1	2	yes	complemented
49	D₁₆	—	23	2	no	—
50	D₁₆	—	46	1	no	—
51	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
52	C₃₂	—	23	2	no	—
53	C₂₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	92	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	46	2	no	—
59	D₈	—	92	1	no	—
60	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
62	C₁₆	C₂²×D₂₃	1	1	yes	characteristic
63	C₂³	—	184	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	92	2	no	—
67	D₄	—	184	1	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	#67272	1	1	yes	characteristic
70	C₈	#67272	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
72	C₂²	—	368	2	no	—
73	C₂²	—	184	2	no	—
74	C₂²	#10625008	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#10625008	1	1	yes	characteristic
77	C₄	C₂×#67272	1	1	yes	characteristic
78	C₂	—	368	2	no	—
79	C₂	#13092254	1	2	yes	direct product factor
80	C₂	C₂×#10625008	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625008
commutator, cosocle	C₁₆×C₂₃	C₂³
Frattini	C₁₆	C₂²×D₂₃
Fitting	C₂×C₂₃×Q₃₂	C₂
socle	C₂²×C₂₃	D₁₆
prime radical	C₂×D₃₆₈	C₂
hypercenter	C₂×Q₃₂	D₂₃
hypocenter	C₂₃	C₂×SD₆₄
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #13092254	C₂	direct (N × H)
3. C₂×C₂₃⋊C₃₂	C₂	semidirect
4. C₂×C₂₃×Q₃₂	C₂	semidirect
8. C₂₃×Q₃₂	C₂²	semidirect
12. C₂₃⋊C₃₂	C₂²	semidirect
38. C₂×Q₃₂	D₂₃	semidirect
42. C₂×C₂₃	SD₆₄	semidirect
48. Q₃₂	C₂×D₂₃	semidirect
53. C₂₃	C₂×SD₆₄	semidirect
79. C₂	#13092254	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×D₃₆₈	2
#13092254	2
C₂×C₂₃⋊C₃₂	2
C₂×C₂₃×Q₃₂	2
C₂×SD₆₄	23

Subgroups — C2×#13092254 #15675697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092254 #15675697