Subgroups — C₂×#20294866 #28365336

Order 13952.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₇₂	C₂	1	1	yes	maximal, characteristic
2	#20294866	C₂	1	4	yes	maximal, direct product factor
3	C₂×#16812605	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₃₆	—	2	1	no	—
6	Dic₈₇₂	—	2	1	no	—
7	Dic₈₇₂	C₂²	1	2	yes	—
8	#16812605	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₁₀₉	—	2	1	no	—
10	Q₃₂×C₁₀₉	—	2	1	no	—
11	Q₃₂×C₁₀₉	C₂²	1	2	yes	—
12	C₂×C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₁₈	—	4	1	no	—
14	Dic₄₃₆	—	2	2	no	—
15	Dic₄₃₆	—	4	1	no	—
16	C₂×Q₈×C₁₀₉	—	4	1	no	—
17	Q₁₆×C₁₀₉	—	2	2	no	—
18	Q₁₆×C₁₀₉	—	4	1	no	—
19	C₂×C₈×C₁₀₉	D₄	1	1	yes	characteristic
20	C₁₆×C₁₀₉	D₄	1	1	yes	characteristic
21	C₁₆×C₁₀₉	C₂³	1	1	yes	characteristic
22	Q₈×C₁₀₉	—	4	2	no	—
23	Q₈×C₁₀₉	—	8	1	no	—
24	C₂×C₄×C₁₀₉	—	8	1	no	—
25	C₂×C₄×C₁₀₉	D₈	1	1	yes	characteristic
26	C₂×Dic₁₀₉	—	8	1	no	—
27	Dic₂₁₈	—	4	2	no	—
28	Dic₂₁₈	—	8	1	no	—
29	C₈×C₁₀₉	D₈	1	1	yes	characteristic
30	C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₀₉	D₁₆	1	1	yes	characteristic
32	C₄×C₁₀₉	—	8	2	no	—
33	C₄×C₁₀₉	D₁₆	1	1	yes	characteristic
34	C₄×C₁₀₉	C₂×D₈	1	1	yes	characteristic
35	Dic₁₀₉	—	8	2	no	—
36	C₂×C₁₀₉	Q₆₄	1	2	yes	complemented
37	C₂×C₁₀₉	C₂×D₁₆	1	1	yes	characteristic
38	C₂×Q₆₄	—	109	1	no	maximal, Sylow
39	C₁₀₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₃₂	—	109	1	no	—
41	C₂×Q₃₂	D₁₀₉	1	1	yes	characteristic
42	Q₆₄	—	109	4	no	—
43	C₂×C₃₂	—	109	1	no	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	—	218	1	no	—
46	Q₃₂	—	2	1	no	—
47	Q₃₂	—	109	2	no	—
48	Q₃₂	—	218	1	no	—
49	Q₃₂	C₂×D₁₀₉	1	2	yes	—
50	C₂×C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
51	C₃₂	—	109	2	no	—
52	C₂×Q₈	—	4	1	no	—
53	C₂×Q₈	—	436	1	no	—
54	Q₁₆	—	2	2	no	—
55	Q₁₆	—	4	1	no	—
56	Q₁₆	—	436	1	no	—
57	Q₁₆	—	218	2	no	—
58	C₂×C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
59	C₁₆	C₂²⋊D₁₀₉	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₀₉	1	1	yes	characteristic
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	872	1	no	—
64	Q₈	—	436	2	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	872	1	no	—
67	C₂×C₄	#13182014	1	1	yes	characteristic
68	C₈	#13182014	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
70	C₂²	#16812640	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	872	2	no	—
73	C₄	#16812640	1	1	yes	characteristic
74	C₄	C₂×#13182014	1	1	yes	characteristic
75	C₂	#20294866	1	2	yes	direct product factor
76	C₂	C₂×#16812640	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812640
commutator, cosocle	C₁₆×C₁₀₉	C₂³
Frattini	C₁₆	C₂²×D₁₀₉
Fitting	C₂×Q₃₂×C₁₀₉	C₂
socle, prime radical	C₂²×C₁₀₉	D₁₆
hypercenter	C₂×Q₃₂	D₁₀₉
hypocenter	C₁₀₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₀₉ ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
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. #20294866	C₂	direct (N × H)
36. C₂×C₁₀₉	Q₆₄	semidirect
39. C₁₀₉	C₂×Q₆₄	semidirect
75. C₂	#20294866	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×Dic₈₇₂	2
#20294866	2
C₂×#16812605	2
C₂×Q₃₂×C₁₀₉	2
C₂×Q₆₄	109

Subgroups — C2×#20294866 #28365336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20294866 #28365336