Subgroups — C₂×#16812769 #20296038

Order 6976.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182039	C₂	1	2	yes	maximal
2	#16812769	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#13182039	—	2	2	no	—
5	#13182039	C₂²	1	4	yes	—
6	C₂×#11724786	—	2	2	no	—
7	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
8	C₂×#11724784	C₄	1	1	yes	characteristic
9	C₈×D₁₀₉	C₄	1	2	yes	—
10	C₈×D₁₀₉	C₂²	1	2	yes	—
11	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
12	C₂²×D₁₀₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
15	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₀₉	D₄	1	1	yes	characteristic
17	C₄×D₁₀₉	Q₈	1	1	yes	characteristic
18	C₄×D₁₀₉	C₂³	1	1	yes	characteristic
19	#11724786	—	2	4	no	—
20	C₈×C₁₀₉	C₂×C₄	1	2	yes	—
21	#11724784	C₂×C₄	1	2	yes	—
22	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₉	—	2	2	no	—
24	C₂×D₁₀₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₁₀₉	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₀₉	C₄⋊C₄	1	1	yes	characteristic
29	Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₁₀₉	#108	1	2	yes	complemented
31	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₁₀₉	—	2	1	no	—
33	D₁₀₉	—	2	1	no	—
34	C₁₀₉	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	109	1	no	maximal, Sylow
36	C₂×M₁₆	—	109	2	no	—
37	C₂²×C₈	—	109	1	no	—
38	#108	—	109	4	no	—
39	C₂²×C₄	—	109	1	no	—
40	M₁₆	—	109	4	no	—
41	M₁₆	—	218	2	no	—
42	C₂×C₈	—	109	1	no	—
43	C₂×C₈	—	109	2	no	—
44	C₂×C₈	—	109	2	no	—
45	C₂×C₈	—	218	2	no	—
46	C₂×C₈	#89137	1	1	yes	characteristic
47	C₂³	—	109	1	no	—
48	C₂×C₄	—	109	1	no	—
49	C₂×C₄	—	109	1	no	—
50	C₂×C₄	—	109	1	no	—
51	C₂×C₄	—	109	1	no	—
52	C₂×C₄	—	109	1	no	—
53	C₂×C₄	C₂×#89137	1	1	yes	characteristic
54	C₈	—	109	2	no	—
55	C₈	—	218	4	no	—
56	C₈	C₂×#89137	1	2	yes	—
57	C₂²	—	109	1	no	—
58	C₂²	—	109	1	no	—
59	C₂²	—	218	2	no	—
60	C₂²	C₄⋊#89137	1	1	yes	characteristic
61	C₄	—	109	1	no	—
62	C₄	—	109	1	no	—
63	C₄	C₄⋊#89137	1	1	yes	characteristic
64	C₄	C₂²×#89137	1	1	yes	characteristic
65	C₂	—	218	1	no	—
66	C₂	—	218	1	no	—
67	C₂	#16812769	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#89137
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₄	C₂²×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₄⋊C₄
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	C₂×#108
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #16812769	C₂	direct (N × H)
30. C₂×C₁₀₉	#108	semidirect
34. C₁₀₉	C₂×#108	semidirect
67. C₂	#16812769	direct (N × H)

Subgroups — C2×#16812769 #20296038

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812769 #20296038