Subgroups — C₂×#16812628 #20295046

Order 6976.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11724784	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#16812628	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₉	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₀₉	C₄	1	1	yes	characteristic
7	C₂×#11724784	—	2	2	no	—
8	C₂×#11724784	C₂²	1	2	yes	—
9	C₄×Dic₁₀₉	C₄	1	2	yes	—
10	C₄×Dic₁₀₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₉	—	2	2	no	—
13	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
14	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
17	C₂×C₄×C₁₀₉	Q₈	1	2	yes	—
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₉	—	2	2	no	—
20	C₂×Dic₁₀₉	C₈	1	4	yes	complemented
21	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
22	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
23	C₈×C₁₀₉	—	2	2	no	—
24	#11724784	—	2	2	no	—
25	C₂²×C₁₀₉	C₄⋊C₄	1	2	yes	—
26	C₂²×C₁₀₉	C₂×C₈	1	2	yes	—
27	C₂²×C₁₀₉	M₁₆	1	2	yes	—
28	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₉	—	2	2	no	—
33	Dic₁₀₉	C₂×C₈	1	4	yes	complemented
34	C₂×C₁₀₉	C₄⋊C₈	1	4	yes	complemented
35	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
38	C₁₀₉	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄⋊C₈	—	109	1	no	maximal, Sylow
40	C₂²×C₈	—	109	1	no	—
41	C₂²×C₈	D₁₀₉	1	1	yes	characteristic
42	C₂×C₄²	—	109	1	no	—
43	C₄⋊C₈	—	109	4	no	—
44	C₂²×C₄	—	109	1	no	—
45	C₂²×C₄	—	109	1	no	—
46	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
47	C₂×C₈	—	2	2	no	—
48	C₂×C₈	—	109	2	no	—
49	C₂×C₈	—	218	2	no	—
50	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
51	C₄²	—	109	2	no	—
52	C₄²	—	109	2	no	—
53	C₂³	C₄×D₁₀₉	1	1	yes	characteristic
54	C₂×C₄	—	109	4	no	—
55	C₂×C₄	—	109	2	no	—
56	C₂×C₄	—	109	2	no	—
57	C₂×C₄	—	218	2	no	—
58	C₂×C₄	Dic₂₁₈	1	2	yes	—
59	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
61	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	218	2	no	—
64	C₂²	#13182008	1	2	yes	—
65	C₂²	C₈×D₁₀₉	1	2	yes	—
66	C₂²	#13182012	1	2	yes	—
67	C₂²	C₂×C₄×D₁₀₉	1	1	yes	characteristic
68	C₄	—	109	4	no	—
69	C₄	—	218	2	no	—
70	C₄	#13182008	1	2	yes	—
71	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
72	C₄	C₂×Dic₂₁₈	1	1	yes	characteristic
73	C₂	#16812628	1	4	yes	direct product factor
74	C₂	C₂×#13182008	1	1	yes	characteristic
75	C₂	C₂×C₈×D₁₀₉	1	1	yes	characteristic
76	C₂	C₂×#13182012	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂²×C₈×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂×C₄
hypercenter	C₂²×C₈	D₁₀₉
hypocenter	C₁₀₉	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #16812628	C₂	direct (N × H)
20. C₂×Dic₁₀₉	C₈	semidirect
33. Dic₁₀₉	C₂×C₈	semidirect
34. C₂×C₁₀₉	C₄⋊C₈	semidirect
38. C₁₀₉	C₂×C₄⋊C₈	semidirect
73. C₂	#16812628	direct (N × H)

Subgroups — C2×#16812628 #20295046

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812628 #20295046