Subgroups — #20295276

Order 6976.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182012	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812670	C₂	1	2	yes	maximal, complemented
3	#16812631	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812620	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
7	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
8	#13182012	—	2	2	no	—
9	C₂×#11724784	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₉	C₂²	1	2	yes	—
11	C₂²⋊Dic₁₀₉	—	2	2	no	—
12	C₂×D₄×C₁₀₉	C₂²	1	2	yes	—
13	D₈×C₁₀₉	—	2	2	no	—
14	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂³×C₁₀₉	—	2	2	no	—
16	C₂²×D₁₀₉	D₄	1	1	yes	characteristic
17	D₄×C₁₀₉	—	2	2	no	—
18	D₄×C₁₀₉	—	2	2	no	—
19	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
20	C₂²⋊D₁₀₉	—	4	4	no	—
21	C₂×Dic₁₀₉	—	2	2	no	—
22	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
23	C₄×D₁₀₉	—	2	1	no	—
24	C₄×D₁₀₉	—	2	1	no	—
25	C₈×C₁₀₉	D₄	1	2	yes	complemented
26	#11724784	—	2	1	no	—
27	C₂²×C₁₀₉	—	4	2	no	—
28	C₂²×C₁₀₉	—	4	2	no	—
29	C₂²×C₁₀₉	—	4	2	no	—
30	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
31	C₂×D₁₀₉	—	2	1	no	—
32	C₂×D₁₀₉	—	2	2	no	—
33	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₀₉	#41	1	1	yes	characteristic
35	Dic₁₀₉	—	2	1	no	—
36	Dic₁₀₉	—	4	2	no	—
37	C₂×C₁₀₉	—	8	2	no	—
38	C₂×C₁₀₉	#121	1	1	yes	characteristic
39	C₂×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
40	D₁₀₉	—	4	1	no	—
41	C₁₀₉	#469	1	1	yes	characteristic, complemented, Sylow
42	#469	—	109	1	no	maximal, Sylow
43	C₂×D₈	D₁₀₉	1	1	yes	characteristic, complemented
44	C₂×M₁₆	—	109	1	no	—
45	#121	—	109	2	no	—
46	#106	—	109	1	no	—
47	#102	—	109	2	no	—
48	C₂×D₄	—	218	2	no	—
49	C₂×D₄	C₂×D₁₀₉	1	2	yes	—
50	C₂²×C₄	—	109	1	no	—
51	D₈	—	2	2	no	—
52	M₁₆	—	218	2	no	—
53	C₂×C₈	—	109	1	no	—
54	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
55	C₄⋊C₄	—	109	2	no	—
56	C₂²⋊C₄	—	218	2	no	—
57	C₂³	—	2	2	no	—
58	C₂³	—	109	1	no	—
59	D₄	—	2	2	no	—
60	D₄	—	2	2	no	—
61	D₄	—	436	4	no	—
62	C₂×C₄	—	109	1	no	—
63	C₂×C₄	—	218	2	no	—
64	C₂×C₄	—	218	1	no	—
65	C₂×C₄	—	218	1	no	—
66	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
67	C₈	—	218	1	no	—
68	C₈	C₂²⋊D₁₀₉	1	2	yes	complemented
69	C₂²	—	4	2	no	—
70	C₂²	—	4	2	no	—
71	C₂²	—	4	2	no	—
72	C₂²	—	218	1	no	—
73	C₂²	—	218	2	no	—
74	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
75	C₄	—	436	2	no	—
76	C₄	—	218	1	no	—
77	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
78	C₄	#13182028	1	1	yes	characteristic
79	C₂	—	8	2	no	—
80	C₂	—	436	1	no	—
81	C₂	#16812670	1	1	yes	characteristic
82	C₂	#16812723	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×D₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	C₂×D₈	D₁₀₉
hypocenter	C₁₀₉	#469
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13182012	C₂	semidirect
2. #16812670	C₂	semidirect
3. #16812631	C₂	semidirect
4. #16812620	C₂	semidirect
5. C₂×D₈×C₁₀₉	C₂	semidirect
25. C₈×C₁₀₉	D₄	semidirect
41. C₁₀₉	#469	semidirect
43. C₂×D₈	D₁₀₉	semidirect
68. C₈	C₂²⋊D₁₀₉	semidirect