Subgroups — #20295073

Order 6976.

102 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
2	M₁₆×D₁₀₉	C₂	1	2	yes	maximal
3	#16812635	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812634	C₂	1	2	yes	maximal, complemented
5	#108×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
7	#13182013	C₂²	1	2	yes	—
8	#13182012	—	2	2	no	—
9	#13182012	C₄	1	4	yes	—
10	C₂×#11724784	C₂²	1	1	yes	characteristic
11	C₈×D₁₀₉	—	2	2	no	—
12	M₁₆×C₁₀₉	C₂²	1	2	yes	—
13	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂²×D₁₀₉	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
16	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
17	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
18	C₄×D₁₀₉	D₄	1	2	yes	—
19	C₈×C₁₀₉	—	2	2	no	—
20	C₈×C₁₀₉	C₂×C₄	1	2	yes	—
21	#11724784	—	2	2	no	—
22	#11724784	C₂×C₄	1	2	yes	—
23	C₂²×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₁₀₉	—	4	1	no	—
25	C₂×D₁₀₉	C₄⋊C₄	1	2	yes	—
26	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
28	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₁₀₉	—	2	1	no	—
30	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₁₀₉	—	2	2	no	—
32	C₁₀₉	#430	1	1	yes	characteristic, complemented, Sylow
33	#430	—	109	1	no	maximal, Sylow
34	C₂×M₁₆	—	109	1	no	—
35	C₂×M₁₆	—	109	2	no	—
36	#108	—	109	2	no	—
37	#108	—	109	1	no	—
38	#108	D₁₀₉	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	109	1	no	—
40	M₁₆	—	109	4	no	—
41	M₁₆	—	109	2	no	—
42	M₁₆	—	218	2	no	—
43	M₁₆	C₂×D₁₀₉	1	2	yes	—
44	C₂×C₈	—	109	1	no	—
45	C₂×C₈	—	218	2	no	—
46	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
47	C₂³	—	109	1	no	—
48	C₂×C₄	—	109	1	no	—
49	C₂×C₄	—	109	2	no	—
50	C₂×C₄	—	109	2	no	—
51	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	109	2	no	—
54	C₈	—	218	2	no	—
55	C₈	C₄×D₁₀₉	1	2	yes	—
56	C₂²	—	109	2	no	—
57	C₂²	—	436	1	no	—
58	C₂²	Q₈×D₁₀₉	1	1	yes	characteristic
59	C₄	—	109	2	no	—
60	C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
61	C₄	D₄×D₁₀₉	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	218	2	no	—
64	C₂	C₄⋊C₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#108×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×C₄⋊C₄
hypercenter	#108	D₁₀₉
hypocenter	C₁₀₉	#430
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #16812635	C₂	semidirect
4. #16812634	C₂	semidirect
5. #108×C₁₀₉	C₂	semidirect
32. C₁₀₉	#430	semidirect
38. #108	D₁₀₉	semidirect