Subgroups — #20295237

Order 6976.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₃₆	C₂	1	2	yes	maximal
2	#16812699	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₂₁₈	C₂	1	1	yes	maximal, characteristic
4	#16812624	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₁₈	C₂²	1	2	yes	—
7	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
8	Dic₄₃₆	—	2	4	no	—
9	C₄⋊Dic₁₀₉	—	2	1	no	—
10	C₄⋊Dic₁₀₉	—	2	1	no	—
11	C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
12	#13182008	—	2	1	no	—
13	C₄×Dic₁₀₉	—	2	1	no	—
14	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
15	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₉	—	2	1	no	—
20	C₂×Dic₁₀₉	—	2	1	no	—
21	C₂×Dic₁₀₉	—	2	2	no	—
22	Dic₂₁₈	—	2	1	no	—
23	Dic₂₁₈	—	2	2	no	—
24	Dic₂₁₈	—	2	2	no	—
25	Dic₂₁₈	D₄	1	2	yes	—
26	C₈×C₁₀₉	—	2	2	no	—
27	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₉	—	2	1	no	—
29	C₄×C₁₀₉	Q₁₆	1	2	yes	complemented
30	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₉	#41	1	1	yes	characteristic
32	Dic₁₀₉	—	2	2	no	—
33	Dic₁₀₉	—	4	2	no	—
34	Dic₁₀₉	—	4	1	no	—
35	C₂×C₁₀₉	#121	1	1	yes	characteristic
36	C₂×C₁₀₉	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₁₀₉	#137	1	1	yes	characteristic
38	C₁₀₉	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	109	1	no	maximal, Sylow
40	C₂×Q₁₆	—	109	2	no	—
41	C₄⋊Q₈	—	109	1	no	—
42	C₄×Q₈	—	109	1	no	—
43	C₄⋊C₈	D₁₀₉	1	1	yes	characteristic
44	#103	—	109	2	no	—
45	C₂×Q₈	—	109	1	no	—
46	C₂×Q₈	—	109	2	no	—
47	Q₁₆	—	218	4	no	—
48	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
49	C₄⋊C₄	—	109	1	no	—
50	C₄⋊C₄	—	218	1	no	—
51	C₄⋊C₄	—	218	1	no	—
52	C₄⋊C₄	—	218	1	no	—
53	C₄²	—	218	1	no	—
54	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
55	Q₈	—	109	2	no	—
56	Q₈	—	218	2	no	—
57	Q₈	—	218	2	no	—
58	Q₈	—	218	1	no	—
59	C₂×C₄	—	218	1	no	—
60	C₂×C₄	—	218	2	no	—
61	C₂×C₄	—	218	1	no	—
62	C₂×C₄	D₄₃₆	1	1	yes	characteristic
63	C₂×C₄	D₄₃₆	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₄₃₆	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	436	2	no	—
69	C₄	—	436	1	no	—
70	C₄	—	218	2	no	—
71	C₄	Dic₄₃₆	1	2	yes	complemented
72	C₄	D₄×D₁₀₉	1	1	yes	characteristic
73	C₄	#13182030	1	1	yes	characteristic
74	C₂	#16812674	1	1	yes	characteristic
75	C₂	C₂×Dic₄₃₆	1	1	yes	characteristic
76	C₂	#16812732	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₃₆
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₄⋊C₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	C₄⋊C₈	D₁₀₉
hypocenter	C₁₀₉	#462
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄×C₁₀₉	Q₁₆	semidirect
38. C₁₀₉	#462	semidirect
71. C₄	Dic₄₃₆	semidirect