Subgroups — #20295201

Order 6976.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812747	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812727	C₂	1	2	yes	maximal, complemented
3	#16812688	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812625	C₂	1	2	yes	maximal, complemented
5	#101×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13182030	—	2	2	no	—
7	#13182029	—	2	2	no	—
8	#13182029	C₂²	1	2	yes	—
9	Q₈×D₁₀₉	—	2	2	no	—
10	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
11	#13182018	—	2	2	no	—
12	D₈₇₂	—	2	2	no	—
13	#13182006	—	2	2	no	—
14	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
16	M₁₆×C₁₀₉	C₂²	1	2	yes	—
17	C₂²×D₁₀₉	—	2	1	no	—
18	Q₈×C₁₀₉	—	2	2	no	—
19	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
20	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
21	C₂²⋊D₁₀₉	—	2	2	no	—
22	C₂×Dic₁₀₉	—	2	1	no	—
23	D₄₃₆	—	2	2	no	—
24	D₄₃₆	—	2	2	no	—
25	D₄₃₆	D₄	1	2	yes	—
26	C₄×D₁₀₉	—	2	4	no	—
27	C₄×D₁₀₉	—	2	2	no	—
28	Dic₂₁₈	—	2	2	no	—
29	Dic₂₁₈	D₄	1	2	yes	—
30	C₈×C₁₀₉	—	2	2	no	—
31	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₀₉	—	2	2	no	—
33	C₂×D₁₀₉	—	4	2	no	—
34	C₂×D₁₀₉	—	4	1	no	—
35	C₄×C₁₀₉	—	2	2	no	—
36	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
37	Dic₁₀₉	—	2	2	no	—
38	Dic₁₀₉	—	4	1	no	—
39	C₂×C₁₀₉	—	2	1	no	—
40	C₂×C₁₀₉	#120	1	1	yes	characteristic
41	D₁₀₉	—	4	2	no	—
42	D₁₀₉	—	8	1	no	—
43	C₁₀₉	#454	1	1	yes	characteristic, complemented, Sylow
44	#454	—	109	1	no	maximal, Sylow
45	2₋¹⁺⁴	—	109	1	no	—
46	AGL(1,ℤ/8)	—	109	2	no	—
47	#124	—	109	1	no	—
48	#104	—	109	2	no	—
49	#101	D₁₀₉	1	1	yes	characteristic, complemented
50	#41	—	109	2	no	—
51	#41	—	218	2	no	—
52	#41	—	218	2	no	—
53	C₂×Q₈	—	218	2	no	—
54	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
55	C₂×D₄	—	109	1	no	—
56	SD₁₆	—	218	2	no	—
57	D₈	—	218	2	no	—
58	M₁₆	C₂×D₁₀₉	1	2	yes	—
59	C₂²⋊C₄	—	218	2	no	—
60	C₄²	—	109	1	no	—
61	C₂³	—	218	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	109	2	no	—
64	Q₈	—	218	2	no	—
65	D₄	—	109	2	no	—
66	D₄	—	218	2	no	—
67	D₄	—	218	2	no	—
68	D₄	—	218	2	no	—
69	C₂×C₄	—	218	4	no	—
70	C₂×C₄	—	218	1	no	—
71	C₂×C₄	—	218	2	no	—
72	C₂×C₄	D₄₃₆	1	2	yes	—
73	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₂²	—	436	2	no	—
76	C₂²	—	436	1	no	—
77	C₂²	—	218	2	no	—
78	C₂²	C₂×D₄₃₆	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	436	1	no	—
81	C₄	—	218	2	no	—
82	C₄	D₄×D₁₀₉	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	872	1	no	—
85	C₂	—	436	2	no	—
86	C₂	#16812669	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812669
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#101×C₁₀₉	C₂
socle	C₂×C₁₀₉	#120
hypercenter	#101	D₁₀₉
hypocenter	C₁₀₉	#454
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
1. #16812747	C₂	semidirect
2. #16812727	C₂	semidirect
3. #16812688	C₂	semidirect
4. #16812625	C₂	semidirect
5. #101×C₁₀₉	C₂	semidirect
43. C₁₀₉	#454	semidirect
49. #101	D₁₀₉	semidirect