Subgroups — #20295297

Order 6976.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812727	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812705	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812615	C₂	1	2	yes	maximal, complemented
5	#108×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13182029	C₂²	1	1	yes	characteristic
7	C₂×D₄₃₆	C₂²	1	2	yes	—
8	#13182018	—	2	2	no	—
9	D₈₇₂	—	2	2	no	—
10	D₈₇₂	—	2	1	no	—
11	D₈₇₂	—	2	1	no	—
12	#13182013	C₂²	1	1	yes	characteristic
13	#13182012	—	2	1	no	—
14	C₈×D₁₀₉	—	2	1	no	—
15	M₁₆×C₁₀₉	C₂²	1	2	yes	—
16	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂²×D₁₀₉	—	2	2	no	—
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂²⋊D₁₀₉	—	2	1	no	—
20	D₄₃₆	—	2	2	no	—
21	D₄₃₆	—	2	2	no	—
22	D₄₃₆	D₄	1	1	yes	characteristic
23	C₄×D₁₀₉	—	2	1	no	—
24	Dic₂₁₈	D₄	1	1	yes	characteristic
25	C₈×C₁₀₉	—	2	2	no	—
26	C₈×C₁₀₉	D₄	1	1	yes	characteristic
27	C₈×C₁₀₉	D₄	1	1	yes	characteristic
28	#11724784	—	2	1	no	—
29	C₂²×C₁₀₉	#41	1	1	yes	characteristic
30	C₂×D₁₀₉	—	2	1	no	—
31	C₂×D₁₀₉	—	4	2	no	—
32	C₂×D₁₀₉	—	8	2	no	—
33	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
35	Dic₁₀₉	—	2	1	no	—
36	C₂×C₁₀₉	—	2	1	no	—
37	C₂×C₁₀₉	#121	1	1	yes	characteristic
38	D₁₀₉	—	4	1	no	—
39	D₁₀₉	—	8	2	no	—
40	C₁₀₉	#472	1	1	yes	characteristic, complemented, Sylow
41	#472	—	109	1	no	maximal, Sylow
42	AGL(1,ℤ/8)	—	109	2	no	—
43	C₂×D₈	—	109	1	no	—
44	#131	—	109	1	no	—
45	#108	D₁₀₉	1	1	yes	characteristic, complemented
46	#100	—	109	2	no	—
47	#41	—	109	1	no	—
48	C₂×D₄	—	109	2	no	—
49	SD₁₆	—	218	2	no	—
50	D₈	—	218	2	no	—
51	D₈	—	218	1	no	—
52	D₈	—	218	1	no	—
53	M₁₆	—	109	1	no	—
54	M₁₆	—	218	1	no	—
55	M₁₆	C₂×D₁₀₉	1	2	yes	—
56	C₂×C₈	—	218	1	no	—
57	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
58	C₂³	—	218	2	no	—
59	Q₈	—	109	1	no	—
60	D₄	—	109	1	no	—
61	D₄	—	218	1	no	—
62	D₄	—	218	2	no	—
63	D₄	—	218	2	no	—
64	C₂×C₄	—	218	1	no	—
65	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	218	1	no	—
68	C₈	D₄₃₆	1	1	yes	characteristic
69	C₈	D₄₃₆	1	1	yes	characteristic
70	C₂²	—	872	2	no	—
71	C₂²	—	436	2	no	—
72	C₂²	—	218	1	no	—
73	C₂²	#13182030	1	1	yes	characteristic
74	C₄	—	218	1	no	—
75	C₄	D₄×D₁₀₉	1	1	yes	characteristic
76	C₄	C₂×D₄₃₆	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	872	2	no	—
79	C₂	—	436	1	no	—
80	C₂	#16812674	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812674
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#108×C₁₀₉	C₂
socle	C₂×C₁₀₉	#121
hypercenter	#108	D₁₀₉
hypocenter	C₁₀₉	#472
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #16812727	C₂	semidirect
2. C₂×D₈₇₂	C₂	semidirect
3. #16812705	C₂	semidirect
4. #16812615	C₂	semidirect
5. #108×C₁₀₉	C₂	semidirect
40. C₁₀₉	#472	semidirect
45. #108	D₁₀₉	semidirect