Subgroups — #20295415

Order 6976.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182018	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₇₂	C₂	1	2	yes	maximal, complemented
3	#16812696	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812687	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
7	C₂×D₄₃₆	—	2	2	no	—
8	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
9	C₂×D₄₃₆	C₂²	1	2	yes	—
10	#13182018	—	2	4	no	—
11	D₈₇₂	—	2	4	no	—
12	#13182006	—	2	2	no	—
13	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
14	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₉	—	2	1	no	—
16	C₂²×D₁₀₉	—	2	2	no	—
17	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₉	—	2	1	no	—
20	D₄₃₆	—	2	2	no	—
21	D₄₃₆	—	2	2	no	—
22	D₄₃₆	—	2	2	no	—
23	D₄₃₆	—	4	4	no	—
24	Dic₂₁₈	—	2	2	no	—
25	C₈×C₁₀₉	D₄	1	4	yes	complemented
26	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₀₉	—	4	1	no	—
28	C₂×D₁₀₉	—	4	2	no	—
29	C₂×D₁₀₉	—	4	4	no	—
30	C₂×D₁₀₉	—	4	2	no	—
31	C₄×C₁₀₉	—	2	2	no	—
32	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
33	Dic₁₀₉	—	4	1	no	—
34	C₂×C₁₀₉	#127	1	1	yes	characteristic
35	C₂×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
36	D₁₀₉	—	8	2	no	—
37	D₁₀₉	—	8	1	no	—
38	C₁₀₉	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	109	1	no	maximal, Sylow
40	C₂×SD₁₆	—	109	2	no	—
41	C₂×D₈	—	109	2	no	—
42	#127	—	109	1	no	—
43	#124	—	109	1	no	—
44	#97	D₁₀₉	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	109	1	no	—
46	C₂×D₄	—	109	1	no	—
47	C₂×D₄	—	109	2	no	—
48	C₂×D₄	—	218	2	no	—
49	SD₁₆	—	218	4	no	—
50	D₈	—	218	4	no	—
51	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
52	C₂²⋊C₄	—	218	2	no	—
53	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
54	C₂³	—	218	1	no	—
55	C₂³	—	218	2	no	—
56	Q₈	—	218	2	no	—
57	D₄	—	436	4	no	—
58	D₄	—	218	2	no	—
59	D₄	—	218	2	no	—
60	D₄	—	218	2	no	—
61	C₂×C₄	—	218	1	no	—
62	C₂×C₄	D₄₃₆	1	2	yes	—
63	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
64	C₈	D₄₃₆	1	4	yes	complemented
65	C₂²	—	436	1	no	—
66	C₂²	—	436	2	no	—
67	C₂²	—	436	4	no	—
68	C₂²	—	436	2	no	—
69	C₂²	C₂×D₄₃₆	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	436	1	no	—
72	C₄	C₂×D₄₃₆	1	2	yes	—
73	C₂	—	872	2	no	—
74	C₂	—	872	1	no	—
75	C₂	#16812696	1	1	yes	characteristic
76	C₂	#16812727	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₃₆
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#97×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	#97	D₁₀₉
hypocenter	C₁₀₉	#496
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×#13182018	C₂	semidirect
2. C₂×D₈₇₂	C₂	semidirect
3. #16812696	C₂	semidirect
4. #16812687	C₂	semidirect
5. #97×C₁₀₉	C₂	semidirect
25. C₈×C₁₀₉	D₄	semidirect
38. C₁₀₉	#496	semidirect
44. #97	D₁₀₉	semidirect
64. C₈	D₄₃₆	semidirect