Subgroups — C₂²×#13182014 #20295795

Order 6976.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13182014	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#11724784	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₉	—	2	1	no	—
6	C₂×D₄₃₆	—	2	3	no	—
7	C₂×D₄₃₆	C₂²	1	6	yes	complemented
8	#13182014	C₂²	1	16	yes	direct product factor
9	C₂×#11724784	C₂²	1	6	yes	complemented
10	C₂⁴×C₁₀₉	—	2	1	no	—
11	C₂×D₄×C₁₀₉	—	2	3	no	—
12	C₂×D₄×C₁₀₉	C₂²	1	6	yes	complemented
13	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂³×C₁₀₉	—	2	6	no	—
15	C₂³×C₁₀₉	—	4	4	no	—
16	C₂³×C₁₀₉	D₄	1	1	yes	characteristic
17	C₂²×D₁₀₉	—	2	6	no	—
18	C₂²×D₁₀₉	—	4	4	no	—
19	D₄×C₁₀₉	—	2	6	no	—
20	D₄×C₁₀₉	C₂³	1	4	yes	complemented
21	C₂×C₄×C₁₀₉	D₄	1	3	yes	—
22	C₂×C₄×C₁₀₉	C₂³	1	3	yes	—
23	D₄₃₆	—	2	6	no	—
24	D₄₃₆	C₂³	1	4	yes	complemented
25	#11724784	C₂³	1	4	yes	complemented
26	C₂²×C₁₀₉	—	2	4	no	—
27	C₂²×C₁₀₉	—	4	12	no	—
28	C₂²×C₁₀₉	D₈	1	4	yes	complemented
29	C₂²×C₁₀₉	C₂×D₄	1	3	yes	—
30	C₂×D₁₀₉	—	2	4	no	—
31	C₂×D₁₀₉	—	4	12	no	—
32	C₄×C₁₀₉	C₂×D₄	1	3	yes	—
33	C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
34	C₂×C₁₀₉	—	4	4	no	—
35	C₂×C₁₀₉	C₂×D₈	1	6	yes	complemented
36	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
37	D₁₀₉	—	4	4	no	—
38	C₁₀₉	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²×D₈	—	109	1	no	maximal, Sylow
40	C₂²×D₄	—	109	1	no	—
41	C₂²×D₄	D₁₀₉	1	1	yes	characteristic, complemented
42	C₂×D₈	—	109	12	no	—
43	C₂²×C₈	—	109	1	no	—
44	C₂⁴	—	2	1	no	—
45	C₂⁴	—	218	1	no	—
46	C₂×D₄	—	2	3	no	—
47	C₂×D₄	—	109	6	no	—
48	C₂×D₄	—	218	3	no	—
49	C₂×D₄	C₂×D₁₀₉	1	6	yes	complemented
50	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
51	D₈	—	109	16	no	—
52	C₂×C₈	—	109	6	no	—
53	C₂³	—	2	6	no	—
54	C₂³	—	4	4	no	—
55	C₂³	—	436	4	no	—
56	C₂³	—	218	6	no	—
57	C₂³	C₂²⋊D₁₀₉	1	1	yes	characteristic
58	D₄	—	2	6	no	—
59	D₄	—	109	4	no	—
60	D₄	—	218	6	no	—
61	D₄	C₂²×D₁₀₉	1	4	yes	complemented
62	C₂×C₄	C₂²⋊D₁₀₉	1	3	yes	—
63	C₂×C₄	C₂²×D₁₀₉	1	3	yes	—
64	C₈	—	109	4	no	—
65	C₂²	—	2	4	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	436	12	no	—
68	C₂²	—	218	4	no	—
69	C₂²	#13182014	1	4	yes	direct product factor
70	C₂²	C₂×C₂²⋊D₁₀₉	1	3	yes	—
71	C₄	C₂×C₂²⋊D₁₀₉	1	3	yes	—
72	C₄	C₂³×D₁₀₉	1	1	yes	characteristic
73	C₂	—	4	4	no	—
74	C₂	—	436	4	no	—
75	C₂	C₂×#13182014	1	6	yes	direct product factor
76	C₂	C₂²×C₂²⋊D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₉
commutator	C₄×C₁₀₉	C₂⁴
Frattini	C₄	C₂³×D₁₀₉
Fitting	C₂²×D₄×C₁₀₉	C₂
socle	C₂³×C₁₀₉	D₄
hypercenter	C₂²×D₄	D₁₀₉
hypocenter	C₁₀₉	C₂²×D₈
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄₃₆	C₂	semidirect
2. C₂×#13182014	C₂	direct (N × H)
3. C₂²×#11724784	C₂	semidirect
4. C₂²×D₄×C₁₀₉	C₂	semidirect
7. C₂×D₄₃₆	C₂²	semidirect
8. #13182014	C₂²	direct (N × H)
9. C₂×#11724784	C₂²	semidirect
12. C₂×D₄×C₁₀₉	C₂²	semidirect
20. D₄×C₁₀₉	C₂³	semidirect
24. D₄₃₆	C₂³	semidirect
25. #11724784	C₂³	semidirect
28. C₂²×C₁₀₉	D₈	semidirect
35. C₂×C₁₀₉	C₂×D₈	semidirect
38. C₁₀₉	C₂²×D₈	semidirect
41. C₂²×D₄	D₁₀₉	semidirect
49. C₂×D₄	C₂×D₁₀₉	semidirect
61. D₄	C₂²×D₁₀₉	semidirect
69. C₂²	#13182014	direct (N × H)
75. C₂	C₂×#13182014	direct (N × H)

Subgroups — C22×#13182014 #20295795

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13182014 #20295795