Subgroups — C₂×#26013578 #36374558

Order 22336.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₃₄₉	C₂	1	1	yes	maximal, characteristic
2	#26013578	C₂	1	4	yes	maximal, direct product factor
3	C₂×#19150208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₃₄₉	C₄	1	1	yes	characteristic
6	C₂×#14584095	C₄	1	1	yes	characteristic
7	C₈×D₃₄₉	C₄	1	2	yes	—
8	C₈×D₃₄₉	C₂²	1	2	yes	—
9	#19150208	C₂²	1	2	yes	complemented
10	C₂×C₈×C₃₄₉	C₂²	1	1	yes	characteristic
11	C₁₆×C₃₄₉	C₂²	1	2	yes	complemented
12	C₂²×D₃₄₉	C₈	1	1	yes	characteristic
13	C₂×Dic₃₄₉	C₈	1	1	yes	characteristic
14	C₄×D₃₄₉	C₈	1	2	yes	—
15	C₄×D₃₄₉	C₂×C₄	1	2	yes	—
16	#14584095	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
18	C₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
19	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
20	C₂²×C₃₄₉	C₂×C₈	1	1	yes	characteristic
21	C₂×D₃₄₉	—	2	2	no	—
22	C₂×D₃₄₉	C₂×C₈	1	2	yes	—
23	C₄×C₃₄₉	C₂×C₈	1	1	yes	characteristic
24	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
25	Dic₃₄₉	C₂×C₈	1	2	yes	—
26	C₂×C₃₄₉	M₃₂	1	2	yes	complemented
27	C₂×C₃₄₉	C₂²×C₈	1	1	yes	characteristic
28	D₃₄₉	—	2	2	no	—
29	C₃₄₉	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×M₃₂	—	349	1	no	maximal, Sylow
31	C₂²×C₈	—	349	1	no	—
32	M₃₂	—	349	4	no	—
33	C₂×C₁₆	—	349	1	no	—
34	C₂×C₁₆	D₃₄₉	1	1	yes	characteristic, complemented
35	C₂²×C₄	—	349	1	no	—
36	C₂×C₈	—	349	1	no	—
37	C₂×C₈	—	349	2	no	—
38	C₂×C₈	—	349	2	no	—
39	C₂×C₈	C₂×D₃₄₉	1	1	yes	characteristic
40	C₁₆	—	349	2	no	—
41	C₁₆	C₂×D₃₄₉	1	2	yes	complemented
42	C₂³	—	349	1	no	—
43	C₂×C₄	—	349	1	no	—
44	C₂×C₄	—	349	2	no	—
45	C₂×C₄	—	349	2	no	—
46	C₂×C₄	C₄×D₃₄₉	1	1	yes	characteristic
47	C₈	—	349	2	no	—
48	C₈	C₄×D₃₄₉	1	1	yes	characteristic
49	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
50	C₂²	—	349	2	no	—
51	C₂²	—	698	2	no	—
52	C₂²	C₈×D₃₄₉	1	1	yes	characteristic
53	C₄	—	349	2	no	—
54	C₄	C₈×D₃₄₉	1	1	yes	characteristic
55	C₄	C₂×C₄×D₃₄₉	1	1	yes	characteristic
56	C₂	—	698	2	no	—
57	C₂	#26013578	1	2	yes	direct product factor
58	C₂	C₂×C₈×D₃₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₄₉
commutator	C₂×C₃₄₉	C₂²×C₈
Frattini	C₈	C₂²×D₃₄₉
Fitting	C₂×C₁₆×C₃₄₉	C₂
socle	C₂²×C₃₄₉	C₂×C₈
prime radical	C₂²×D₃₄₉	C₈
cosocle	C₈×C₃₄₉	C₂³
hypercenter	C₂×C₁₆	D₃₄₉
hypocenter	C₃₄₉	C₂×M₃₂
LCS	G ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #26013578	C₂	direct (N × H)
3. C₂×#19150208	C₂	semidirect
4. C₂×C₁₆×C₃₄₉	C₂	semidirect
9. #19150208	C₂²	semidirect
11. C₁₆×C₃₄₉	C₂²	semidirect
26. C₂×C₃₄₉	M₃₂	semidirect
29. C₃₄₉	C₂×M₃₂	semidirect
34. C₂×C₁₆	D₃₄₉	semidirect
41. C₁₆	C₂×D₃₄₉	semidirect
57. C₂	#26013578	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×D₃₄₉	2
#26013578	2
C₂×#19150208	2
C₂×C₁₆×C₃₄₉	2
C₂×M₃₂	349

Subgroups — C2×#26013578 #36374558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26013578 #36374558