Subgroups — C₂×#26013549 #36374092

Order 22336.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14584095	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₄₉	C₂	1	1	yes	maximal, characteristic
3	#26013549	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₄₉	C₄	1	2	yes	—
6	C₂×#14584095	C₄	1	4	yes	complemented
7	C₂×#14584095	C₂²	1	2	yes	—
8	C₄×Dic₃₄₉	C₄	1	2	yes	—
9	C₄×Dic₃₄₉	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₄₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₄₉	C₄	1	4	yes	complemented
12	C₂×C₈×C₃₄₉	C₂²	1	2	yes	—
13	C₂×Dic₃₄₉	—	2	4	no	—
14	C₂×Dic₃₄₉	C₂×C₄	1	4	yes	—
15	#14584095	C₂×C₄	1	4	yes	complemented
16	C₂³×C₃₄₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₄₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₄₉	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₃₄₉	C₂³	1	1	yes	characteristic
21	C₈×C₃₄₉	C₂×C₄	1	4	yes	complemented
22	C₂²×C₃₄₉	C₄²	1	2	yes	—
23	C₂²×C₃₄₉	M₁₆	1	4	yes	—
24	C₂²×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₄₉	C₄²	1	2	yes	—
26	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₃₄₉	—	2	4	no	—
29	C₂×C₃₄₉	#97	1	4	yes	complemented
30	C₂×C₃₄₉	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₃₄₉	C₂×M₁₆	1	2	yes	—
32	C₃₄₉	C₂×#97	1	1	yes	characteristic, complemented, Sylow
33	C₂×#97	—	349	1	no	maximal, Sylow
34	C₂²×C₈	—	349	1	no	—
35	C₂²×C₈	D₃₄₉	1	1	yes	characteristic
36	C₂×C₄²	—	349	1	no	—
37	#97	—	349	4	no	—
38	C₂²×C₄	—	349	2	no	—
39	C₂²×C₄	C₂×D₃₄₉	1	1	yes	characteristic
40	C₂×C₈	—	349	4	no	—
41	C₂×C₈	—	349	2	no	—
42	C₂×C₈	Dic₃₄₉	1	4	yes	complemented
43	C₂×C₈	C₂×D₃₄₉	1	2	yes	—
44	C₄²	—	349	2	no	—
45	C₄²	—	349	2	no	—
46	C₂³	C₄×D₃₄₉	1	1	yes	characteristic
47	C₂×C₄	—	349	4	no	—
48	C₂×C₄	—	698	4	no	—
49	C₂×C₄	C₄×D₃₄₉	1	1	yes	characteristic
50	C₂×C₄	C₄×D₃₄₉	1	2	yes	—
51	C₂×C₄	C₂×Dic₃₄₉	1	2	yes	—
52	C₂×C₄	C₂²×D₃₄₉	1	1	yes	characteristic
53	C₈	—	349	4	no	—
54	C₈	C₂×Dic₃₄₉	1	4	yes	complemented
55	C₂²	C₄×Dic₃₄₉	1	2	yes	—
56	C₂²	#19150216	1	4	yes	—
57	C₂²	C₂×C₄×D₃₄₉	1	1	yes	characteristic
58	C₄	—	698	4	no	—
59	C₄	C₄×Dic₃₄₉	1	2	yes	—
60	C₄	C₂×C₄×D₃₄₉	1	1	yes	characteristic
61	C₄	C₂²×Dic₃₄₉	1	1	yes	characteristic
62	C₂	#26013549	1	4	yes	direct product factor
63	C₂	C₂×C₄×Dic₃₄₉	1	1	yes	characteristic
64	C₂	C₂×#19150216	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₄₉
commutator	C₂×C₃₄₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃₄₉
Fitting	C₂²×C₈×C₃₄₉	C₂
socle, prime radical	C₂³×C₃₄₉	C₂×C₄
cosocle	C₂×C₄×C₃₄₉	C₂³
hypercenter	C₂²×C₈	D₃₄₉
hypocenter	C₃₄₉	C₂×#97
LCS	G ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #26013549	C₂	direct (N × H)
6. C₂×#14584095	C₄	semidirect
11. C₂×C₈×C₃₄₉	C₄	semidirect
15. #14584095	C₂×C₄	semidirect
21. C₈×C₃₄₉	C₂×C₄	semidirect
29. C₂×C₃₄₉	#97	semidirect
32. C₃₄₉	C₂×#97	semidirect
42. C₂×C₈	Dic₃₄₉	semidirect
54. C₈	C₂×Dic₃₄₉	semidirect
62. C₂	#26013549	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14584095	2
C₂×C₄×Dic₃₄₉	2
#26013549	2
C₂²×C₈×C₃₄₉	2
C₂×#97	349

Subgroups — C2×#26013549 #36374092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26013549 #36374092