Subgroups — C₂×#26013580 #36374564

Order 22336.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#26013580	C₂	1	4	yes	maximal, direct product factor
3	C₂×#19150208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₃₉₆	—	2	1	no	—
6	D₂₇₉₂	—	2	1	no	—
7	D₂₇₉₂	C₂²	1	2	yes	complemented
8	#19150208	C₂²	1	2	yes	complemented
9	C₂×D₄×C₃₄₉	—	2	1	no	—
10	D₈×C₃₄₉	—	2	1	no	—
11	D₈×C₃₄₉	C₂²	1	2	yes	complemented
12	C₂×C₈×C₃₄₉	C₂²	1	1	yes	characteristic
13	C₂²×D₃₄₉	—	4	1	no	—
14	D₁₃₉₆	—	2	2	no	—
15	D₁₃₉₆	—	4	1	no	—
16	C₂³×C₃₄₉	—	4	1	no	—
17	D₄×C₃₄₉	—	2	2	no	—
18	D₄×C₃₄₉	—	4	1	no	—
19	C₂×C₄×C₃₄₉	D₄	1	1	yes	characteristic
20	C₈×C₃₄₉	D₄	1	1	yes	characteristic
21	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
22	C₂²×C₃₄₉	—	4	2	no	—
23	C₂²×C₃₄₉	—	8	2	no	—
24	C₂²×C₃₄₉	D₈	1	1	yes	characteristic
25	C₂×D₃₄₉	—	4	2	no	—
26	C₂×D₃₄₉	—	8	2	no	—
27	C₄×C₃₄₉	D₈	1	1	yes	characteristic
28	C₄×C₃₄₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃₄₉	—	8	2	no	—
30	C₂×C₃₄₉	D₁₆	1	2	yes	complemented
31	C₂×C₃₄₉	C₂×D₈	1	1	yes	characteristic
32	D₃₄₉	—	8	2	no	—
33	C₃₄₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	—	349	1	no	maximal, Sylow
35	C₂×D₈	—	349	1	no	—
36	C₂×D₈	D₃₄₉	1	1	yes	characteristic, complemented
37	D₁₆	—	349	4	no	—
38	C₂×C₁₆	—	349	1	no	—
39	C₂×D₄	—	2	1	no	—
40	C₂×D₄	—	698	1	no	—
41	D₈	—	2	1	no	—
42	D₈	—	349	2	no	—
43	D₈	—	698	1	no	—
44	D₈	C₂×D₃₄₉	1	2	yes	complemented
45	C₂×C₈	C₂×D₃₄₉	1	1	yes	characteristic
46	C₁₆	—	349	2	no	—
47	C₂³	—	4	1	no	—
48	C₂³	—	1396	1	no	—
49	D₄	—	2	2	no	—
50	D₄	—	4	1	no	—
51	D₄	—	1396	1	no	—
52	D₄	—	698	2	no	—
53	C₂×C₄	C₂²⋊D₃₄₉	1	1	yes	characteristic
54	C₈	C₂²⋊D₃₄₉	1	1	yes	characteristic
55	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
56	C₂²	—	4	2	no	—
57	C₂²	—	8	2	no	—
58	C₂²	—	1396	2	no	—
59	C₂²	—	2792	2	no	—
60	C₂²	#19150218	1	1	yes	characteristic
61	C₄	#19150218	1	1	yes	characteristic
62	C₄	C₂×C₂²⋊D₃₄₉	1	1	yes	characteristic
63	C₂	—	8	2	no	—
64	C₂	—	2792	2	no	—
65	C₂	#26013580	1	2	yes	direct product factor
66	C₂	C₂×#19150218	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19150218
commutator, cosocle	C₈×C₃₄₉	C₂³
Frattini	C₈	C₂²×D₃₄₉
Fitting	C₂×D₈×C₃₄₉	C₂
socle	C₂²×C₃₄₉	D₈
hypercenter	C₂×D₈	D₃₄₉
hypocenter	C₃₄₉	C₂×D₁₆
LCS	G ▷ C₈×C₃₄₉ ▷ C₄×C₃₄₉ ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₇₉₂	C₂	semidirect
2. #26013580	C₂	direct (N × H)
3. C₂×#19150208	C₂	semidirect
4. C₂×D₈×C₃₄₉	C₂	semidirect
7. D₂₇₉₂	C₂²	semidirect
8. #19150208	C₂²	semidirect
11. D₈×C₃₄₉	C₂²	semidirect
30. C₂×C₃₄₉	D₁₆	semidirect
33. C₃₄₉	C₂×D₁₆	semidirect
36. C₂×D₈	D₃₄₉	semidirect
44. D₈	C₂×D₃₄₉	semidirect
65. C₂	#26013580	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×D₂₇₉₂	2
#26013580	2
C₂×#19150208	2
C₂×D₈×C₃₄₉	2
C₂×D₁₆	349

Subgroups — C2×#26013580 #36374564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26013580 #36374564