Subgroups — SD₃₂×D₃₄₉ #36374566

Order 22336.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₃₄₉	C₂	1	1	yes	maximal, characteristic
3	#26013584	C₂	1	1	yes	maximal, characteristic, complemented
4	#26013583	C₂	1	1	yes	maximal, characteristic, complemented
5	#26013582	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₃₄₉	—	2	1	no	—
9	D₄×D₃₄₉	—	2	1	no	—
10	Dic₁₃₉₆	C₂²	1	1	yes	characteristic, complemented
11	#19150223	—	2	1	no	—
12	D₂₇₉₂	C₂²	1	1	yes	characteristic
13	#19150218	—	2	1	no	—
14	C₈×D₃₄₉	C₂²	1	1	yes	characteristic
15	#19150208	C₂²	1	1	yes	characteristic, complemented
16	Q₁₆×C₃₄₉	C₂²	1	1	yes	characteristic, complemented
17	D₈×C₃₄₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₃₄₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₃₄₉	—	4	1	no	—
20	Dic₆₉₈	—	2	1	no	—
21	Dic₆₉₈	—	4	1	no	—
22	D₁₃₉₆	—	2	1	no	—
23	C₂²⋊D₃₄₉	—	4	1	no	—
24	C₄×D₃₄₉	—	4	1	no	—
25	C₄×D₃₄₉	D₄	1	1	yes	characteristic
26	#14584095	D₄	1	1	yes	characteristic
27	Q₈×C₃₄₉	—	2	1	no	—
28	D₄×C₃₄₉	—	2	1	no	—
29	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
30	C₂²×C₃₄₉	—	4	1	no	—
31	C₂×D₃₄₉	—	4	1	no	—
32	C₂×D₃₄₉	—	8	2	no	—
33	C₂×D₃₄₉	D₈	1	1	yes	characteristic
34	C₄×C₃₄₉	—	4	1	no	—
35	C₄×C₃₄₉	C₂×D₄	1	1	yes	characteristic
36	Dic₃₄₉	—	4	1	no	—
37	Dic₃₄₉	D₈	1	1	yes	characteristic
38	C₂×C₃₄₉	—	8	1	no	—
39	C₂×C₃₄₉	C₂×D₈	1	1	yes	characteristic
40	D₃₄₉	—	8	1	no	—
41	D₃₄₉	SD₃₂	1	2	yes	direct product factor
42	C₃₄₉	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂×SD₃₂	—	349	1	no	maximal, Sylow
44	C₂×Q₁₆	—	349	1	no	—
45	C₂×D₈	—	349	1	no	—
46	SD₃₂	—	349	1	no	—
47	SD₃₂	—	349	1	no	—
48	SD₃₂	—	349	1	no	—
49	SD₃₂	D₃₄₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₆	—	349	1	no	—
51	C₂×Q₈	—	698	1	no	—
52	C₂×D₄	—	698	1	no	—
53	Q₁₆	—	349	1	no	—
54	Q₁₆	—	698	1	no	—
55	Q₁₆	C₂×D₃₄₉	1	1	yes	characteristic, complemented
56	D₈	—	349	1	no	—
57	D₈	—	698	1	no	—
58	D₈	C₂×D₃₄₉	1	1	yes	characteristic
59	C₂×C₈	—	349	1	no	—
60	C₁₆	—	349	1	no	—
61	C₁₆	C₂×D₃₄₉	1	1	yes	characteristic, complemented
62	C₂³	—	1396	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	1396	1	no	—
65	Q₈	—	698	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	1396	1	no	—
68	D₄	—	698	1	no	—
69	C₂×C₄	—	349	1	no	—
70	C₂×C₄	—	1396	1	no	—
71	C₈	—	349	1	no	—
72	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	349	1	no	—
75	C₂²	—	1396	1	no	—
76	C₂²	—	2792	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	349	1	no	—
79	C₄	—	1396	1	no	—
80	C₄	D₄×D₃₄₉	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	349	2	no	—
83	C₂	—	2792	1	no	—
84	C₂	D₈×D₃₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₄₉
commutator, cosocle	C₈×C₃₄₉	C₂³
Frattini	C₈	C₂²×D₃₄₉
Fitting	SD₃₂×C₃₄₉	C₂
socle	C₂×C₃₄₉	C₂×D₈
prime radical	D₈×D₃₄₉	C₂
hypercenter	SD₃₂	D₃₄₉
hypocenter	C₃₄₉	C₂×SD₃₂
LCS	G ▷ C₈×C₃₄₉ ▷ C₄×C₃₄₉ ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₃₄₉	C₂	semidirect
3. #26013584	C₂	semidirect
4. #26013583	C₂	semidirect
5. #26013582	C₂	semidirect
6. C₁₆×D₃₄₉	C₂	semidirect
7. SD₃₂×C₃₄₉	C₂	semidirect
10. Dic₁₃₉₆	C₂²	semidirect
15. #19150208	C₂²	semidirect
16. Q₁₆×C₃₄₉	C₂²	semidirect
18. C₁₆×C₃₄₉	C₂²	semidirect
41. D₃₄₉	SD₃₂	direct (N × H)
42. C₃₄₉	C₂×SD₃₂	semidirect
49. SD₃₂	D₃₄₉	direct (N × H)
55. Q₁₆	C₂×D₃₄₉	semidirect
61. C₁₆	C₂×D₃₄₉	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₃₄₉	2
D₈×D₃₄₉	2
#26013584	2
#26013583	2
#26013582	2
C₁₆×D₃₄₉	2
SD₃₂×C₃₄₉	2
C₂×SD₃₂	349

Subgroups — SD32×D349 #36374566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×D₃₄₉ #36374566