Subgroups — D₃₄₉⋊#131 #36375220

Order 22336.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013727	C₂	1	2	yes	maximal, complemented
2	#26013726	C₂	1	6	yes	maximal, complemented
3	D₃₄₉⋊M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂×D₃₄₉⋊C₈	C₂	1	3	yes	maximal, complemented
5	#41×D₃₄₉	C₂	1	1	yes	maximal, characteristic
6	#19150243	C₂²	1	6	yes	complemented
7	#19150242	C₂²	1	6	yes	complemented
8	D₃₄₉⋊C₈	C₂²	1	1	yes	characteristic
9	D₃₄₉⋊C₈	C₂²	1	3	yes	—
10	D₃₄₉⋊C₈	C₂²	1	6	yes	complemented
11	C₂×#14584102	C₂²	1	6	yes	complemented
12	#19150234	C₂²	1	1	yes	characteristic
13	#19150233	C₄	1	3	yes	—
14	#19150232	C₂²	1	3	yes	—
15	Q₈×D₃₄₉	C₄	1	1	yes	characteristic
16	D₄×D₃₄₉	C₄	1	3	yes	—
17	C₂×C₄×D₃₄₉	C₂²	1	3	yes	—
18	#41×C₃₄₉	C₄	1	1	yes	characteristic
19	#14584102	C₂³	1	2	yes	—
20	#14584102	C₂³	1	6	yes	—
21	C₂²×D₃₄₉	C₂×C₄	1	3	yes	—
22	Dic₆₉₈	C₂×C₄	1	3	yes	—
23	D₁₃₉₆	C₂×C₄	1	3	yes	—
24	C₂²⋊D₃₄₉	C₂×C₄	1	6	yes	—
25	C₂×Dic₃₄₉	C₂³	1	3	yes	—
26	C₄×D₃₄₉	C₂×C₄	1	3	yes	—
27	C₄×D₃₄₉	C₂×C₄	1	3	yes	—
28	C₄×D₃₄₉	C₂³	1	1	yes	characteristic
29	C₄×D₃₄₉	C₂³	1	3	yes	—
30	Q₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
31	D₄×C₃₄₉	C₂×C₄	1	3	yes	—
32	C₂×C₄×C₃₄₉	C₂×C₄	1	3	yes	—
33	C₂²×C₃₄₉	C₂²×C₄	1	3	yes	—
34	C₂×D₃₄₉	—	2	6	no	—
35	C₂×D₃₄₉	C₂²×C₄	1	3	yes	—
36	C₂×D₃₄₉	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₃₄₉	C₂²×C₄	1	3	yes	—
38	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
39	Dic₃₄₉	C₂²×C₄	1	3	yes	—
40	Dic₃₄₉	C₂⁴	1	1	yes	characteristic
41	C₂×C₃₄₉	—	2	3	no	—
42	C₂×C₃₄₉	C₂³×C₄	1	1	yes	characteristic
43	D₃₄₉	—	2	3	no	—
44	D₃₄₉	#131	1	2	yes	complemented
45	C₃₄₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
46	C₂×#131	—	349	1	no	maximal, Sylow
47	C₂×#41	—	349	1	no	—
48	#131	—	349	6	no	—
49	#131	—	349	2	no	—
50	C₂×M₁₆	—	349	3	no	—
51	C₂²×C₈	—	349	3	no	—
52	#41	—	349	1	no	—
53	#41	—	349	3	no	—
54	#41	—	349	3	no	—
55	#41	#13063703	1	1	yes	characteristic
56	C₂×Q₈	—	349	1	no	—
57	C₂×D₄	—	349	3	no	—
58	C₂²×C₄	—	349	3	no	—
59	M₁₆	—	349	6	no	—
60	M₁₆	—	349	6	no	—
61	C₂×C₈	—	349	1	no	—
62	C₂×C₈	—	349	3	no	—
63	C₂×C₈	—	349	6	no	—
64	C₂×C₈	—	349	6	no	—
65	C₂³	—	349	3	no	—
66	Q₈	—	349	3	no	—
67	Q₈	C₂×#13063703	1	1	yes	characteristic
68	D₄	—	349	6	no	—
69	D₄	—	349	3	no	—
70	D₄	C₂×#13063703	1	3	yes	—
71	C₂×C₄	—	349	3	no	—
72	C₂×C₄	—	349	3	no	—
73	C₂×C₄	—	349	3	no	—
74	C₂×C₄	—	349	3	no	—
75	C₂×C₄	—	349	1	no	—
76	C₂×C₄	C₂×#13063703	1	3	yes	—
77	C₈	—	349	2	no	—
78	C₈	—	349	6	no	—
79	C₂²	—	349	1	no	—
80	C₂²	—	349	3	no	—
81	C₂²	—	698	6	no	—
82	C₂²	C₂²×#13063703	1	3	yes	—
83	C₄	—	349	1	no	—
84	C₄	—	349	3	no	—
85	C₄	C₂²×#13063703	1	3	yes	—
86	C₄	C₂²×#13063703	1	1	yes	characteristic
87	C₂	—	2	3	no	—
88	C₂	—	349	2	no	—
89	C₂	—	698	3	no	—
90	C₂	C₂³×#13063703	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#13063703
commutator, socle	C₂×C₃₄₉	C₂³×C₄
Frattini	C₂	C₂³×#13063703
Fitting	#41×C₃₄₉	C₄
prime radical	#41×D₃₄₉	C₂
cosocle	Dic₃₄₉	C₂⁴
hypercenter	#41	#13063703
hypocenter	C₃₄₉	C₂×#131
LCS	G ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #26013727	C₂	semidirect
2. #26013726	C₂	semidirect
3. D₃₄₉⋊M₁₆	C₂	semidirect
4. C₂×D₃₄₉⋊C₈	C₂	semidirect
6. #19150243	C₂²	semidirect
7. #19150242	C₂²	semidirect
10. D₃₄₉⋊C₈	C₂²	semidirect
11. C₂×#14584102	C₂²	semidirect
44. D₃₄₉	#131	semidirect
45. C₃₄₉	C₂×#131	semidirect

Maximal subgroups

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

subgroup	index
#26013727	2
#26013726	2
D₃₄₉⋊M₁₆	2
C₂×D₃₄₉⋊C₈	2
#41×D₃₄₉	2
C₂×#131	349

Subgroups — D349⋊#131 #36375220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₄₉⋊#131 #36375220