Subgroups — D₁₄₉⋊M₆₄ #34061112

Order 19072.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750558	C₂	1	2	yes	maximal, complemented
2	#23750557	C₂	1	2	yes	maximal, complemented
3	D₁₄₉⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic
5	#18011961	C₂²	1	4	yes	complemented
6	C₂×C₈×D₁₄₉	C₄	1	1	yes	characteristic
7	C₂×#14558711	C₂²	1	1	yes	characteristic
8	C₁₆×D₁₄₉	C₄	1	1	yes	characteristic
9	C₁₆×D₁₄₉	C₄	1	1	yes	characteristic
10	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
11	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×C₄×D₁₄₉	C₈	1	1	yes	characteristic
14	C₂×#11924746	C₈	1	1	yes	characteristic
15	C₈×D₁₄₉	C₈	1	1	yes	characteristic
16	C₈×D₁₄₉	C₈	1	1	yes	characteristic
17	C₈×D₁₄₉	C₂×C₄	1	1	yes	characteristic
18	C₈×D₁₄₉	C₂×C₄	1	1	yes	characteristic
19	#14558711	C₂×C₄	1	1	yes	characteristic
20	#14558711	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₁₄₉	C₁₆	1	1	yes	characteristic
25	C₂×Dic₁₄₉	C₁₆	1	1	yes	characteristic
26	C₄×D₁₄₉	C₁₆	1	1	yes	characteristic
27	C₄×D₁₄₉	C₁₆	1	1	yes	characteristic
28	C₄×D₁₄₉	C₂×C₈	1	1	yes	characteristic
29	C₄×D₁₄₉	C₂×C₈	1	1	yes	characteristic
30	#11924746	C₂×C₈	1	1	yes	characteristic
31	#11924746	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
34	C₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
36	C₂×D₁₄₉	—	2	2	no	—
37	C₂×D₁₄₉	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₁₄₉	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
41	Dic₁₄₉	C₂×C₁₆	1	1	yes	characteristic
42	Dic₁₄₉	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₁₄₉	—	2	1	no	—
44	C₂×C₁₄₉	C₂²×C₁₆	1	1	yes	characteristic
45	D₁₄₉	—	2	1	no	—
46	D₁₄₉	M₆₄	1	2	yes	complemented
47	C₁₄₉	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₆₄	—	149	1	no	maximal, Sylow
49	C₂²×C₁₆	—	149	1	no	—
50	M₆₄	—	149	2	no	—
51	M₆₄	—	149	2	no	—
52	C₂×C₃₂	—	149	2	no	—
53	C₂²×C₈	—	149	1	no	—
54	C₂×C₁₆	—	149	1	no	—
55	C₂×C₁₆	—	149	1	no	—
56	C₂×C₁₆	—	149	1	no	—
57	C₂×C₁₆	—	149	1	no	—
58	C₂×C₁₆	—	149	1	no	—
59	C₂×C₁₆	#10597010	1	1	yes	characteristic
60	C₃₂	—	149	4	no	—
61	C₂²×C₄	—	149	1	no	—
62	C₂×C₈	—	149	1	no	—
63	C₂×C₈	—	149	1	no	—
64	C₂×C₈	—	149	1	no	—
65	C₂×C₈	—	149	1	no	—
66	C₂×C₈	—	149	1	no	—
67	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
68	C₁₆	—	149	1	no	—
69	C₁₆	—	149	1	no	—
70	C₁₆	C₂×#10597010	1	1	yes	characteristic
71	C₁₆	C₂×#10597010	1	1	yes	characteristic
72	C₂³	—	149	1	no	—
73	C₂×C₄	—	149	1	no	—
74	C₂×C₄	—	149	1	no	—
75	C₂×C₄	—	149	1	no	—
76	C₂×C₄	—	149	1	no	—
77	C₂×C₄	—	149	1	no	—
78	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
79	C₈	—	149	1	no	—
80	C₈	—	149	1	no	—
81	C₈	D₁₄₉⋊C₈	1	1	yes	characteristic
82	C₈	C₂²×#10597010	1	1	yes	characteristic
83	C₂²	—	298	2	no	—
84	C₂²	—	149	1	no	—
85	C₂²	—	149	1	no	—
86	C₂²	D₁₄₉⋊C₁₆	1	1	yes	characteristic
87	C₄	—	149	1	no	—
88	C₄	—	149	1	no	—
89	C₄	D₁₄₉⋊C₁₆	1	1	yes	characteristic
90	C₄	C₂×D₁₄₉⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	298	1	no	—
93	C₂	—	149	2	no	—
94	C₂	C₂×D₁₄₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×#10597010
commutator, socle	C₂×C₁₄₉	C₂²×C₁₆
Frattini	C₈	C₂²×#10597010
Fitting	C₂×C₁₆×C₁₄₉	C₄
prime radical	C₂²×D₁₄₉	C₁₆
cosocle	#14558711	C₂³
hypercenter	C₂×C₁₆	#10597010
hypocenter	C₁₄₉	C₂×M₆₄
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #23750558	C₂	semidirect
2. #23750557	C₂	semidirect
3. D₁₄₉⋊C₃₂	C₂	semidirect
5. #18011961	C₂²	semidirect
46. D₁₄₉	M₆₄	semidirect
47. C₁₄₉	C₂×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
#23750558	2
#23750557	2
D₁₄₉⋊C₃₂	2
C₂×C₁₆×D₁₄₉	2
C₂×M₆₄	149

Subgroups — D149⋊M64 #34061112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₉⋊M₆₄ #34061112