Subgroups — #34059840

Order 19072.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750551	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#18011980	—	2	1	no	—
5	#18011961	—	2	1	no	—
6	D₈×D₁₄₉	—	2	1	no	—
7	D₂₃₈₄	C₄	1	1	yes	characteristic, complemented
8	#18011852	—	2	1	no	—
9	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
10	D₁₆×C₁₄₉	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10597010	—	4	1	no	—
12	D₄×D₁₄₉	—	4	1	no	—
13	D₁₁₉₂	—	2	1	no	—
14	#14558721	—	4	1	no	—
15	C₈×D₁₄₉	D₄	1	1	yes	characteristic
16	#14558711	D₄	1	1	yes	characteristic
17	D₈×C₁₄₉	—	2	1	no	—
18	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂×#10597010	—	8	1	no	—
20	C₂²×D₁₄₉	—	8	1	no	—
21	D₅₉₆	—	4	1	no	—
22	C₂²⋊D₁₄₉	—	8	1	no	—
23	C₄×D₁₄₉	D₈	1	1	yes	characteristic
24	#11924746	SD₁₆	1	1	yes	characteristic
25	D₄×C₁₄₉	—	4	1	no	—
26	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₄₉	—	8	1	no	—
28	C₂×D₁₄₉	—	8	1	no	—
29	C₂×D₁₄₉	—	16	1	no	—
30	C₂×D₁₄₉	—	16	1	no	—
31	C₂×D₁₄₉	D₁₆	1	1	yes	characteristic
32	#10597010	—	16	1	no	—
33	C₄×C₁₄₉	#102	1	1	yes	characteristic
34	Dic₁₄₉	SD₃₂	1	1	yes	characteristic
35	C₂×C₁₄₉	—	16	1	no	—
36	C₂×C₁₄₉	#357	1	1	yes	characteristic
37	D₁₄₉	—	16	1	no	—
38	D₁₄₉	D₃₂	1	1	yes	characteristic
39	D₁₄₉	SD₆₄	1	1	yes	characteristic
40	C₁₄₉	#1415	1	1	yes	characteristic, complemented, Sylow
41	#1415	—	149	1	no	maximal, Sylow
42	C₂×D₁₆	—	149	1	no	—
43	C₂×C₃₂	—	149	1	no	—
44	#366	—	149	1	no	—
45	C₂×D₈	—	298	1	no	—
46	D₁₆	—	298	1	no	—
47	D₁₆	—	149	1	no	—
48	D₁₆	#10597010	1	1	yes	characteristic, complemented
49	C₂×C₁₆	—	149	1	no	—
50	#107	—	298	1	no	—
51	C₃₂	—	298	1	no	—
52	C₂×D₄	—	596	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	298	1	no	—
55	D₈	—	596	1	no	—
56	C₂×C₈	—	149	1	no	—
57	C₄⋊C₄	—	596	1	no	—
58	C₁₆	—	149	1	no	—
59	C₁₆	C₂×#10597010	1	1	yes	characteristic
60	C₂³	—	1192	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	596	1	no	—
63	D₄	—	1192	1	no	—
64	C₂×C₄	—	149	1	no	—
65	C₂×C₄	—	1192	1	no	—
66	C₈	—	149	1	no	—
67	C₈	C₂²⋊#10597010	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	2384	1	no	—
70	C₂²	—	2384	1	no	—
71	C₂²	—	149	1	no	—
72	C₂²	—	1192	1	no	—
73	C₄	—	2384	1	no	—
74	C₄	—	149	1	no	—
75	C₄	#18011973	1	1	yes	characteristic
76	C₂	—	16	1	no	—
77	C₂	—	2384	1	no	—
78	C₂	—	149	1	no	—
79	C₂	—	149	1	no	—
80	C₂	#23750537	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750537
commutator	C₁₆×C₁₄₉	C₂×C₄
Frattini	C₁₆	C₂×#10597010
Fitting	D₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	#357
prime radical	D₁₆×D₁₄₉	C₂
cosocle	C₁₆×D₁₄₉	C₂²
hypercenter	D₁₆	#10597010
hypocenter	C₁₄₉	#1415
LCS	G ▷ C₁₆×C₁₄₉ ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₁₄₉⋊C₃₂	C₂	semidirect
2. #23750551	C₂	semidirect
7. D₂₃₈₄	C₄	semidirect
10. D₁₆×C₁₄₉	C₄	semidirect
40. C₁₄₉	#1415	semidirect
48. D₁₆	#10597010	semidirect

Maximal subgroups

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

subgroup	index
D₁₄₉⋊C₃₂	2
#23750551	2
D₁₆×D₁₄₉	2
#1415	149