Subgroups — #34042832

Order 19072.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750041	C₂	1	1	yes	maximal, characteristic
2	#23749459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#18011917	C₄	1	1	yes	characteristic
5	#18011851	C₄	1	1	yes	characteristic
6	#18011850	—	2	1	no	—
7	C₁₆×D₁₄₉	—	2	1	no	—
8	#18011817	—	2	1	no	—
9	C₂×C₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₃₂×C₁₄₉	—	2	1	no	—
11	#14558736	C₈	1	1	yes	characteristic
12	#14558720	C₈	1	1	yes	characteristic
13	#14558719	—	2	1	no	—
14	C₈×D₁₄₉	—	2	1	no	—
15	#14558711	—	2	1	no	—
16	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₄₉	D₄	1	1	yes	characteristic
18	C₁₆×C₁₄₉	D₄	1	1	yes	characteristic
19	Dic₂₉₈	C₁₆	1	1	yes	characteristic
20	D₅₉₆	C₁₆	1	1	yes	characteristic
21	C₂²⋊D₁₄₉	—	2	1	no	—
22	C₄×D₁₄₉	—	2	1	no	—
23	#11924746	—	2	1	no	—
24	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
25	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
27	C₂²×C₁₄₉	M₃₂	1	1	yes	characteristic
28	C₂×D₁₄₉	—	2	1	no	—
29	C₄×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
31	Dic₁₄₉	—	2	1	no	—
32	C₂×C₁₄₉	—	2	1	no	—
33	C₂×C₁₄₉	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₁₄₉	—	4	1	no	—
35	C₁₄₉	#1401	1	1	yes	characteristic, complemented, Sylow
36	#1401	—	149	1	no	maximal, Sylow
37	#504	—	149	1	no	—
38	M₆₄	—	149	1	no	—
39	C₂×C₃₂	D₁₄₉	1	1	yes	characteristic, complemented
40	#131	—	149	1	no	—
41	M₃₂	—	298	1	no	—
42	M₃₂	—	149	1	no	—
43	C₂×C₁₆	—	298	1	no	—
44	C₂×C₁₆	C₂×D₁₄₉	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	298	1	no	—
47	#41	—	149	1	no	—
48	M₁₆	—	298	1	no	—
49	M₁₆	—	149	1	no	—
50	C₂×C₈	—	298	1	no	—
51	C₂×C₈	C₄×D₁₄₉	1	1	yes	characteristic
52	C₁₆	—	298	1	no	—
53	C₁₆	C₂²⋊D₁₄₉	1	1	yes	characteristic
54	C₁₆	D₅₉₆	1	1	yes	characteristic
55	Q₈	—	149	1	no	—
56	D₄	—	298	1	no	—
57	D₄	—	149	1	no	—
58	C₂×C₄	—	298	1	no	—
59	C₂×C₄	C₈×D₁₄₉	1	1	yes	characteristic
60	C₈	—	298	1	no	—
61	C₈	#14558713	1	1	yes	characteristic
62	C₈	#14558719	1	1	yes	characteristic
63	C₂²	—	298	1	no	—
64	C₂²	#18011850	1	1	yes	characteristic
65	C₄	—	298	1	no	—
66	C₄	#18011823	1	1	yes	characteristic
67	C₄	C₁₆×D₁₄₉	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	596	1	no	—
70	C₂	#23749404	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₅₉₆
commutator	C₄×C₁₄₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₄₉
Fitting	C₂×C₃₂×C₁₄₉	C₂
socle	C₂×C₁₄₉	C₂²⋊C₁₆
prime radical	#14558736	C₈
cosocle	C₂×C₁₆×C₁₄₉	C₂²
hypercenter	C₂×C₃₂	D₁₄₉
hypocenter	C₁₄₉	#1401
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #23749459	C₂	semidirect
3. C₂×C₃₂×C₁₄₉	C₂	semidirect
35. C₁₄₉	#1401	semidirect
39. C₂×C₃₂	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750041	2
#23749459	2
C₂×C₃₂×C₁₄₉	2
#1401	149