Subgroups — #34059807

Order 19072.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750557	C₂	1	2	yes	maximal, complemented
2	C₂×#18011850	C₂	1	1	yes	maximal, characteristic
3	#18011961	—	2	2	no	—
4	C₂×C₈×D₁₄₉	C₄	1	1	yes	characteristic
5	#18011850	—	2	2	no	—
6	C₂×#14558711	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₄₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₄₉	C₈	1	1	yes	characteristic
9	C₂×#11924746	C₈	1	1	yes	characteristic
10	C₈×D₁₄₉	—	2	1	no	—
11	C₈×D₁₄₉	—	2	1	no	—
12	#14558711	D₄	1	2	yes	—
13	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₄₉	—	2	1	no	—
15	C₂²×D₁₄₉	C₁₆	1	1	yes	characteristic
16	C₂×Dic₁₄₉	C₁₆	1	1	yes	characteristic
17	C₄×D₁₄₉	—	2	1	no	—
18	C₄×D₁₄₉	—	2	1	no	—
19	#11924746	—	2	1	no	—
20	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₁₄₉	—	2	1	no	—
25	C₂×D₁₄₉	—	4	1	no	—
26	C₄×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₁₄₉	M₃₂	1	1	yes	characteristic
28	Dic₁₄₉	—	2	1	no	—
29	C₂×C₁₄₉	—	2	1	no	—
30	C₂×C₁₄₉	C₂²⋊C₁₆	1	1	yes	characteristic
31	D₁₄₉	—	4	1	no	—
32	C₁₄₉	#1400	1	1	yes	characteristic, complemented, Sylow
33	#1400	—	149	1	no	maximal, Sylow
34	C₂×M₃₂	—	149	1	no	—
35	M₆₄	—	149	2	no	—
36	C₂²×C₈	—	149	1	no	—
37	M₃₂	—	298	2	no	—
38	C₂×C₁₆	—	149	1	no	—
39	C₂×C₁₆	#10597010	1	1	yes	characteristic
40	C₃₂	—	298	2	no	—
41	C₂²×C₄	—	149	1	no	—
42	C₂×C₈	—	298	1	no	—
43	C₂×C₈	—	298	1	no	—
44	C₂×C₈	—	149	1	no	—
45	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	—	149	2	no	—
48	C₂³	—	149	1	no	—
49	C₂×C₄	—	298	1	no	—
50	C₂×C₄	—	298	1	no	—
51	C₂×C₄	—	149	1	no	—
52	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
53	C₈	—	298	1	no	—
54	C₈	C₂²⋊#10597010	1	1	yes	characteristic
55	C₈	#14558746	1	1	yes	characteristic
56	C₂²	—	298	1	no	—
57	C₂²	—	596	1	no	—
58	C₂²	D₁₄₉⋊C₁₆	1	1	yes	characteristic
59	C₄	—	298	1	no	—
60	C₄	#18011968	1	1	yes	characteristic
61	C₄	#18011986	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	596	1	no	—
64	C₂	#23750520	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#10597010
commutator	C₂²×C₁₄₉	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10597010
Fitting	C₂×C₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂²⋊C₁₆
prime radical	C₂²×D₁₄₉	C₁₆
cosocle	C₂×#14558711	C₂²
hypercenter	C₂×C₁₆	#10597010
hypocenter	C₁₄₉	#1400
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #23750557	C₂	semidirect
32. C₁₄₉	#1400	semidirect

Maximal subgroups

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

subgroup	index
#23750557	2
C₂×#18011850	2
#1400	149