Subgroups — #34059852

Order 19072.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750551	C₂	1	2	yes	maximal
2	C₃₂×D₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#18011980	—	2	2	no	—
4	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
5	#18011817	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₄₉	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#10597010	—	4	2	no	—
8	C₈×D₁₄₉	D₄	1	1	yes	characteristic
9	#14558711	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
11	C₂×#10597010	—	8	2	no	—
12	C₄×D₁₄₉	D₈	1	1	yes	characteristic
13	#11924746	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₄₉	D₁₆	1	1	yes	characteristic
16	#10597010	—	16	2	no	—
17	C₄×C₁₄₉	#107	1	1	yes	characteristic
18	Dic₁₄₉	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₄₉	#366	1	1	yes	characteristic
20	D₁₄₉	D₃₂	1	1	yes	characteristic
21	D₁₄₉	Q₆₄	1	1	yes	characteristic
22	C₁₄₉	#1423	1	1	yes	characteristic, complemented, Sylow
23	#1423	—	149	1	no	maximal, Sylow
24	C₂×C₃₂	—	149	1	no	—
25	#366	—	149	2	no	—
26	C₂×C₁₆	—	149	1	no	—
27	#107	—	298	2	no	—
28	C₃₂	—	149	1	no	—
29	C₃₂	#10597010	1	1	yes	characteristic, complemented
30	C₂×C₈	—	149	1	no	—
31	C₄⋊C₄	—	596	2	no	—
32	C₁₆	—	149	1	no	—
33	C₁₆	C₂×#10597010	1	1	yes	characteristic
34	C₂×C₄	—	149	1	no	—
35	C₂×C₄	—	1192	2	no	—
36	C₈	—	149	1	no	—
37	C₈	C₄⋊#10597010	1	1	yes	characteristic
38	C₂²	—	149	1	no	—
39	C₄	—	2384	2	no	—
40	C₄	—	149	1	no	—
41	C₄	#18011980	1	1	yes	characteristic
42	C₂	—	149	1	no	—
43	C₂	—	149	1	no	—
44	C₂	#23750551	1	1	yes	characteristic

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

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