Subgroups — #34059847

Order 19072.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750558	C₂	1	1	yes	maximal, characteristic
2	#23750554	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#18011982	—	2	1	no	—
5	#18011961	—	2	1	no	—
6	Q₁₆×D₁₄₉	—	2	1	no	—
7	Dic₁₁₉₂	C₄	1	1	yes	characteristic
8	#18011857	—	2	1	no	—
9	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
10	Q₃₂×C₁₄₉	C₄	1	1	yes	characteristic
11	#14558746	—	4	1	no	—
12	Q₈×D₁₄₉	—	4	1	no	—
13	Dic₅₉₆	—	2	1	no	—
14	#14558726	—	4	1	no	—
15	C₈×D₁₄₉	D₄	1	1	yes	characteristic
16	#14558711	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₄₉	—	2	1	no	—
18	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	#11924753	—	8	1	no	—
20	Dic₂₉₈	—	4	1	no	—
21	Dic₂₉₈	—	8	1	no	—
22	C₄×D₁₄₉	—	8	1	no	—
23	C₄×D₁₄₉	D₈	1	1	yes	characteristic
24	#11924746	SD₁₆	1	1	yes	characteristic
25	Q₈×C₁₄₉	—	4	1	no	—
26	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₁₄₉	SD₃₂	1	1	yes	characteristic
28	C₄×C₁₄₉	—	8	1	no	—
29	C₄×C₁₄₉	#102	1	1	yes	characteristic
30	Dic₁₄₉	—	8	1	no	—
31	Dic₁₄₉	D₁₆	1	1	yes	characteristic
32	C₂×C₁₄₉	#357	1	1	yes	characteristic
33	D₁₄₉	—	2	1	no	—
34	C₁₄₉	#1420	1	1	yes	characteristic, complemented, Sylow
35	#1420	—	149	1	no	maximal, Sylow
36	C₂×Q₃₂	—	149	1	no	—
37	M₆₄	—	149	1	no	—
38	#368	—	149	1	no	—
39	C₂×Q₁₆	—	298	1	no	—
40	Q₃₂	—	298	1	no	—
41	Q₃₂	—	149	1	no	—
42	Q₃₂	#10597010	1	1	yes	characteristic
43	C₂×C₁₆	—	149	1	no	—
44	#108	—	298	1	no	—
45	C₃₂	—	298	1	no	—
46	C₂×Q₈	—	596	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	298	1	no	—
49	Q₁₆	—	596	1	no	—
50	M₁₆	—	596	1	no	—
51	C₂×C₈	—	149	1	no	—
52	C₁₆	—	149	1	no	—
53	C₁₆	C₂×#10597010	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	596	1	no	—
56	Q₈	—	1192	1	no	—
57	C₂×C₄	—	149	1	no	—
58	C₂×C₄	—	1192	1	no	—
59	C₈	—	149	1	no	—
60	C₈	—	1192	1	no	—
61	C₈	C₂²⋊#10597010	1	1	yes	characteristic
62	C₂²	—	149	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	149	1	no	—
65	C₄	—	1192	1	no	—
66	C₄	#18011973	1	1	yes	characteristic
67	C₂	—	298	1	no	—
68	C₂	#23750537	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750537
commutator	C₁₆×C₁₄₉	C₂×C₄
Frattini	C₁₆	C₂×#10597010
Fitting	Q₃₂×C₁₄₉	C₄
socle	C₂×C₁₄₉	#357
prime radical	C₂×D₁₄₉	SD₃₂
cosocle	C₁₆×D₁₄₉	C₂²
hypercenter	Q₃₂	#10597010
hypocenter	C₁₄₉	#1420
LCS	G ▷ C₁₆×C₁₄₉ ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
34. C₁₄₉	#1420	semidirect

Maximal subgroups

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

subgroup	index
#23750558	2
#23750554	2
Q₃₂×D₁₄₉	2
#1420	149