Subgroups — #34059844

Order 19072.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750558	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750552	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750054	C₂	1	1	yes	maximal, characteristic
4	#18011980	—	2	1	no	—
5	#18011961	—	2	1	no	—
6	#18011930	—	2	1	no	—
7	Dic₁₁₉₂	C₄	1	1	yes	characteristic, complemented
8	#18011855	—	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	#14558735	—	4	1	no	—
13	Dic₅₉₆	—	2	1	no	—
14	#14558724	—	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	Dic₂₉₈	—	4	1	no	—
21	C₂²⋊D₁₄₉	—	8	1	no	—
22	C₂×Dic₁₄₉	—	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	D₁₆	1	1	yes	characteristic
29	#10597010	—	16	1	no	—
30	C₄×C₁₄₉	#102	1	1	yes	characteristic
31	Dic₁₄₉	—	8	1	no	—
32	Dic₁₄₉	SD₃₂	1	1	yes	characteristic
33	C₂×C₁₄₉	—	16	1	no	—
34	C₂×C₁₄₉	#357	1	1	yes	characteristic
35	D₁₄₉	—	2	1	no	—
36	C₁₄₉	#1418	1	1	yes	characteristic, complemented, Sylow
37	#1418	—	149	1	no	maximal, Sylow
38	#508	—	149	1	no	—
39	M₆₄	—	149	1	no	—
40	#367	—	149	1	no	—
41	#135	—	298	1	no	—
42	Q₃₂	—	149	1	no	—
43	SD₃₂	—	298	1	no	—
44	D₁₆	#10597010	1	1	yes	characteristic, complemented
45	C₂×C₁₆	—	149	1	no	—
46	#107	—	298	1	no	—
47	C₃₂	—	298	1	no	—
48	#41	—	596	1	no	—
49	Q₁₆	—	298	1	no	—
50	SD₁₆	—	596	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	—	149	1	no	—
53	C₄⋊C₄	—	596	1	no	—
54	C₁₆	—	149	1	no	—
55	C₁₆	C₂×#10597010	1	1	yes	characteristic
56	Q₈	—	596	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	1192	1	no	—
59	C₂×C₄	—	149	1	no	—
60	C₂×C₄	—	1192	1	no	—
61	C₂×C₄	—	1192	1	no	—
62	C₈	—	149	1	no	—
63	C₈	C₂²⋊#10597010	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	—	149	1	no	—
66	C₄	—	2384	1	no	—
67	C₄	—	149	1	no	—
68	C₄	—	1192	1	no	—
69	C₄	#18011973	1	1	yes	characteristic
70	C₂	—	16	1	no	—
71	C₂	—	298	1	no	—
72	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	#23750054	C₂
cosocle	C₁₆×D₁₄₉	C₂²
hypercenter	D₁₆	#10597010
hypocenter	C₁₄₉	#1418
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. #23750558	C₂	semidirect
2. #23750552	C₂	semidirect
7. Dic₁₁₉₂	C₄	semidirect
10. D₁₆×C₁₄₉	C₄	semidirect
36. C₁₄₉	#1418	semidirect
44. D₁₆	#10597010	semidirect

Maximal subgroups

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

subgroup	index
#23750558	2
#23750552	2
#23750054	2
#1418	149