Subgroups — #34042793

Order 19072.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23749663	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#18011870	—	2	2	no	—
4	#18011845	—	2	2	no	—
5	#18011843	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
7	M₃₂×C₁₄₉	—	2	2	no	—
8	C₂×C₁₆×C₁₄₉	C₄	1	2	yes	complemented
9	C₄⋊Dic₁₄₉	—	2	4	no	—
10	C₂²⋊Dic₁₄₉	—	4	2	no	—
11	C₄×Dic₁₄₉	—	4	2	no	—
12	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₄₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₄₉	D₄	1	2	yes	—
16	C₂×C₈×C₁₄₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₄₉	—	2	2	no	—
18	C₂×Dic₁₄₉	—	4	4	no	—
19	C₂³×C₁₄₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₄₉	SD₁₆	1	2	yes	—
23	C₂×C₄×C₁₄₉	Q₁₆	1	1	yes	characteristic
24	C₈×C₁₄₉	C₄²	1	1	yes	characteristic
25	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₄₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₁₄₉	—	4	1	no	—
28	C₂²×C₁₄₉	#102	1	2	yes	—
29	C₂²×C₁₄₉	#107	1	1	yes	characteristic
30	C₄×C₁₄₉	#95	1	1	yes	characteristic
31	C₄×C₁₄₉	#103	1	2	yes	—
32	C₄×C₁₄₉	#106	1	1	yes	characteristic
33	Dic₁₄₉	—	8	4	no	—
34	C₂×C₁₄₉	—	2	2	no	—
35	C₂×C₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	#340	1	1	yes	characteristic
37	C₁₄₉	#1384	1	1	yes	characteristic, complemented, Sylow
38	#1384	—	149	1	no	maximal, Sylow
39	C₂×M₃₂	D₁₄₉	1	1	yes	characteristic
40	#427	—	149	2	no	—
41	C₂²×C₈	C₂×D₁₄₉	1	1	yes	characteristic
42	#117	—	298	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₁₄₉	1	2	yes	complemented
45	#107	—	298	2	no	—
46	#106	—	149	4	no	—
47	C₂²×C₄	D₅₉₆	1	1	yes	characteristic
48	C₂×C₈	C₄×D₁₄₉	1	2	yes	—
49	C₂×C₈	C₂×Dic₁₄₉	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₁₄₉	1	2	yes	—
51	C₂×C₈	Dic₂₉₈	1	1	yes	characteristic
52	C₄⋊C₄	—	298	4	no	—
53	C₂²⋊C₄	—	596	2	no	—
54	C₄²	—	596	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₁₁₉₂	1	1	yes	characteristic
57	C₂×C₄	—	596	4	no	—
58	C₂×C₄	#14558713	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₁₄₉	1	1	yes	characteristic
60	C₂×C₄	#14558725	1	2	yes	—
61	C₂×C₄	Dic₅₉₆	1	1	yes	characteristic
62	C₈	C₄×Dic₁₄₉	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₁₄₉	1	1	yes	characteristic
64	C₈	#14558715	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#18011833	1	2	yes	—
67	C₂²	#18011845	1	1	yes	characteristic
68	C₄	—	1192	4	no	—
69	C₄	#18011818	1	1	yes	characteristic
70	C₄	#18011836	1	2	yes	—
71	C₄	#18011843	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#23749388	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#18011843
commutator	C₈×C₁₄₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₄₉
Fitting	C₂×M₃₂×C₁₄₉	C₂
socle	C₂×C₁₄₉	#340
prime radical	C₂³×C₁₄₉	D₈
cosocle	C₂²×C₈×C₁₄₉	C₂²
hypercenter	C₂×M₃₂	D₁₄₉
hypocenter	C₁₄₉	#1384
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #18011843	C₄	semidirect
8. C₂×C₁₆×C₁₄₉	C₄	semidirect
37. C₁₄₉	#1384	semidirect
44. C₂×C₁₆	Dic₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23749663	2
C₂×M₃₂×C₁₄₉	2
#1384	149