Subgroups — #23749665

Order 9536.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558720	C₂	1	1	yes	maximal, characteristic
2	#18011870	C₂	1	1	yes	maximal, characteristic
3	#18011844	C₂	1	2	yes	maximal, complemented
4	#18011842	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
6	#14558720	C₄	1	4	yes	complemented
7	C₂×#11924746	C₂²	1	2	yes	—
8	C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₁₄₉	—	2	1	no	—
11	C₄×Dic₁₄₉	—	2	1	no	—
12	C₂²×C₄×C₁₄₉	—	2	1	no	—
13	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₄₉	—	2	1	no	—
15	C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
16	C₂×Dic₁₄₉	—	2	1	no	—
17	C₂×Dic₁₄₉	—	2	1	no	—
18	#11924746	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₄₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₄₉	—	2	2	no	—
21	C₂×C₄×C₁₄₉	—	4	2	no	—
22	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₄₉	Q₈	1	2	yes	—
25	C₂×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₄₉	—	2	1	no	—
27	C₂²×C₁₄₉	—	2	1	no	—
28	C₂²×C₁₄₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₄₉	—	4	2	no	—
31	C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
32	C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₄₉	—	4	1	no	—
35	Dic₁₄₉	—	4	1	no	—
36	C₂×C₁₄₉	—	2	2	no	—
37	C₂×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₄₉	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₁₄₉	#137	1	1	yes	characteristic
40	C₁₄₉	#428	1	1	yes	characteristic, complemented, Sylow
41	#428	—	149	1	no	maximal, Sylow
42	C₂×M₁₆	—	149	1	no	—
43	#117	—	149	1	no	—
44	C₂×C₄⋊C₄	D₁₄₉	1	1	yes	characteristic
45	#107	—	149	2	no	—
46	#106	—	149	2	no	—
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
49	M₁₆	—	149	4	no	—
50	C₂×C₈	—	149	2	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	149	1	no	—
53	C₄⋊C₄	—	149	1	no	—
54	C₄⋊C₄	C₂×D₁₄₉	1	2	yes	—
55	C₂²⋊C₄	—	298	1	no	—
56	C₄²	—	298	1	no	—
57	C₂³	C₂²⋊D₁₄₉	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	298	1	no	—
61	C₂×C₄	—	298	1	no	—
62	C₂×C₄	C₄×D₁₄₉	1	2	yes	—
63	C₂×C₄	C₂²⋊D₁₄₉	1	1	yes	characteristic
64	C₂×C₄	Dic₂₉₈	1	2	yes	—
65	C₂×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
66	C₈	—	149	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	#14558715	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₄₉	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	596	1	no	—
73	C₄	—	596	1	no	—
74	C₄	#14558715	1	2	yes	—
75	C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
76	C₄	C₂×Dic₂₉₈	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×#14558715	1	1	yes	characteristic
79	C₂	#18011937	1	1	yes	characteristic
80	C₂	#18011942	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₄₉
commutator	C₄×C₁₄₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₄₉
Fitting	C₂×C₄⋊C₄×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂×D₄
prime radical	C₂³×C₁₄₉	D₄
cosocle	C₂×C₄×C₁₄₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₁₄₉
hypocenter	C₁₄₉	#428
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #18011844	C₂	semidirect
4. #18011842	C₂	semidirect
6. #14558720	C₄	semidirect
18. #11924746	C₂×C₄	semidirect
40. C₁₄₉	#428	semidirect