Subgroups — #23749990

Order 9536.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011908	C₂	1	1	yes	maximal, characteristic
2	#18011903	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011833	C₂	1	4	yes	maximal, complemented
4	#97×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅₉₆	—	2	2	no	—
6	C₂×D₅₉₆	C₂²	1	2	yes	—
7	C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
8	#14558715	—	2	2	no	—
9	C₂×C₈×C₁₄₉	C₂²	1	2	yes	—
10	C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
11	C₂²×D₁₄₉	—	2	2	no	—
12	D₅₉₆	—	2	4	no	—
13	D₅₉₆	—	4	4	no	—
14	C₂×Dic₁₄₉	—	2	2	no	—
15	C₂×C₄×C₁₄₉	D₄	1	2	yes	—
16	C₂×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
17	C₈×C₁₄₉	—	2	2	no	—
18	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
19	C₂×D₁₄₉	—	4	2	no	—
20	C₂×D₁₄₉	—	4	4	no	—
21	C₄×C₁₄₉	—	2	2	no	—
22	C₄×C₁₄₉	#41	1	2	yes	—
23	Dic₁₄₉	—	4	2	no	—
24	C₂×C₁₄₉	#124	1	1	yes	characteristic
25	C₂×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
26	D₁₄₉	—	8	2	no	—
27	C₁₄₉	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	149	1	no	maximal, Sylow
29	#127	—	149	1	no	—
30	#125	—	149	1	no	—
31	#102	—	149	4	no	—
32	#97	D₁₄₉	1	1	yes	characteristic, complemented
33	C₂×D₄	—	298	2	no	—
34	C₂×D₄	—	149	2	no	—
35	C₂×C₈	C₂×D₁₄₉	1	2	yes	—
36	C₄⋊C₄	—	298	2	no	—
37	C₄⋊C₄	—	149	2	no	—
38	C₄²	C₂×D₁₄₉	1	1	yes	characteristic
39	C₂³	—	298	2	no	—
40	D₄	—	298	4	no	—
41	D₄	—	596	4	no	—
42	C₂×C₄	—	298	2	no	—
43	C₂×C₄	D₅₉₆	1	2	yes	—
44	C₂×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	596	4	no	—
47	C₂²	—	596	2	no	—
48	C₂²	C₂×D₅₉₆	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	596	2	no	—
51	C₄	#14558736	1	2	yes	—
52	C₂	—	1192	2	no	—
53	C₂	#18011899	1	1	yes	characteristic
54	C₂	#18011939	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₅₉₆
commutator, cosocle	C₂×C₄×C₁₄₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₄₉
Fitting	#97×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂×D₄
prime radical	#18011908	C₂
hypercenter	#97	D₁₄₉
hypocenter	C₁₄₉	#490
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #18011903	C₂	semidirect
3. #18011833	C₂	semidirect
4. #97×C₁₄₉	C₂	semidirect
27. C₁₄₉	#490	semidirect
32. #97	D₁₄₉	semidirect