Subgroups — #23749352

Order 9536.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₅₉₆	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924746	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₉₆	C₄	1	1	yes	characteristic
5	C₂×C₄×D₁₄₉	—	2	1	no	—
6	C₂×#11924746	—	2	1	no	—
7	C₄⋊Dic₁₄₉	C₄	1	1	yes	characteristic
8	#14558713	—	2	1	no	—
9	C₂×C₈×C₁₄₉	—	2	1	no	—
10	C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
11	C₂²×D₁₄₉	—	2	1	no	—
12	D₅₉₆	—	2	1	no	—
13	D₅₉₆	C₈	1	2	yes	complemented
14	C₂×Dic₁₄₉	—	2	1	no	—
15	C₄×D₁₄₉	—	4	1	no	—
16	C₄×D₁₄₉	—	4	1	no	—
17	#11924746	—	2	2	no	—
18	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
21	C₈×C₁₄₉	—	4	1	no	—
22	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₄₉	—	2	2	no	—
24	C₂×D₁₄₉	—	4	1	no	—
25	C₂×D₁₄₉	—	4	1	no	—
26	C₄×C₁₄₉	—	2	1	no	—
27	C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
29	C₄×C₁₄₉	D₈	1	1	yes	characteristic
30	C₄×C₁₄₉	SD₁₆	1	1	yes	characteristic
31	Dic₁₄₉	—	4	1	no	—
32	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₁₄₉	#102	1	1	yes	characteristic
34	C₂×C₁₄₉	#104	1	1	yes	characteristic
35	D₁₄₉	—	4	2	no	—
36	C₁₄₉	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	149	1	no	maximal, Sylow
38	C₄×D₄	—	149	1	no	—
39	C₄⋊C₈	D₁₄₉	1	1	yes	characteristic, complemented
40	C₄×C₈	—	149	1	no	—
41	C₂×D₄	—	149	1	no	—
42	C₂²×C₄	—	298	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	—	298	1	no	—
45	C₄⋊C₄	—	149	1	no	—
46	C₂²⋊C₄	—	298	1	no	—
47	C₄²	C₂×D₁₄₉	1	1	yes	characteristic
48	C₂³	—	298	1	no	—
49	D₄	—	298	1	no	—
50	D₄	—	149	2	no	—
51	C₂×C₄	—	298	1	no	—
52	C₂×C₄	—	596	1	no	—
53	C₂×C₄	—	596	1	no	—
54	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₁₄₉	1	1	yes	characteristic
56	C₂×C₄	D₅₉₆	1	1	yes	characteristic
57	C₈	—	4	1	no	—
58	C₈	—	298	2	no	—
59	C₂²	—	298	2	no	—
60	C₂²	—	596	1	no	—
61	C₂²	—	596	1	no	—
62	C₂²	#14558713	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	596	1	no	—
65	C₄	C₈×D₁₄₉	1	1	yes	characteristic
66	C₄	#14558719	1	1	yes	characteristic
67	C₄	#14558721	1	1	yes	characteristic
68	C₄	#14558723	1	1	yes	characteristic
69	C₂	—	596	2	no	—
70	C₂	#18011823	1	1	yes	characteristic
71	C₂	#18011831	1	1	yes	characteristic
72	C₂	#18011837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₄₉
commutator	C₄×C₁₄₉	C₂×C₈
Frattini	C₄²	C₂×D₁₄₉
Fitting	C₄⋊C₈×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂²⋊C₄
prime radical	C₂×D₅₉₆	C₄
cosocle	C₄²×C₁₄₉	C₂²
hypercenter	C₄⋊C₈	D₁₄₉
hypocenter	C₁₄₉	D₄⋊C₈
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄×#11924746	C₂	semidirect
3. C₄⋊C₈×C₁₄₉	C₂	semidirect
13. D₅₉₆	C₈	semidirect
36. C₁₄₉	D₄⋊C₈	semidirect
39. C₄⋊C₈	D₁₄₉	semidirect