Subgroups — #23750477

Order 9536.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011968	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#10597010)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011886	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10597010	—	2	1	no	—
5	C₂×#11924753	—	2	1	no	—
6	C₂×D₅₉₆	—	2	1	no	—
7	C₂×D₅₉₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
9	#14558713	—	2	1	no	—
10	C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#10597010	—	2	2	no	—
12	C₂×#10597010	—	4	1	no	—
13	C₂×#10597010	—	4	1	no	—
14	#11924753	—	4	1	no	—
15	C₂²×D₁₄₉	—	2	1	no	—
16	C₂²×D₁₄₉	D₄	1	1	yes	characteristic
17	D₅₉₆	—	4	1	no	—
18	D₅₉₆	—	4	1	no	—
19	D₅₉₆	—	4	1	no	—
20	C₂×Dic₁₄₉	D₄	1	1	yes	characteristic
21	C₄×D₁₄₉	—	4	1	no	—
22	C₂×C₄×C₁₄₉	—	2	1	no	—
23	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₁₄₉	—	2	1	no	—
26	C₂×D₁₄₉	—	2	1	no	—
27	C₂×D₁₄₉	—	4	1	no	—
28	C₂×D₁₄₉	—	4	1	no	—
29	C₂×D₁₄₉	—	4	1	no	—
30	C₂×D₁₄₉	D₈	1	1	yes	characteristic
31	C₂×D₁₄₉	SD₁₆	1	1	yes	characteristic
32	#10597010	—	4	2	no	—
33	C₄×C₁₄₉	—	2	1	no	—
34	C₄×C₁₄₉	—	4	1	no	—
35	Dic₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	#99	1	1	yes	characteristic
37	C₂×C₁₄₉	#102	1	1	yes	characteristic
38	C₂×C₁₄₉	#104	1	1	yes	characteristic
39	D₁₄₉	—	2	1	no	—
40	D₁₄₉	—	2	1	no	—
41	D₁₄₉	—	8	1	no	—
42	C₁₄₉	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	149	1	no	maximal, Sylow
44	#121	—	149	1	no	—
45	C₂²⋊C₈	—	149	1	no	—
46	#95	—	149	1	no	—
47	C₂×D₄	—	298	1	no	—
48	C₂×D₄	—	149	1	no	—
49	C₂²×C₄	—	298	1	no	—
50	C₂²×C₄	—	149	1	no	—
51	C₂×C₈	—	298	1	no	—
52	C₄⋊C₄	#10597010	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	298	1	no	—
54	C₂³	—	298	1	no	—
55	C₂³	—	149	1	no	—
56	D₄	—	596	1	no	—
57	D₄	—	596	1	no	—
58	D₄	—	596	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	298	2	no	—
61	C₂×C₄	—	596	1	no	—
62	C₂×C₄	—	596	1	no	—
63	C₂×C₄	—	596	1	no	—
64	C₂×C₄	—	149	1	no	—
65	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
66	C₈	—	596	1	no	—
67	C₂²	—	298	1	no	—
68	C₂²	—	298	1	no	—
69	C₂²	—	596	1	no	—
70	C₂²	—	596	1	no	—
71	C₂²	—	596	1	no	—
72	C₂²	—	149	1	no	—
73	C₂²	—	149	1	no	—
74	C₂²	C₂²⋊#10597010	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	298	1	no	—
78	C₄	—	596	2	no	—
79	C₂	—	298	1	no	—
80	C₂	—	298	1	no	—
81	C₂	—	1192	1	no	—
82	C₂	#18011970	1	1	yes	characteristic
83	C₂	#18011973	1	1	yes	characteristic
84	C₂	#18011976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10597010
commutator	C₂×C₄×C₁₄₉	C₂×C₄
Frattini	C₂×C₄	C₂×#10597010
Fitting	C₄⋊C₄×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²⋊C₄
prime radical	#18011886	C₂
cosocle	C₂×C₄×D₁₄₉	C₂²
hypercenter	C₄⋊C₄	#10597010
hypocenter	C₁₄₉	#327
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #18011968	C₂	semidirect
2. (C₂×#10597010)⋊C₄	C₂	semidirect
7. C₂×D₅₉₆	C₄	semidirect
10. C₄⋊C₄×C₁₄₉	C₄	semidirect
42. C₁₄₉	#327	semidirect
52. C₄⋊C₄	#10597010	semidirect