Subgroups — D₁₄₉⋊#101 #23750610

Order 9536.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₉⋊M₁₆	C₂	1	2	yes	maximal
2	#18011972	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#14558746	—	2	2	no	—
5	#14558745	C₂²	1	4	yes	—
6	D₁₄₉⋊C₈	—	2	2	no	—
7	C₂×Dic₂₉₈	C₄	1	1	yes	characteristic
8	C₂×Dic₂₉₈	C₂²	1	2	yes	—
9	Q₈×D₁₄₉	—	2	2	no	—
10	Q₈×D₁₄₉	—	2	2	no	—
11	C₂×C₄×D₁₄₉	C₄	1	2	yes	—
12	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
14	#11924753	—	2	4	no	—
15	C₂²×D₁₄₉	C₂×C₄	1	1	yes	characteristic
16	Dic₂₉₈	—	2	2	no	—
17	Dic₂₉₈	—	2	4	no	—
18	C₂×Dic₁₄₉	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
20	C₄×D₁₄₉	—	2	2	no	—
21	C₄×D₁₄₉	—	2	2	no	—
22	C₄×D₁₄₉	D₄	1	2	yes	—
23	C₄×D₁₄₉	D₄	1	2	yes	—
24	Q₈×C₁₄₉	—	2	2	no	—
25	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₁₄₉	—	2	2	no	—
29	C₂×D₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₁₄₉	—	2	2	no	—
32	C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
33	Dic₁₄₉	—	2	2	no	—
34	Dic₁₄₉	C₂×D₄	1	2	yes	—
35	C₂×C₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₁₄₉	—	2	1	no	—
38	D₁₄₉	#101	1	2	yes	complemented
39	C₁₄₉	C₂×#101	1	1	yes	characteristic, complemented, Sylow
40	C₂×#101	—	149	1	no	maximal, Sylow
41	C₂²×Q₈	—	149	1	no	—
42	C₂×M₁₆	—	149	2	no	—
43	#101	—	149	4	no	—
44	C₂×Q₈	—	298	2	no	—
45	C₂×Q₈	—	298	2	no	—
46	C₂×Q₈	—	149	2	no	—
47	C₂×Q₈	—	149	1	no	—
48	C₂×Q₈	#10597010	1	1	yes	characteristic
49	C₂²×C₄	—	149	2	no	—
50	C₂²×C₄	—	149	1	no	—
51	M₁₆	—	298	2	no	—
52	M₁₆	—	149	4	no	—
53	C₂×C₈	—	298	2	no	—
54	C₂³	—	149	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	298	4	no	—
57	Q₈	—	298	2	no	—
58	C₂×C₄	—	298	2	no	—
59	C₂×C₄	—	298	2	no	—
60	C₂×C₄	—	149	2	no	—
61	C₂×C₄	—	149	1	no	—
62	C₂×C₄	—	149	2	no	—
63	C₂×C₄	—	149	2	no	—
64	C₂×C₄	C₂×#10597010	1	2	yes	—
65	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
66	C₈	—	298	4	no	—
67	C₂²	—	298	2	no	—
68	C₂²	—	149	1	no	—
69	C₂²	—	149	1	no	—
70	C₂²	C₂²×#10597010	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	298	2	no	—
73	C₄	—	149	2	no	—
74	C₄	C₂²⋊#10597010	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	298	1	no	—
77	C₂	—	149	2	no	—
78	C₂	C₂×C₂²⋊#10597010	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#10597010
commutator	C₂²×C₁₄₉	C₂²×C₄
Frattini	C₂²	C₂²×#10597010
Fitting	C₂×Q₈×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₄₉	C₂×C₄
cosocle	C₂×Dic₁₄₉	C₂³
hypercenter	C₂×Q₈	#10597010
hypocenter	C₁₄₉	C₂×#101
LCS	G ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #18011972	C₂	semidirect
38. D₁₄₉	#101	semidirect
39. C₁₄₉	C₂×#101	semidirect

Subgroups — D149⋊#101 #23750610

Conjugacy classes of subgroups

Complements

Subgroups — D₁₄₉⋊#101 #23750610