Subgroups — C₂×#341×C₁₄₉ #34040650

Order 19072.

392 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆×C₁₄₉	C₂	1	2	yes	maximal
2	C₂³×C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#341×C₁₄₉	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₁₄₉	—	2	4	no	—
6	C₂×M₁₆×C₁₄₉	—	2	2	no	—
7	C₂×M₁₆×C₁₄₉	C₄	1	8	yes	—
8	C₂×M₁₆×C₁₄₉	C₂²	1	4	yes	—
9	C₂²×C₈×C₁₄₉	—	2	4	no	—
10	C₂²×C₈×C₁₄₉	—	2	2	no	—
11	C₂²×C₈×C₁₄₉	C₄	1	2	yes	—
12	C₂²×C₈×C₁₄₉	C₄	1	2	yes	—
13	C₂²×C₈×C₁₄₉	C₂²	1	2	yes	—
14	C₂⁴×C₁₄₉	Q₈	1	1	yes	characteristic
15	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₄₉	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₁₄₉	D₄	1	4	yes	—
19	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₄₉	Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₁₄₉	—	2	8	no	—
24	M₁₆×C₁₄₉	—	2	4	no	—
25	M₁₆×C₁₄₉	C₂×C₄	1	8	yes	—
26	C₂×C₈×C₁₄₉	—	2	4	no	—
27	C₂×C₈×C₁₄₉	—	2	4	no	—
28	C₂×C₈×C₁₄₉	—	2	8	no	—
29	C₂×C₈×C₁₄₉	—	2	4	no	—
30	C₂×C₈×C₁₄₉	—	2	4	no	—
31	C₂×C₈×C₁₄₉	C₂×C₄	1	4	yes	—
32	C₂³×C₁₄₉	—	2	4	no	—
33	C₂³×C₁₄₉	C₄⋊C₄	1	4	yes	—
34	C₂³×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂³×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂³×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₄₉	C₄²	1	2	yes	—
38	C₂×C₄×C₁₄₉	C₄²	1	2	yes	—
39	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
42	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
43	C₂×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
44	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
50	C₈×C₁₄₉	—	2	4	no	—
51	C₈×C₁₄₉	—	2	8	no	—
52	C₂²×C₁₄₉	—	2	8	no	—
53	C₂²×C₁₄₉	—	2	2	no	—
54	C₂²×C₁₄₉	—	2	2	no	—
55	C₂²×C₁₄₉	#95	1	2	yes	—
56	C₂²×C₁₄₉	#95	1	2	yes	—
57	C₂²×C₁₄₉	#108	1	4	yes	—
58	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	2	yes	—
59	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₁₄₉	#95	1	2	yes	—
61	C₄×C₁₄₉	#95	1	2	yes	—
62	C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
63	C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
65	C₂×C₁₄₉	—	2	2	no	—
66	C₂×C₁₄₉	—	2	2	no	—
67	C₂×C₁₄₉	#341	1	4	yes	direct product factor
68	C₂×C₁₄₉	C₂×#95	1	1	yes	characteristic
69	C₂×C₁₄₉	C₂×#108	1	2	yes	—
70	C₁₄₉	C₂×#341	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×#341	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂²×M₁₆	C₂×C₁₄₉	1	2	yes	—
73	C₂³×C₈	C₂×C₁₄₉	1	1	yes	characteristic
74	#341	C₂×C₁₄₉	1	4	yes	direct product factor
75	C₂³×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
76	C₂×M₁₆	—	2	4	no	—
77	C₂×M₁₆	—	2	2	no	—
78	C₂×M₁₆	C₄×C₁₄₉	1	8	yes	—
79	C₂×M₁₆	C₂²×C₁₄₉	1	4	yes	—
80	C₂²×C₈	—	2	4	no	—
81	C₂²×C₈	—	2	2	no	—
82	C₂²×C₈	C₄×C₁₄₉	1	2	yes	—
83	C₂²×C₈	C₄×C₁₄₉	1	2	yes	—
84	C₂²×C₈	C₂²×C₁₄₉	1	2	yes	—
85	C₂⁴	Q₈×C₁₄₉	1	1	yes	characteristic
86	C₂²×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
87	C₂²×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
88	C₂²×C₄	C₂×C₄×C₁₄₉	1	4	yes	—
89	C₂²×C₄	D₄×C₁₄₉	1	1	yes	characteristic
90	C₂²×C₄	D₄×C₁₄₉	1	4	yes	—
91	C₂²×C₄	D₄×C₁₄₉	1	1	yes	characteristic
92	C₂²×C₄	Q₈×C₁₄₉	1	1	yes	characteristic
93	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
94	M₁₆	—	2	8	no	—
95	M₁₆	—	2	4	no	—
96	M₁₆	C₂×C₄×C₁₄₉	1	8	yes	—
97	C₂×C₈	—	2	4	no	—
98	C₂×C₈	—	2	4	no	—
99	C₂×C₈	—	2	8	no	—
100	C₂×C₈	—	2	4	no	—
101	C₂×C₈	—	2	4	no	—
102	C₂×C₈	C₂×C₄×C₁₄₉	1	4	yes	—
103	C₂³	—	2	4	no	—
104	C₂³	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
105	C₂³	C₄⋊C₄×C₁₄₉	1	4	yes	—
106	C₂³	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
107	C₂³	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
108	C₂×C₄	C₄²×C₁₄₉	1	2	yes	—
109	C₂×C₄	C₄²×C₁₄₉	1	2	yes	—
110	C₂×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
111	C₂×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
112	C₂×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
113	C₂×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
114	C₂×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
115	C₂×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
116	C₂×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
117	C₂×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
118	C₂×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
119	C₂×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
120	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
121	C₈	—	2	4	no	—
122	C₈	—	2	8	no	—
123	C₂²	—	2	2	no	—
124	C₂²	—	2	2	no	—
125	C₂²	—	2	8	no	—
126	C₂²	#95×C₁₄₉	1	2	yes	—
127	C₂²	#95×C₁₄₉	1	2	yes	—
128	C₂²	#108×C₁₄₉	1	4	yes	—
129	C₂²	C₂×C₄⋊C₄×C₁₄₉	1	2	yes	—
130	C₂²	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
131	C₄	#95×C₁₄₉	1	2	yes	—
132	C₄	#95×C₁₄₉	1	2	yes	—
133	C₄	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
134	C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
135	C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
136	C₂	—	2	2	no	—
137	C₂	—	2	2	no	—
138	C₂	#341×C₁₄₉	1	4	yes	direct product factor
139	C₂	C₂×#95×C₁₄₉	1	1	yes	characteristic
140	C₂	C₂×#108×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	D₄
commutator	C₄	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₄⋊C₄
prime radical	C₂⁴×C₁₄₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂³×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #341×C₁₄₉	C₂	direct (N × H)
67. C₂×C₁₄₉	#341	direct (N × H)
70. C₁₄₉	C₂×#341	direct (N × H)
71. C₂×#341	C₁₄₉	direct (N × H)
74. #341	C₂×C₁₄₉	direct (N × H)
138. C₂	#341×C₁₄₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×M₁₆×C₁₄₉	2
C₂³×C₈×C₁₄₉	2
#341×C₁₄₉	2
C₂×#341	149

Subgroups — C2×#341×C149 #34040650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#341×C₁₄₉ #34040650