Subgroups — C₂×C₇×#1839 #13197986

Order 1792.

1134 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×#1839	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₇×#336	C₂	1	6	yes	maximal
4	C₂³×C₇×C₈	C₂²	1	4	yes	—
5	C₂²×C₄²×C₇	C₄	1	3	yes	—
6	C₂²×C₄²×C₇	C₄	1	1	yes	characteristic
7	C₂²×C₄²×C₇	C₂²	1	3	yes	—
8	C₄³×C₇	C₄	1	4	yes	—
9	C₄³×C₇	C₂²	1	4	yes	—
10	C₇×#336	C₂²	1	24	yes	—
11	C₂×#1839	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₄×C₇	C₂×C₄	1	3	yes	—
13	C₂³×C₄×C₇	C₂×C₄	1	3	yes	—
14	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
15	C₂²×C₇×C₈	—	2	24	no	—
16	C₂²×C₇×C₈	C₂³	1	8	yes	—
17	C₂×C₄²×C₇	—	2	12	no	—
18	C₂×C₄²×C₇	—	2	12	no	—
19	C₂×C₄²×C₇	C₈	1	8	yes	complemented
20	C₂×C₄²×C₇	C₂×C₄	1	6	yes	—
21	C₂×C₄²×C₇	C₂×C₄	1	12	yes	—
22	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₇	C₂³	1	6	yes	—
24	C₂×C₄³	C₂×C₇	1	1	yes	characteristic
25	#1839	C₂×C₇	1	8	yes	direct product factor
26	C₂×#336	C₂×C₇	1	6	yes	—
27	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₇	—	2	6	no	—
29	C₂²×C₄×C₇	—	2	6	no	—
30	C₂²×C₄×C₇	—	2	6	no	—
31	C₂²×C₄×C₇	—	2	6	no	—
32	C₂²×C₄×C₇	C₂×C₈	1	12	yes	—
33	C₂²×C₄×C₇	M₁₆	1	12	yes	—
34	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
35	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
36	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₇	#41	1	12	yes	—
38	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
39	C₂×C₇×C₈	—	2	24	no	—
40	C₂×C₇×C₈	—	4	16	no	—
41	C₄²×C₇	—	2	12	no	—
42	C₄²×C₇	—	2	24	no	—
43	C₄²×C₇	—	2	12	no	—
44	C₄²×C₇	C₂×C₈	1	16	yes	complemented
45	C₂³×C₈	C₂²×C₇	1	4	yes	—
46	C₂²×C₄²	C₄×C₇	1	3	yes	—
47	C₂²×C₄²	C₄×C₇	1	1	yes	characteristic
48	C₂²×C₄²	C₂²×C₇	1	3	yes	—
49	C₄³	C₄×C₇	1	4	yes	—
50	C₄³	C₂²×C₇	1	4	yes	—
51	#336	C₂²×C₇	1	24	yes	—
52	C₂³×C₇	#117	1	6	yes	—
53	C₂³×C₇	C₂²×C₈	1	2	yes	—
54	C₂³×C₇	C₂×M₁₆	1	6	yes	—
55	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
56	C₂×C₄×C₇	—	2	6	no	—
57	C₂×C₄×C₇	—	2	6	no	—
58	C₂×C₄×C₇	—	2	6	no	—
59	C₂×C₄×C₇	—	2	6	no	—
60	C₂×C₄×C₇	—	2	24	no	—
61	C₂×C₄×C₇	—	2	24	no	—
62	C₂×C₄×C₇	#117	1	6	yes	—
63	C₂×C₄×C₇	#126	1	16	yes	—
64	C₂×C₄×C₇	C₂²×C₈	1	12	yes	—
65	C₂×C₄×C₇	C₂×M₁₆	1	12	yes	—
66	C₂×C₄×C₇	C₂×#41	1	6	yes	—
67	C₇×C₈	—	4	8	no	—
68	C₂³×C₄	C₂×C₄×C₇	1	3	yes	—
69	C₂³×C₄	C₂×C₄×C₇	1	3	yes	—
70	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
71	C₂²×C₈	—	2	24	no	—
72	C₂²×C₈	C₂³×C₇	1	8	yes	—
73	C₂×C₄²	—	2	12	no	—
74	C₂×C₄²	—	2	12	no	—
75	C₂×C₄²	C₇×C₈	1	8	yes	complemented
76	C₂×C₄²	C₂×C₄×C₇	1	6	yes	—
77	C₂×C₄²	C₂×C₄×C₇	1	12	yes	—
78	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
79	C₂×C₄²	C₂³×C₇	1	6	yes	—
80	C₂²×C₇	#383	1	4	yes	—
81	C₂²×C₇	#431	1	12	yes	—
82	C₂²×C₇	#432	1	12	yes	—
83	C₂²×C₇	C₂×#117	1	3	yes	—
84	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
85	C₂²×C₇	C₂²×M₁₆	1	3	yes	—
86	C₄×C₇	—	2	12	no	—
87	C₄×C₇	—	2	12	no	—
88	C₄×C₇	#383	1	4	yes	—
89	C₄×C₇	C₂×#126	1	4	yes	—
90	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
91	C₂²×C₄	—	2	6	no	—
92	C₂²×C₄	—	2	6	no	—
93	C₂²×C₄	—	2	6	no	—
94	C₂²×C₄	—	2	6	no	—
95	C₂²×C₄	C₂×C₇×C₈	1	12	yes	—
96	C₂²×C₄	C₇×M₁₆	1	12	yes	—
97	C₂²×C₄	C₂²×C₄×C₇	1	6	yes	—
98	C₂²×C₄	C₂²×C₄×C₇	1	6	yes	—
99	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
100	C₂²×C₄	C₇×#41	1	12	yes	—
101	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
102	C₂×C₈	—	2	24	no	—
103	C₂×C₈	—	4	16	no	—
104	C₄²	—	2	12	no	—
105	C₄²	—	2	24	no	—
106	C₄²	—	2	12	no	—
107	C₄²	C₂×C₇×C₈	1	16	yes	complemented
108	C₂×C₇	#1839	1	8	yes	direct product factor
109	C₂×C₇	C₂×#383	1	1	yes	characteristic
110	C₂×C₇	C₂×#431	1	3	yes	—
111	C₂×C₇	C₂×#432	1	3	yes	—
112	C₂³	C₇×#117	1	6	yes	—
113	C₂³	C₂²×C₇×C₈	1	2	yes	—
114	C₂³	C₂×C₇×M₁₆	1	6	yes	—
115	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
116	C₂×C₄	—	2	6	no	—
117	C₂×C₄	—	2	6	no	—
118	C₂×C₄	—	2	6	no	—
119	C₂×C₄	—	2	6	no	—
120	C₂×C₄	—	2	24	no	—
121	C₂×C₄	—	2	24	no	—
122	C₂×C₄	C₇×#117	1	6	yes	—
123	C₂×C₄	C₇×#126	1	16	yes	—
124	C₂×C₄	C₂²×C₇×C₈	1	12	yes	—
125	C₂×C₄	C₂×C₇×M₁₆	1	12	yes	—
126	C₂×C₄	C₂×C₇×#41	1	6	yes	—
127	C₈	—	4	8	no	—
128	C₇	C₂×#1839	1	1	yes	characteristic, direct product factor, Sylow
129	C₂²	C₇×#383	1	4	yes	—
130	C₂²	C₇×#431	1	12	yes	—
131	C₂²	C₇×#432	1	12	yes	—
132	C₂²	C₂×C₇×#117	1	3	yes	—
133	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
134	C₂²	C₂²×C₇×M₁₆	1	3	yes	—
135	C₄	—	2	12	no	—
136	C₄	—	2	12	no	—
137	C₄	C₇×#383	1	4	yes	—
138	C₄	C₂×C₇×#126	1	4	yes	—
139	C₂	C₇×#1839	1	8	yes	direct product factor
140	C₂	C₂×C₇×#383	1	1	yes	characteristic
141	C₂	C₂×C₇×#431	1	3	yes	—
142	C₂	C₂×C₇×#432	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄×C₇	C₂³
commutator	C₂²	C₂³×C₇×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle, prime radical	C₂⁴×C₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#1839	C₂	direct (N × H)
11. C₂×#1839	C₇	direct (N × H)
19. C₂×C₄²×C₇	C₈	semidirect
25. #1839	C₂×C₇	direct (N × H)
44. C₄²×C₇	C₂×C₈	semidirect
75. C₂×C₄²	C₇×C₈	semidirect
107. C₄²	C₂×C₇×C₈	semidirect
108. C₂×C₇	#1839	direct (N × H)
128. C₇	C₂×#1839	direct (N × H)
139. C₂	C₇×#1839	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄³×C₇	2
C₇×#1839	2
C₂×C₇×#336	2
C₂×#1839	7

Subgroups — C2×C7×#1839 #13197986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1839 #13197986