Subgroups — C₂×C₇×#2859 #13213844

Order 1792.

2558 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#125	C₂	1	2	yes	maximal
2	C₇×#2859	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#389	C₂	1	8	yes	maximal
4	C₂×C₇×#384	C₂	1	2	yes	maximal
5	C₂×C₇×#382	C₂	1	2	yes	maximal
6	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic
7	C₂×C₇×#125	—	2	16	no	—
8	C₂×C₇×#125	C₂²	1	16	yes	—
9	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	—
11	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	—
12	C₂²×C₄²×C₇	C₂²	1	4	yes	—
13	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₇×#389	C₂²	1	64	yes	—
17	C₇×#384	C₂²	1	16	yes	—
18	C₇×#382	C₂²	1	16	yes	—
19	C₂×C₇×#95	C₂²	1	8	yes	—
20	C₄³×C₇	C₂²	1	8	yes	—
21	C₂×#2859	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₄×C₇	C₂³	1	8	yes	—
23	C₂³×C₄×C₇	C₂³	1	2	yes	—
24	C₂³×C₄×C₇	C₂³	1	2	yes	—
25	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₇	C₂³	1	2	yes	—
27	C₇×#125	—	2	64	no	—
28	C₂×C₇×C₄⋊C₄	—	2	32	no	—
29	C₂×C₇×C₄⋊C₄	—	2	16	no	—
30	C₂×C₇×C₄⋊C₄	—	2	32	no	—
31	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
32	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	—
33	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	—
34	C₂×C₄²×C₇	—	2	16	no	—
35	C₂×C₄²×C₇	D₄	1	8	yes	—
36	C₂×C₄²×C₇	Q₈	1	8	yes	—
37	C₂×C₄²×C₇	Q₈	1	8	yes	—
38	C₂×C₄²×C₇	C₂³	1	16	yes	—
39	C₂×C₄²×C₇	C₂³	1	4	yes	—
40	C₂×C₄²×C₇	C₂³	1	4	yes	—
41	C₂×C₄²×C₇	C₂³	1	4	yes	—
42	C₇×#95	C₂³	1	32	yes	—
43	C₂²×#125	C₂×C₇	1	2	yes	—
44	#2859	C₂×C₇	1	16	yes	direct product factor
45	C₂×#389	C₂×C₇	1	8	yes	—
46	C₂×#384	C₂×C₇	1	2	yes	—
47	C₂×#382	C₂×C₇	1	2	yes	—
48	C₂×C₄³	C₂×C₇	1	1	yes	characteristic
49	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
50	C₂²×C₄×C₇	—	2	8	no	—
51	C₂²×C₄×C₇	—	2	8	no	—
52	C₂²×C₄×C₇	—	2	16	no	—
53	C₂²×C₄×C₇	—	2	32	no	—
54	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
55	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
56	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
57	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
58	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
59	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
60	C₂²×C₄×C₇	#41	1	16	yes	—
61	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
62	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
63	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
64	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
65	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
66	C₇×C₄⋊C₄	—	2	64	no	—
67	C₇×C₄⋊C₄	—	2	32	no	—
68	C₇×C₄⋊C₄	—	2	64	no	—
69	C₄²×C₇	—	2	32	no	—
70	C₄²×C₇	C₂×D₄	1	16	yes	—
71	C₄²×C₇	C₂×Q₈	1	16	yes	—
72	C₄²×C₇	C₂×Q₈	1	16	yes	—
73	C₂×#125	—	2	16	no	—
74	C₂×#125	C₂²×C₇	1	16	yes	—
75	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
76	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	—
77	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	—
78	C₂²×C₄²	C₂²×C₇	1	4	yes	—
79	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
80	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
81	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
82	#389	C₂²×C₇	1	64	yes	—
83	#384	C₂²×C₇	1	16	yes	—
84	#382	C₂²×C₇	1	16	yes	—
85	C₂×#95	C₂²×C₇	1	8	yes	—
86	C₄³	C₂²×C₇	1	8	yes	—
87	C₂³×C₇	C₂²×D₄	1	2	yes	—
88	C₂³×C₇	C₂²×Q₈	1	2	yes	—
89	C₂³×C₇	C₂²×Q₈	1	2	yes	—
90	C₂³×C₇	C₂×#41	1	8	yes	—
91	C₂³×C₇	C₂⁵	1	1	yes	characteristic
92	C₂×C₄×C₇	—	2	16	no	—
93	C₂×C₄×C₇	—	2	16	no	—
94	C₂×C₄×C₇	—	2	8	no	—
95	C₂×C₄×C₇	—	2	8	no	—
96	C₂×C₄×C₇	—	2	16	no	—
97	C₂×C₄×C₇	—	2	32	no	—
98	C₂×C₄×C₇	—	4	32	no	—
99	C₂×C₄×C₇	#125	1	32	yes	complemented
100	C₂×C₄×C₇	C₄⋊Q₈	1	16	yes	—
101	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
102	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
103	C₂×C₄×C₇	C₂²×Q₈	1	8	yes	—
104	C₂×C₄×C₇	C₂²×Q₈	1	8	yes	—
105	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
106	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
107	C₂×C₄×C₇	C₂×#41	1	16	yes	—
108	C₂³×C₄	C₂³×C₇	1	8	yes	—
109	C₂³×C₄	C₂³×C₇	1	2	yes	—
110	C₂³×C₄	C₂³×C₇	1	2	yes	—
111	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
112	C₂³×C₄	C₂³×C₇	1	2	yes	—
113	#125	—	2	64	no	—
114	C₂×C₄⋊C₄	—	2	32	no	—
115	C₂×C₄⋊C₄	—	2	16	no	—
116	C₂×C₄⋊C₄	—	2	32	no	—
117	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
118	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	—
119	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	—
120	C₂×C₄²	—	2	16	no	—
121	C₂×C₄²	C₇×D₄	1	8	yes	—
122	C₂×C₄²	C₇×Q₈	1	8	yes	—
123	C₂×C₄²	C₇×Q₈	1	8	yes	—
124	C₂×C₄²	C₂³×C₇	1	16	yes	—
125	C₂×C₄²	C₂³×C₇	1	4	yes	—
126	C₂×C₄²	C₂³×C₇	1	4	yes	—
127	C₂×C₄²	C₂³×C₇	1	4	yes	—
128	#95	C₂³×C₇	1	32	yes	—
129	C₂²×C₇	C₂×#125	1	8	yes	—
130	C₂²×C₇	C₂×C₄⋊Q₈	1	4	yes	—
131	C₂²×C₇	#532	1	8	yes	—
132	C₂²×C₇	#533	1	8	yes	—
133	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
134	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
135	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
136	C₂²×C₇	C₂²×#41	1	4	yes	—
137	C₄×C₇	—	2	8	no	—
138	C₄×C₇	—	2	8	no	—
139	C₄×C₇	—	4	16	no	—
140	C₄×C₇	C₂×#125	1	16	yes	complemented
141	C₄×C₇	C₂×C₄⋊Q₈	1	8	yes	—
142	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
143	C₂²×C₄	—	2	8	no	—
144	C₂²×C₄	—	2	8	no	—
145	C₂²×C₄	—	2	16	no	—
146	C₂²×C₄	—	2	32	no	—
147	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
148	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
149	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
150	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
151	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
152	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
153	C₂²×C₄	C₇×#41	1	16	yes	—
154	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
155	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
156	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
157	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
158	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
159	C₄⋊C₄	—	2	64	no	—
160	C₄⋊C₄	—	2	32	no	—
161	C₄⋊C₄	—	2	64	no	—
162	C₄²	—	2	32	no	—
163	C₄²	C₂×C₇×D₄	1	16	yes	—
164	C₄²	C₂×C₇×Q₈	1	16	yes	—
165	C₄²	C₂×C₇×Q₈	1	16	yes	—
166	C₂×C₇	#2859	1	8	yes	direct product factor
167	C₂×C₇	C₂²×#125	1	2	yes	—
168	C₂×C₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
169	C₂×C₇	C₂×#532	1	2	yes	—
170	C₂×C₇	C₂×#533	1	2	yes	—
171	C₂³	C₂²×C₇×D₄	1	2	yes	—
172	C₂³	C₂²×C₇×Q₈	1	2	yes	—
173	C₂³	C₂²×C₇×Q₈	1	2	yes	—
174	C₂³	C₂×C₇×#41	1	8	yes	—
175	C₂³	C₂⁵×C₇	1	1	yes	characteristic
176	C₂×C₄	—	2	8	no	—
177	C₂×C₄	—	2	8	no	—
178	C₂×C₄	—	2	16	no	—
179	C₂×C₄	—	2	16	no	—
180	C₂×C₄	—	2	16	no	—
181	C₂×C₄	—	2	32	no	—
182	C₂×C₄	—	4	32	no	—
183	C₂×C₄	C₇×#125	1	32	yes	complemented
184	C₂×C₄	C₇×C₄⋊Q₈	1	16	yes	—
185	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
186	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
187	C₂×C₄	C₂²×C₇×Q₈	1	8	yes	—
188	C₂×C₄	C₂²×C₇×Q₈	1	8	yes	—
189	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
190	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
191	C₂×C₄	C₂×C₇×#41	1	16	yes	—
192	C₇	C₂×#2859	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²	C₂×C₇×#125	1	8	yes	—
194	C₂²	C₂×C₇×C₄⋊Q₈	1	4	yes	—
195	C₂²	C₇×#532	1	8	yes	—
196	C₂²	C₇×#533	1	8	yes	—
197	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
198	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
199	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
200	C₂²	C₂²×C₇×#41	1	4	yes	—
201	C₄	—	2	8	no	—
202	C₄	—	2	8	no	—
203	C₄	—	4	16	no	—
204	C₄	C₂×C₇×#125	1	16	yes	complemented
205	C₄	C₂×C₇×C₄⋊Q₈	1	8	yes	—
206	C₂	C₇×#2859	1	8	yes	direct product factor
207	C₂	C₂²×C₇×#125	1	2	yes	—
208	C₂	C₂²×C₇×C₄⋊Q₈	1	1	yes	characteristic
209	C₂	C₂×C₇×#532	1	2	yes	—
210	C₂	C₂×C₇×#533	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2859	C₂	direct (N × H)
21. C₂×#2859	C₇	direct (N × H)
44. #2859	C₂×C₇	direct (N × H)
99. C₂×C₄×C₇	#125	semidirect
140. C₄×C₇	C₂×#125	semidirect
166. C₂×C₇	#2859	direct (N × H)
183. C₂×C₄	C₇×#125	semidirect
192. C₇	C₂×#2859	direct (N × H)
204. C₄	C₂×C₇×#125	semidirect
206. C₂	C₇×#2859	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×C₇×#125	2
C₇×#2859	2
C₂×C₇×#389	2
C₂×C₇×#384	2
C₂×C₇×#382	2
C₂×C₄³×C₇	2
C₂×#2859	7

Subgroups — C2×C7×#2859 #13213844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2859 #13213844