Subgroups — C₂×C₇×#1290 #13185201

Order 1792.

602 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#432	C₂	1	2	yes	maximal
2	C₂²×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#1290	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇×C₈	C₄	1	2	yes	—
5	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₇×#432	—	2	2	no	—
7	C₇×#432	—	2	2	no	—
8	C₇×#432	C₄	1	4	yes	—
9	C₇×#432	C₂²	1	4	yes	—
10	C₂×C₇×C₄⋊C₈	—	2	2	no	—
11	C₂×C₇×C₄⋊C₈	—	2	2	no	—
12	C₂×C₇×C₄⋊C₈	—	2	2	no	—
13	C₂×C₇×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₇×C₂²⋊C₈	—	2	2	no	—
16	C₂×C₇×#97	C₄	1	4	yes	—
17	C₂×#1290	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
21	C₂²×C₇×C₈	—	2	4	no	—
22	C₂²×C₇×C₈	—	2	2	no	—
23	C₂²×C₇×C₈	—	2	2	no	—
24	C₂²×C₇×C₈	—	4	4	no	—
25	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₇	D₄	1	2	yes	—
31	C₂×C₄²×C₇	D₄	1	2	yes	—
32	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
33	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
34	C₇×C₄⋊C₈	—	2	4	no	—
35	C₇×C₄⋊C₈	—	2	4	no	—
36	C₇×C₄⋊C₈	—	2	4	no	—
37	C₇×C₄⋊C₈	—	2	4	no	—
38	C₇×C₂²⋊C₈	—	2	4	no	—
39	C₇×C₂²⋊C₈	—	2	4	no	—
40	C₇×#97	—	2	4	no	—
41	C₇×#97	C₂×C₄	1	8	yes	—
42	C₂×#432	C₂×C₇	1	2	yes	—
43	C₂²×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
44	#1290	C₂×C₇	1	4	yes	direct product factor
45	C₂⁴×C₇	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₇	—	2	4	no	—
47	C₂²×C₄×C₇	—	2	2	no	—
48	C₂²×C₄×C₇	—	2	2	no	—
49	C₂²×C₄×C₇	—	4	2	no	—
50	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
52	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
59	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₇×C₈	—	2	8	no	—
65	C₂×C₇×C₈	—	2	4	no	—
66	C₂×C₇×C₈	—	4	8	no	—
67	C₂×C₇×C₈	—	4	4	no	—
68	C₂×C₇×C₈	—	4	4	no	—
69	C₂×C₇×C₈	—	4	4	no	—
70	C₄²×C₇	C₄²	1	2	yes	—
71	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₇	C₄⋊C₄	1	2	yes	—
75	C₄²×C₇	C₄⋊C₄	1	2	yes	—
76	C₄²×C₇	C₂²×C₄	1	2	yes	—
77	C₄²×C₇	C₂×D₄	1	2	yes	—
78	C₂³×C₈	C₄×C₇	1	2	yes	—
79	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
80	#432	—	2	2	no	—
81	#432	—	2	2	no	—
82	#432	C₄×C₇	1	4	yes	—
83	#432	C₂²×C₇	1	4	yes	—
84	C₂×C₄⋊C₈	—	2	2	no	—
85	C₂×C₄⋊C₈	—	2	2	no	—
86	C₂×C₄⋊C₈	—	2	2	no	—
87	C₂×C₄⋊C₈	C₄×C₇	1	2	yes	—
88	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
89	C₂×C₂²⋊C₈	—	2	2	no	—
90	C₂×#97	C₄×C₇	1	4	yes	—
91	C₂³×C₇	—	2	2	no	—
92	C₂³×C₇	—	2	2	no	—
93	C₂³×C₇	#95	1	1	yes	characteristic
94	C₂³×C₇	#95	1	1	yes	characteristic
95	C₂³×C₇	#108	1	4	yes	—
96	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₇	—	2	4	no	—
98	C₂×C₄×C₇	—	2	4	no	—
99	C₂×C₄×C₇	—	2	4	no	—
100	C₂×C₄×C₇	—	2	2	no	—
101	C₂×C₄×C₇	—	2	2	no	—
102	C₂×C₄×C₇	—	2	2	no	—
103	C₂×C₄×C₇	—	2	2	no	—
104	C₂×C₄×C₇	—	2	2	no	—
105	C₂×C₄×C₇	—	2	1	no	—
106	C₂×C₄×C₇	—	2	1	no	—
107	C₂×C₄×C₇	—	2	1	no	—
108	C₂×C₄×C₇	—	2	1	no	—
109	C₂×C₄×C₇	—	4	2	no	—
110	C₂×C₄×C₇	—	4	1	no	—
111	C₂×C₄×C₇	—	4	1	no	—
112	C₂×C₄×C₇	#95	1	2	yes	—
113	C₂×C₄×C₇	#95	1	2	yes	—
114	C₂×C₄×C₇	#95	1	1	yes	characteristic
115	C₂×C₄×C₇	#95	1	1	yes	characteristic
116	C₂×C₄×C₇	#100	1	2	yes	—
117	C₂×C₄×C₇	#101	1	2	yes	—
118	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
119	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
122	C₇×C₈	—	4	8	no	—
123	C₇×C₈	—	4	4	no	—
124	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
125	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
126	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
127	C₂²×C₈	—	2	2	no	—
128	C₂²×C₈	—	2	2	no	—
129	C₂²×C₈	—	2	4	no	—
130	C₂²×C₈	—	4	4	no	—
131	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
132	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
133	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
134	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
135	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
136	C₂×C₄²	C₇×D₄	1	2	yes	—
137	C₂×C₄²	C₇×D₄	1	2	yes	—
138	C₂×C₄²	C₇×Q₈	1	1	yes	characteristic
139	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
140	C₄⋊C₈	—	2	4	no	—
141	C₄⋊C₈	—	2	4	no	—
142	C₄⋊C₈	—	2	4	no	—
143	C₄⋊C₈	—	2	4	no	—
144	C₂²⋊C₈	—	2	4	no	—
145	C₂²⋊C₈	—	2	4	no	—
146	#97	—	2	4	no	—
147	#97	C₂×C₄×C₇	1	8	yes	—
148	C₂²×C₇	—	2	8	no	—
149	C₂²×C₇	—	2	1	no	—
150	C₂²×C₇	—	2	1	no	—
151	C₂²×C₇	—	2	1	no	—
152	C₂²×C₇	—	2	1	no	—
153	C₂²×C₇	H(3,ℤ/4)	1	2	yes	—
154	C₂²×C₇	#341	1	2	yes	—
155	C₂²×C₇	#341	1	2	yes	—
156	C₂²×C₇	#343	1	2	yes	—
157	C₂²×C₇	C₂×#95	1	1	yes	characteristic
158	C₂²×C₇	C₂×#108	1	2	yes	—
159	C₄×C₇	—	2	2	no	—
160	C₄×C₇	—	2	2	no	—
161	C₄×C₇	—	2	2	no	—
162	C₄×C₇	—	2	2	no	—
163	C₄×C₇	—	2	1	no	—
164	C₄×C₇	—	2	1	no	—
165	C₄×C₇	#343	1	2	yes	—
166	C₄×C₇	C₂×#100	1	1	yes	characteristic
167	C₄×C₇	C₂×#101	1	1	yes	characteristic
168	C₂⁴	C₇×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₄	—	2	4	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
174	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
175	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
176	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
178	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
182	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
183	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
187	C₂×C₈	—	2	8	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	8	no	—
190	C₂×C₈	—	4	4	no	—
191	C₂×C₈	—	4	4	no	—
192	C₂×C₈	—	4	4	no	—
193	C₄²	C₄²×C₇	1	2	yes	—
194	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
195	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
196	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
197	C₄²	C₇×C₄⋊C₄	1	2	yes	—
198	C₄²	C₇×C₄⋊C₄	1	2	yes	—
199	C₄²	C₂²×C₄×C₇	1	2	yes	—
200	C₄²	C₂×C₇×D₄	1	2	yes	—
201	C₂×C₇	—	2	2	no	—
202	C₂×C₇	—	2	2	no	—
203	C₂×C₇	#1290	1	4	yes	direct product factor
204	C₂×C₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
205	C₂×C₇	C₂×#341	1	1	yes	characteristic
206	C₂×C₇	C₂×#343	1	1	yes	characteristic
207	C₂³	—	2	2	no	—
208	C₂³	—	2	2	no	—
209	C₂³	C₇×#95	1	1	yes	characteristic
210	C₂³	C₇×#95	1	1	yes	characteristic
211	C₂³	C₇×#108	1	4	yes	—
212	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	C₇×#95	1	2	yes	—
229	C₂×C₄	C₇×#95	1	2	yes	—
230	C₂×C₄	C₇×#95	1	1	yes	characteristic
231	C₂×C₄	C₇×#95	1	1	yes	characteristic
232	C₂×C₄	C₇×#100	1	2	yes	—
233	C₂×C₄	C₇×#101	1	2	yes	—
234	C₂×C₄	C₂×C₄²×C₇	1	1	yes	characteristic
235	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
236	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
238	C₈	—	4	8	no	—
239	C₈	—	4	4	no	—
240	C₇	C₂×#1290	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	8	no	—
246	C₂²	C₇×H(3,ℤ/4)	1	2	yes	—
247	C₂²	C₇×#341	1	2	yes	—
248	C₂²	C₇×#341	1	2	yes	—
249	C₂²	C₇×#343	1	2	yes	—
250	C₂²	C₂×C₇×#95	1	1	yes	characteristic
251	C₂²	C₂×C₇×#108	1	2	yes	—
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	C₇×#343	1	2	yes	—
259	C₄	C₂×C₇×#100	1	1	yes	characteristic
260	C₄	C₂×C₇×#101	1	1	yes	characteristic
261	C₂	—	2	2	no	—
262	C₂	—	2	2	no	—
263	C₂	C₇×#1290	1	4	yes	direct product factor
264	C₂	C₂×C₇×H(3,ℤ/4)	1	1	yes	characteristic
265	C₂	C₂×C₇×#341	1	1	yes	characteristic
266	C₂	C₂×C₇×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	#95
commutator	C₂×C₄	C₂×C₄²×C₇
Frattini, cosocle	C₂×C₄²	C₂³×C₇
prime radical	C₂⁴×C₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1290	C₂	direct (N × H)
17. C₂×#1290	C₇	direct (N × H)
44. #1290	C₂×C₇	direct (N × H)
203. C₂×C₇	#1290	direct (N × H)
240. C₇	C₂×#1290	direct (N × H)
263. C₂	C₇×#1290	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×C₇×#432	2
C₂²×C₇×C₄⋊C₈	2
C₇×#1290	2
C₂×#1290	7

Subgroups — C2×C7×#1290 #13185201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1290 #13185201