Subgroups — C₂×C₇×#2494 #13212001

Order 1792.

2182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2494	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₇×#401	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#397	C₂	1	2	yes	maximal
4	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#388	C₂	1	2	yes	maximal
7	C₂×C₇×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
14	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇	C₂²	1	2	yes	—
27	C₇×#401	C₂²	1	16	yes	complemented
28	C₇×#397	C₂²	1	16	yes	—
29	C₇×#389	C₂²	1	8	yes	complemented
30	C₇×#389	C₂²	1	8	yes	complemented
31	C₇×#388	C₂²	1	16	yes	—
32	C₇×#387	C₂²	1	16	yes	complemented
33	C₇×#382	C₂²	1	8	yes	complemented
34	C₇×#380	C₂²	1	8	yes	—
35	C₇×#380	C₂²	1	8	yes	—
36	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
37	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
38	C₂×C₇×#95	C₂²	1	2	yes	—
39	C₂×C₇×#95	C₂²	1	2	yes	—
40	C₂×C₇×#95	C₂²	1	2	yes	—
41	C₂×C₇×#95	C₂²	1	1	yes	characteristic
42	C₂×C₇×#95	C₂²	1	2	yes	—
43	C₂×C₇×#95	C₂²	1	2	yes	—
44	C₂×C₇×#95	C₂²	1	2	yes	—
45	C₂×C₇×#95	C₂²	1	2	yes	—
46	C₂×C₇×#95	C₂²	1	1	yes	characteristic
47	C₂×#2494	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁵×C₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇	—	2	4	no	—
50	C₂³×C₄×C₇	—	2	4	no	—
51	C₂³×C₄×C₇	—	2	4	no	—
52	C₂³×C₄×C₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	—	2	8	no	—
64	C₂×C₇×C₄⋊C₄	—	2	4	no	—
65	C₂×C₇×C₄⋊C₄	—	2	4	no	—
66	C₂×C₇×C₄⋊C₄	—	2	4	no	—
67	C₂×C₇×C₄⋊C₄	—	2	4	no	—
68	C₂×C₇×C₄⋊C₄	—	4	4	no	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
78	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
79	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₄²×C₇	—	2	4	no	—
84	C₂×C₄²×C₇	—	2	4	no	—
85	C₂×C₄²×C₇	—	4	4	no	—
86	C₂×C₄²×C₇	C₂³	1	4	yes	—
87	C₂×C₄²×C₇	C₂³	1	4	yes	—
88	C₂×C₄²×C₇	C₂³	1	8	yes	—
89	C₇×#95	C₂³	1	4	yes	—
90	C₇×#95	C₂³	1	4	yes	—
91	C₇×#95	C₂³	1	8	yes	—
92	C₇×#95	C₂³	1	8	yes	—
93	C₇×#95	C₂³	1	8	yes	—
94	C₇×#95	C₂³	1	8	yes	—
95	C₇×#95	C₂³	1	8	yes	—
96	C₇×#95	C₂³	1	8	yes	—
97	C₇×#95	C₂³	1	8	yes	—
98	#2494	C₂×C₇	1	16	yes	direct product factor
99	C₂×#401	C₂×C₇	1	2	yes	complemented
100	C₂×#397	C₂×C₇	1	2	yes	—
101	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
102	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
103	C₂×#388	C₂×C₇	1	2	yes	—
104	C₂×#387	C₂×C₇	1	2	yes	complemented
105	C₂×#382	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂×#380	C₂×C₇	1	1	yes	characteristic
107	C₂×#380	C₂×C₇	1	1	yes	characteristic
108	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
110	C₂⁴×C₇	—	2	2	no	—
111	C₂⁴×C₇	—	2	2	no	—
112	C₂⁴×C₇	—	2	2	no	—
113	C₂⁴×C₇	—	2	2	no	—
114	C₂⁴×C₇	—	2	2	no	—
115	C₂⁴×C₇	—	2	2	no	—
116	C₂⁴×C₇	#41	1	4	yes	—
117	C₂⁴×C₇	C₂⁴	1	2	yes	—
118	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	4	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	4	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	4	no	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	4	no	—
132	C₂²×C₄×C₇	—	2	4	no	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	2	4	no	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	8	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	—	2	8	no	—
148	C₂²×C₄×C₇	—	4	16	no	—
149	C₂²×C₄×C₇	#41	1	4	yes	—
150	C₂²×C₄×C₇	#41	1	4	yes	—
151	C₂²×C₄×C₇	#41	1	4	yes	—
152	C₂²×C₄×C₇	#41	1	4	yes	—
153	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
163	C₇×C₄⋊C₄	—	2	16	no	—
164	C₇×C₄⋊C₄	—	2	8	no	—
165	C₇×C₄⋊C₄	—	2	8	no	—
166	C₇×C₄⋊C₄	—	2	8	no	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	—	4	8	no	—
169	C₇×C₂²⋊C₄	—	2	8	no	—
170	C₇×C₂²⋊C₄	—	2	16	no	—
171	C₇×C₂²⋊C₄	—	2	8	no	—
172	C₇×C₂²⋊C₄	—	4	8	no	—
173	C₄²×C₇	—	2	8	no	—
174	C₄²×C₇	—	2	8	no	—
175	C₄²×C₇	—	4	8	no	—
176	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
177	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
178	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
187	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
188	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
189	C₂²×C₄²	C₂²×C₇	1	2	yes	—
190	#401	C₂²×C₇	1	16	yes	complemented
191	#397	C₂²×C₇	1	16	yes	—
192	#389	C₂²×C₇	1	8	yes	complemented
193	#389	C₂²×C₇	1	8	yes	complemented
194	#388	C₂²×C₇	1	16	yes	—
195	#387	C₂²×C₇	1	16	yes	complemented
196	#382	C₂²×C₇	1	8	yes	complemented
197	#380	C₂²×C₇	1	8	yes	—
198	#380	C₂²×C₇	1	8	yes	—
199	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
200	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
201	C₂×#95	C₂²×C₇	1	2	yes	—
202	C₂×#95	C₂²×C₇	1	2	yes	—
203	C₂×#95	C₂²×C₇	1	2	yes	—
204	C₂×#95	C₂²×C₇	1	1	yes	characteristic
205	C₂×#95	C₂²×C₇	1	2	yes	—
206	C₂×#95	C₂²×C₇	1	2	yes	—
207	C₂×#95	C₂²×C₇	1	2	yes	—
208	C₂×#95	C₂²×C₇	1	2	yes	—
209	C₂×#95	C₂²×C₇	1	1	yes	characteristic
210	C₂³×C₇	—	2	8	no	—
211	C₂³×C₇	—	2	8	no	—
212	C₂³×C₇	—	2	8	no	—
213	C₂³×C₇	—	2	2	no	—
214	C₂³×C₇	—	2	2	no	—
215	C₂³×C₇	—	2	2	no	—
216	C₂³×C₇	—	2	2	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	4	4	no	—
220	C₂³×C₇	—	4	4	no	—
221	C₂³×C₇	—	4	4	no	—
222	C₂³×C₇	—	4	4	no	—
223	C₂³×C₇	C₂×#41	1	4	yes	—
224	C₂³×C₇	C₂×#41	1	2	yes	—
225	C₂³×C₇	C₂×#41	1	2	yes	—
226	C₂³×C₇	C₂×#41	1	2	yes	—
227	C₂³×C₇	C₂×#41	1	2	yes	—
228	C₂³×C₇	C₂×#41	1	2	yes	—
229	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
230	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
231	C₂³×C₇	C₂⁵	1	1	yes	characteristic
232	C₂×C₄×C₇	—	2	8	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	4	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	2	4	no	—
248	C₂×C₄×C₇	—	2	4	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	4	no	—
253	C₂×C₄×C₇	—	2	4	no	—
254	C₂×C₄×C₇	—	2	4	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	4	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	2	no	—
259	C₂×C₄×C₇	—	4	4	no	—
260	C₂×C₄×C₇	—	4	8	no	—
261	C₂×C₄×C₇	—	4	8	no	—
262	C₂×C₄×C₇	—	4	4	no	—
263	C₂×C₄×C₇	—	4	8	no	—
264	C₂×C₄×C₇	—	4	4	no	—
265	C₂×C₄×C₇	—	4	8	no	—
266	C₂×C₄×C₇	—	4	4	no	—
267	C₂×C₄×C₇	—	4	16	no	—
268	C₂×C₄×C₇	#126	1	16	yes	—
269	C₂×C₄×C₇	C₂×#41	1	4	yes	—
270	C₂×C₄×C₇	C₂×#41	1	4	yes	—
271	C₂×C₄×C₇	C₂×#41	1	4	yes	—
272	C₂×C₄×C₇	C₂×#41	1	4	yes	—
273	C₂⁵	C₂³×C₇	1	1	yes	characteristic
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	4	no	—
277	C₂³×C₄	C₂³×C₇	1	2	yes	—
278	C₂³×C₄	C₂³×C₇	1	2	yes	—
279	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₇	1	2	yes	—
281	C₂³×C₄	C₂³×C₇	1	2	yes	—
282	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₇	1	4	yes	—
286	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	4	4	no	—
294	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
296	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
299	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	—	4	4	no	—
304	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	—	4	4	no	—
311	C₂×C₄²	C₂³×C₇	1	4	yes	—
312	C₂×C₄²	C₂³×C₇	1	4	yes	—
313	C₂×C₄²	C₂³×C₇	1	8	yes	—
314	#95	C₂³×C₇	1	4	yes	—
315	#95	C₂³×C₇	1	4	yes	—
316	#95	C₂³×C₇	1	8	yes	—
317	#95	C₂³×C₇	1	8	yes	—
318	#95	C₂³×C₇	1	8	yes	—
319	#95	C₂³×C₇	1	8	yes	—
320	#95	C₂³×C₇	1	8	yes	—
321	#95	C₂³×C₇	1	8	yes	—
322	#95	C₂³×C₇	1	8	yes	—
323	C₂²×C₇	—	2	4	no	—
324	C₂²×C₇	—	2	4	no	—
325	C₂²×C₇	—	2	4	no	—
326	C₂²×C₇	—	4	2	no	—
327	C₂²×C₇	—	4	2	no	—
328	C₂²×C₇	—	4	2	no	—
329	C₂²×C₇	—	4	2	no	—
330	C₂²×C₇	—	4	16	no	—
331	C₂²×C₇	C₂×#126	1	4	yes	—
332	C₂²×C₇	#529	1	4	yes	—
333	C₂²×C₇	#542	1	4	yes	—
334	C₂²×C₇	#552	1	4	yes	—
335	C₂²×C₇	#553	1	4	yes	—
336	C₂²×C₇	#553	1	4	yes	—
337	C₂²×C₇	#556	1	4	yes	—
338	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₄×C₇	—	2	4	no	—
346	C₄×C₇	—	4	2	no	—
347	C₄×C₇	—	4	4	no	—
348	C₄×C₇	—	4	4	no	—
349	C₄×C₇	—	4	2	no	—
350	C₄×C₇	—	4	4	no	—
351	C₄×C₇	—	4	2	no	—
352	C₄×C₇	—	4	4	no	—
353	C₄×C₇	—	4	2	no	—
354	C₄×C₇	C₂×#126	1	8	yes	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	2	2	no	—
361	C₂⁴	C₇×#41	1	4	yes	—
362	C₂⁴	C₂⁴×C₇	1	2	yes	—
363	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	4	16	no	—
394	C₂²×C₄	C₇×#41	1	4	yes	—
395	C₂²×C₄	C₇×#41	1	4	yes	—
396	C₂²×C₄	C₇×#41	1	4	yes	—
397	C₂²×C₄	C₇×#41	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
408	C₄⋊C₄	—	2	16	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	4	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	16	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	2	8	no	—
420	C₄²	—	4	8	no	—
421	C₂×C₇	—	4	4	no	—
422	C₂×C₇	#2494	1	8	yes	direct product factor
423	C₂×C₇	C₂²×#126	1	1	yes	characteristic
424	C₂×C₇	C₂×#529	1	1	yes	characteristic
425	C₂×C₇	C₂×#542	1	1	yes	characteristic
426	C₂×C₇	C₂×#552	1	1	yes	characteristic
427	C₂×C₇	C₂×#553	1	1	yes	characteristic
428	C₂×C₇	C₂×#553	1	1	yes	characteristic
429	C₂×C₇	C₂×#556	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	8	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	C₂×C₇×#41	1	4	yes	—
444	C₂³	C₂×C₇×#41	1	2	yes	—
445	C₂³	C₂×C₇×#41	1	2	yes	—
446	C₂³	C₂×C₇×#41	1	2	yes	—
447	C₂³	C₂×C₇×#41	1	2	yes	—
448	C₂³	C₂×C₇×#41	1	2	yes	—
449	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
450	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
451	C₂³	C₂⁵×C₇	1	1	yes	characteristic
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	C₇×#126	1	16	yes	—
489	C₂×C₄	C₂×C₇×#41	1	4	yes	—
490	C₂×C₄	C₂×C₇×#41	1	4	yes	—
491	C₂×C₄	C₂×C₇×#41	1	4	yes	—
492	C₂×C₄	C₂×C₇×#41	1	4	yes	—
493	C₇	C₂×#2494	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	16	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	C₂×C₇×#126	1	4	yes	—
503	C₂²	C₇×#529	1	4	yes	—
504	C₂²	C₇×#542	1	4	yes	—
505	C₂²	C₇×#552	1	4	yes	—
506	C₂²	C₇×#553	1	4	yes	—
507	C₂²	C₇×#553	1	4	yes	—
508	C₂²	C₇×#556	1	4	yes	—
509	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
510	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
511	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
512	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
513	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
514	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	C₂×C₇×#126	1	8	yes	—
526	C₂	—	4	4	no	—
527	C₂	C₇×#2494	1	8	yes	direct product factor
528	C₂	C₂²×C₇×#126	1	1	yes	characteristic
529	C₂	C₂×C₇×#529	1	1	yes	characteristic
530	C₂	C₂×C₇×#542	1	1	yes	characteristic
531	C₂	C₂×C₇×#552	1	1	yes	characteristic
532	C₂	C₂×C₇×#553	1	1	yes	characteristic
533	C₂	C₂×C₇×#553	1	1	yes	characteristic
534	C₂	C₂×C₇×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
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
1. C₇×#2494	C₂	direct (N × H)
2. C₂×C₇×#401	C₂	semidirect
4. C₂×C₇×#389	C₂	semidirect
5. C₂×C₇×#389	C₂	semidirect
7. C₂×C₇×#387	C₂	semidirect
8. C₂×C₇×#382	C₂	semidirect
11. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
27. C₇×#401	C₂²	semidirect
29. C₇×#389	C₂²	semidirect
30. C₇×#389	C₂²	semidirect
32. C₇×#387	C₂²	semidirect
33. C₇×#382	C₂²	semidirect
36. C₄×C₇×C₄⋊C₄	C₂²	semidirect
47. C₂×#2494	C₇	direct (N × H)
98. #2494	C₂×C₇	direct (N × H)
99. C₂×#401	C₂×C₇	semidirect
101. C₂×#389	C₂×C₇	semidirect
102. C₂×#389	C₂×C₇	semidirect
104. C₂×#387	C₂×C₇	semidirect
105. C₂×#382	C₂×C₇	semidirect
108. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
190. #401	C₂²×C₇	semidirect
192. #389	C₂²×C₇	semidirect
193. #389	C₂²×C₇	semidirect
195. #387	C₂²×C₇	semidirect
196. #382	C₂²×C₇	semidirect
199. C₄×C₄⋊C₄	C₂²×C₇	semidirect
422. C₂×C₇	#2494	direct (N × H)
493. C₇	C₂×#2494	direct (N × H)
527. C₂	C₇×#2494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2494	2
C₂×C₇×#401	2
C₂×C₇×#397	2
C₂×C₇×#389	2
C₂×C₇×#388	2
C₂×C₇×#387	2
C₂×C₇×#382	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₄⋊C₄	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2494	7

Subgroups — C2×C7×#2494 #13212001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2494 #13212001