Subgroups — C₂×C₇×#2081 #13200866

Order 1792.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₇×#100	C₂	1	1	yes	maximal, characteristic
5	C₇×#2081	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	C₂²	1	1	yes	characteristic
16	C₇×#430	—	2	2	no	—
17	C₇×#430	C₂²	1	4	yes	complemented
18	C₂×C₇×#108	—	2	2	no	—
19	C₇×#418	—	2	2	no	—
20	C₇×#418	—	2	2	no	—
21	C₇×#418	C₂²	1	4	yes	—
22	C₇×#418	C₂²	1	4	yes	—
23	C₂×C₇×#102	—	2	2	no	—
24	C₂×C₇×#102	—	2	2	no	—
25	C₂×C₇×#100	—	2	2	no	—
26	C₂×C₇×#100	—	2	2	no	—
27	C₂×C₇×#100	C₂²	1	4	yes	—
28	C₇×#344	C₂²	1	4	yes	complemented
29	C₇×#344	C₂²	1	4	yes	complemented
30	C₇×H(3,ℤ/4)	C₂²	1	4	yes	complemented
31	C₂×#2081	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁵×C₇	—	2	1	no	—
33	C₂²×C₇×D₄	—	2	1	no	—
34	C₂²×C₇×D₄	—	2	1	no	—
35	C₂²×C₇×D₄	—	2	1	no	—
36	C₂²×C₇×D₄	—	2	1	no	—
37	C₂²×C₇×D₄	—	2	1	no	—
38	C₂²×C₇×D₄	—	2	1	no	—
39	C₂²×C₇×D₄	—	2	1	no	—
40	C₂²×C₇×D₄	—	2	1	no	—
41	C₂²×C₇×D₄	—	2	1	no	—
42	C₂²×C₇×D₄	—	2	1	no	—
43	C₂²×C₇×D₄	—	2	1	no	—
44	C₂²×C₇×D₄	D₄	1	2	yes	—
45	C₂²×C₇×D₄	D₄	1	2	yes	—
46	C₂²×C₇×D₄	C₂³	1	2	yes	—
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂×C₇×M₁₆	—	2	1	no	—
49	C₂×C₇×M₁₆	—	2	1	no	—
50	C₂×C₇×M₁₆	—	2	1	no	—
51	C₂×C₇×M₁₆	—	2	1	no	—
52	C₂×C₇×M₁₆	—	2	1	no	—
53	C₂×C₇×M₁₆	—	2	1	no	—
54	C₂×C₇×M₁₆	—	2	1	no	—
55	C₂×C₇×M₁₆	—	2	1	no	—
56	C₂×C₇×M₁₆	—	2	1	no	—
57	C₂×C₇×M₁₆	—	2	1	no	—
58	C₂×C₇×M₁₆	—	2	1	no	—
59	C₂×C₇×M₁₆	—	2	1	no	—
60	C₂×C₇×M₁₆	—	2	1	no	—
61	C₂×C₇×M₁₆	—	2	1	no	—
62	C₂×C₇×M₁₆	—	2	1	no	—
63	C₂×C₇×M₁₆	—	2	1	no	—
64	C₂×C₇×M₁₆	—	2	1	no	—
65	C₂×C₇×M₁₆	—	2	1	no	—
66	C₂×C₇×M₁₆	—	2	1	no	—
67	C₂×C₇×M₁₆	D₄	1	2	yes	—
68	C₂×C₇×M₁₆	C₂³	1	2	yes	—
69	C₂×C₇×M₁₆	C₂³	1	2	yes	—
70	C₂×C₇×M₁₆	C₂³	1	2	yes	—
71	C₂×C₇×M₁₆	C₂³	1	2	yes	—
72	C₂²×C₇×C₈	—	2	1	no	—
73	C₂²×C₇×C₈	—	2	1	no	—
74	C₂²×C₇×C₈	—	2	1	no	—
75	C₂²×C₇×C₈	D₄	1	2	yes	—
76	C₇×#117	—	2	1	no	—
77	C₇×#117	—	2	1	no	—
78	C₇×#117	—	2	1	no	—
79	C₇×#117	—	2	1	no	—
80	C₇×#117	—	2	1	no	—
81	C₇×#117	—	2	1	no	—
82	C₇×#117	C₂³	1	2	yes	—
83	C₇×#117	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₇	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₇×#108	—	2	8	no	—
91	C₇×#102	—	2	8	no	—
92	C₇×#102	—	2	8	no	—
93	C₇×#100	—	2	8	no	—
94	C₂×#430	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×#418	C₂×C₇	1	1	yes	characteristic
96	C₂×#418	C₂×C₇	1	1	yes	characteristic
97	C₂²×#100	C₂×C₇	1	1	yes	characteristic
98	#2081	C₂×C₇	1	8	yes	direct product factor
99	C₂×#344	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂×#344	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂×H(3,ℤ/4)	C₂×C₇	1	1	yes	characteristic, complemented
102	C₂⁴×C₇	—	2	2	no	—
103	C₂⁴×C₇	—	2	2	no	—
104	C₂⁴×C₇	—	2	2	no	—
105	C₂⁴×C₇	—	4	1	no	—
106	C₂⁴×C₇	—	4	1	no	—
107	C₂⁴×C₇	—	4	1	no	—
108	C₂⁴×C₇	—	4	1	no	—
109	C₂⁴×C₇	—	8	4	no	—
110	C₂⁴×C₇	#41	1	1	yes	characteristic
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	2	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	—	2	2	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	4	1	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂×C₇×D₄	—	4	1	no	—
130	C₂×C₇×D₄	—	4	1	no	—
131	C₂×C₇×D₄	—	4	1	no	—
132	C₂×C₇×D₄	—	4	1	no	—
133	C₂×C₇×D₄	—	4	1	no	—
134	C₂×C₇×D₄	—	4	1	no	—
135	C₂×C₇×D₄	—	4	1	no	—
136	C₂×C₇×D₄	—	4	1	no	—
137	C₂×C₇×D₄	—	4	1	no	—
138	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₇	—	4	1	no	—
140	C₂²×C₄×C₇	—	4	1	no	—
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	#41	1	1	yes	characteristic
146	C₂²×C₄×C₇	#41	1	1	yes	characteristic
147	C₂²×C₄×C₇	#41	1	1	yes	characteristic
148	C₂²×C₄×C₇	#41	1	1	yes	characteristic
149	C₂²×C₄×C₇	#41	1	1	yes	characteristic
150	C₂²×C₄×C₇	#41	1	1	yes	characteristic
151	C₂²×C₄×C₇	#41	1	1	yes	characteristic
152	C₂²×C₄×C₇	#41	1	1	yes	characteristic
153	C₂²×C₄×C₇	#41	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
155	C₇×M₁₆	—	2	2	no	—
156	C₇×M₁₆	—	2	2	no	—
157	C₇×M₁₆	—	2	2	no	—
158	C₇×M₁₆	—	2	2	no	—
159	C₇×M₁₆	—	2	2	no	—
160	C₇×M₁₆	—	2	2	no	—
161	C₇×M₁₆	—	2	2	no	—
162	C₇×M₁₆	—	2	2	no	—
163	C₇×M₁₆	—	2	2	no	—
164	C₇×M₁₆	—	2	2	no	—
165	C₇×M₁₆	—	4	1	no	—
166	C₇×M₁₆	—	4	1	no	—
167	C₇×M₁₆	—	4	1	no	—
168	C₇×M₁₆	—	4	1	no	—
169	C₇×M₁₆	—	4	1	no	—
170	C₇×M₁₆	—	4	1	no	—
171	C₂×C₇×C₈	—	2	2	no	—
172	C₂×C₇×C₈	—	2	2	no	—
173	C₂×C₇×C₈	—	2	2	no	—
174	C₂×C₇×C₈	—	2	2	no	—
175	C₂×C₇×C₈	—	2	2	no	—
176	C₂×C₇×C₈	—	4	1	no	—
177	C₂×C₇×C₈	—	4	1	no	—
178	C₂×C₇×C₈	—	4	1	no	—
179	C₂×C₇×C₈	—	4	1	no	—
180	C₂×C₇×C₈	—	4	1	no	—
181	C₂×C₇×C₈	—	4	1	no	—
182	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
183	C₇×C₄⋊C₄	—	2	2	no	—
184	C₇×C₄⋊C₄	—	2	2	no	—
185	C₇×C₄⋊C₄	—	4	1	no	—
186	C₇×C₄⋊C₄	—	4	1	no	—
187	C₇×C₂²⋊C₄	—	2	2	no	—
188	C₇×C₂²⋊C₄	—	2	2	no	—
189	C₇×C₂²⋊C₄	—	4	1	no	—
190	C₇×C₂²⋊C₄	—	4	1	no	—
191	C₄²×C₇	—	2	2	no	—
192	C₄²×C₇	—	2	2	no	—
193	C₄²×C₇	—	4	1	no	—
194	C₄²×C₇	—	4	1	no	—
195	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
198	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
200	C₂×#117	C₂²×C₇	1	1	yes	characteristic
201	C₂×#117	C₂²×C₇	1	1	yes	characteristic
202	#430	—	2	2	no	—
203	#430	C₂²×C₇	1	4	yes	complemented
204	C₂×#108	—	2	2	no	—
205	#418	—	2	2	no	—
206	#418	—	2	2	no	—
207	#418	C₂²×C₇	1	4	yes	—
208	#418	C₂²×C₇	1	4	yes	—
209	C₂×#102	—	2	2	no	—
210	C₂×#102	—	2	2	no	—
211	C₂×#100	—	2	2	no	—
212	C₂×#100	—	2	2	no	—
213	C₂×#100	C₂²×C₇	1	4	yes	—
214	#344	C₂²×C₇	1	4	yes	complemented
215	#344	C₂²×C₇	1	4	yes	complemented
216	H(3,ℤ/4)	C₂²×C₇	1	4	yes	complemented
217	C₂³×C₇	—	2	4	no	—
218	C₂³×C₇	—	4	2	no	—
219	C₂³×C₇	—	4	2	no	—
220	C₂³×C₇	—	4	2	no	—
221	C₂³×C₇	—	4	2	no	—
222	C₂³×C₇	—	4	2	no	—
223	C₂³×C₇	—	4	2	no	—
224	C₂³×C₇	—	4	2	no	—
225	C₂³×C₇	—	8	4	no	—
226	C₂³×C₇	—	8	4	no	—
227	C₂³×C₇	—	8	4	no	—
228	C₂³×C₇	—	8	4	no	—
229	C₂³×C₇	—	8	4	no	—
230	C₂³×C₇	—	8	4	no	—
231	C₂³×C₇	—	8	4	no	—
232	C₂³×C₇	#123	1	1	yes	characteristic
233	C₂³×C₇	#123	1	1	yes	characteristic
234	C₂³×C₇	#124	1	1	yes	characteristic
235	C₂³×C₇	#124	1	1	yes	characteristic
236	C₂³×C₇	#126	1	1	yes	characteristic
237	C₂³×C₇	#126	1	1	yes	characteristic
238	C₂³×C₇	C₂×#41	1	1	yes	characteristic
239	C₇×D₄	—	2	4	no	—
240	C₇×D₄	—	2	4	no	—
241	C₇×D₄	—	4	2	no	—
242	C₇×D₄	—	4	2	no	—
243	C₇×D₄	—	4	2	no	—
244	C₇×D₄	—	4	2	no	—
245	C₇×D₄	—	4	2	no	—
246	C₇×D₄	—	4	2	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	2	no	—
249	C₂×C₄×C₇	—	8	2	no	—
250	C₂×C₄×C₇	—	8	2	no	—
251	C₂×C₄×C₇	#121	1	1	yes	characteristic
252	C₂×C₄×C₇	#121	1	1	yes	characteristic
253	C₂×C₄×C₇	#121	1	1	yes	characteristic
254	C₂×C₄×C₇	#121	1	1	yes	characteristic
255	C₂×C₄×C₇	#123	1	1	yes	characteristic
256	C₂×C₄×C₇	#123	1	1	yes	characteristic
257	C₂×C₄×C₇	#123	1	1	yes	characteristic
258	C₂×C₄×C₇	#123	1	1	yes	characteristic
259	C₂×C₄×C₇	#123	1	1	yes	characteristic
260	C₂×C₄×C₇	#123	1	1	yes	characteristic
261	C₂×C₄×C₇	#123	1	1	yes	characteristic
262	C₂×C₄×C₇	#123	1	1	yes	characteristic
263	C₂×C₄×C₇	#123	1	1	yes	characteristic
264	C₂×C₄×C₇	#123	1	1	yes	characteristic
265	C₂×C₄×C₇	#124	1	1	yes	characteristic
266	C₂×C₄×C₇	#124	1	1	yes	characteristic
267	C₂×C₄×C₇	#126	1	1	yes	characteristic
268	C₂×C₄×C₇	#126	1	1	yes	characteristic
269	C₂×C₄×C₇	#126	1	1	yes	characteristic
270	C₂×C₄×C₇	#126	1	1	yes	characteristic
271	C₂×C₄×C₇	#126	1	1	yes	characteristic
272	C₂×C₄×C₇	#126	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
279	C₇×C₈	—	2	4	no	—
280	C₇×C₈	—	4	2	no	—
281	C₇×C₈	—	4	2	no	—
282	C₇×C₈	—	4	2	no	—
283	C₂⁵	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₇×D₄	1	2	yes	—
296	C₂²×D₄	C₇×D₄	1	2	yes	—
297	C₂²×D₄	C₂³×C₇	1	2	yes	—
298	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	C₇×D₄	1	2	yes	—
319	C₂×M₁₆	C₂³×C₇	1	2	yes	—
320	C₂×M₁₆	C₂³×C₇	1	2	yes	—
321	C₂×M₁₆	C₂³×C₇	1	2	yes	—
322	C₂×M₁₆	C₂³×C₇	1	2	yes	—
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	C₇×D₄	1	2	yes	—
327	#117	—	2	1	no	—
328	#117	—	2	1	no	—
329	#117	—	2	1	no	—
330	#117	—	2	1	no	—
331	#117	—	2	1	no	—
332	#117	—	2	1	no	—
333	#117	C₂³×C₇	1	2	yes	—
334	#117	C₂³×C₇	1	2	yes	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	#108	—	2	8	no	—
342	#102	—	2	8	no	—
343	#102	—	2	8	no	—
344	#100	—	2	8	no	—
345	C₂²×C₇	—	2	2	no	—
346	C₂²×C₇	—	2	2	no	—
347	C₂²×C₇	—	2	2	no	—
348	C₂²×C₇	—	4	1	no	—
349	C₂²×C₇	—	4	1	no	—
350	C₂²×C₇	—	4	1	no	—
351	C₂²×C₇	—	4	1	no	—
352	C₂²×C₇	—	4	4	no	—
353	C₂²×C₇	—	8	4	no	—
354	C₂²×C₇	—	8	4	no	—
355	C₂²×C₇	—	8	4	no	—
356	C₂²×C₇	—	8	4	no	—
357	C₂²×C₇	—	8	4	no	—
358	C₂²×C₇	—	8	4	no	—
359	C₂²×C₇	—	8	4	no	—
360	C₂²×C₇	#397	1	1	yes	characteristic
361	C₂²×C₇	#397	1	1	yes	characteristic
362	C₂²×C₇	#397	1	1	yes	characteristic
363	C₂²×C₇	#397	1	1	yes	characteristic
364	C₂²×C₇	C₂×#123	1	1	yes	characteristic
365	C₂²×C₇	C₂×#124	1	1	yes	characteristic
366	C₂²×C₇	C₂×#126	1	1	yes	characteristic
367	C₄×C₇	—	8	2	no	—
368	C₄×C₇	—	8	2	no	—
369	C₄×C₇	#397	1	1	yes	characteristic
370	C₄×C₇	#397	1	1	yes	characteristic
371	C₄×C₇	#397	1	1	yes	characteristic
372	C₄×C₇	#397	1	1	yes	characteristic
373	C₄×C₇	C₂×#121	1	1	yes	characteristic
374	C₄×C₇	C₂×#123	1	1	yes	characteristic
375	C₄×C₇	C₂×#123	1	1	yes	characteristic
376	C₄×C₇	C₂×#126	1	1	yes	characteristic
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	4	1	no	—
381	C₂⁴	—	4	1	no	—
382	C₂⁴	—	4	1	no	—
383	C₂⁴	—	4	1	no	—
384	C₂⁴	—	8	4	no	—
385	C₂⁴	C₇×#41	1	1	yes	characteristic
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	4	1	no	—
416	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₇×#41	1	1	yes	characteristic
421	C₂²×C₄	C₇×#41	1	1	yes	characteristic
422	C₂²×C₄	C₇×#41	1	1	yes	characteristic
423	C₂²×C₄	C₇×#41	1	1	yes	characteristic
424	C₂²×C₄	C₇×#41	1	1	yes	characteristic
425	C₂²×C₄	C₇×#41	1	1	yes	characteristic
426	C₂²×C₄	C₇×#41	1	1	yes	characteristic
427	C₂²×C₄	C₇×#41	1	1	yes	characteristic
428	C₂²×C₄	C₇×#41	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	4	1	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	4	1	no	—
452	C₂×C₈	—	4	1	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	—	4	1	no	—
455	C₂×C₈	—	4	1	no	—
456	C₂×C₈	—	4	1	no	—
457	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	4	1	no	—
469	C₄²	—	4	1	no	—
470	C₂×C₇	—	2	1	no	—
471	C₂×C₇	—	2	1	no	—
472	C₂×C₇	—	2	1	no	—
473	C₂×C₇	—	2	1	no	—
474	C₂×C₇	—	2	1	no	—
475	C₂×C₇	—	2	1	no	—
476	C₂×C₇	—	8	4	no	—
477	C₂×C₇	#2081	1	2	yes	direct product factor
478	C₂×C₇	C₂×#397	1	1	yes	characteristic
479	C₂³	—	2	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	8	4	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	—	8	4	no	—
494	C₂³	C₇×#123	1	1	yes	characteristic
495	C₂³	C₇×#123	1	1	yes	characteristic
496	C₂³	C₇×#124	1	1	yes	characteristic
497	C₂³	C₇×#124	1	1	yes	characteristic
498	C₂³	C₇×#126	1	1	yes	characteristic
499	C₂³	C₇×#126	1	1	yes	characteristic
500	C₂³	C₂×C₇×#41	1	1	yes	characteristic
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	C₇×#121	1	1	yes	characteristic
514	C₂×C₄	C₇×#121	1	1	yes	characteristic
515	C₂×C₄	C₇×#121	1	1	yes	characteristic
516	C₂×C₄	C₇×#121	1	1	yes	characteristic
517	C₂×C₄	C₇×#123	1	1	yes	characteristic
518	C₂×C₄	C₇×#123	1	1	yes	characteristic
519	C₂×C₄	C₇×#123	1	1	yes	characteristic
520	C₂×C₄	C₇×#123	1	1	yes	characteristic
521	C₂×C₄	C₇×#123	1	1	yes	characteristic
522	C₂×C₄	C₇×#123	1	1	yes	characteristic
523	C₂×C₄	C₇×#123	1	1	yes	characteristic
524	C₂×C₄	C₇×#123	1	1	yes	characteristic
525	C₂×C₄	C₇×#123	1	1	yes	characteristic
526	C₂×C₄	C₇×#123	1	1	yes	characteristic
527	C₂×C₄	C₇×#124	1	1	yes	characteristic
528	C₂×C₄	C₇×#124	1	1	yes	characteristic
529	C₂×C₄	C₇×#126	1	1	yes	characteristic
530	C₂×C₄	C₇×#126	1	1	yes	characteristic
531	C₂×C₄	C₇×#126	1	1	yes	characteristic
532	C₂×C₄	C₇×#126	1	1	yes	characteristic
533	C₂×C₄	C₇×#126	1	1	yes	characteristic
534	C₂×C₄	C₇×#126	1	1	yes	characteristic
535	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
536	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
538	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
539	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
540	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₈	—	4	2	no	—
544	C₈	—	4	2	no	—
545	C₇	C₂×#2081	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	8	4	no	—
555	C₂²	—	8	4	no	—
556	C₂²	—	8	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	C₇×#397	1	1	yes	characteristic
562	C₂²	C₇×#397	1	1	yes	characteristic
563	C₂²	C₇×#397	1	1	yes	characteristic
564	C₂²	C₇×#397	1	1	yes	characteristic
565	C₂²	C₂×C₇×#123	1	1	yes	characteristic
566	C₂²	C₂×C₇×#124	1	1	yes	characteristic
567	C₂²	C₂×C₇×#126	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	C₇×#397	1	1	yes	characteristic
571	C₄	C₇×#397	1	1	yes	characteristic
572	C₄	C₇×#397	1	1	yes	characteristic
573	C₄	C₇×#397	1	1	yes	characteristic
574	C₄	C₂×C₇×#121	1	1	yes	characteristic
575	C₄	C₂×C₇×#123	1	1	yes	characteristic
576	C₄	C₂×C₇×#123	1	1	yes	characteristic
577	C₄	C₂×C₇×#126	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	8	4	no	—
585	C₂	C₇×#2081	1	2	yes	direct product factor
586	C₂	C₂×C₇×#397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#430	C₂	semidirect
5. C₇×#2081	C₂	direct (N × H)
6. C₂×C₇×#344	C₂	semidirect
7. C₂×C₇×#344	C₂	semidirect
8. C₂×C₇×H(3,ℤ/4)	C₂	semidirect
17. C₇×#430	C₂²	semidirect
28. C₇×#344	C₂²	semidirect
29. C₇×#344	C₂²	semidirect
30. C₇×H(3,ℤ/4)	C₂²	semidirect
31. C₂×#2081	C₇	direct (N × H)
94. C₂×#430	C₂×C₇	semidirect
98. #2081	C₂×C₇	direct (N × H)
99. C₂×#344	C₂×C₇	semidirect
100. C₂×#344	C₂×C₇	semidirect
101. C₂×H(3,ℤ/4)	C₂×C₇	semidirect
203. #430	C₂²×C₇	semidirect
214. #344	C₂²×C₇	semidirect
215. #344	C₂²×C₇	semidirect
216. H(3,ℤ/4)	C₂²×C₇	semidirect
477. C₂×C₇	#2081	direct (N × H)
545. C₇	C₂×#2081	direct (N × H)
585. C₂	C₇×#2081	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×#430	2
C₂×C₇×#418	2
C₂²×C₇×#100	2
C₇×#2081	2
C₂×C₇×#344	2
C₂×C₇×H(3,ℤ/4)	2
C₂×#2081	7

Subgroups — C2×C7×#2081 #13200866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2081 #13200866