Subgroups — C₄×C₇×#469 #13198749

Order 1792.

1170 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×#121	C₂	1	2	yes	maximal, complemented
5	C₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₇×#1895	C₂	1	2	yes	maximal, complemented
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₇×#121	C₂²	1	2	yes	—
16	C₂×C₄×C₇×D₄	—	2	2	no	—
17	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
18	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
19	C₇×#469	C₄	1	8	yes	direct product factor
20	C₄×C₇×D₈	—	2	4	no	—
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#102	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₂×C₇×#102	C₂²	1	2	yes	—
27	C₄×C₇×M₁₆	—	2	4	no	—
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#389	C₂²	1	2	yes	—
34	C₇×#388	—	2	2	no	—
35	C₇×#386	—	2	2	no	—
36	C₇×#380	C₂²	1	2	yes	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₄×#469	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	—	2	2	no	—
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₂×C₇×D₈	—	2	2	no	—
50	C₂×C₇×D₈	—	2	2	no	—
51	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂×C₇×M₁₆	—	2	2	no	—
54	C₂×C₇×M₁₆	—	2	2	no	—
55	C₂×C₇×M₁₆	—	2	2	no	—
56	C₂×C₇×M₁₆	—	2	2	no	—
57	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₇×#121	—	2	4	no	—
63	C₇×#121	C₂×C₄	1	8	yes	complemented
64	C₄×C₇×D₄	—	2	4	no	—
65	C₄×C₇×D₄	—	2	4	no	—
66	C₄×C₇×D₄	—	4	8	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	—	2	2	no	—
78	C₂×C₄²×C₇	—	2	2	no	—
79	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#107	—	2	2	no	—
84	C₇×#106	—	2	2	no	—
85	C₇×#106	C₂×C₄	1	4	yes	complemented
86	C₇×#102	—	2	4	no	—
87	C₇×#102	—	2	4	no	—
88	C₇×#102	C₂×C₄	1	8	yes	complemented
89	C₇×#97	—	2	2	no	—
90	C₇×#97	—	2	2	no	—
91	C₄×C₇×C₈	—	2	2	no	—
92	C₄×C₇×C₈	D₄	1	4	yes	complemented
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₇×#95	—	2	2	no	—
96	C₂×#469	C₂×C₇	1	1	yes	characteristic
97	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
99	C₄×#121	C₂×C₇	1	2	yes	complemented
100	#1972	C₂×C₇	1	1	yes	characteristic, complemented
101	#1944	C₂×C₇	1	1	yes	characteristic, complemented
102	#1936	C₂×C₇	1	2	yes	complemented
103	#1895	C₂×C₇	1	2	yes	complemented
104	#1809	C₂×C₇	1	1	yes	characteristic, complemented
105	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
106	C₄×#102	C₂×C₇	1	2	yes	complemented
107	C₂⁴×C₇	—	2	2	no	—
108	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₇×D₄	—	2	8	no	—
110	C₂×C₇×D₄	—	2	2	no	—
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	—	4	4	no	—
116	C₂×C₇×D₄	—	4	4	no	—
117	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	4	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	4	2	no	—
129	C₂²×C₄×C₇	—	4	4	no	—
130	C₂²×C₄×C₇	—	4	4	no	—
131	C₂²×C₄×C₇	—	4	4	no	—
132	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	#41	1	2	yes	—
139	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
140	C₇×D₈	—	2	8	no	—
141	C₇×M₁₆	—	2	8	no	—
142	C₇×M₁₆	—	2	8	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₇×C₈	#41	1	2	yes	—
154	C₂×C₇×C₈	#41	1	2	yes	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	4	4	no	—
161	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
162	C₇×C₂²⋊C₄	—	2	8	no	—
163	C₇×C₂²⋊C₄	—	4	4	no	—
164	C₇×C₂²⋊C₄	—	4	4	no	—
165	C₇×C₂²⋊C₄	—	4	4	no	—
166	C₇×C₂²⋊C₄	—	4	4	no	—
167	C₄²×C₇	—	2	2	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	1	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	4	4	no	—
172	C₄²×C₇	C₂×D₄	1	2	yes	—
173	C₄²×C₇	#41	1	2	yes	—
174	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
175	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
176	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
177	C₂×#121	C₂²×C₇	1	2	yes	—
178	C₂×C₄×D₄	—	2	2	no	—
179	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
180	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
181	#469	C₄×C₇	1	8	yes	direct product factor
182	C₄×D₈	—	2	4	no	—
183	C₂×#107	C₂²×C₇	1	1	yes	characteristic
184	C₂×#106	C₂²×C₇	1	1	yes	characteristic
185	C₂×#106	C₂²×C₇	1	1	yes	characteristic
186	C₂×#102	C₂²×C₇	1	2	yes	—
187	C₂×#102	C₂²×C₇	1	2	yes	—
188	C₂×#102	C₂²×C₇	1	2	yes	—
189	C₄×M₁₆	—	2	4	no	—
190	C₂×#97	C₂²×C₇	1	1	yes	characteristic
191	C₂×#97	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
194	#390	C₂²×C₇	1	2	yes	—
195	#389	C₂²×C₇	1	2	yes	—
196	#388	—	2	2	no	—
197	#386	—	2	2	no	—
198	#380	C₂²×C₇	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
200	C₄×C₂²⋊C₄	—	2	2	no	—
201	#340	C₂²×C₇	1	2	yes	—
202	#340	C₂²×C₇	1	2	yes	—
203	#340	C₂²×C₇	1	2	yes	—
204	C₂³×C₇	—	2	1	no	—
205	C₂³×C₇	—	2	1	no	—
206	C₂³×C₇	—	2	2	no	—
207	C₂³×C₇	—	2	2	no	—
208	C₂³×C₇	—	2	4	no	—
209	C₂³×C₇	—	4	2	no	—
210	C₂³×C₇	—	4	2	no	—
211	C₂³×C₇	—	4	2	no	—
212	C₂³×C₇	—	4	2	no	—
213	C₂³×C₇	—	4	2	no	—
214	C₂³×C₇	—	4	2	no	—
215	C₂³×C₇	C₄×D₄	1	2	yes	—
216	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
217	C₇×D₄	—	2	4	no	—
218	C₇×D₄	—	2	4	no	—
219	C₇×D₄	—	4	16	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	2	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	4	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	4	4	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	4	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	—	4	2	no	—
242	C₂×C₄×C₇	—	4	2	no	—
243	C₂×C₄×C₇	—	4	2	no	—
244	C₂×C₄×C₇	—	8	8	no	—
245	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₇	#121	1	2	yes	—
247	C₂×C₄×C₇	#121	1	2	yes	—
248	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
249	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
255	C₇×C₈	—	2	2	no	—
256	C₇×C₈	—	2	2	no	—
257	C₇×C₈	—	2	2	no	—
258	C₇×C₈	C₄×D₄	1	4	yes	complemented
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	C₂³×C₇	1	2	yes	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
263	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
274	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
278	#121	—	2	4	no	—
279	#121	C₂×C₄×C₇	1	8	yes	complemented
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	4	8	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
296	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	#106	C₂×C₄×C₇	1	4	yes	complemented
302	#102	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	C₂×C₄×C₇	1	8	yes	complemented
305	#97	—	2	2	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	C₇×D₄	1	4	yes	complemented
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂²×C₇	—	2	4	no	—
313	C₂²×C₇	—	2	2	no	—
314	C₂²×C₇	—	4	2	no	—
315	C₂²×C₇	—	4	1	no	—
316	C₂²×C₇	—	4	1	no	—
317	C₂²×C₇	—	4	4	no	—
318	C₂²×C₇	—	4	4	no	—
319	C₂²×C₇	—	4	4	no	—
320	C₂²×C₇	—	8	2	no	—
321	C₂²×C₇	—	8	2	no	—
322	C₂²×C₇	—	8	2	no	—
323	C₂²×C₇	—	8	2	no	—
324	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₇	C₂×#121	1	1	yes	characteristic
326	C₂²×C₇	#532	1	1	yes	characteristic
327	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
328	C₂²×C₇	#575	1	2	yes	—
329	C₄×C₇	—	2	2	no	—
330	C₄×C₇	—	2	2	no	—
331	C₄×C₇	—	4	4	no	—
332	C₄×C₇	—	4	1	no	—
333	C₄×C₇	—	4	1	no	—
334	C₄×C₇	—	8	2	no	—
335	C₄×C₇	—	8	2	no	—
336	C₄×C₇	#469	1	4	yes	direct product factor
337	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₇	C₄×#41	1	1	yes	characteristic
339	C₄×C₇	#525	1	1	yes	characteristic
340	C₄×C₇	#529	1	1	yes	characteristic
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
367	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₇×#41	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
374	D₈	—	2	8	no	—
375	M₁₆	—	2	8	no	—
376	M₁₆	—	2	8	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
384	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
385	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
386	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
387	C₂×C₈	C₇×#41	1	2	yes	—
388	C₂×C₈	C₇×#41	1	2	yes	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	4	no	—
406	C₄²	C₂×C₇×D₄	1	2	yes	—
407	C₄²	C₇×#41	1	2	yes	—
408	C₂×C₇	—	4	2	no	—
409	C₂×C₇	—	8	4	no	—
410	C₂×C₇	C₄×#121	1	1	yes	characteristic
411	C₂×C₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
412	C₂×C₇	C₂×#469	1	1	yes	characteristic
413	C₂×C₇	#3054	1	1	yes	characteristic
414	C₂×C₇	#3171	1	2	yes	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	C₄×C₇×D₄	1	2	yes	—
427	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	16	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	8	no	—
456	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
457	C₂×C₄	C₇×#121	1	2	yes	—
458	C₂×C₄	C₇×#121	1	2	yes	—
459	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
460	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
463	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
464	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
465	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	C₄×C₇×D₄	1	4	yes	complemented
470	C₇	C₄×#469	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
484	C₂²	C₂×C₇×#121	1	1	yes	characteristic
485	C₂²	C₇×#532	1	1	yes	characteristic
486	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
487	C₂²	C₇×#575	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₇×#469	1	4	yes	direct product factor
496	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
497	C₄	C₄×C₇×#41	1	1	yes	characteristic
498	C₄	C₇×#525	1	1	yes	characteristic
499	C₄	C₇×#529	1	1	yes	characteristic
500	C₂	—	4	2	no	—
501	C₂	—	8	4	no	—
502	C₂	C₄×C₇×#121	1	1	yes	characteristic
503	C₂	C₄×C₇×AGL(1,ℤ/8)	1	2	yes	—
504	C₂	C₂×C₇×#469	1	1	yes	characteristic
505	C₂	C₇×#3054	1	1	yes	characteristic
506	C₂	C₇×#3171	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂×C₇×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×D₈	C₂	semidirect
3. C₂×C₄×C₇×M₁₆	C₂	semidirect
4. C₄×C₇×#121	C₂	semidirect
5. C₇×#1972	C₂	semidirect
6. C₇×#1944	C₂	semidirect
7. C₇×#1936	C₂	semidirect
8. C₇×#1895	C₂	semidirect
9. C₇×#1809	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₄×C₇×#102	C₂	semidirect
19. C₇×#469	C₄	direct (N × H)
42. C₄×#469	C₇	direct (N × H)
51. C₂×C₇×D₈	C₂×C₄	semidirect
57. C₂×C₇×M₁₆	C₂×C₄	semidirect
63. C₇×#121	C₂×C₄	semidirect
85. C₇×#106	C₂×C₄	semidirect
88. C₇×#102	C₂×C₄	semidirect
92. C₄×C₇×C₈	D₄	semidirect
97. C₂×C₄×D₈	C₂×C₇	semidirect
98. C₂×C₄×M₁₆	C₂×C₇	semidirect
99. C₄×#121	C₂×C₇	semidirect
100. #1972	C₂×C₇	semidirect
101. #1944	C₂×C₇	semidirect
102. #1936	C₂×C₇	semidirect
103. #1895	C₂×C₇	semidirect
104. #1809	C₂×C₇	semidirect
105. C₄×#106	C₂×C₇	semidirect
106. C₄×#102	C₂×C₇	semidirect
181. #469	C₄×C₇	direct (N × H)
258. C₇×C₈	C₄×D₄	semidirect
267. C₂×D₈	C₂×C₄×C₇	semidirect
273. C₂×M₁₆	C₂×C₄×C₇	semidirect
279. #121	C₂×C₄×C₇	semidirect
301. #106	C₂×C₄×C₇	semidirect
304. #102	C₂×C₄×C₇	semidirect
308. C₄×C₈	C₇×D₄	semidirect
336. C₄×C₇	#469	direct (N × H)
469. C₈	C₄×C₇×D₄	semidirect
470. C₇	C₄×#469	direct (N × H)
495. C₄	C₇×#469	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×#469	2
C₂×C₄×C₇×D₈	2
C₂×C₄×C₇×M₁₆	2
C₄×C₇×#121	2
C₇×#1972	2
C₇×#1944	2
C₇×#1936	2
C₇×#1895	2
C₇×#1809	2
C₄×C₇×#106	2
C₄×C₇×#102	2
C₄×#469	7

Subgroups — C4×C7×#469 #13198749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#469 #13198749