Subgroups — C₄×C₇×#470 #13198750

Order 1792.

1002 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1935	C₂	1	2	yes	maximal, complemented
8	C₇×#1894	C₂	1	2	yes	maximal
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×Q₁₆	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×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
17	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
18	C₇×#470	C₄	1	8	yes	direct product factor
19	C₄×C₇×Q₁₆	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	2	yes	—
26	C₄×C₇×M₁₆	—	2	4	no	—
27	C₂×C₇×#97	C₂²	1	1	yes	characteristic
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#391	C₂²	1	2	yes	—
32	C₇×#389	C₂²	1	2	yes	—
33	C₇×#387	—	2	2	no	—
34	C₇×#385	—	2	2	no	—
35	C₇×#380	C₂²	1	2	yes	—
36	C₄×C₇×C₄⋊C₄	—	2	2	no	—
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×#470	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂×C₇×Q₁₆	—	2	2	no	—
48	C₂×C₇×Q₁₆	—	2	2	no	—
49	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
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	C₂×C₄	1	4	yes	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
60	C₇×C₂²⋊Q₈	—	2	4	no	—
61	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
62	C₄×C₇×Q₈	—	2	4	no	—
63	C₄×C₇×Q₈	—	2	4	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₇	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#107	—	2	2	no	—
81	C₇×#106	—	2	2	no	—
82	C₇×#106	C₂×C₄	1	4	yes	complemented
83	C₇×#103	—	2	4	no	—
84	C₇×#103	—	2	4	no	—
85	C₇×#103	C₂×C₄	1	8	yes	complemented
86	C₇×#97	—	2	2	no	—
87	C₇×#97	—	2	2	no	—
88	C₄×C₇×C₈	—	2	2	no	—
89	C₄×C₇×C₈	D₄	1	4	yes	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₂×#470	C₂×C₇	1	1	yes	characteristic
96	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic
98	C₄×C₂²⋊Q₈	C₂×C₇	1	2	yes	—
99	#1971	C₂×C₇	1	1	yes	characteristic, complemented
100	#1944	C₂×C₇	1	1	yes	characteristic, complemented
101	#1935	C₂×C₇	1	2	yes	complemented
102	#1894	C₂×C₇	1	2	yes	—
103	#1809	C₂×C₇	1	1	yes	characteristic
104	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
105	C₄×#103	C₂×C₇	1	2	yes	complemented
106	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	—	2	2	no	—
111	C₂×C₇×Q₈	—	2	2	no	—
112	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	4	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	4	2	no	—
125	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	#41	1	2	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
133	C₇×Q₁₆	—	2	8	no	—
134	C₇×M₁₆	—	2	8	no	—
135	C₇×M₁₆	—	2	8	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₇×C₈	#41	1	2	yes	—
147	C₂×C₇×C₈	#41	1	2	yes	—
148	C₇×C₄⋊C₄	—	2	8	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	4	4	no	—
155	C₇×C₄⋊C₄	—	4	4	no	—
156	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
157	C₇×C₂²⋊C₄	—	2	8	no	—
158	C₇×C₂²⋊C₄	—	4	4	no	—
159	C₄²×C₇	—	2	2	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	—	2	1	no	—
162	C₄²×C₇	—	2	1	no	—
163	C₄²×C₇	—	4	4	no	—
164	C₄²×C₇	—	4	4	no	—
165	C₄²×C₇	C₂×D₄	1	2	yes	—
166	C₄²×C₇	#41	1	2	yes	—
167	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
168	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
169	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
171	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
172	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
173	#470	C₄×C₇	1	8	yes	direct product factor
174	C₄×Q₁₆	—	2	4	no	—
175	C₂×#107	C₂²×C₇	1	1	yes	characteristic
176	C₂×#106	C₂²×C₇	1	1	yes	characteristic
177	C₂×#106	C₂²×C₇	1	1	yes	characteristic
178	C₂×#103	C₂²×C₇	1	2	yes	—
179	C₂×#103	C₂²×C₇	1	2	yes	—
180	C₂×#103	C₂²×C₇	1	2	yes	—
181	C₄×M₁₆	—	2	4	no	—
182	C₂×#97	C₂²×C₇	1	1	yes	characteristic
183	C₂×#97	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
186	#391	C₂²×C₇	1	2	yes	—
187	#389	C₂²×C₇	1	2	yes	—
188	#387	—	2	2	no	—
189	#385	—	2	2	no	—
190	#380	C₂²×C₇	1	2	yes	—
191	C₄×C₄⋊C₄	—	2	2	no	—
192	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
193	C₄×C₂²⋊C₄	—	2	2	no	—
194	#340	C₂²×C₇	1	2	yes	—
195	#340	C₂²×C₇	1	2	yes	—
196	#340	C₂²×C₇	1	2	yes	—
197	C₂³×C₇	—	2	1	no	—
198	C₂³×C₇	—	2	1	no	—
199	C₂³×C₇	—	2	2	no	—
200	C₂³×C₇	—	2	2	no	—
201	C₂³×C₇	C₄×D₄	1	2	yes	—
202	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₇×Q₈	—	2	4	no	—
204	C₇×Q₈	—	2	4	no	—
205	C₇×Q₈	—	4	2	no	—
206	C₇×Q₈	—	4	2	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	4	4	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	4	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₇	#121	1	2	yes	—
234	C₂×C₄×C₇	#121	1	2	yes	—
235	C₂×C₄×C₇	#137	1	4	yes	—
236	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
242	C₇×C₈	—	2	2	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	C₄×D₄	1	4	yes	—
246	C₂²×Q₈	C₂³×C₇	1	2	yes	—
247	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
248	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
259	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₂²⋊Q₈	—	2	4	no	—
264	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
280	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	#107	—	2	2	no	—
284	#106	—	2	2	no	—
285	#106	C₂×C₄×C₇	1	4	yes	complemented
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#103	C₂×C₄×C₇	1	8	yes	complemented
289	#97	—	2	2	no	—
290	#97	—	2	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	C₇×D₄	1	4	yes	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂²×C₇	—	2	4	no	—
299	C₂²×C₇	—	2	2	no	—
300	C₂²×C₇	—	4	2	no	—
301	C₂²×C₇	—	4	1	no	—
302	C₂²×C₇	—	4	1	no	—
303	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₇	C₂×#121	1	1	yes	characteristic
305	C₂²×C₇	#532	1	1	yes	characteristic
306	C₂²×C₇	C₂×#137	1	2	yes	—
307	C₂²×C₇	#575	1	2	yes	—
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	4	4	no	—
311	C₄×C₇	—	4	1	no	—
312	C₄×C₇	—	4	1	no	—
313	C₄×C₇	—	4	4	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	—	8	2	no	—
316	C₄×C₇	#470	1	4	yes	direct product factor
317	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₇	C₄×#41	1	1	yes	characteristic
319	C₄×C₇	#525	1	1	yes	characteristic
320	C₄×C₇	#529	1	1	yes	characteristic
321	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₇×#41	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	Q₁₆	—	2	8	no	—
349	M₁₆	—	2	8	no	—
350	M₁₆	—	2	8	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
358	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
359	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
360	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
361	C₂×C₈	C₇×#41	1	2	yes	—
362	C₂×C₈	C₇×#41	1	2	yes	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	4	4	no	—
380	C₄²	C₂×C₇×D₄	1	2	yes	—
381	C₄²	C₇×#41	1	2	yes	—
382	C₂×C₇	—	4	2	no	—
383	C₂×C₇	C₄×#121	1	1	yes	characteristic
384	C₂×C₇	C₄×#137	1	2	yes	—
385	C₂×C₇	C₂×#470	1	1	yes	characteristic
386	C₂×C₇	#3054	1	1	yes	characteristic
387	C₂×C₇	#3172	1	2	yes	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	C₄×C₇×D₄	1	2	yes	—
393	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
394	Q₈	—	2	4	no	—
395	Q₈	—	2	4	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
424	C₂×C₄	C₇×#121	1	2	yes	—
425	C₂×C₄	C₇×#121	1	2	yes	—
426	C₂×C₄	C₇×#137	1	4	yes	—
427	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
430	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	C₄×C₇×D₄	1	4	yes	—
437	C₇	C₄×#470	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
444	C₂²	C₂×C₇×#121	1	1	yes	characteristic
445	C₂²	C₇×#532	1	1	yes	characteristic
446	C₂²	C₂×C₇×#137	1	2	yes	—
447	C₂²	C₇×#575	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	C₇×#470	1	4	yes	direct product factor
457	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
458	C₄	C₄×C₇×#41	1	1	yes	characteristic
459	C₄	C₇×#525	1	1	yes	characteristic
460	C₄	C₇×#529	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	C₄×C₇×#121	1	1	yes	characteristic
463	C₂	C₄×C₇×#137	1	2	yes	—
464	C₂	C₂×C₇×#470	1	1	yes	characteristic
465	C₂	C₇×#3054	1	1	yes	characteristic
466	C₂	C₇×#3172	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	C₂⁴×C₇	C₂×D₄
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×Q₁₆	C₂	semidirect
5. C₇×#1971	C₂	semidirect
6. C₇×#1944	C₂	semidirect
7. C₇×#1935	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₄×C₇×#103	C₂	semidirect
18. C₇×#470	C₄	direct (N × H)
42. C₄×#470	C₇	direct (N × H)
49. C₂×C₇×Q₁₆	C₂×C₄	semidirect
82. C₇×#106	C₂×C₄	semidirect
85. C₇×#103	C₂×C₄	semidirect
96. C₂×C₄×Q₁₆	C₂×C₇	semidirect
99. #1971	C₂×C₇	semidirect
100. #1944	C₂×C₇	semidirect
101. #1935	C₂×C₇	semidirect
104. C₄×#106	C₂×C₇	semidirect
105. C₄×#103	C₂×C₇	semidirect
173. #470	C₄×C₇	direct (N × H)
252. C₂×Q₁₆	C₂×C₄×C₇	semidirect
285. #106	C₂×C₄×C₇	semidirect
288. #103	C₂×C₄×C₇	semidirect
316. C₄×C₇	#470	direct (N × H)
437. C₇	C₄×#470	direct (N × H)
456. C₄	C₇×#470	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×#470	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×M₁₆	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#1971	2
C₇×#1944	2
C₇×#1935	2
C₇×#1894	2
C₇×#1809	2
C₄×C₇×#106	2
C₄×C₇×#103	2
C₄×#470	7

Subgroups — C4×C7×#470 #13198750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#470 #13198750