Subgroups — C₇×#24764 #13201980

Order 1792.

904 conjugacy classes of subgroups.

The subgroup lattice has 686 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×C₇×#467	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic
5	C₇×#2621	C₂	1	1	yes	maximal, characteristic
6	C₇×#2323	C₂	1	1	yes	maximal, characteristic
7	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1894	C₂	1	1	yes	maximal, characteristic
14	C₇×#1892	C₂	1	1	yes	maximal, characteristic
15	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#117	C₂²	1	1	yes	characteristic
26	C₇×#470	—	2	4	no	—
27	C₇×#467	—	2	4	no	—
28	C₇×#462	—	2	4	no	—
29	C₂×C₇×#107	C₂²	1	1	yes	characteristic
30	C₂×C₇×#106	C₂²	1	1	yes	characteristic
31	C₇×#424	—	2	4	no	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#103	C₂²	1	1	yes	characteristic
42	C₂×C₇×#103	C₂²	1	1	yes	characteristic
43	C₂×C₇×#103	C₂²	1	1	yes	characteristic
44	C₇×#398	—	2	1	no	—
45	C₇×#398	—	2	1	no	—
46	C₇×#397	—	2	1	no	—
47	C₇×#397	—	2	1	no	—
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#389	—	2	1	no	—
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#388	—	2	1	no	—
54	C₇×#388	—	2	1	no	—
55	C₇×#387	—	2	1	no	—
56	C₇×#382	C₂²	1	1	yes	characteristic
57	C₇×#380	C₂²	1	1	yes	characteristic
58	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	C₇×#340	C₂²	1	1	yes	characteristic
63	#24764	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₇×Q₁₆	—	2	2	no	—
69	C₂×C₇×Q₁₆	—	2	2	no	—
70	C₂×C₇×Q₁₆	—	2	2	no	—
71	C₂×C₇×Q₁₆	—	2	2	no	—
72	C₂×C₇×Q₁₆	—	4	1	no	—
73	C₂×C₇×Q₁₆	—	4	1	no	—
74	C₂×C₇×M₁₆	—	2	2	no	—
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	4	1	no	—
77	C₂²×C₇×C₈	—	2	2	no	—
78	C₂²×C₇×C₈	—	2	2	no	—
79	C₂²×C₇×C₈	—	4	1	no	—
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊Q₈	—	2	2	no	—
85	C₇×C₄⋊Q₈	—	2	2	no	—
86	C₇×C₂²⋊Q₈	—	2	2	no	—
87	C₇×C₂²⋊Q₈	—	2	2	no	—
88	C₇×C₂²⋊Q₈	—	2	2	no	—
89	C₇×C₂²⋊Q₈	—	2	2	no	—
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₇×C₂²⋊Q₈	D₄	1	4	yes	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	2	2	no	—
94	C₇×#117	—	2	2	no	—
95	C₇×#117	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	—	2	1	no	—
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₇×#107	—	2	2	no	—
121	C₇×#106	—	2	2	no	—
122	C₇×C₄⋊C₈	—	2	2	no	—
123	C₇×C₄⋊C₈	—	2	2	no	—
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	D₄	1	4	yes	—
126	C₇×#103	—	2	2	no	—
127	C₇×#103	—	2	2	no	—
128	C₇×#103	—	2	2	no	—
129	C₇×#103	—	2	2	no	—
130	C₇×#103	—	2	2	no	—
131	C₇×#103	—	2	2	no	—
132	C₇×#103	—	4	1	no	—
133	C₇×#103	—	4	1	no	—
134	C₇×#95	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	—	2	1	no	—
143	C₇×#95	—	2	1	no	—
144	C₇×#95	—	2	1	no	—
145	C₂×#470	C₂×C₇	1	1	yes	characteristic
146	C₂×#467	C₂×C₇	1	1	yes	characteristic
147	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#424	C₂×C₇	1	1	yes	characteristic
149	#2621	C₂×C₇	1	1	yes	characteristic
150	#2323	C₂×C₇	1	1	yes	characteristic
151	#2068	C₂×C₇	1	1	yes	characteristic, complemented
152	#2066	C₂×C₇	1	1	yes	characteristic, complemented
153	#2056	C₂×C₇	1	1	yes	characteristic, complemented
154	#2056	C₂×C₇	1	1	yes	characteristic, complemented
155	#1981	C₂×C₇	1	1	yes	characteristic, complemented
156	#1949	C₂×C₇	1	1	yes	characteristic, complemented
157	#1894	C₂×C₇	1	1	yes	characteristic
158	#1892	C₂×C₇	1	1	yes	characteristic
159	#1805	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	2	1	no	—
172	C₂×C₇×Q₈	—	2	1	no	—
173	C₂×C₇×Q₈	—	2	1	no	—
174	C₂×C₇×Q₈	—	2	1	no	—
175	C₂×C₇×Q₈	—	2	1	no	—
176	C₂×C₇×Q₈	—	2	1	no	—
177	C₂×C₇×Q₈	—	2	1	no	—
178	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₇	#41	1	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₇×Q₁₆	—	4	4	no	—
200	C₇×Q₁₆	—	4	4	no	—
201	C₇×M₁₆	—	4	4	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	4	4	no	—
213	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
214	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
215	C₇×C₄⋊C₄	—	2	4	no	—
216	C₇×C₄⋊C₄	—	2	2	no	—
217	C₇×C₄⋊C₄	—	2	2	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	—	4	2	no	—
229	C₇×C₄⋊C₄	—	4	2	no	—
230	C₇×C₄⋊C₄	—	4	2	no	—
231	C₇×C₄⋊C₄	—	4	2	no	—
232	C₇×C₄⋊C₄	—	8	1	no	—
233	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
234	C₇×C₂²⋊C₄	—	2	4	no	—
235	C₇×C₂²⋊C₄	—	2	2	no	—
236	C₇×C₂²⋊C₄	—	2	2	no	—
237	C₇×C₂²⋊C₄	—	4	2	no	—
238	C₇×C₂²⋊C₄	—	4	2	no	—
239	C₇×C₂²⋊C₄	—	8	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	4	2	no	—
243	C₄²×C₇	—	8	1	no	—
244	C₄²×C₇	C₂×D₄	1	2	yes	—
245	C₄²×C₇	#41	1	2	yes	—
246	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
247	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
255	C₂×#117	C₂²×C₇	1	1	yes	characteristic
256	#470	—	2	4	no	—
257	#467	—	2	4	no	—
258	#462	—	2	4	no	—
259	C₂×#107	C₂²×C₇	1	1	yes	characteristic
260	C₂×#106	C₂²×C₇	1	1	yes	characteristic
261	#424	—	2	4	no	—
262	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₇	1	1	yes	characteristic
267	C₂×#103	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇	1	1	yes	characteristic
274	#398	—	2	1	no	—
275	#398	—	2	1	no	—
276	#397	—	2	1	no	—
277	#397	—	2	1	no	—
278	#391	C₂²×C₇	1	1	yes	characteristic
279	#391	C₂²×C₇	1	1	yes	characteristic
280	#391	C₂²×C₇	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	C₂²×C₇	1	1	yes	characteristic
283	#388	—	2	1	no	—
284	#388	—	2	1	no	—
285	#387	—	2	1	no	—
286	#382	C₂²×C₇	1	1	yes	characteristic
287	#380	C₂²×C₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	C₂³×C₇	—	2	1	no	—
294	C₂³×C₇	—	2	1	no	—
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	#121	1	2	yes	—
300	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
301	C₇×Q₈	—	2	2	no	—
302	C₇×Q₈	—	2	2	no	—
303	C₇×Q₈	—	4	1	no	—
304	C₇×Q₈	—	4	1	no	—
305	C₇×Q₈	—	4	1	no	—
306	C₇×Q₈	—	4	1	no	—
307	C₇×Q₈	—	4	1	no	—
308	C₇×Q₈	—	4	1	no	—
309	C₇×Q₈	—	4	1	no	—
310	C₇×Q₈	—	4	1	no	—
311	C₇×Q₈	—	4	1	no	—
312	C₇×Q₈	—	4	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	2	no	—
321	C₂×C₄×C₇	—	2	2	no	—
322	C₂×C₄×C₇	—	2	2	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	2	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	—	4	1	no	—
335	C₂×C₄×C₇	—	4	1	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	#121	1	2	yes	—
354	C₂×C₄×C₇	#121	1	2	yes	—
355	C₂×C₄×C₇	#121	1	2	yes	—
356	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
362	C₇×C₈	—	2	2	no	—
363	C₇×C₈	—	2	2	no	—
364	C₇×C₈	—	4	1	no	—
365	C₇×C₈	—	4	1	no	—
366	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
370	C₂×Q₁₆	—	2	2	no	—
371	C₂×Q₁₆	—	2	2	no	—
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	—	2	2	no	—
374	C₂×Q₁₆	—	4	1	no	—
375	C₂×Q₁₆	—	4	1	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	4	1	no	—
379	C₂²×C₈	—	2	2	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	—	4	1	no	—
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	C₇×D₄	1	4	yes	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
422	#107	—	2	2	no	—
423	#106	—	2	2	no	—
424	C₄⋊C₈	—	2	2	no	—
425	C₄⋊C₈	—	2	2	no	—
426	C₄⋊C₈	—	2	2	no	—
427	C₄⋊C₈	C₇×D₄	1	4	yes	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	4	1	no	—
435	#103	—	4	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	C₂²×C₇	—	2	2	no	—
448	C₂²×C₇	—	2	2	no	—
449	C₂²×C₇	—	2	2	no	—
450	C₂²×C₇	—	4	1	no	—
451	C₂²×C₇	—	4	1	no	—
452	C₂²×C₇	—	4	1	no	—
453	C₂²×C₇	—	4	1	no	—
454	C₂²×C₇	C₂×#121	1	1	yes	characteristic
455	C₂²×C₇	C₂×#121	1	1	yes	characteristic
456	C₂²×C₇	#537	1	1	yes	characteristic
457	C₂²×C₇	#577	1	1	yes	characteristic
458	C₂²×C₇	#578	1	1	yes	characteristic
459	C₂²×C₇	#578	1	1	yes	characteristic
460	C₂²×C₇	#578	1	1	yes	characteristic
461	C₄×C₇	—	2	2	no	—
462	C₄×C₇	—	2	2	no	—
463	C₄×C₇	—	2	2	no	—
464	C₄×C₇	—	4	2	no	—
465	C₄×C₇	—	4	2	no	—
466	C₄×C₇	—	4	1	no	—
467	C₄×C₇	—	4	1	no	—
468	C₄×C₇	—	8	1	no	—
469	C₄×C₇	—	8	1	no	—
470	C₄×C₇	—	8	1	no	—
471	C₄×C₇	—	8	1	no	—
472	C₄×C₇	—	8	1	no	—
473	C₄×C₇	—	8	1	no	—
474	C₄×C₇	D₄²	1	1	yes	characteristic
475	C₄×C₇	#547	1	1	yes	characteristic
476	C₄×C₇	#548	1	1	yes	characteristic
477	C₄×C₇	#553	1	1	yes	characteristic
478	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
515	C₂²×C₄	C₇×#41	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
517	Q₁₆	—	4	4	no	—
518	Q₁₆	—	4	4	no	—
519	M₁₆	—	4	4	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	4	4	no	—
531	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
532	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	8	1	no	—
551	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	8	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	8	1	no	—
562	C₄²	C₂×C₇×D₄	1	2	yes	—
563	C₄²	C₇×#41	1	2	yes	—
564	C₂×C₇	—	4	2	no	—
565	C₂×C₇	#2416	1	1	yes	characteristic
566	C₂×C₇	#3044	1	1	yes	characteristic
567	C₂×C₇	#3046	1	1	yes	characteristic
568	C₂×C₇	#3059	1	1	yes	characteristic
569	C₂×C₇	#3063	1	1	yes	characteristic
570	C₂×C₇	#3258	1	1	yes	characteristic
571	C₂×C₇	#3261	1	1	yes	characteristic
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	C₇×#121	1	2	yes	—
579	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	C₇×#121	1	2	yes	—
633	C₂×C₄	C₇×#121	1	2	yes	—
634	C₂×C₄	C₇×#121	1	2	yes	—
635	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
636	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
637	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
638	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
639	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	2	2	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₇	#24764	1	1	yes	characteristic, direct product factor, Sylow
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	C₂×C₇×#121	1	1	yes	characteristic
654	C₂²	C₂×C₇×#121	1	1	yes	characteristic
655	C₂²	C₇×#537	1	1	yes	characteristic
656	C₂²	C₇×#577	1	1	yes	characteristic
657	C₂²	C₇×#578	1	1	yes	characteristic
658	C₂²	C₇×#578	1	1	yes	characteristic
659	C₂²	C₇×#578	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₇×D₄²	1	1	yes	characteristic
674	C₄	C₇×#547	1	1	yes	characteristic
675	C₄	C₇×#548	1	1	yes	characteristic
676	C₄	C₇×#553	1	1	yes	characteristic
677	C₂	—	4	2	no	—
678	C₂	C₇×#2416	1	1	yes	characteristic
679	C₂	C₇×#3044	1	1	yes	characteristic
680	C₂	C₇×#3046	1	1	yes	characteristic
681	C₂	C₇×#3059	1	1	yes	characteristic
682	C₂	C₇×#3063	1	1	yes	characteristic
683	C₂	C₇×#3258	1	1	yes	characteristic
684	C₂	C₇×#3261	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#462	C₂	semidirect
7. C₇×#2068	C₂	semidirect
8. C₇×#2066	C₂	semidirect
9. C₇×#2056	C₂	semidirect
10. C₇×#2056	C₂	semidirect
11. C₇×#1981	C₂	semidirect
12. C₇×#1949	C₂	semidirect
15. C₇×#1805	C₂	semidirect
63. #24764	C₇	direct (N × H)
147. C₂×#462	C₂×C₇	semidirect
151. #2068	C₂×C₇	semidirect
152. #2066	C₂×C₇	semidirect
153. #2056	C₂×C₇	semidirect
154. #2056	C₂×C₇	semidirect
155. #1981	C₂×C₇	semidirect
156. #1949	C₂×C₇	semidirect
159. #1805	C₂×C₇	semidirect
645. C₇	#24764	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×C₇×#467	2
C₂×C₇×#462	2
C₂×C₇×#424	2
C₇×#2621	2
C₇×#2323	2
C₇×#2068	2
C₇×#2066	2
C₇×#2056	2
C₇×#1981	2
C₇×#1949	2
C₇×#1894	2
C₇×#1892	2
C₇×#1805	2
#24764	7

Subgroups — C7×#24764 #13201980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24764 #13201980