Subgroups — C₇×#60719 #13237935

Order 1792.

1966 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3180	C₂	1	4	yes	maximal, complemented
4	C₇×#3179	C₂	1	8	yes	maximal, complemented
5	C₇×#3171	C₂	1	4	yes	maximal, complemented
6	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3058	C₂	1	2	yes	maximal, complemented
11	C₇×#3057	C₂	1	2	yes	maximal, complemented
12	C₇×#2949	C₂	1	2	yes	maximal, complemented
13	C₇×#2948	C₂	1	2	yes	maximal, complemented
14	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×D₈	C₂²	1	2	yes	—
17	C₂×C₇×#131	C₂²	1	2	yes	—
18	C₇×#559	—	2	2	no	—
19	C₇×#559	—	2	2	no	—
20	C₇×#556	—	2	2	no	—
21	C₇×#551	—	2	4	no	—
22	C₇×#550	—	2	2	no	—
23	C₇×#546	—	2	4	no	—
24	C₇×#542	C₂²	1	4	yes	complemented
25	C₇×#540	C₂²	1	4	yes	complemented
26	C₇×#536	C₂²	1	1	yes	characteristic
27	C₇×#535	C₂²	1	2	yes	—
28	C₇×#535	C₂²	1	1	yes	characteristic
29	C₇×#533	C₂²	1	1	yes	characteristic
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#532	C₂²	1	4	yes	complemented
32	C₂×C₇×#127	C₂²	1	1	yes	characteristic
33	C₇×#529	C₂²	1	4	yes	complemented
34	C₂×C₇×#124	C₂²	1	1	yes	characteristic
35	C₇×#519	C₂²	1	1	yes	characteristic
36	C₇×#518	C₂²	1	1	yes	characteristic
37	C₇×#518	C₂²	1	2	yes	—
38	C₄×C₇×#41	C₂²	1	1	yes	characteristic
39	C₇×#501	C₂²	1	2	yes	complemented
40	C₇×#501	C₂²	1	4	yes	complemented
41	C₇×#501	C₂²	1	2	yes	complemented
42	C₇×#496	C₂²	1	2	yes	—
43	C₇×#496	C₂²	1	4	yes	—
44	C₇×#496	C₂²	1	2	yes	—
45	C₇×#490	C₂²	1	4	yes	complemented
46	C₇×#489	C₂²	1	4	yes	complemented
47	C₇×#488	C₂²	1	4	yes	complemented
48	C₇×#486	C₂²	1	4	yes	complemented
49	C₇×#469	C₂²	1	8	yes	complemented
50	C₇×#468	C₂²	1	8	yes	complemented
51	C₇×#466	C₂²	1	8	yes	complemented
52	C₇×#465	C₂²	1	8	yes	complemented
53	C₇×#442	C₂²	1	8	yes	complemented
54	C₇×#440	C₂²	1	8	yes	complemented
55	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
56	C₄×C₇×D₈	C₂²	1	8	yes	complemented
57	C₇×#427	C₂²	1	2	yes	—
58	C₇×#427	C₂²	1	2	yes	—
59	C₇×#419	C₂²	1	2	yes	—
60	C₇×#418	C₂²	1	2	yes	—
61	C₇×#418	C₂²	1	2	yes	—
62	C₇×#418	C₂²	1	2	yes	—
63	C₇×#405	C₂²	1	2	yes	—
64	C₇×#405	C₂²	1	4	yes	complemented
65	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
67	C₂×C₇×#97	C₂²	1	1	yes	characteristic
68	C₂×C₇×#97	C₂²	1	2	yes	complemented
69	#60719	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₇×#41	—	2	4	no	—
71	C₂×C₇×#41	C₂³	1	1	yes	characteristic
72	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×D₄	—	2	2	no	—
74	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
75	C₂²×C₇×D₄	C₂³	1	2	yes	—
76	C₂×C₇×SD₁₆	—	2	8	no	—
77	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
79	C₂×C₇×D₈	—	2	8	no	—
80	C₂×C₇×D₈	C₂³	1	4	yes	—
81	C₂×C₇×D₈	C₂³	1	4	yes	—
82	C₇×#131	—	2	8	no	—
83	C₂×C₇×M₁₆	C₂³	1	4	yes	—
84	C₂×C₇×M₁₆	C₂³	1	2	yes	—
85	C₂²×C₇×C₈	C₂³	1	4	yes	—
86	C₂²×C₇×C₈	C₂³	1	2	yes	—
87	C₇×C₄⋊Q₈	—	2	1	no	—
88	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₇×#127	—	2	2	no	—
91	C₇×#127	—	2	1	no	—
92	C₇×#127	—	2	2	no	—
93	C₇×#127	C₂³	1	2	yes	—
94	C₇×#127	C₂³	1	2	yes	—
95	C₇×#126	—	2	4	no	—
96	C₇×#126	—	2	4	no	—
97	C₇×#125	C₂³	1	2	yes	—
98	C₇×#125	C₂³	1	2	yes	—
99	C₇×#124	—	2	1	no	—
100	C₇×#124	—	2	2	no	—
101	C₇×#124	—	2	1	no	—
102	C₇×#124	—	2	4	no	—
103	C₇×#124	—	2	2	no	—
104	C₇×#124	—	2	4	no	—
105	C₇×#124	C₂³	1	2	yes	—
106	C₇×#124	C₂³	1	2	yes	—
107	C₇×#123	—	2	2	no	—
108	C₇×#123	—	2	4	no	—
109	C₇×#123	—	2	8	no	—
110	C₇×#123	—	2	4	no	—
111	C₇×C₂²⋊Q₈	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	4	no	—
114	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₇×#121	—	2	4	no	—
116	C₇×#121	—	2	8	no	—
117	C₇×#121	C₂³	1	4	yes	—
118	C₇×#121	C₂³	1	8	yes	—
119	C₇×#120	—	2	4	no	—
120	C₇×#120	—	2	2	no	—
121	C₄×C₇×Q₈	—	2	2	no	—
122	C₄×C₇×Q₈	—	2	2	no	—
123	C₄×C₇×Q₈	—	2	2	no	—
124	C₄×C₇×Q₈	D₄	1	2	yes	—
125	C₄×C₇×Q₈	C₂³	1	4	yes	—
126	C₄×C₇×D₄	—	2	4	no	—
127	C₄×C₇×D₄	—	2	4	no	—
128	C₄×C₇×D₄	—	2	2	no	—
129	C₄×C₇×D₄	—	2	4	no	—
130	C₄×C₇×D₄	D₄	1	4	yes	—
131	C₄×C₇×D₄	D₄	1	2	yes	—
132	C₄×C₇×D₄	C₂³	1	4	yes	—
133	C₄×C₇×D₄	C₂³	1	8	yes	—
134	C₇×#117	—	2	2	no	—
135	C₇×#117	—	2	4	no	—
136	C₇×#117	C₂³	1	2	yes	—
137	C₇×#117	C₂³	1	1	yes	characteristic
138	C₇×#117	C₂³	1	1	yes	characteristic
139	C₇×#117	C₂³	1	1	yes	characteristic
140	C₇×#117	C₂³	1	2	yes	—
141	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₇	C₂³	1	2	yes	—
146	C₇×#107	C₂³	1	4	yes	—
147	C₇×#107	C₂³	1	4	yes	—
148	C₇×#106	C₂³	1	4	yes	—
149	C₇×#106	C₂³	1	4	yes	—
150	C₇×#103	C₂³	1	8	yes	—
151	C₇×#102	C₂³	1	8	yes	—
152	C₇×#102	C₂³	1	8	yes	—
153	C₇×#102	C₂³	1	8	yes	—
154	C₇×#97	C₂³	1	2	yes	—
155	C₇×#97	C₂³	1	1	yes	characteristic
156	C₇×#97	C₂³	1	1	yes	characteristic
157	C₇×#97	C₂³	1	2	yes	—
158	C₇×#97	C₂³	1	4	yes	—
159	C₄×C₇×C₈	C₂³	1	2	yes	—
160	C₄×C₇×C₈	C₂³	1	4	yes	—
161	#3510	C₂×C₇	1	1	yes	characteristic, complemented
162	#3508	C₂×C₇	1	1	yes	characteristic, complemented
163	#3180	C₂×C₇	1	4	yes	complemented
164	#3179	C₂×C₇	1	8	yes	complemented
165	#3171	C₂×C₇	1	4	yes	complemented
166	#3162	C₂×C₇	1	1	yes	characteristic, complemented
167	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
168	#3140	C₂×C₇	1	1	yes	characteristic, complemented
169	#3138	C₂×C₇	1	1	yes	characteristic, complemented
170	#3058	C₂×C₇	1	2	yes	complemented
171	#3057	C₂×C₇	1	2	yes	complemented
172	#2949	C₂×C₇	1	2	yes	complemented
173	#2948	C₂×C₇	1	2	yes	complemented
174	#2875	C₂×C₇	1	1	yes	characteristic, complemented
175	C₂⁴×C₇	—	2	1	no	—
176	C₂⁴×C₇	—	2	2	no	—
177	C₇×#41	—	2	4	no	—
178	C₇×#41	—	8	8	no	—
179	C₂×C₇×Q₈	—	2	1	no	—
180	C₂×C₇×Q₈	—	2	2	no	—
181	C₂×C₇×Q₈	—	2	2	no	—
182	C₂×C₇×Q₈	—	2	4	no	—
183	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
185	C₂×C₇×D₄	—	2	4	no	—
186	C₂×C₇×D₄	—	2	8	no	—
187	C₂×C₇×D₄	—	2	1	no	—
188	C₂×C₇×D₄	—	2	2	no	—
189	C₂×C₇×D₄	—	2	4	no	—
190	C₂×C₇×D₄	—	2	4	no	—
191	C₂×C₇×D₄	—	2	4	no	—
192	C₂×C₇×D₄	—	2	4	no	—
193	C₂×C₇×D₄	—	2	4	no	—
194	C₂×C₇×D₄	—	8	4	no	—
195	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
196	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂×C₇×D₄	C₂⁴	1	2	yes	—
198	C₂×C₇×D₄	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	2	4	no	—
201	C₂²×C₄×C₇	—	2	8	no	—
202	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
206	C₇×SD₁₆	—	2	8	no	—
207	C₇×SD₁₆	—	2	8	no	—
208	C₇×D₈	—	2	8	no	—
209	C₇×D₈	—	2	8	no	—
210	C₇×M₁₆	—	2	4	no	—
211	C₇×M₁₆	—	2	8	no	—
212	C₂×C₇×C₈	—	2	8	no	—
213	C₂×C₇×C₈	#41	1	8	yes	complemented
214	C₂×C₇×C₈	C₂⁴	1	4	yes	—
215	C₂×C₇×C₈	C₂⁴	1	2	yes	—
216	C₂×C₇×C₈	C₂⁴	1	2	yes	—
217	C₇×C₄⋊C₄	—	2	2	no	—
218	C₇×C₄⋊C₄	—	2	4	no	—
219	C₇×C₄⋊C₄	—	2	4	no	—
220	C₇×C₄⋊C₄	—	2	2	no	—
221	C₇×C₄⋊C₄	—	2	2	no	—
222	C₇×C₄⋊C₄	—	2	4	no	—
223	C₇×C₄⋊C₄	—	2	2	no	—
224	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
225	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
226	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
227	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
228	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
229	C₇×C₂²⋊C₄	—	2	2	no	—
230	C₇×C₂²⋊C₄	—	2	1	no	—
231	C₇×C₂²⋊C₄	—	2	1	no	—
232	C₇×C₂²⋊C₄	—	2	4	no	—
233	C₇×C₂²⋊C₄	—	2	4	no	—
234	C₇×C₂²⋊C₄	—	2	8	no	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	2	4	no	—
238	C₇×C₂²⋊C₄	—	2	8	no	—
239	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
240	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
241	C₄²×C₇	—	2	4	no	—
242	C₄²×C₇	—	2	2	no	—
243	C₄²×C₇	—	2	1	no	—
244	C₄²×C₇	—	2	1	no	—
245	C₄²×C₇	C₂×D₄	1	4	yes	—
246	C₄²×C₇	C₂×D₄	1	2	yes	—
247	C₄²×C₇	C₂⁴	1	2	yes	—
248	C₄²×C₇	C₂⁴	1	1	yes	characteristic
249	C₄²×C₇	C₂⁴	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
251	C₂²×D₈	C₂²×C₇	1	2	yes	—
252	C₂×#131	C₂²×C₇	1	2	yes	—
253	#559	—	2	2	no	—
254	#559	—	2	2	no	—
255	#556	—	2	2	no	—
256	#551	—	2	4	no	—
257	#550	—	2	2	no	—
258	#546	—	2	4	no	—
259	#542	C₂²×C₇	1	4	yes	complemented
260	#540	C₂²×C₇	1	4	yes	complemented
261	#536	C₂²×C₇	1	1	yes	characteristic
262	#535	C₂²×C₇	1	2	yes	—
263	#535	C₂²×C₇	1	1	yes	characteristic
264	#533	C₂²×C₇	1	1	yes	characteristic
265	#533	C₂²×C₇	1	1	yes	characteristic
266	#532	C₂²×C₇	1	4	yes	complemented
267	C₂×#127	C₂²×C₇	1	1	yes	characteristic
268	#529	C₂²×C₇	1	4	yes	complemented
269	C₂×#124	C₂²×C₇	1	1	yes	characteristic
270	#519	C₂²×C₇	1	1	yes	characteristic
271	#518	C₂²×C₇	1	1	yes	characteristic
272	#518	C₂²×C₇	1	2	yes	—
273	C₄×#41	C₂²×C₇	1	1	yes	characteristic
274	#501	C₂²×C₇	1	2	yes	complemented
275	#501	C₂²×C₇	1	4	yes	complemented
276	#501	C₂²×C₇	1	2	yes	complemented
277	#496	C₂²×C₇	1	2	yes	—
278	#496	C₂²×C₇	1	4	yes	—
279	#496	C₂²×C₇	1	2	yes	—
280	#490	C₂²×C₇	1	4	yes	complemented
281	#489	C₂²×C₇	1	4	yes	complemented
282	#488	C₂²×C₇	1	4	yes	complemented
283	#486	C₂²×C₇	1	4	yes	complemented
284	#469	C₂²×C₇	1	8	yes	complemented
285	#468	C₂²×C₇	1	8	yes	complemented
286	#466	C₂²×C₇	1	8	yes	complemented
287	#465	C₂²×C₇	1	8	yes	complemented
288	#442	C₂²×C₇	1	8	yes	complemented
289	#440	C₂²×C₇	1	8	yes	complemented
290	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
291	C₄×D₈	C₂²×C₇	1	8	yes	complemented
292	#427	C₂²×C₇	1	2	yes	—
293	#427	C₂²×C₇	1	2	yes	—
294	#419	C₂²×C₇	1	2	yes	—
295	#418	C₂²×C₇	1	2	yes	—
296	#418	C₂²×C₇	1	2	yes	—
297	#418	C₂²×C₇	1	2	yes	—
298	#405	C₂²×C₇	1	2	yes	—
299	#405	C₂²×C₇	1	4	yes	complemented
300	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
301	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
302	C₂×#97	C₂²×C₇	1	1	yes	characteristic
303	C₂×#97	C₂²×C₇	1	2	yes	complemented
304	C₂³×C₇	—	2	2	no	—
305	C₂³×C₇	—	2	4	no	—
306	C₂³×C₇	—	4	2	no	—
307	C₂³×C₇	—	4	4	no	—
308	C₂³×C₇	—	8	4	no	—
309	C₂³×C₇	—	8	2	no	—
310	C₂³×C₇	C₂²×D₄	1	2	yes	—
311	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
312	C₇×Q₈	—	2	2	no	—
313	C₇×Q₈	—	2	4	no	—
314	C₇×Q₈	—	4	4	no	—
315	C₇×Q₈	—	4	2	no	—
316	C₇×Q₈	—	8	2	no	—
317	C₇×D₄	—	2	4	no	—
318	C₇×D₄	—	2	2	no	—
319	C₇×D₄	—	2	4	no	—
320	C₇×D₄	—	2	4	no	—
321	C₇×D₄	—	2	4	no	—
322	C₇×D₄	—	4	8	no	—
323	C₇×D₄	—	4	2	no	—
324	C₇×D₄	—	4	4	no	—
325	C₇×D₄	—	8	4	no	—
326	C₇×D₄	—	8	4	no	—
327	C₇×D₄	—	8	8	no	—
328	C₂×C₄×C₇	—	2	4	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	4	no	—
333	C₂×C₄×C₇	—	4	2	no	—
334	C₂×C₄×C₇	—	4	4	no	—
335	C₂×C₄×C₇	—	4	2	no	—
336	C₂×C₄×C₇	—	8	4	no	—
337	C₂×C₄×C₇	—	8	8	no	—
338	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₇	C₂×#41	1	4	yes	—
344	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
345	C₇×C₈	—	2	4	no	—
346	C₇×C₈	C₂×#41	1	4	yes	—
347	C₇×C₈	C₂×#41	1	4	yes	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	C₂³×C₇	1	1	yes	characteristic
350	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
353	C₂²×D₄	C₂³×C₇	1	2	yes	—
354	C₂×SD₁₆	—	2	8	no	—
355	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
356	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
357	C₂×D₈	—	2	8	no	—
358	C₂×D₈	C₂³×C₇	1	4	yes	—
359	C₂×D₈	C₂³×C₇	1	4	yes	—
360	#131	—	2	8	no	—
361	C₂×M₁₆	C₂³×C₇	1	2	yes	—
362	C₂×M₁₆	C₂³×C₇	1	4	yes	—
363	C₂²×C₈	C₂³×C₇	1	4	yes	—
364	C₂²×C₈	C₂³×C₇	1	2	yes	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
367	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
368	#127	—	2	2	no	—
369	#127	—	2	1	no	—
370	#127	—	2	2	no	—
371	#127	C₂³×C₇	1	2	yes	—
372	#127	C₂³×C₇	1	2	yes	—
373	#126	—	2	4	no	—
374	#126	—	2	4	no	—
375	#125	C₂³×C₇	1	2	yes	—
376	#125	C₂³×C₇	1	2	yes	—
377	#124	—	2	1	no	—
378	#124	—	2	2	no	—
379	#124	—	2	1	no	—
380	#124	—	2	4	no	—
381	#124	—	2	2	no	—
382	#124	—	2	4	no	—
383	#124	C₂³×C₇	1	2	yes	—
384	#124	C₂³×C₇	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	2	4	no	—
387	#123	—	2	8	no	—
388	#123	—	2	4	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	4	no	—
392	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
393	#121	—	2	4	no	—
394	#121	—	2	8	no	—
395	#121	C₂³×C₇	1	4	yes	—
396	#121	C₂³×C₇	1	8	yes	—
397	#120	—	2	4	no	—
398	#120	—	2	2	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	C₇×D₄	1	2	yes	—
403	C₄×Q₈	C₂³×C₇	1	4	yes	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	C₇×D₄	1	4	yes	—
409	C₄×D₄	C₇×D₄	1	2	yes	—
410	C₄×D₄	C₂³×C₇	1	4	yes	—
411	C₄×D₄	C₂³×C₇	1	8	yes	—
412	#117	—	2	2	no	—
413	#117	—	2	4	no	—
414	#117	C₂³×C₇	1	2	yes	—
415	#117	C₂³×C₇	1	1	yes	characteristic
416	#117	C₂³×C₇	1	1	yes	characteristic
417	#117	C₂³×C₇	1	1	yes	characteristic
418	#117	C₂³×C₇	1	2	yes	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	4	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₇	1	2	yes	—
424	#107	C₂³×C₇	1	4	yes	—
425	#107	C₂³×C₇	1	4	yes	—
426	#106	C₂³×C₇	1	4	yes	—
427	#106	C₂³×C₇	1	4	yes	—
428	#103	C₂³×C₇	1	8	yes	—
429	#102	C₂³×C₇	1	8	yes	—
430	#102	C₂³×C₇	1	8	yes	—
431	#102	C₂³×C₇	1	8	yes	—
432	#97	C₂³×C₇	1	1	yes	characteristic
433	#97	C₂³×C₇	1	1	yes	characteristic
434	#97	C₂³×C₇	1	2	yes	—
435	#97	C₂³×C₇	1	2	yes	—
436	#97	C₂³×C₇	1	4	yes	—
437	C₄×C₈	C₂³×C₇	1	2	yes	—
438	C₄×C₈	C₂³×C₇	1	4	yes	—
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	4	no	—
441	C₂²×C₇	—	2	2	no	—
442	C₂²×C₇	—	4	8	no	—
443	C₂²×C₇	—	4	4	no	—
444	C₂²×C₇	—	4	2	no	—
445	C₂²×C₇	—	4	4	no	—
446	C₂²×C₇	—	16	4	no	—
447	C₂²×C₇	—	16	2	no	—
448	C₂²×C₇	#532	1	2	yes	—
449	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
450	C₄×C₇	—	2	2	no	—
451	C₄×C₇	—	2	4	no	—
452	C₄×C₇	—	2	2	no	—
453	C₄×C₇	—	2	2	no	—
454	C₄×C₇	—	4	4	no	—
455	C₄×C₇	—	4	2	no	—
456	C₄×C₇	—	4	2	no	—
457	C₄×C₇	—	4	2	no	—
458	C₄×C₇	#532	1	2	yes	—
459	C₄×C₇	C₂²×#41	1	2	yes	—
460	C₂⁴	—	2	1	no	—
461	C₂⁴	—	2	2	no	—
462	#41	—	2	4	no	—
463	#41	—	8	8	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	4	no	—
468	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
469	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	8	4	no	—
480	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
481	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
482	C₂×D₄	C₂⁴×C₇	1	2	yes	—
483	C₂×D₄	C₂⁴×C₇	1	4	yes	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
488	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
491	SD₁₆	—	2	8	no	—
492	SD₁₆	—	2	8	no	—
493	D₈	—	2	8	no	—
494	D₈	—	2	8	no	—
495	M₁₆	—	2	4	no	—
496	M₁₆	—	2	8	no	—
497	C₂×C₈	—	2	8	no	—
498	C₂×C₈	C₇×#41	1	8	yes	complemented
499	C₂×C₈	C₂⁴×C₇	1	4	yes	—
500	C₂×C₈	C₂⁴×C₇	1	2	yes	—
501	C₂×C₈	C₂⁴×C₇	1	2	yes	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
510	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
511	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
512	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
513	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
525	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	C₂×C₇×D₄	1	4	yes	—
531	C₄²	C₂×C₇×D₄	1	2	yes	—
532	C₄²	C₂⁴×C₇	1	2	yes	—
533	C₄²	C₂⁴×C₇	1	1	yes	characteristic
534	C₄²	C₂⁴×C₇	1	1	yes	characteristic
535	C₂×C₇	—	2	2	no	—
536	C₂×C₇	—	4	2	no	—
537	C₂×C₇	—	8	4	no	—
538	C₂×C₇	—	8	2	no	—
539	C₂×C₇	C₂×#532	1	1	yes	characteristic
540	C₂×C₇	#3585	1	2	yes	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	8	4	no	—
546	C₂³	—	8	2	no	—
547	C₂³	C₂²×C₇×D₄	1	2	yes	—
548	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	2	4	no	—
551	Q₈	—	4	4	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	8	2	no	—
554	D₄	—	2	4	no	—
555	D₄	—	2	4	no	—
556	D₄	—	2	4	no	—
557	D₄	—	2	4	no	—
558	D₄	—	2	2	no	—
559	D₄	—	4	8	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	4	no	—
562	D₄	—	8	4	no	—
563	D₄	—	8	4	no	—
564	D₄	—	8	8	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	8	4	no	—
574	C₂×C₄	—	8	8	no	—
575	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
576	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
577	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
578	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
579	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂×C₇×#41	1	4	yes	—
581	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
582	C₈	—	2	4	no	—
583	C₈	C₂×C₇×#41	1	4	yes	—
584	C₈	C₂×C₇×#41	1	4	yes	—
585	C₇	#60719	1	1	yes	characteristic, direct product factor, Sylow
586	C₂²	—	2	2	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	16	4	no	—
594	C₂²	—	16	2	no	—
595	C₂²	C₇×#532	1	2	yes	—
596	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	4	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	4	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	C₇×#532	1	2	yes	—
606	C₄	C₂²×C₇×#41	1	2	yes	—
607	C₂	—	2	2	no	—
608	C₂	—	4	2	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₂×C₇×#532	1	1	yes	characteristic
612	C₂	C₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3510	C₂	semidirect
2. C₇×#3508	C₂	semidirect
3. C₇×#3180	C₂	semidirect
4. C₇×#3179	C₂	semidirect
5. C₇×#3171	C₂	semidirect
6. C₇×#3162	C₂	semidirect
7. C₂×C₇×#496	C₂	semidirect
8. C₇×#3140	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3058	C₂	semidirect
11. C₇×#3057	C₂	semidirect
12. C₇×#2949	C₂	semidirect
13. C₇×#2948	C₂	semidirect
14. C₇×#2875	C₂	semidirect
24. C₇×#542	C₂²	semidirect
25. C₇×#540	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
33. C₇×#529	C₂²	semidirect
39. C₇×#501	C₂²	semidirect
40. C₇×#501	C₂²	semidirect
41. C₇×#501	C₂²	semidirect
45. C₇×#490	C₂²	semidirect
46. C₇×#489	C₂²	semidirect
47. C₇×#488	C₂²	semidirect
48. C₇×#486	C₂²	semidirect
49. C₇×#469	C₂²	semidirect
50. C₇×#468	C₂²	semidirect
51. C₇×#466	C₂²	semidirect
52. C₇×#465	C₂²	semidirect
53. C₇×#442	C₂²	semidirect
54. C₇×#440	C₂²	semidirect
55. C₄×C₇×SD₁₆	C₂²	semidirect
56. C₄×C₇×D₈	C₂²	semidirect
64. C₇×#405	C₂²	semidirect
66. C₄×C₇×M₁₆	C₂²	semidirect
68. C₂×C₇×#97	C₂²	semidirect
69. #60719	C₇	direct (N × H)
161. #3510	C₂×C₇	semidirect
162. #3508	C₂×C₇	semidirect
163. #3180	C₂×C₇	semidirect
164. #3179	C₂×C₇	semidirect
165. #3171	C₂×C₇	semidirect
166. #3162	C₂×C₇	semidirect
167. C₂×#496	C₂×C₇	semidirect
168. #3140	C₂×C₇	semidirect
169. #3138	C₂×C₇	semidirect
170. #3058	C₂×C₇	semidirect
171. #3057	C₂×C₇	semidirect
172. #2949	C₂×C₇	semidirect
173. #2948	C₂×C₇	semidirect
174. #2875	C₂×C₇	semidirect
213. C₂×C₇×C₈	#41	semidirect
259. #542	C₂²×C₇	semidirect
260. #540	C₂²×C₇	semidirect
266. #532	C₂²×C₇	semidirect
268. #529	C₂²×C₇	semidirect
274. #501	C₂²×C₇	semidirect
275. #501	C₂²×C₇	semidirect
276. #501	C₂²×C₇	semidirect
280. #490	C₂²×C₇	semidirect
281. #489	C₂²×C₇	semidirect
282. #488	C₂²×C₇	semidirect
283. #486	C₂²×C₇	semidirect
284. #469	C₂²×C₇	semidirect
285. #468	C₂²×C₇	semidirect
286. #466	C₂²×C₇	semidirect
287. #465	C₂²×C₇	semidirect
288. #442	C₂²×C₇	semidirect
289. #440	C₂²×C₇	semidirect
290. C₄×SD₁₆	C₂²×C₇	semidirect
291. C₄×D₈	C₂²×C₇	semidirect
299. #405	C₂²×C₇	semidirect
301. C₄×M₁₆	C₂²×C₇	semidirect
303. C₂×#97	C₂²×C₇	semidirect
498. C₂×C₈	C₇×#41	semidirect
585. C₇	#60719	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×#3510	2
C₇×#3508	2
C₇×#3180	2
C₇×#3179	2
C₇×#3171	2
C₇×#3162	2
C₂×C₇×#496	2
C₇×#3140	2
C₇×#3138	2
C₇×#3058	2
C₇×#3057	2
C₇×#2949	2
C₇×#2948	2
C₇×#2875	2
#60719	7

Subgroups — C7×#60719 #13237935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60719 #13237935