Subgroups — C₇×#19735 #13196951

Order 1792.

780 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1721	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1721	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1720	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1719	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1717	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1715	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1709	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#533	C₂²	1	1	yes	characteristic
17	C₇×#532	C₂²	1	1	yes	characteristic
18	C₇×#532	C₂²	1	1	yes	characteristic
19	C₂×C₇×#127	C₂²	1	1	yes	characteristic
20	C₇×#500	C₂²	1	1	yes	characteristic, complemented
21	C₇×#498	C₂²	1	1	yes	characteristic, complemented
22	C₇×#494	C₂²	1	1	yes	characteristic, complemented
23	C₇×#493	C₂²	1	1	yes	characteristic
24	C₇×#493	C₂²	1	1	yes	characteristic
25	C₇×#493	C₂²	1	1	yes	characteristic
26	C₇×#493	C₂²	1	1	yes	characteristic
27	C₇×#493	C₂²	1	1	yes	characteristic, complemented
28	C₇×#492	C₂²	1	1	yes	characteristic
29	C₇×#492	C₂²	1	1	yes	characteristic
30	C₇×#492	C₂²	1	1	yes	characteristic, complemented
31	C₇×#492	C₂²	1	1	yes	characteristic, complemented
32	C₇×#487	C₂²	1	1	yes	characteristic, complemented
33	C₇×#487	C₂²	1	1	yes	characteristic, complemented
34	C₇×#486	C₂²	1	1	yes	characteristic
35	C₇×#486	C₂²	1	1	yes	characteristic
36	C₇×#486	C₂²	1	1	yes	characteristic
37	C₇×#486	C₂²	1	1	yes	characteristic
38	C₇×#486	C₂²	1	1	yes	characteristic
39	C₇×#486	C₂²	1	1	yes	characteristic
40	C₇×#486	C₂²	1	1	yes	characteristic, complemented
41	C₇×#486	C₂²	1	1	yes	characteristic, complemented
42	C₇×#486	C₂²	1	1	yes	characteristic, complemented
43	C₇×#486	C₂²	1	1	yes	characteristic, complemented
44	C₇×#482	—	2	2	no	—
45	C₇×#478	—	2	2	no	—
46	C₇×#464	—	2	2	no	—
47	C₇×#463	—	2	2	no	—
48	C₇×#460	—	2	2	no	—
49	C₇×#459	—	2	2	no	—
50	C₇×#459	—	2	2	no	—
51	C₇×#452	—	2	2	no	—
52	C₇×#450	—	2	2	no	—
53	C₇×#449	—	2	2	no	—
54	C₇×#447	—	2	2	no	—
55	C₇×#447	—	2	2	no	—
56	C₇×#431	C₂²	1	1	yes	characteristic
57	C₇×#431	C₂²	1	1	yes	characteristic
58	C₇×#431	C₂²	1	1	yes	characteristic
59	C₇×#322	C₂²	1	1	yes	characteristic, complemented
60	C₇×#322	C₂²	1	1	yes	characteristic, complemented
61	C₇×#322	C₂²	1	1	yes	characteristic, complemented
62	C₇×C₈²	C₂²	1	1	yes	characteristic, complemented
63	#19735	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₇×#41	—	2	1	no	—
65	C₂×C₇×#41	—	2	1	no	—
66	C₂²×C₇×D₄	—	2	1	no	—
67	C₂²×C₇×D₄	—	2	1	no	—
68	C₂²×C₇×D₄	—	2	1	no	—
69	C₂×C₇×Q₁₆	—	2	2	no	—
70	C₂×C₇×SD₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	—	2	2	no	—
73	C₂×C₇×SD₁₆	—	2	2	no	—
74	C₂×C₇×D₈	—	2	2	no	—
75	C₂×C₇×D₈	—	2	2	no	—
76	C₂×C₇×D₈	—	2	2	no	—
77	C₂×C₇×D₈	—	2	2	no	—
78	C₂×C₇×D₈	—	2	2	no	—
79	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₇×#127	—	2	1	no	—
84	C₇×#127	—	2	1	no	—
85	C₇×#127	—	2	1	no	—
86	C₇×#127	C₂³	1	1	yes	characteristic
87	C₇×#127	C₂³	1	1	yes	characteristic
88	C₇×#127	C₂³	1	1	yes	characteristic
89	C₇×#127	C₂³	1	1	yes	characteristic
90	C₇×#125	—	2	1	no	—
91	C₇×#124	—	2	1	no	—
92	C₇×#124	—	2	1	no	—
93	C₇×C₂²⋊Q₈	—	2	1	no	—
94	C₇×C₂²⋊Q₈	—	2	1	no	—
95	C₇×#121	—	2	1	no	—
96	C₇×#121	—	2	1	no	—
97	C₇×#121	—	2	1	no	—
98	C₇×#121	—	2	1	no	—
99	C₄×C₇×Q₈	—	2	1	no	—
100	C₄×C₇×Q₈	—	2	1	no	—
101	C₄×C₇×D₄	—	2	1	no	—
102	C₄×C₇×D₄	—	2	1	no	—
103	C₄×C₇×D₄	—	2	1	no	—
104	C₄×C₇×D₄	—	2	1	no	—
105	C₇×#117	—	2	1	no	—
106	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
107	C₇×#107	—	2	2	no	—
108	C₇×#106	—	2	2	no	—
109	C₇×C₄⋊C₈	D₄	1	2	yes	—
110	C₇×C₄⋊C₈	D₄	1	2	yes	—
111	C₇×C₄⋊C₈	D₄	1	2	yes	—
112	C₇×#103	—	2	2	no	—
113	C₇×#103	—	2	2	no	—
114	C₇×#102	—	2	2	no	—
115	C₇×#102	—	2	2	no	—
116	C₇×#102	—	2	2	no	—
117	C₇×#102	—	2	2	no	—
118	C₇×#102	—	2	2	no	—
119	C₇×#102	—	2	2	no	—
120	C₇×#102	—	2	2	no	—
121	C₇×#102	—	2	2	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×C₂²⋊C₈	D₄	1	2	yes	—
125	C₇×C₂²⋊C₈	D₄	1	2	yes	—
126	C₇×C₂²⋊C₈	D₄	1	2	yes	—
127	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
128	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
129	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
130	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
131	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
132	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
133	#3228	C₂×C₇	1	1	yes	characteristic, complemented
134	#3210	C₂×C₇	1	1	yes	characteristic, complemented
135	#3208	C₂×C₇	1	1	yes	characteristic, complemented
136	#3207	C₂×C₇	1	1	yes	characteristic, complemented
137	#3205	C₂×C₇	1	1	yes	characteristic, complemented
138	#3205	C₂×C₇	1	1	yes	characteristic, complemented
139	#1721	C₂×C₇	1	1	yes	characteristic, complemented
140	#1721	C₂×C₇	1	1	yes	characteristic, complemented
141	#1720	C₂×C₇	1	1	yes	characteristic, complemented
142	#1719	C₂×C₇	1	1	yes	characteristic, complemented
143	#1717	C₂×C₇	1	1	yes	characteristic, complemented
144	#1715	C₂×C₇	1	1	yes	characteristic, complemented
145	#1709	C₂×C₇	1	1	yes	characteristic, complemented
146	#1706	C₂×C₇	1	1	yes	characteristic, complemented
147	#1454	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂⁴×C₇	—	4	1	no	—
149	C₇×#41	—	8	2	no	—
150	C₇×#41	—	8	2	no	—
151	C₂×C₇×Q₈	—	2	1	no	—
152	C₂×C₇×Q₈	—	2	1	no	—
153	C₂×C₇×Q₈	—	2	1	no	—
154	C₂×C₇×Q₈	—	2	1	no	—
155	C₂×C₇×D₄	—	2	1	no	—
156	C₂×C₇×D₄	—	2	1	no	—
157	C₂×C₇×D₄	—	2	1	no	—
158	C₂×C₇×D₄	—	2	1	no	—
159	C₂×C₇×D₄	—	2	1	no	—
160	C₂×C₇×D₄	—	2	1	no	—
161	C₂×C₇×D₄	—	2	1	no	—
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	4	1	no	—
168	C₂×C₇×D₄	—	4	1	no	—
169	C₂×C₇×D₄	—	4	1	no	—
170	C₂×C₇×D₄	—	4	1	no	—
171	C₂×C₇×D₄	—	4	1	no	—
172	C₂×C₇×D₄	—	8	2	no	—
173	C₂×C₇×D₄	—	8	2	no	—
174	C₂×C₇×D₄	—	8	2	no	—
175	C₂²×C₄×C₇	—	4	1	no	—
176	C₂²×C₄×C₇	—	4	1	no	—
177	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
180	C₇×Q₁₆	—	8	2	no	—
181	C₇×SD₁₆	—	8	2	no	—
182	C₇×SD₁₆	—	8	2	no	—
183	C₇×SD₁₆	—	8	2	no	—
184	C₇×SD₁₆	—	8	2	no	—
185	C₇×D₈	—	8	2	no	—
186	C₇×D₈	—	8	2	no	—
187	C₇×D₈	—	8	2	no	—
188	C₇×D₈	—	8	2	no	—
189	C₇×D₈	—	8	2	no	—
190	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
191	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
192	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
193	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
194	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
195	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
196	C₇×C₄⋊C₄	—	2	1	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	2	1	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	2	1	no	—
202	C₇×C₄⋊C₄	—	2	1	no	—
203	C₇×C₄⋊C₄	—	2	1	no	—
204	C₇×C₄⋊C₄	—	4	1	no	—
205	C₇×C₄⋊C₄	—	4	1	no	—
206	C₇×C₂²⋊C₄	—	4	1	no	—
207	C₇×C₂²⋊C₄	—	4	1	no	—
208	C₇×C₂²⋊C₄	—	4	1	no	—
209	C₇×C₂²⋊C₄	—	4	1	no	—
210	C₇×C₂²⋊C₄	—	4	1	no	—
211	C₄²×C₇	—	4	1	no	—
212	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₇	C₂⁴	1	1	yes	characteristic
216	#533	C₂²×C₇	1	1	yes	characteristic
217	#532	C₂²×C₇	1	1	yes	characteristic
218	#532	C₂²×C₇	1	1	yes	characteristic
219	C₂×#127	C₂²×C₇	1	1	yes	characteristic
220	#500	C₂²×C₇	1	1	yes	characteristic, complemented
221	#498	C₂²×C₇	1	1	yes	characteristic, complemented
222	#494	C₂²×C₇	1	1	yes	characteristic, complemented
223	#493	C₂²×C₇	1	1	yes	characteristic
224	#493	C₂²×C₇	1	1	yes	characteristic
225	#493	C₂²×C₇	1	1	yes	characteristic
226	#493	C₂²×C₇	1	1	yes	characteristic
227	#493	C₂²×C₇	1	1	yes	characteristic, complemented
228	#492	C₂²×C₇	1	1	yes	characteristic
229	#492	C₂²×C₇	1	1	yes	characteristic
230	#492	C₂²×C₇	1	1	yes	characteristic, complemented
231	#492	C₂²×C₇	1	1	yes	characteristic, complemented
232	#487	C₂²×C₇	1	1	yes	characteristic, complemented
233	#487	C₂²×C₇	1	1	yes	characteristic, complemented
234	#486	C₂²×C₇	1	1	yes	characteristic
235	#486	C₂²×C₇	1	1	yes	characteristic
236	#486	C₂²×C₇	1	1	yes	characteristic
237	#486	C₂²×C₇	1	1	yes	characteristic
238	#486	C₂²×C₇	1	1	yes	characteristic
239	#486	C₂²×C₇	1	1	yes	characteristic
240	#486	C₂²×C₇	1	1	yes	characteristic, complemented
241	#486	C₂²×C₇	1	1	yes	characteristic, complemented
242	#486	C₂²×C₇	1	1	yes	characteristic, complemented
243	#486	C₂²×C₇	1	1	yes	characteristic, complemented
244	#482	—	2	2	no	—
245	#478	—	2	2	no	—
246	#464	—	2	2	no	—
247	#463	—	2	2	no	—
248	#460	—	2	2	no	—
249	#459	—	2	2	no	—
250	#459	—	2	2	no	—
251	#452	—	2	2	no	—
252	#450	—	2	2	no	—
253	#449	—	2	2	no	—
254	#447	—	2	2	no	—
255	#447	—	2	2	no	—
256	#431	C₂²×C₇	1	1	yes	characteristic
257	#431	C₂²×C₇	1	1	yes	characteristic
258	#431	C₂²×C₇	1	1	yes	characteristic
259	#322	C₂²×C₇	1	1	yes	characteristic, complemented
260	#322	C₂²×C₇	1	1	yes	characteristic, complemented
261	#322	C₂²×C₇	1	1	yes	characteristic, complemented
262	C₈²	C₂²×C₇	1	1	yes	characteristic, complemented
263	C₂³×C₇	—	4	1	no	—
264	C₂³×C₇	—	4	1	no	—
265	C₂³×C₇	—	4	1	no	—
266	C₂³×C₇	—	4	1	no	—
267	C₂³×C₇	—	8	2	no	—
268	C₂³×C₇	—	8	2	no	—
269	C₂³×C₇	—	8	2	no	—
270	C₂³×C₇	#127	1	1	yes	characteristic
271	C₇×Q₈	—	4	2	no	—
272	C₇×Q₈	—	4	2	no	—
273	C₇×Q₈	—	4	2	no	—
274	C₇×Q₈	—	4	2	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	—	4	2	no	—
279	C₇×D₄	—	4	2	no	—
280	C₇×D₄	—	4	2	no	—
281	C₇×D₄	—	4	2	no	—
282	C₇×D₄	—	4	2	no	—
283	C₇×D₄	—	4	2	no	—
284	C₇×D₄	—	4	2	no	—
285	C₇×D₄	—	4	2	no	—
286	C₇×D₄	—	4	2	no	—
287	C₇×D₄	—	8	2	no	—
288	C₇×D₄	—	8	2	no	—
289	C₇×D₄	—	8	2	no	—
290	C₇×D₄	—	8	2	no	—
291	C₇×D₄	—	8	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	2	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	8	2	no	—
300	C₂×C₄×C₇	—	8	2	no	—
301	C₂×C₄×C₇	#127	1	1	yes	characteristic
302	C₂×C₄×C₇	#127	1	1	yes	characteristic
303	C₂×C₄×C₇	#127	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
307	C₇×C₈	—	2	2	no	—
308	C₇×C₈	—	2	2	no	—
309	C₇×C₈	—	2	2	no	—
310	C₇×C₈	—	2	2	no	—
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	2	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
330	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
332	#127	—	2	1	no	—
333	#127	—	2	1	no	—
334	#127	—	2	1	no	—
335	#127	C₂³×C₇	1	1	yes	characteristic
336	#127	C₂³×C₇	1	1	yes	characteristic
337	#127	C₂³×C₇	1	1	yes	characteristic
338	#127	C₂³×C₇	1	1	yes	characteristic
339	#125	—	2	1	no	—
340	#124	—	2	1	no	—
341	#124	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	#117	—	2	1	no	—
355	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
356	#107	—	2	2	no	—
357	#106	—	2	2	no	—
358	C₄⋊C₈	C₇×D₄	1	2	yes	—
359	C₄⋊C₈	C₇×D₄	1	2	yes	—
360	C₄⋊C₈	C₇×D₄	1	2	yes	—
361	#103	—	2	2	no	—
362	#103	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	2	2	no	—
373	C₂²⋊C₈	C₇×D₄	1	2	yes	—
374	C₂²⋊C₈	C₇×D₄	1	2	yes	—
375	C₂²⋊C₈	C₇×D₄	1	2	yes	—
376	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
377	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
378	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
379	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
380	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₇	—	2	1	no	—
383	C₂²×C₇	—	2	1	no	—
384	C₂²×C₇	—	2	1	no	—
385	C₂²×C₇	—	8	1	no	—
386	C₂²×C₇	—	8	1	no	—
387	C₂²×C₇	—	8	1	no	—
388	C₂²×C₇	—	8	1	no	—
389	C₂²×C₇	—	8	1	no	—
390	C₂²×C₇	—	8	1	no	—
391	C₂²×C₇	—	8	1	no	—
392	C₂²×C₇	—	8	1	no	—
393	C₂²×C₇	—	8	1	no	—
394	C₂²×C₇	—	8	1	no	—
395	C₂²×C₇	—	8	1	no	—
396	C₂²×C₇	—	8	1	no	—
397	C₂²×C₇	—	16	4	no	—
398	C₂²×C₇	C₂×#127	1	1	yes	characteristic
399	C₄×C₇	—	2	1	no	—
400	C₄×C₇	—	2	1	no	—
401	C₄×C₇	—	2	1	no	—
402	C₄×C₇	—	8	1	no	—
403	C₄×C₇	—	8	1	no	—
404	C₄×C₇	—	8	1	no	—
405	C₄×C₇	—	8	1	no	—
406	C₄×C₇	#576	1	2	yes	—
407	C₄×C₇	#576	1	2	yes	—
408	C₄×C₇	#577	1	2	yes	—
409	C₂⁴	—	4	1	no	—
410	#41	—	8	2	no	—
411	#41	—	8	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	8	2	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	—	8	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
441	Q₁₆	—	8	2	no	—
442	SD₁₆	—	8	2	no	—
443	SD₁₆	—	8	2	no	—
444	SD₁₆	—	8	2	no	—
445	SD₁₆	—	8	2	no	—
446	D₈	—	8	2	no	—
447	D₈	—	8	2	no	—
448	D₈	—	8	2	no	—
449	D₈	—	8	2	no	—
450	D₈	—	8	2	no	—
451	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
452	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
453	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
454	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
455	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
456	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
474	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
475	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
476	C₄²	C₂⁴×C₇	1	1	yes	characteristic
477	C₂×C₇	—	4	1	no	—
478	C₂×C₇	—	16	1	no	—
479	C₂×C₇	—	16	1	no	—
480	C₂×C₇	—	16	1	no	—
481	C₂×C₇	—	16	1	no	—
482	C₂×C₇	#3154	1	1	yes	characteristic
483	C₂×C₇	#3155	1	1	yes	characteristic
484	C₂×C₇	#3155	1	1	yes	characteristic
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	8	2	no	—
490	C₂³	—	8	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	C₇×#127	1	1	yes	characteristic
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	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	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	C₇×#127	1	1	yes	characteristic
524	C₂×C₄	C₇×#127	1	1	yes	characteristic
525	C₂×C₄	C₇×#127	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₇	#19735	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	16	4	no	—
552	C₂²	C₂×C₇×#127	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	C₇×#576	1	2	yes	—
561	C₄	C₇×#576	1	2	yes	—
562	C₄	C₇×#577	1	2	yes	—
563	C₂	—	4	1	no	—
564	C₂	—	16	1	no	—
565	C₂	—	16	1	no	—
566	C₂	—	16	1	no	—
567	C₂	—	16	1	no	—
568	C₂	C₇×#3154	1	1	yes	characteristic
569	C₂	C₇×#3155	1	1	yes	characteristic
570	C₂	C₇×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3228	C₂	semidirect
2. C₇×#3210	C₂	semidirect
3. C₇×#3208	C₂	semidirect
4. C₇×#3207	C₂	semidirect
5. C₇×#3205	C₂	semidirect
6. C₇×#3205	C₂	semidirect
7. C₇×#1721	C₂	semidirect
8. C₇×#1721	C₂	semidirect
9. C₇×#1720	C₂	semidirect
10. C₇×#1719	C₂	semidirect
11. C₇×#1717	C₂	semidirect
12. C₇×#1715	C₂	semidirect
13. C₇×#1709	C₂	semidirect
14. C₇×#1706	C₂	semidirect
15. C₇×#1454	C₂	semidirect
20. C₇×#500	C₂²	semidirect
21. C₇×#498	C₂²	semidirect
22. C₇×#494	C₂²	semidirect
27. C₇×#493	C₂²	semidirect
30. C₇×#492	C₂²	semidirect
31. C₇×#492	C₂²	semidirect
32. C₇×#487	C₂²	semidirect
33. C₇×#487	C₂²	semidirect
40. C₇×#486	C₂²	semidirect
41. C₇×#486	C₂²	semidirect
42. C₇×#486	C₂²	semidirect
43. C₇×#486	C₂²	semidirect
59. C₇×#322	C₂²	semidirect
60. C₇×#322	C₂²	semidirect
61. C₇×#322	C₂²	semidirect
62. C₇×C₈²	C₂²	semidirect
63. #19735	C₇	direct (N × H)
133. #3228	C₂×C₇	semidirect
134. #3210	C₂×C₇	semidirect
135. #3208	C₂×C₇	semidirect
136. #3207	C₂×C₇	semidirect
137. #3205	C₂×C₇	semidirect
138. #3205	C₂×C₇	semidirect
139. #1721	C₂×C₇	semidirect
140. #1721	C₂×C₇	semidirect
141. #1720	C₂×C₇	semidirect
142. #1719	C₂×C₇	semidirect
143. #1717	C₂×C₇	semidirect
144. #1715	C₂×C₇	semidirect
145. #1709	C₂×C₇	semidirect
146. #1706	C₂×C₇	semidirect
147. #1454	C₂×C₇	semidirect
220. #500	C₂²×C₇	semidirect
221. #498	C₂²×C₇	semidirect
222. #494	C₂²×C₇	semidirect
227. #493	C₂²×C₇	semidirect
230. #492	C₂²×C₇	semidirect
231. #492	C₂²×C₇	semidirect
232. #487	C₂²×C₇	semidirect
233. #487	C₂²×C₇	semidirect
240. #486	C₂²×C₇	semidirect
241. #486	C₂²×C₇	semidirect
242. #486	C₂²×C₇	semidirect
243. #486	C₂²×C₇	semidirect
259. #322	C₂²×C₇	semidirect
260. #322	C₂²×C₇	semidirect
261. #322	C₂²×C₇	semidirect
262. C₈²	C₂²×C₇	semidirect
535. C₇	#19735	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×#3228	2
C₇×#3210	2
C₇×#3208	2
C₇×#3207	2
C₇×#3205	2
C₇×#1721	2
C₇×#1720	2
C₇×#1719	2
C₇×#1717	2
C₇×#1715	2
C₇×#1709	2
C₇×#1706	2
C₇×#1454	2
#19735	7

Subgroups — C7×#19735 #13196951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19735 #13196951