Subgroups — C₇×#60883 #13238099

Order 1792.

1742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3508	C₂	1	1	yes	maximal, characteristic
2	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3241	C₂	1	8	yes	maximal, complemented
4	C₇×#3235	C₂	1	4	yes	maximal, complemented
5	C₇×#3234	C₂	1	4	yes	maximal, complemented
6	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3096	C₂	1	4	yes	maximal, complemented
11	C₇×#3081	C₂	1	4	yes	maximal, complemented
12	C₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#559	—	2	2	no	—
14	C₇×#557	—	2	2	no	—
15	C₇×#554	—	2	4	no	—
16	C₇×#554	—	2	2	no	—
17	C₇×#550	—	2	2	no	—
18	C₇×#546	—	2	4	no	—
19	C₇×#544	C₂²	1	2	yes	—
20	C₇×#544	C₂²	1	4	yes	complemented
21	C₇×#540	C₂²	1	4	yes	—
22	C₇×#535	C₂²	1	2	yes	—
23	C₇×#533	C₂²	1	1	yes	characteristic
24	C₇×#533	C₂²	1	1	yes	characteristic
25	C₇×#533	C₂²	1	2	yes	complemented
26	C₇×#532	C₂²	1	4	yes	—
27	C₂×C₇×#127	C₂²	1	1	yes	characteristic
28	C₂×C₇×#125	C₂²	1	1	yes	characteristic
29	C₂×C₇×#125	C₂²	1	2	yes	complemented
30	C₇×#520	C₂²	1	2	yes	—
31	C₇×#518	C₂²	1	2	yes	—
32	C₄×C₇×#41	C₂²	1	1	yes	characteristic
33	C₇×#501	C₂²	1	2	yes	complemented
34	C₇×#501	C₂²	1	2	yes	complemented
35	C₇×#501	C₂²	1	4	yes	complemented
36	C₇×#501	C₂²	1	4	yes	complemented
37	C₇×#499	C₂²	1	4	yes	complemented
38	C₇×#490	C₂²	1	2	yes	—
39	C₇×#490	C₂²	1	4	yes	—
40	C₇×#490	C₂²	1	2	yes	—
41	C₇×#490	C₂²	1	4	yes	—
42	C₇×#486	C₂²	1	4	yes	—
43	C₇×#482	C₂²	1	8	yes	complemented
44	C₇×#482	C₂²	1	8	yes	complemented
45	C₇×#481	C₂²	1	8	yes	complemented
46	C₇×#480	C₂²	1	8	yes	complemented
47	C₇×#478	C₂²	1	8	yes	complemented
48	C₇×#478	C₂²	1	8	yes	complemented
49	C₇×#476	C₂²	1	8	yes	complemented
50	C₇×#474	C₂²	1	8	yes	complemented
51	C₇×#433	C₂²	1	4	yes	complemented
52	C₇×#432	C₂²	1	4	yes	complemented
53	C₇×#428	C₂²	1	4	yes	—
54	C₇×#427	C₂²	1	4	yes	—
55	C₇×#424	C₂²	1	2	yes	—
56	C₇×#418	C₂²	1	4	yes	—
57	C₂×C₇×#102	C₂²	1	4	yes	—
58	C₇×#408	C₂²	1	2	yes	—
59	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₇×#97	C₂²	1	1	yes	characteristic
61	#60883	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₇×#41	—	2	4	no	—
63	C₂×C₇×#41	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	C₂³	1	2	yes	—
66	C₂×C₇×M₁₆	C₂³	1	2	yes	—
67	C₂²×C₇×C₈	C₂³	1	2	yes	—
68	C₇×C₄⋊Q₈	—	2	2	no	—
69	C₇×C₄⋊Q₈	—	2	4	no	—
70	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₇×#127	—	2	2	no	—
74	C₇×#127	—	2	2	no	—
75	C₇×#127	C₂³	1	2	yes	—
76	C₇×#127	C₂³	1	2	yes	—
77	C₇×#125	—	2	2	no	—
78	C₇×#125	—	2	4	no	—
79	C₇×#125	—	2	2	no	—
80	C₇×#125	—	2	4	no	—
81	C₇×#125	C₂³	1	4	yes	—
82	C₇×#125	C₂³	1	2	yes	—
83	C₇×#125	C₂³	1	2	yes	—
84	C₇×#125	C₂³	1	1	yes	characteristic
85	C₇×#125	C₂³	1	1	yes	characteristic
86	C₇×#125	C₂³	1	2	yes	—
87	C₇×#124	—	2	2	no	—
88	C₇×#124	—	2	4	no	—
89	C₇×#123	—	2	8	no	—
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₇×C₂²⋊Q₈	—	2	2	no	—
92	C₇×C₂²⋊Q₈	—	2	4	no	—
93	C₇×C₂²⋊Q₈	—	2	4	no	—
94	C₇×C₂²⋊Q₈	—	2	4	no	—
95	C₇×C₂²⋊Q₈	—	2	4	no	—
96	C₇×#121	—	2	4	no	—
97	C₇×#121	—	2	8	no	—
98	C₇×#121	C₂³	1	8	yes	—
99	C₇×#120	—	2	4	no	—
100	C₄×C₇×Q₈	—	2	2	no	—
101	C₄×C₇×Q₈	—	2	2	no	—
102	C₄×C₇×Q₈	—	2	2	no	—
103	C₄×C₇×Q₈	—	2	4	no	—
104	C₄×C₇×Q₈	D₄	1	2	yes	—
105	C₄×C₇×D₄	—	2	4	no	—
106	C₄×C₇×D₄	—	2	2	no	—
107	C₄×C₇×D₄	—	2	4	no	—
108	C₄×C₇×D₄	—	2	4	no	—
109	C₄×C₇×D₄	D₄	1	4	yes	—
110	C₄×C₇×D₄	D₄	1	2	yes	—
111	C₄×C₇×D₄	C₂³	1	8	yes	—
112	C₇×#117	C₂³	1	4	yes	—
113	C₇×#117	C₂³	1	2	yes	—
114	C₇×#117	C₂³	1	2	yes	—
115	C₇×#117	C₂³	1	1	yes	characteristic
116	C₇×#117	C₂³	1	2	yes	—
117	C₂×C₇×C₄⋊C₄	—	2	2	no	—
118	C₂×C₇×C₄⋊C₄	—	2	4	no	—
119	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	2	yes	—
124	C₇×#107	C₂³	1	4	yes	—
125	C₇×#107	C₂³	1	8	yes	—
126	C₇×#107	C₂³	1	4	yes	—
127	C₇×#106	C₂³	1	4	yes	—
128	C₇×#106	C₂³	1	8	yes	—
129	C₇×#106	C₂³	1	4	yes	—
130	C₇×C₄⋊C₈	C₂³	1	8	yes	—
131	C₇×#102	C₂³	1	8	yes	—
132	C₇×#102	C₂³	1	8	yes	—
133	C₇×#102	C₂³	1	8	yes	—
134	C₇×#102	C₂³	1	8	yes	—
135	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
136	C₇×#97	C₂³	1	2	yes	—
137	C₇×#97	C₂³	1	2	yes	—
138	C₇×#97	C₂³	1	2	yes	—
139	C₄×C₇×C₈	C₂³	1	2	yes	—
140	#3508	C₂×C₇	1	1	yes	characteristic
141	#3504	C₂×C₇	1	1	yes	characteristic, complemented
142	#3241	C₂×C₇	1	8	yes	complemented
143	#3235	C₂×C₇	1	4	yes	complemented
144	#3234	C₂×C₇	1	4	yes	complemented
145	#3166	C₂×C₇	1	1	yes	characteristic, complemented
146	#3162	C₂×C₇	1	1	yes	characteristic, complemented
147	#3138	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
149	#3096	C₂×C₇	1	4	yes	complemented
150	#3081	C₂×C₇	1	4	yes	complemented
151	#2923	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂⁴×C₇	—	2	2	no	—
153	C₇×#41	—	2	4	no	—
154	C₇×#41	—	8	8	no	—
155	C₂×C₇×Q₈	—	2	2	no	—
156	C₂×C₇×Q₈	—	2	4	no	—
157	C₂×C₇×Q₈	—	2	2	no	—
158	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇×D₄	—	2	8	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	4	no	—
163	C₂×C₇×D₄	—	2	8	no	—
164	C₂×C₇×D₄	—	8	4	no	—
165	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
166	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
167	C₂×C₇×D₄	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₇	—	2	4	no	—
169	C₂²×C₄×C₇	—	2	2	no	—
170	C₂²×C₄×C₇	—	2	8	no	—
171	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
175	C₇×M₁₆	—	2	4	no	—
176	C₂×C₇×C₈	—	2	4	no	—
177	C₂×C₇×C₈	C₂⁴	1	4	yes	—
178	C₂×C₇×C₈	C₂⁴	1	4	yes	—
179	C₇×C₄⋊C₄	—	2	4	no	—
180	C₇×C₄⋊C₄	—	2	2	no	—
181	C₇×C₄⋊C₄	—	2	4	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	4	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	4	no	—
190	C₇×C₄⋊C₄	—	2	2	no	—
191	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₇×C₂²⋊C₄	—	2	2	no	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	2	2	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	8	no	—
202	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
203	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
204	C₄²×C₇	—	2	2	no	—
205	C₄²×C₇	—	2	4	no	—
206	C₄²×C₇	—	2	2	no	—
207	C₄²×C₇	C₂×D₄	1	4	yes	—
208	C₄²×C₇	C₂×D₄	1	2	yes	—
209	C₄²×C₇	C₂⁴	1	1	yes	characteristic
210	C₄²×C₇	C₂⁴	1	1	yes	characteristic
211	C₄²×C₇	C₂⁴	1	2	yes	—
212	#559	—	2	2	no	—
213	#557	—	2	2	no	—
214	#554	—	2	4	no	—
215	#554	—	2	2	no	—
216	#550	—	2	2	no	—
217	#546	—	2	4	no	—
218	#544	C₂²×C₇	1	2	yes	—
219	#544	C₂²×C₇	1	4	yes	complemented
220	#540	C₂²×C₇	1	4	yes	—
221	#535	C₂²×C₇	1	2	yes	—
222	#533	C₂²×C₇	1	1	yes	characteristic
223	#533	C₂²×C₇	1	1	yes	characteristic
224	#533	C₂²×C₇	1	2	yes	complemented
225	#532	C₂²×C₇	1	4	yes	—
226	C₂×#127	C₂²×C₇	1	1	yes	characteristic
227	C₂×#125	C₂²×C₇	1	1	yes	characteristic
228	C₂×#125	C₂²×C₇	1	2	yes	complemented
229	#520	C₂²×C₇	1	2	yes	—
230	#518	C₂²×C₇	1	2	yes	—
231	C₄×#41	C₂²×C₇	1	1	yes	characteristic
232	#501	C₂²×C₇	1	2	yes	complemented
233	#501	C₂²×C₇	1	2	yes	complemented
234	#501	C₂²×C₇	1	4	yes	complemented
235	#501	C₂²×C₇	1	4	yes	complemented
236	#499	C₂²×C₇	1	4	yes	complemented
237	#490	C₂²×C₇	1	4	yes	—
238	#490	C₂²×C₇	1	4	yes	—
239	#490	C₂²×C₇	1	2	yes	—
240	#490	C₂²×C₇	1	2	yes	—
241	#486	C₂²×C₇	1	4	yes	—
242	#482	C₂²×C₇	1	8	yes	complemented
243	#482	C₂²×C₇	1	8	yes	complemented
244	#481	C₂²×C₇	1	8	yes	complemented
245	#480	C₂²×C₇	1	8	yes	complemented
246	#478	C₂²×C₇	1	8	yes	complemented
247	#478	C₂²×C₇	1	8	yes	complemented
248	#476	C₂²×C₇	1	8	yes	complemented
249	#474	C₂²×C₇	1	8	yes	complemented
250	#433	C₂²×C₇	1	4	yes	complemented
251	#432	C₂²×C₇	1	4	yes	complemented
252	#428	C₂²×C₇	1	4	yes	—
253	#427	C₂²×C₇	1	4	yes	—
254	#424	C₂²×C₇	1	2	yes	—
255	#418	C₂²×C₇	1	4	yes	—
256	C₂×#102	C₂²×C₇	1	4	yes	—
257	#408	C₂²×C₇	1	2	yes	—
258	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
259	C₂×#97	C₂²×C₇	1	1	yes	characteristic
260	C₂³×C₇	—	2	4	no	—
261	C₂³×C₇	—	4	4	no	—
262	C₂³×C₇	—	8	4	no	—
263	C₂³×C₇	C₂²×D₄	1	2	yes	—
264	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
265	C₇×Q₈	—	2	2	no	—
266	C₇×Q₈	—	4	4	no	—
267	C₇×Q₈	—	8	4	no	—
268	C₇×Q₈	—	8	2	no	—
269	C₇×D₄	—	2	4	no	—
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	2	8	no	—
272	C₇×D₄	—	4	8	no	—
273	C₇×D₄	—	4	4	no	—
274	C₇×D₄	—	8	4	no	—
275	C₇×D₄	—	8	8	no	—
276	C₂×C₄×C₇	—	2	4	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	4	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	4	2	no	—
282	C₂×C₄×C₇	—	4	4	no	—
283	C₂×C₄×C₇	—	8	8	no	—
284	C₂×C₄×C₇	—	8	2	no	—
285	C₂×C₄×C₇	—	8	4	no	—
286	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
292	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
293	C₇×C₈	—	2	4	no	—
294	C₇×C₈	—	2	4	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	C₂³×C₇	1	1	yes	characteristic
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	C₂³×C₇	1	2	yes	—
299	C₂×M₁₆	C₂³×C₇	1	2	yes	—
300	C₂²×C₈	C₂³×C₇	1	2	yes	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
304	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
305	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
306	#127	—	2	2	no	—
307	#127	—	2	2	no	—
308	#127	C₂³×C₇	1	2	yes	—
309	#127	C₂³×C₇	1	2	yes	—
310	#125	—	2	2	no	—
311	#125	—	2	4	no	—
312	#125	—	2	2	no	—
313	#125	—	2	4	no	—
314	#125	C₂³×C₇	1	2	yes	—
315	#125	C₂³×C₇	1	2	yes	—
316	#125	C₂³×C₇	1	1	yes	characteristic
317	#125	C₂³×C₇	1	4	yes	—
318	#125	C₂³×C₇	1	1	yes	characteristic
319	#125	C₂³×C₇	1	2	yes	—
320	#124	—	2	2	no	—
321	#124	—	2	4	no	—
322	#123	—	2	8	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	#121	—	2	4	no	—
330	#121	—	2	8	no	—
331	#121	C₂³×C₇	1	8	yes	—
332	#120	—	2	4	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	4	no	—
337	C₄×Q₈	C₇×D₄	1	2	yes	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	C₇×D₄	1	4	yes	—
343	C₄×D₄	C₇×D₄	1	2	yes	—
344	C₄×D₄	C₂³×C₇	1	8	yes	—
345	#117	C₂³×C₇	1	2	yes	—
346	#117	C₂³×C₇	1	2	yes	—
347	#117	C₂³×C₇	1	4	yes	—
348	#117	C₂³×C₇	1	1	yes	characteristic
349	#117	C₂³×C₇	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₇	1	2	yes	—
357	#107	C₂³×C₇	1	4	yes	—
358	#107	C₂³×C₇	1	4	yes	—
359	#107	C₂³×C₇	1	8	yes	—
360	#106	C₂³×C₇	1	4	yes	—
361	#106	C₂³×C₇	1	4	yes	—
362	#106	C₂³×C₇	1	8	yes	—
363	C₄⋊C₈	C₂³×C₇	1	8	yes	—
364	#102	C₂³×C₇	1	8	yes	—
365	#102	C₂³×C₇	1	8	yes	—
366	#102	C₂³×C₇	1	8	yes	—
367	#102	C₂³×C₇	1	8	yes	—
368	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
369	#97	C₂³×C₇	1	2	yes	—
370	#97	C₂³×C₇	1	2	yes	—
371	#97	C₂³×C₇	1	2	yes	—
372	C₄×C₈	C₂³×C₇	1	2	yes	—
373	C₂²×C₇	—	2	2	no	—
374	C₂²×C₇	—	2	4	no	—
375	C₂²×C₇	—	2	2	no	—
376	C₂²×C₇	—	4	8	no	—
377	C₂²×C₇	—	4	4	no	—
378	C₂²×C₇	—	16	4	no	—
379	C₂²×C₇	#536	1	2	yes	—
380	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₇	—	2	2	no	—
382	C₄×C₇	—	2	4	no	—
383	C₄×C₇	—	2	2	no	—
384	C₄×C₇	—	2	2	no	—
385	C₄×C₇	—	4	4	no	—
386	C₄×C₇	—	4	4	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	—	4	2	no	—
389	C₄×C₇	#536	1	2	yes	—
390	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
391	C₂⁴	—	2	2	no	—
392	#41	—	2	4	no	—
393	#41	—	8	8	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	8	4	no	—
404	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
405	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
406	C₂×D₄	C₂⁴×C₇	1	4	yes	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
411	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
414	M₁₆	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	C₂⁴×C₇	1	4	yes	—
417	C₂×C₈	C₂⁴×C₇	1	4	yes	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
431	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
433	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
434	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
435	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
442	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	2	no	—
446	C₄²	C₂×C₇×D₄	1	4	yes	—
447	C₄²	C₂×C₇×D₄	1	2	yes	—
448	C₄²	C₂⁴×C₇	1	1	yes	characteristic
449	C₄²	C₂⁴×C₇	1	1	yes	characteristic
450	C₄²	C₂⁴×C₇	1	2	yes	—
451	C₂×C₇	—	2	2	no	—
452	C₂×C₇	—	4	2	no	—
453	C₂×C₇	—	8	4	no	—
454	C₂×C₇	C₂×#536	1	1	yes	characteristic
455	C₂×C₇	#3585	1	2	yes	—
456	C₂³	—	2	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	8	4	no	—
459	C₂³	C₂²×C₇×D₄	1	2	yes	—
460	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	8	4	no	—
464	Q₈	—	8	2	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	8	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	4	no	—
470	D₄	—	8	4	no	—
471	D₄	—	8	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	8	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	4	no	—
482	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
483	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
484	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
485	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
486	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
487	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
488	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	2	4	no	—
491	C₇	#60883	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	16	4	no	—
498	C₂²	C₇×#536	1	2	yes	—
499	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	C₇×#536	1	2	yes	—
509	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	4	no	—
513	C₂	C₂×C₇×#536	1	1	yes	characteristic
514	C₂	C₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3508	C₂
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
2. C₇×#3504	C₂	semidirect
3. C₇×#3241	C₂	semidirect
4. C₇×#3235	C₂	semidirect
5. C₇×#3234	C₂	semidirect
6. C₇×#3166	C₂	semidirect
7. C₇×#3162	C₂	semidirect
8. C₇×#3138	C₂	semidirect
9. C₂×C₇×#490	C₂	semidirect
10. C₇×#3096	C₂	semidirect
11. C₇×#3081	C₂	semidirect
12. C₇×#2923	C₂	semidirect
20. C₇×#544	C₂²	semidirect
25. C₇×#533	C₂²	semidirect
29. C₂×C₇×#125	C₂²	semidirect
33. C₇×#501	C₂²	semidirect
34. C₇×#501	C₂²	semidirect
35. C₇×#501	C₂²	semidirect
36. C₇×#501	C₂²	semidirect
37. C₇×#499	C₂²	semidirect
43. C₇×#482	C₂²	semidirect
44. C₇×#482	C₂²	semidirect
45. C₇×#481	C₂²	semidirect
46. C₇×#480	C₂²	semidirect
47. C₇×#478	C₂²	semidirect
48. C₇×#478	C₂²	semidirect
49. C₇×#476	C₂²	semidirect
50. C₇×#474	C₂²	semidirect
51. C₇×#433	C₂²	semidirect
52. C₇×#432	C₂²	semidirect
61. #60883	C₇	direct (N × H)
141. #3504	C₂×C₇	semidirect
142. #3241	C₂×C₇	semidirect
143. #3235	C₂×C₇	semidirect
144. #3234	C₂×C₇	semidirect
145. #3166	C₂×C₇	semidirect
146. #3162	C₂×C₇	semidirect
147. #3138	C₂×C₇	semidirect
148. C₂×#490	C₂×C₇	semidirect
149. #3096	C₂×C₇	semidirect
150. #3081	C₂×C₇	semidirect
151. #2923	C₂×C₇	semidirect
219. #544	C₂²×C₇	semidirect
224. #533	C₂²×C₇	semidirect
228. C₂×#125	C₂²×C₇	semidirect
232. #501	C₂²×C₇	semidirect
233. #501	C₂²×C₇	semidirect
234. #501	C₂²×C₇	semidirect
235. #501	C₂²×C₇	semidirect
236. #499	C₂²×C₇	semidirect
242. #482	C₂²×C₇	semidirect
243. #482	C₂²×C₇	semidirect
244. #481	C₂²×C₇	semidirect
245. #480	C₂²×C₇	semidirect
246. #478	C₂²×C₇	semidirect
247. #478	C₂²×C₇	semidirect
248. #476	C₂²×C₇	semidirect
249. #474	C₂²×C₇	semidirect
250. #433	C₂²×C₇	semidirect
251. #432	C₂²×C₇	semidirect
491. C₇	#60883	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×#3508	2
C₇×#3504	2
C₇×#3241	2
C₇×#3235	2
C₇×#3234	2
C₇×#3166	2
C₇×#3162	2
C₇×#3138	2
C₂×C₇×#490	2
C₇×#3096	2
C₇×#3081	2
C₇×#2923	2
#60883	7

Subgroups — C7×#60883 #13238099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60883 #13238099