Subgroups — C₇×#21518 #13198734

Order 1792.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3035	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#444	C₂	1	2	yes	maximal, complemented
3	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1929	C₂	1	2	yes	maximal, complemented
8	C₇×#1876	C₂	1	2	yes	maximal, complemented
9	C₇×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#135	C₂²	1	2	yes	—
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	C₂×C₇×#131	C₂²	1	1	yes	characteristic
15	C₂×C₇×#131	C₂²	1	1	yes	characteristic
16	C₇×#532	C₂²	1	1	yes	characteristic
17	C₄×C₇×#41	C₂²	1	1	yes	characteristic
18	C₇×#464	C₄	1	2	yes	complemented
19	C₇×#463	C₄	1	2	yes	complemented
20	C₇×#462	C₄	1	1	yes	characteristic, complemented
21	C₇×#461	C₄	1	1	yes	characteristic, complemented
22	C₇×#460	C₄	1	1	yes	characteristic, complemented
23	C₇×#459	C₄	1	1	yes	characteristic, complemented
24	C₇×#444	—	2	8	no	—
25	C₇×#436	—	2	1	no	—
26	C₇×#436	—	2	1	no	—
27	C₇×C₈×D₄	—	2	1	no	—
28	C₇×C₈×D₄	—	2	1	no	—
29	C₂×C₇×#108	C₂²	1	2	yes	—
30	C₇×#423	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×#104	C₂²	1	2	yes	—
33	C₂×C₇×#104	C₂²	1	2	yes	—
34	C₂×C₇×#104	C₂²	1	2	yes	—
35	C₇×#416	C₂²	1	2	yes	—
36	C₇×#408	C₂²	1	2	yes	—
37	C₇×#405	—	2	1	no	—
38	C₇×#405	—	2	1	no	—
39	C₇×#405	C₂²	1	1	yes	characteristic
40	C₇×#405	C₂²	1	1	yes	characteristic
41	C₄×C₇×M₁₆	—	2	1	no	—
42	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₇×#97	C₂²	1	2	yes	—
44	C₂×C₄×C₇×C₈	—	2	1	no	—
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#341	C₂²	1	2	yes	—
48	C₇×#339	C₂²	1	2	yes	—
49	C₇×#336	C₂²	1	2	yes	—
50	#21518	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₇×#41	C₂³	1	2	yes	—
52	C₂×C₇×#41	C₂³	1	1	yes	characteristic
53	C₇×#135	—	2	4	no	—
54	C₇×#135	—	2	4	no	—
55	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
59	C₇×#131	—	2	2	no	—
60	C₇×#131	—	2	2	no	—
61	C₇×#131	—	2	2	no	—
62	C₇×#131	—	2	4	no	—
63	C₇×#131	—	2	4	no	—
64	C₇×#131	D₄	1	4	yes	complemented
65	C₂×C₇×M₁₆	—	2	1	no	—
66	C₂×C₇×M₁₆	—	2	1	no	—
67	C₂×C₇×M₁₆	—	2	2	no	—
68	C₂×C₇×M₁₆	C₂³	1	2	yes	—
69	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	—	2	1	no	—
72	C₂²×C₇×C₈	—	2	1	no	—
73	C₂²×C₇×C₈	—	2	2	no	—
74	C₂²×C₇×C₈	C₂³	1	2	yes	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₇×#127	C₂×C₄	1	1	yes	characteristic
79	C₇×#124	C₂×C₄	1	2	yes	—
80	C₇×#121	—	2	1	no	—
81	C₇×#121	—	2	1	no	—
82	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₇×D₄	—	2	1	no	—
85	C₄×C₇×D₄	—	2	1	no	—
86	C₄×C₇×D₄	—	2	1	no	—
87	C₄×C₇×D₄	—	2	1	no	—
88	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
89	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
90	C₇×#117	—	2	1	no	—
91	C₇×#117	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₄²×C₇	—	2	1	no	—
94	C₂×C₄²×C₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₇×#108	—	2	4	no	—
97	C₇×C₄⋊C₈	—	2	1	no	—
98	C₇×C₄⋊C₈	—	2	1	no	—
99	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
102	C₇×#104	—	2	4	no	—
103	C₇×#104	—	2	4	no	—
104	C₇×#104	—	2	4	no	—
105	C₇×#103	C₂×C₄	1	2	yes	—
106	C₇×#103	C₂×C₄	1	2	yes	—
107	C₇×#102	C₂×C₄	1	2	yes	—
108	C₇×#102	C₂×C₄	1	2	yes	—
109	C₇×C₂²⋊C₈	—	2	2	no	—
110	C₇×C₂²⋊C₈	—	2	2	no	—
111	C₇×#97	—	2	4	no	—
112	C₇×#97	—	2	1	no	—
113	C₇×#97	—	2	1	no	—
114	C₇×#97	—	2	1	no	—
115	C₄×C₇×C₈	—	2	1	no	—
116	C₄×C₇×C₈	—	2	1	no	—
117	C₄×C₇×C₈	—	2	1	no	—
118	C₄×C₇×C₈	D₄	1	1	yes	characteristic
119	C₄×C₇×C₈	D₄	1	1	yes	characteristic
120	C₄×C₇×C₈	D₄	1	1	yes	characteristic
121	C₄×C₇×C₈	D₄	1	1	yes	characteristic
122	C₇×#95	—	2	1	no	—
123	#3035	C₂×C₇	1	1	yes	characteristic
124	C₂×#444	C₂×C₇	1	2	yes	complemented
125	#2931	C₂×C₇	1	1	yes	characteristic, complemented
126	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
127	#1980	C₂×C₇	1	1	yes	characteristic, complemented
128	#1950	C₂×C₇	1	1	yes	characteristic, complemented
129	#1929	C₂×C₇	1	2	yes	complemented
130	#1876	C₂×C₇	1	2	yes	complemented
131	#1806	C₂×C₇	1	1	yes	characteristic, complemented
132	#1770	C₂×C₇	1	1	yes	characteristic, complemented
133	#1765	C₂×C₇	1	2	yes	complemented
134	C₇×#41	—	2	1	no	—
135	C₇×#41	—	2	1	no	—
136	C₇×#41	—	2	2	no	—
137	C₇×#41	—	2	2	no	—
138	C₇×#41	—	2	2	no	—
139	C₇×#41	—	2	2	no	—
140	C₇×#41	C₂×D₄	1	2	yes	—
141	C₇×#41	#41	1	2	yes	—
142	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
143	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	2	no	—
146	C₂×C₇×D₄	—	2	1	no	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
149	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	2	no	—
154	C₂²×C₄×C₇	—	2	2	no	—
155	C₂²×C₄×C₇	#41	1	1	yes	characteristic
156	C₂²×C₄×C₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
158	C₇×Q₁₆	—	2	4	no	—
159	C₇×SD₁₆	—	2	4	no	—
160	C₇×SD₁₆	—	2	4	no	—
161	C₇×D₈	—	2	4	no	—
162	C₇×M₁₆	—	2	4	no	—
163	C₇×M₁₆	—	2	1	no	—
164	C₇×M₁₆	—	2	1	no	—
165	C₇×M₁₆	—	2	4	no	—
166	C₇×M₁₆	—	2	2	no	—
167	C₇×M₁₆	—	2	2	no	—
168	C₇×M₁₆	—	4	4	no	—
169	C₇×M₁₆	C₂×D₄	1	2	yes	—
170	C₇×M₁₆	#41	1	2	yes	—
171	C₂×C₇×C₈	—	2	4	no	—
172	C₂×C₇×C₈	—	2	2	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	2	no	—
178	C₂×C₇×C₈	—	2	4	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	—	4	4	no	—
181	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
182	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
183	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₇×C₈	#41	1	2	yes	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	4	2	no	—
194	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₇×C₂²⋊C₄	—	2	1	no	—
197	C₇×C₂²⋊C₄	—	2	1	no	—
198	C₇×C₂²⋊C₄	—	2	1	no	—
199	C₇×C₂²⋊C₄	—	2	2	no	—
200	C₇×C₂²⋊C₄	—	2	2	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	2	no	—
205	C₄²×C₇	—	2	2	no	—
206	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
210	C₂×#135	C₂²×C₇	1	2	yes	—
211	C₂×#131	C₂²×C₇	1	1	yes	characteristic
212	C₂×#131	C₂²×C₇	1	2	yes	—
213	C₂×#131	C₂²×C₇	1	1	yes	characteristic
214	#532	C₂²×C₇	1	1	yes	characteristic
215	C₄×#41	C₂²×C₇	1	1	yes	characteristic
216	#464	C₄×C₇	1	2	yes	complemented
217	#463	C₄×C₇	1	2	yes	complemented
218	#462	C₄×C₇	1	1	yes	characteristic, complemented
219	#461	C₄×C₇	1	1	yes	characteristic, complemented
220	#460	C₄×C₇	1	1	yes	characteristic, complemented
221	#459	C₄×C₇	1	1	yes	characteristic, complemented
222	#444	—	2	8	no	—
223	#436	—	2	1	no	—
224	#436	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	C₈×D₄	—	2	1	no	—
227	C₂×#108	C₂²×C₇	1	2	yes	—
228	#423	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×#104	C₂²×C₇	1	2	yes	—
231	C₂×#104	C₂²×C₇	1	2	yes	—
232	C₂×#104	C₂²×C₇	1	2	yes	—
233	#416	C₂²×C₇	1	2	yes	—
234	#408	C₂²×C₇	1	2	yes	—
235	#405	—	2	1	no	—
236	#405	—	2	1	no	—
237	#405	C₂²×C₇	1	1	yes	characteristic
238	#405	C₂²×C₇	1	1	yes	characteristic
239	C₄×M₁₆	—	2	1	no	—
240	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
241	C₂×#97	C₂²×C₇	1	2	yes	—
242	C₂×C₄×C₈	—	2	1	no	—
243	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
245	#341	C₂²×C₇	1	2	yes	—
246	#339	C₂²×C₇	1	2	yes	—
247	#336	C₂²×C₇	1	2	yes	—
248	C₂³×C₇	—	2	1	no	—
249	C₂³×C₇	—	2	2	no	—
250	C₂³×C₇	C₂×#41	1	1	yes	characteristic
251	C₇×Q₈	—	2	1	no	—
252	C₇×Q₈	—	2	2	no	—
253	C₇×Q₈	—	2	2	no	—
254	C₇×Q₈	C₄×D₄	1	2	yes	—
255	C₇×D₄	—	2	2	no	—
256	C₇×D₄	—	2	2	no	—
257	C₇×D₄	—	2	2	no	—
258	C₇×D₄	—	2	1	no	—
259	C₇×D₄	—	2	2	no	—
260	C₇×D₄	—	4	2	no	—
261	C₇×D₄	—	4	2	no	—
262	C₇×D₄	—	4	2	no	—
263	C₇×D₄	—	4	2	no	—
264	C₇×D₄	C₄×D₄	1	2	yes	—
265	C₂×C₄×C₇	—	2	1	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	1	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	4	1	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	—	4	2	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	—	4	2	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
281	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
283	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
290	C₇×C₈	—	2	2	no	—
291	C₇×C₈	—	2	2	no	—
292	C₇×C₈	—	2	2	no	—
293	C₇×C₈	—	2	1	no	—
294	C₇×C₈	—	2	2	no	—
295	C₇×C₈	—	2	1	no	—
296	C₇×C₈	—	4	2	no	—
297	C₇×C₈	#121	1	2	yes	—
298	C₇×C₈	#121	1	2	yes	—
299	C₂×#41	C₂³×C₇	1	2	yes	—
300	C₂×#41	C₂³×C₇	1	1	yes	characteristic
301	#135	—	2	4	no	—
302	#135	—	2	4	no	—
303	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
304	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
305	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
306	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
307	#131	—	2	2	no	—
308	#131	—	2	2	no	—
309	#131	—	2	2	no	—
310	#131	—	2	4	no	—
311	#131	—	2	4	no	—
312	#131	C₇×D₄	1	4	yes	complemented
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	C₂³×C₇	1	2	yes	—
317	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
318	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	C₂³×C₇	1	2	yes	—
323	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
325	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
326	#127	C₂×C₄×C₇	1	1	yes	characteristic
327	#124	C₂×C₄×C₇	1	2	yes	—
328	#121	—	2	1	no	—
329	#121	—	2	1	no	—
330	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
331	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
337	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
338	#117	—	2	1	no	—
339	#117	C₂³×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₇	1	2	yes	—
343	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
344	#108	—	2	4	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
348	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
349	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
350	#104	—	2	4	no	—
351	#104	—	2	4	no	—
352	#104	—	2	4	no	—
353	#103	C₂×C₄×C₇	1	2	yes	—
354	#103	C₂×C₄×C₇	1	2	yes	—
355	#102	C₂×C₄×C₇	1	2	yes	—
356	#102	C₂×C₄×C₇	1	2	yes	—
357	C₂²⋊C₈	—	2	2	no	—
358	C₂²⋊C₈	—	2	2	no	—
359	#97	—	2	4	no	—
360	#97	—	2	1	no	—
361	#97	—	2	1	no	—
362	#97	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	C₇×D₄	1	1	yes	characteristic
367	C₄×C₈	C₇×D₄	1	1	yes	characteristic
368	C₄×C₈	C₇×D₄	1	1	yes	characteristic
369	C₄×C₈	C₇×D₄	1	1	yes	characteristic
370	#95	—	2	1	no	—
371	C₂²×C₇	—	2	1	no	—
372	C₂²×C₇	—	2	1	no	—
373	C₂²×C₇	—	2	2	no	—
374	C₂²×C₇	—	4	1	no	—
375	C₂²×C₇	—	4	1	no	—
376	C₂²×C₇	—	4	2	no	—
377	C₂²×C₇	—	4	2	no	—
378	C₂²×C₇	—	4	2	no	—
379	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
380	C₂²×C₇	#529	1	1	yes	characteristic
381	C₂²×C₇	#532	1	1	yes	characteristic
382	C₄×C₇	—	2	1	no	—
383	C₄×C₇	—	2	1	no	—
384	C₄×C₇	—	2	1	no	—
385	C₄×C₇	—	2	2	no	—
386	C₄×C₇	—	4	1	no	—
387	C₄×C₇	—	4	1	no	—
388	C₄×C₇	—	4	2	no	—
389	C₄×C₇	—	8	2	no	—
390	C₄×C₇	#444	1	2	yes	complemented
391	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
392	C₄×C₇	C₄×#41	1	1	yes	characteristic
393	C₄×C₇	C₂×#121	1	1	yes	characteristic
394	C₄×C₇	#525	1	1	yes	characteristic
395	#41	—	2	1	no	—
396	#41	—	2	1	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	C₂×C₇×D₄	1	2	yes	—
402	#41	C₇×#41	1	2	yes	—
403	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
404	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
410	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	C₇×#41	1	1	yes	characteristic
417	C₂²×C₄	C₇×#41	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
419	Q₁₆	—	2	4	no	—
420	SD₁₆	—	2	4	no	—
421	SD₁₆	—	2	4	no	—
422	D₈	—	2	4	no	—
423	M₁₆	—	2	4	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	4	4	no	—
430	M₁₆	C₂×C₇×D₄	1	2	yes	—
431	M₁₆	C₇×#41	1	2	yes	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	4	4	no	—
442	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
443	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
444	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
445	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
446	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
447	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
448	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
449	C₂×C₈	C₇×#41	1	2	yes	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
468	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
469	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
470	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂×C₇	—	2	1	no	—
472	C₂×C₇	—	2	1	no	—
473	C₂×C₇	—	4	2	no	—
474	C₂×C₇	—	8	2	no	—
475	C₂×C₇	C₄×#121	1	1	yes	characteristic
476	C₂×C₇	C₂×#444	1	1	yes	characteristic
477	C₂×C₇	#2955	1	1	yes	characteristic
478	C₂³	—	2	1	no	—
479	C₂³	—	2	2	no	—
480	C₂³	C₂×C₇×#41	1	1	yes	characteristic
481	Q₈	—	2	1	no	—
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	C₄×C₇×D₄	1	2	yes	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	C₄×C₇×D₄	1	2	yes	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
511	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
512	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
513	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
517	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
518	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
519	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	2	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	2	no	—
527	C₈	C₇×#121	1	2	yes	—
528	C₈	C₇×#121	1	2	yes	—
529	C₇	#21518	1	1	yes	characteristic, direct product factor, Sylow
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
539	C₂²	C₇×#529	1	1	yes	characteristic
540	C₂²	C₇×#532	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	2	no	—
549	C₄	C₇×#444	1	2	yes	complemented
550	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
551	C₄	C₄×C₇×#41	1	1	yes	characteristic
552	C₄	C₂×C₇×#121	1	1	yes	characteristic
553	C₄	C₇×#525	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₄×C₇×#121	1	1	yes	characteristic
559	C₂	C₂×C₇×#444	1	1	yes	characteristic
560	C₂	C₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#444	C₂	semidirect
3. C₇×#2931	C₂	semidirect
4. C₄×C₇×#131	C₂	semidirect
5. C₇×#1980	C₂	semidirect
6. C₇×#1950	C₂	semidirect
7. C₇×#1929	C₂	semidirect
8. C₇×#1876	C₂	semidirect
9. C₇×#1806	C₂	semidirect
10. C₇×#1770	C₂	semidirect
11. C₇×#1765	C₂	semidirect
18. C₇×#464	C₄	semidirect
19. C₇×#463	C₄	semidirect
20. C₇×#462	C₄	semidirect
21. C₇×#461	C₄	semidirect
22. C₇×#460	C₄	semidirect
23. C₇×#459	C₄	semidirect
50. #21518	C₇	direct (N × H)
64. C₇×#131	D₄	semidirect
124. C₂×#444	C₂×C₇	semidirect
125. #2931	C₂×C₇	semidirect
126. C₄×#131	C₂×C₇	semidirect
127. #1980	C₂×C₇	semidirect
128. #1950	C₂×C₇	semidirect
129. #1929	C₂×C₇	semidirect
130. #1876	C₂×C₇	semidirect
131. #1806	C₂×C₇	semidirect
132. #1770	C₂×C₇	semidirect
133. #1765	C₂×C₇	semidirect
216. #464	C₄×C₇	semidirect
217. #463	C₄×C₇	semidirect
218. #462	C₄×C₇	semidirect
219. #461	C₄×C₇	semidirect
220. #460	C₄×C₇	semidirect
221. #459	C₄×C₇	semidirect
312. #131	C₇×D₄	semidirect
390. C₄×C₇	#444	semidirect
529. C₇	#21518	direct (N × H)
549. C₄	C₇×#444	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3035	2
C₂×C₇×#444	2
C₇×#2931	2
C₄×C₇×#131	2
C₇×#1980	2
C₇×#1950	2
C₇×#1929	2
C₇×#1876	2
C₇×#1806	2
C₇×#1770	2
C₇×#1765	2
#21518	7

Subgroups — C7×#21518 #13198734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21518 #13198734