Subgroups — C₇×#25201 #13202417

Order 1792.

806 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic
3	C₇×#2499	C₂	1	1	yes	maximal, characteristic
4	C₇×#2362	C₂	1	1	yes	maximal, characteristic
5	C₇×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1873	C₂	1	1	yes	maximal, characteristic
13	C₇×#1850	C₂	1	1	yes	maximal, characteristic
14	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1735	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₂×C₇×#117	C₂²	1	1	yes	characteristic
23	C₇×#485	—	2	4	no	—
24	C₇×#467	—	2	4	no	—
25	C₂×C₇×#107	C₂²	1	1	yes	characteristic
26	C₂×C₇×#107	C₂²	1	1	yes	characteristic
27	C₂×C₇×#106	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#103	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₇×#397	—	2	1	no	—
38	C₇×#397	—	2	1	no	—
39	C₇×#391	C₂²	1	1	yes	characteristic
40	C₇×#391	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	1	yes	characteristic
42	C₇×#389	C₂²	1	1	yes	characteristic
43	C₇×#388	—	2	1	no	—
44	C₇×#388	—	2	1	no	—
45	C₇×#387	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#387	—	2	1	no	—
48	C₇×#384	C₂²	1	1	yes	characteristic
49	C₇×#382	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	—	2	1	no	—
51	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#25201	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₇×Q₁₆	—	2	2	no	—
66	C₂×C₇×Q₁₆	—	2	2	no	—
67	C₂×C₇×Q₁₆	—	4	1	no	—
68	C₂²×C₇×C₈	—	2	2	no	—
69	C₂²×C₇×C₈	—	2	2	no	—
70	C₂²×C₇×C₈	—	4	1	no	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₇×C₂²⋊Q₈	—	2	2	no	—
76	C₇×C₂²⋊Q₈	—	2	2	no	—
77	C₇×C₂²⋊Q₈	—	2	2	no	—
78	C₇×C₂²⋊Q₈	D₄	1	4	yes	—
79	C₄×C₇×Q₈	—	2	2	no	—
80	C₄×C₇×Q₈	—	4	1	no	—
81	C₇×#117	—	2	2	no	—
82	C₇×#117	—	2	2	no	—
83	C₇×#117	—	2	2	no	—
84	C₇×#117	—	4	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	—	2	1	no	—
87	C₂×C₇×C₄⋊C₄	—	2	1	no	—
88	C₂×C₇×C₄⋊C₄	—	2	1	no	—
89	C₂×C₇×C₄⋊C₄	—	2	1	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₇	—	2	1	no	—
104	C₂×C₄²×C₇	—	2	1	no	—
105	C₂×C₄²×C₇	—	2	1	no	—
106	C₂×C₄²×C₇	—	2	1	no	—
107	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₇×#107	—	2	2	no	—
110	C₇×#107	—	2	2	no	—
111	C₇×#106	—	2	2	no	—
112	C₇×C₄⋊C₈	—	2	2	no	—
113	C₇×C₄⋊C₈	—	4	1	no	—
114	C₇×#103	—	2	2	no	—
115	C₇×#103	—	2	2	no	—
116	C₇×#103	—	2	2	no	—
117	C₇×#103	—	2	2	no	—
118	C₇×#103	—	2	2	no	—
119	C₇×#103	—	4	1	no	—
120	C₇×C₂²⋊C₈	—	2	2	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	C₇×#95	—	2	1	no	—
124	C₇×#95	—	2	1	no	—
125	C₇×#95	—	2	1	no	—
126	C₇×#95	—	2	1	no	—
127	C₇×#95	—	2	1	no	—
128	C₇×#95	—	2	1	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₇×#95	D₄	1	1	yes	characteristic
132	C₇×#95	D₄	1	1	yes	characteristic
133	C₂×#485	C₂×C₇	1	1	yes	characteristic
134	C₂×#467	C₂×C₇	1	1	yes	characteristic
135	#2499	C₂×C₇	1	1	yes	characteristic
136	#2362	C₂×C₇	1	1	yes	characteristic
137	#2083	C₂×C₇	1	1	yes	characteristic, complemented
138	#2074	C₂×C₇	1	1	yes	characteristic, complemented
139	#2066	C₂×C₇	1	1	yes	characteristic, complemented
140	#2056	C₂×C₇	1	1	yes	characteristic, complemented
141	#1949	C₂×C₇	1	1	yes	characteristic, complemented
142	#1928	C₂×C₇	1	1	yes	characteristic, complemented
143	#1878	C₂×C₇	1	1	yes	characteristic, complemented
144	#1873	C₂×C₇	1	1	yes	characteristic
145	#1850	C₂×C₇	1	1	yes	characteristic
146	#1803	C₂×C₇	1	1	yes	characteristic, complemented
147	#1735	C₂×C₇	1	1	yes	characteristic
148	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₇×Q₈	—	2	1	no	—
150	C₂×C₇×Q₈	—	2	1	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×Q₈	—	2	1	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	1	no	—
158	C₂×C₇×Q₈	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	1	no	—
160	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	#41	1	2	yes	—
180	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
181	C₇×Q₁₆	—	4	4	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₂×C₇×C₈	—	2	1	no	—
189	C₂×C₇×C₈	—	2	1	no	—
190	C₂×C₇×C₈	—	2	1	no	—
191	C₂×C₇×C₈	—	2	1	no	—
192	C₂×C₇×C₈	—	2	1	no	—
193	C₂×C₇×C₈	—	4	4	no	—
194	C₂×C₇×C₈	#41	1	2	yes	—
195	C₇×C₄⋊C₄	—	2	4	no	—
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	—	2	1	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	—	4	2	no	—
207	C₇×C₄⋊C₄	—	4	2	no	—
208	C₇×C₄⋊C₄	—	4	2	no	—
209	C₇×C₄⋊C₄	—	4	2	no	—
210	C₇×C₄⋊C₄	—	4	2	no	—
211	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
212	C₇×C₄⋊C₄	#41	1	2	yes	—
213	C₇×C₂²⋊C₄	—	2	4	no	—
214	C₇×C₂²⋊C₄	—	2	2	no	—
215	C₇×C₂²⋊C₄	—	4	1	no	—
216	C₇×C₂²⋊C₄	—	4	2	no	—
217	C₇×C₂²⋊C₄	—	4	2	no	—
218	C₇×C₂²⋊C₄	—	4	2	no	—
219	C₄²×C₇	—	2	1	no	—
220	C₄²×C₇	—	2	1	no	—
221	C₄²×C₇	—	2	1	no	—
222	C₄²×C₇	—	2	1	no	—
223	C₄²×C₇	—	4	2	no	—
224	C₄²×C₇	—	4	2	no	—
225	C₄²×C₇	—	4	2	no	—
226	C₄²×C₇	—	4	2	no	—
227	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
232	C₂×#117	C₂²×C₇	1	1	yes	characteristic
233	C₂×#117	C₂²×C₇	1	1	yes	characteristic
234	#485	—	2	4	no	—
235	#467	—	2	4	no	—
236	C₂×#107	C₂²×C₇	1	1	yes	characteristic
237	C₂×#107	C₂²×C₇	1	1	yes	characteristic
238	C₂×#106	C₂²×C₇	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
241	C₂×#103	C₂²×C₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₇	1	1	yes	characteristic
243	C₂×#103	C₂²×C₇	1	1	yes	characteristic
244	C₂×#103	C₂²×C₇	1	1	yes	characteristic
245	C₂×#103	C₂²×C₇	1	1	yes	characteristic
246	C₂×#103	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
248	#397	—	2	1	no	—
249	#397	—	2	1	no	—
250	#391	C₂²×C₇	1	1	yes	characteristic
251	#391	C₂²×C₇	1	1	yes	characteristic
252	#391	C₂²×C₇	1	1	yes	characteristic
253	#389	C₂²×C₇	1	1	yes	characteristic
254	#388	—	2	1	no	—
255	#388	—	2	1	no	—
256	#387	—	2	1	no	—
257	#387	—	2	1	no	—
258	#387	—	2	1	no	—
259	#384	C₂²×C₇	1	1	yes	characteristic
260	#382	C₂²×C₇	1	1	yes	characteristic
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
264	#340	C₂²×C₇	1	1	yes	characteristic
265	#340	C₂²×C₇	1	1	yes	characteristic
266	#340	C₂²×C₇	1	1	yes	characteristic
267	#340	C₂²×C₇	1	1	yes	characteristic
268	#340	C₂²×C₇	1	1	yes	characteristic
269	#340	C₂²×C₇	1	1	yes	characteristic
270	#336	C₂²×C₇	1	1	yes	characteristic
271	#336	C₂²×C₇	1	1	yes	characteristic
272	C₂³×C₇	—	2	1	no	—
273	C₂³×C₇	—	2	1	no	—
274	C₂³×C₇	—	2	1	no	—
275	C₂³×C₇	—	2	1	no	—
276	C₂³×C₇	—	2	1	no	—
277	C₂³×C₇	—	2	1	no	—
278	C₂³×C₇	#121	1	2	yes	—
279	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
280	C₇×Q₈	—	2	2	no	—
281	C₇×Q₈	—	2	2	no	—
282	C₇×Q₈	—	4	1	no	—
283	C₇×Q₈	—	4	1	no	—
284	C₇×Q₈	—	4	1	no	—
285	C₇×Q₈	—	4	1	no	—
286	C₇×Q₈	—	4	1	no	—
287	C₇×Q₈	—	4	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	2	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	—	4	1	no	—
322	C₂×C₄×C₇	—	4	1	no	—
323	C₂×C₄×C₇	—	4	1	no	—
324	C₂×C₄×C₇	—	4	1	no	—
325	C₂×C₄×C₇	—	4	1	no	—
326	C₂×C₄×C₇	—	4	1	no	—
327	C₂×C₄×C₇	—	4	1	no	—
328	C₂×C₄×C₇	—	4	1	no	—
329	C₂×C₄×C₇	#121	1	2	yes	—
330	C₂×C₄×C₇	#135	1	2	yes	—
331	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
337	C₇×C₈	—	2	2	no	—
338	C₇×C₈	—	4	1	no	—
339	C₇×C₈	—	4	1	no	—
340	C₇×C₈	—	4	1	no	—
341	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
344	C₂×Q₁₆	—	2	2	no	—
345	C₂×Q₁₆	—	2	2	no	—
346	C₂×Q₁₆	—	4	1	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	—	4	1	no	—
350	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	C₇×D₄	1	4	yes	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	4	1	no	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	#117	—	2	2	no	—
363	#117	—	4	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
388	#107	—	2	2	no	—
389	#107	—	2	2	no	—
390	#106	—	2	2	no	—
391	C₄⋊C₈	—	2	2	no	—
392	C₄⋊C₈	—	4	1	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	4	1	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	C₇×D₄	1	1	yes	characteristic
411	#95	C₇×D₄	1	1	yes	characteristic
412	C₂²×C₇	—	2	2	no	—
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	—	4	1	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	—	4	1	no	—
419	C₂²×C₇	C₂×#121	1	1	yes	characteristic
420	C₂²×C₇	#546	1	1	yes	characteristic
421	C₂²×C₇	#547	1	1	yes	characteristic
422	C₂²×C₇	C₂×#135	1	1	yes	characteristic
423	C₂²×C₇	#575	1	1	yes	characteristic
424	C₂²×C₇	#578	1	1	yes	characteristic
425	C₂²×C₇	#578	1	1	yes	characteristic
426	C₄×C₇	—	2	2	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	4	1	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	—	4	2	no	—
431	C₄×C₇	—	4	2	no	—
432	C₄×C₇	—	4	1	no	—
433	C₄×C₇	—	4	2	no	—
434	C₄×C₇	—	8	1	no	—
435	C₄×C₇	—	8	1	no	—
436	C₄×C₇	—	8	1	no	—
437	C₄×C₇	—	8	1	no	—
438	C₄×C₇	—	8	1	no	—
439	C₄×C₇	#529	1	1	yes	characteristic
440	C₄×C₇	#539	1	1	yes	characteristic
441	C₄×C₇	#546	1	1	yes	characteristic
442	C₄×C₇	#547	1	1	yes	characteristic
443	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
473	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
474	C₂²×C₄	C₇×#41	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
476	Q₁₆	—	4	4	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	4	4	no	—
489	C₂×C₈	C₇×#41	1	2	yes	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
507	C₄⋊C₄	C₇×#41	1	2	yes	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	4	2	no	—
522	C₂×C₇	—	4	2	no	—
523	C₂×C₇	#2425	1	1	yes	characteristic
524	C₂×C₇	#3035	1	1	yes	characteristic
525	C₂×C₇	#3044	1	1	yes	characteristic
526	C₂×C₇	#3300	1	1	yes	characteristic
527	C₂×C₇	#3315	1	1	yes	characteristic
528	C₂×C₇	#3342	1	1	yes	characteristic
529	C₂×C₇	#3349	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	C₇×#121	1	2	yes	—
537	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
538	Q₈	—	2	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	C₇×#121	1	2	yes	—
588	C₂×C₄	C₇×#135	1	2	yes	—
589	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
593	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₇	#25201	1	1	yes	characteristic, direct product factor, Sylow
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	C₂×C₇×#121	1	1	yes	characteristic
608	C₂²	C₇×#546	1	1	yes	characteristic
609	C₂²	C₇×#547	1	1	yes	characteristic
610	C₂²	C₂×C₇×#135	1	1	yes	characteristic
611	C₂²	C₇×#575	1	1	yes	characteristic
612	C₂²	C₇×#578	1	1	yes	characteristic
613	C₂²	C₇×#578	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	C₇×#529	1	1	yes	characteristic
628	C₄	C₇×#539	1	1	yes	characteristic
629	C₄	C₇×#546	1	1	yes	characteristic
630	C₄	C₇×#547	1	1	yes	characteristic
631	C₂	—	4	2	no	—
632	C₂	C₇×#2425	1	1	yes	characteristic
633	C₂	C₇×#3035	1	1	yes	characteristic
634	C₂	C₇×#3044	1	1	yes	characteristic
635	C₂	C₇×#3300	1	1	yes	characteristic
636	C₂	C₇×#3315	1	1	yes	characteristic
637	C₂	C₇×#3342	1	1	yes	characteristic
638	C₂	C₇×#3349	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 ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇×#2083	C₂	semidirect
6. C₇×#2074	C₂	semidirect
7. C₇×#2066	C₂	semidirect
8. C₇×#2056	C₂	semidirect
9. C₇×#1949	C₂	semidirect
10. C₇×#1928	C₂	semidirect
11. C₇×#1878	C₂	semidirect
14. C₇×#1803	C₂	semidirect
61. #25201	C₇	direct (N × H)
137. #2083	C₂×C₇	semidirect
138. #2074	C₂×C₇	semidirect
139. #2066	C₂×C₇	semidirect
140. #2056	C₂×C₇	semidirect
141. #1949	C₂×C₇	semidirect
142. #1928	C₂×C₇	semidirect
143. #1878	C₂×C₇	semidirect
146. #1803	C₂×C₇	semidirect
599. C₇	#25201	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×#485	2
C₂×C₇×#467	2
C₇×#2499	2
C₇×#2362	2
C₇×#2083	2
C₇×#2074	2
C₇×#2066	2
C₇×#2056	2
C₇×#1949	2
C₇×#1928	2
C₇×#1878	2
C₇×#1873	2
C₇×#1850	2
C₇×#1803	2
C₇×#1735	2
#25201	7

Subgroups — C7×#25201 #13202417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#25201 #13202417