Subgroups — C₇×#29442 #13206658

Order 1792.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2644	C₂	1	1	yes	maximal, characteristic
2	C₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2065	C₂	1	1	yes	maximal, characteristic
6	C₇×#2055	C₂	1	1	yes	maximal, characteristic
7	C₇×#1968	C₂	1	1	yes	maximal, characteristic
8	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1936	C₂	1	1	yes	maximal, characteristic
10	C₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1926	C₂	1	1	yes	maximal, characteristic
12	C₇×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1880	C₂	1	1	yes	maximal, characteristic
14	C₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#106	C₂²	1	1	yes	characteristic
19	C₂×C₇×#106	C₂²	1	1	yes	characteristic
20	C₂×C₇×#106	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#397	—	2	1	no	—
32	C₇×#397	—	2	1	no	—
33	C₇×#397	—	2	1	no	—
34	C₇×#396	—	2	1	no	—
35	C₇×#391	C₂²	1	1	yes	characteristic
36	C₇×#391	C₂²	1	1	yes	characteristic
37	C₇×#390	C₂²	1	1	yes	characteristic
38	C₇×#390	C₂²	1	1	yes	characteristic
39	C₇×#390	C₂²	1	1	yes	characteristic
40	C₇×#389	C₂²	1	1	yes	characteristic
41	C₇×#389	C₂²	1	1	yes	characteristic
42	C₇×#389	C₂²	1	1	yes	characteristic
43	C₇×#389	C₂²	1	1	yes	characteristic
44	C₇×#389	C₂²	1	1	yes	characteristic
45	C₇×#387	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#383	—	2	1	no	—
48	C₇×#382	—	2	1	no	—
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₇×#376	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#29442	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₇×SD₁₆	—	2	2	no	—
63	C₂×C₇×SD₁₆	—	2	2	no	—
64	C₂×C₇×SD₁₆	—	4	1	no	—
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	—	2	2	no	—
71	C₂×C₇×C₄⋊C₄	—	2	1	no	—
72	C₂×C₇×C₄⋊C₄	—	2	1	no	—
73	C₂×C₇×C₄⋊C₄	—	2	1	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₂×C₄²×C₇	—	2	1	no	—
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₇×#106	—	2	2	no	—
95	C₇×#106	—	2	2	no	—
96	C₇×#106	—	4	1	no	—
97	C₇×C₄⋊C₈	—	2	2	no	—
98	C₇×C₄⋊C₈	—	2	2	no	—
99	C₇×#103	—	2	2	no	—
100	C₇×#103	—	2	2	no	—
101	C₇×#103	—	4	1	no	—
102	C₇×#102	—	2	2	no	—
103	C₇×#102	—	2	2	no	—
104	C₇×#102	—	4	1	no	—
105	C₇×#97	—	4	1	no	—
106	C₄×C₇×C₈	—	4	1	no	—
107	C₇×#95	—	2	1	no	—
108	C₇×#95	—	2	1	no	—
109	C₇×#95	—	2	1	no	—
110	C₇×#95	—	2	1	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	—	2	1	no	—
114	C₇×#95	—	2	1	no	—
115	C₇×#95	—	2	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	D₄	1	1	yes	characteristic
118	C₇×#95	D₄	1	1	yes	characteristic
119	C₇×#95	D₄	1	1	yes	characteristic
120	C₇×#95	D₄	1	1	yes	characteristic
121	#2644	C₂×C₇	1	1	yes	characteristic
122	#2320	C₂×C₇	1	1	yes	characteristic, complemented
123	#2088	C₂×C₇	1	1	yes	characteristic, complemented
124	#2066	C₂×C₇	1	1	yes	characteristic, complemented
125	#2065	C₂×C₇	1	1	yes	characteristic
126	#2055	C₂×C₇	1	1	yes	characteristic
127	#1968	C₂×C₇	1	1	yes	characteristic
128	#1941	C₂×C₇	1	1	yes	characteristic, complemented
129	#1936	C₂×C₇	1	1	yes	characteristic
130	#1935	C₂×C₇	1	1	yes	characteristic, complemented
131	#1926	C₂×C₇	1	1	yes	characteristic
132	#1920	C₂×C₇	1	1	yes	characteristic, complemented
133	#1880	C₂×C₇	1	1	yes	characteristic
134	#1865	C₂×C₇	1	1	yes	characteristic, complemented
135	#1768	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂⁴×C₇	—	2	1	no	—
137	C₂×C₇×Q₈	—	2	1	no	—
138	C₂×C₇×Q₈	—	2	1	no	—
139	C₂×C₇×Q₈	—	2	1	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	1	no	—
142	C₂×C₇×Q₈	#41	1	2	yes	—
143	C₂×C₇×D₄	—	2	1	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	1	no	—
146	C₂×C₇×D₄	—	2	1	no	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
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	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₇×SD₁₆	—	4	4	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	1	no	—
166	C₂×C₇×C₈	—	2	1	no	—
167	C₂×C₇×C₈	—	2	1	no	—
168	C₂×C₇×C₈	—	2	1	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	#41	1	2	yes	—
175	C₂×C₇×C₈	#41	1	2	yes	—
176	C₇×C₄⋊C₄	—	2	4	no	—
177	C₇×C₄⋊C₄	—	2	1	no	—
178	C₇×C₄⋊C₄	—	2	1	no	—
179	C₇×C₄⋊C₄	—	2	1	no	—
180	C₇×C₄⋊C₄	—	2	1	no	—
181	C₇×C₄⋊C₄	—	2	1	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	8	1	no	—
189	C₇×C₄⋊C₄	—	8	1	no	—
190	C₇×C₄⋊C₄	—	8	1	no	—
191	C₇×C₄⋊C₄	—	8	1	no	—
192	C₇×C₄⋊C₄	—	8	1	no	—
193	C₇×C₄⋊C₄	#41	1	2	yes	—
194	C₇×C₂²⋊C₄	—	8	1	no	—
195	C₇×C₂²⋊C₄	—	8	1	no	—
196	C₇×C₂²⋊C₄	—	8	1	no	—
197	C₇×C₂²⋊C₄	—	8	1	no	—
198	C₇×C₂²⋊C₄	—	8	1	no	—
199	C₇×C₂²⋊C₄	—	8	1	no	—
200	C₄²×C₇	—	2	4	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	—	2	1	no	—
206	C₄²×C₇	—	2	1	no	—
207	C₄²×C₇	—	8	1	no	—
208	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×#106	C₂²×C₇	1	1	yes	characteristic
211	C₂×#106	C₂²×C₇	1	1	yes	characteristic
212	C₂×#106	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×#103	C₂²×C₇	1	1	yes	characteristic
216	C₂×#103	C₂²×C₇	1	1	yes	characteristic
217	C₂×#103	C₂²×C₇	1	1	yes	characteristic
218	C₂×#102	C₂²×C₇	1	1	yes	characteristic
219	C₂×#102	C₂²×C₇	1	1	yes	characteristic
220	C₂×#102	C₂²×C₇	1	1	yes	characteristic
221	C₂×#97	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
223	#397	—	2	1	no	—
224	#397	—	2	1	no	—
225	#397	—	2	1	no	—
226	#396	—	2	1	no	—
227	#391	C₂²×C₇	1	1	yes	characteristic
228	#391	C₂²×C₇	1	1	yes	characteristic
229	#390	C₂²×C₇	1	1	yes	characteristic
230	#390	C₂²×C₇	1	1	yes	characteristic
231	#390	C₂²×C₇	1	1	yes	characteristic
232	#389	C₂²×C₇	1	1	yes	characteristic
233	#389	C₂²×C₇	1	1	yes	characteristic
234	#389	C₂²×C₇	1	1	yes	characteristic
235	#389	C₂²×C₇	1	1	yes	characteristic
236	#389	C₂²×C₇	1	1	yes	characteristic
237	#387	—	2	1	no	—
238	#387	—	2	1	no	—
239	#383	—	2	1	no	—
240	#382	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
242	#376	C₂²×C₇	1	1	yes	characteristic
243	#340	C₂²×C₇	1	1	yes	characteristic
244	#340	C₂²×C₇	1	1	yes	characteristic
245	#340	C₂²×C₇	1	1	yes	characteristic
246	#340	C₂²×C₇	1	1	yes	characteristic
247	#340	C₂²×C₇	1	1	yes	characteristic
248	#340	C₂²×C₇	1	1	yes	characteristic
249	#336	C₂²×C₇	1	1	yes	characteristic
250	#336	C₂²×C₇	1	1	yes	characteristic
251	C₂³×C₇	—	4	1	no	—
252	C₂³×C₇	—	4	1	no	—
253	C₂³×C₇	—	4	1	no	—
254	C₂³×C₇	—	4	1	no	—
255	C₂³×C₇	—	4	1	no	—
256	C₂³×C₇	—	4	1	no	—
257	C₂³×C₇	—	4	1	no	—
258	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
259	C₇×Q₈	—	2	2	no	—
260	C₇×Q₈	—	2	2	no	—
261	C₇×Q₈	—	4	1	no	—
262	C₇×Q₈	—	4	1	no	—
263	C₇×D₄	—	4	1	no	—
264	C₇×D₄	—	4	1	no	—
265	C₇×D₄	—	4	1	no	—
266	C₇×D₄	—	4	1	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	4	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	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	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
312	C₇×C₈	—	2	2	no	—
313	C₇×C₈	—	2	2	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	4	1	no	—
321	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
350	#106	—	2	2	no	—
351	#106	—	2	2	no	—
352	#106	—	4	1	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	#103	—	2	2	no	—
356	#103	—	2	2	no	—
357	#103	—	4	1	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#102	—	4	1	no	—
361	#97	—	4	1	no	—
362	C₄×C₈	—	4	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	C₇×D₄	1	1	yes	characteristic
374	#95	C₇×D₄	1	1	yes	characteristic
375	#95	C₇×D₄	1	1	yes	characteristic
376	#95	C₇×D₄	1	1	yes	characteristic
377	C₂²×C₇	—	8	1	no	—
378	C₂²×C₇	—	8	1	no	—
379	C₂²×C₇	—	8	1	no	—
380	C₂²×C₇	—	8	1	no	—
381	C₂²×C₇	—	8	1	no	—
382	C₂²×C₇	—	8	1	no	—
383	C₂²×C₇	—	8	1	no	—
384	C₂²×C₇	#525	1	1	yes	characteristic
385	C₂²×C₇	#532	1	1	yes	characteristic
386	C₂²×C₇	#537	1	1	yes	characteristic
387	C₂²×C₇	#577	1	1	yes	characteristic
388	C₂²×C₇	#577	1	1	yes	characteristic
389	C₂²×C₇	#577	1	1	yes	characteristic
390	C₂²×C₇	#577	1	1	yes	characteristic
391	C₄×C₇	—	4	2	no	—
392	C₄×C₇	—	4	1	no	—
393	C₄×C₇	—	4	2	no	—
394	C₄×C₇	—	4	1	no	—
395	C₄×C₇	—	4	1	no	—
396	C₄×C₇	—	4	1	no	—
397	C₄×C₇	—	4	1	no	—
398	C₄×C₇	—	4	1	no	—
399	C₄×C₇	—	8	1	no	—
400	C₄×C₇	—	8	1	no	—
401	C₄×C₇	—	8	1	no	—
402	C₄×C₇	—	8	1	no	—
403	C₄×C₇	—	8	1	no	—
404	C₄×C₇	#551	1	1	yes	characteristic
405	C₄×C₇	#552	1	1	yes	characteristic
406	C₄×C₇	#553	1	1	yes	characteristic
407	C₄×C₇	#556	1	1	yes	characteristic
408	C₂⁴	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	C₇×#41	1	2	yes	—
415	C₂×D₄	—	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	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
435	SD₁₆	—	4	4	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	C₇×#41	1	2	yes	—
447	C₂×C₈	C₇×#41	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	8	1	no	—
461	C₄⋊C₄	—	8	1	no	—
462	C₄⋊C₄	—	8	1	no	—
463	C₄⋊C₄	—	8	1	no	—
464	C₄⋊C₄	—	8	1	no	—
465	C₄⋊C₄	C₇×#41	1	2	yes	—
466	C₂²⋊C₄	—	8	1	no	—
467	C₂²⋊C₄	—	8	1	no	—
468	C₂²⋊C₄	—	8	1	no	—
469	C₂²⋊C₄	—	8	1	no	—
470	C₂²⋊C₄	—	8	1	no	—
471	C₂²⋊C₄	—	8	1	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	8	1	no	—
480	C₂×C₇	—	16	1	no	—
481	C₂×C₇	#2601	1	1	yes	characteristic
482	C₂×C₇	#3125	1	1	yes	characteristic
483	C₂×C₇	#3126	1	1	yes	characteristic
484	C₂×C₇	#3173	1	1	yes	characteristic
485	C₂×C₇	#3174	1	1	yes	characteristic
486	C₂×C₇	#3260	1	1	yes	characteristic
487	C₂×C₇	#3263	1	1	yes	characteristic
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
544	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
545	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
546	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
547	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
549	C₈	—	2	2	no	—
550	C₈	—	2	2	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₇	#29442	1	1	yes	characteristic, direct product factor, Sylow
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	C₇×#525	1	1	yes	characteristic
562	C₂²	C₇×#532	1	1	yes	characteristic
563	C₂²	C₇×#537	1	1	yes	characteristic
564	C₂²	C₇×#577	1	1	yes	characteristic
565	C₂²	C₇×#577	1	1	yes	characteristic
566	C₂²	C₇×#577	1	1	yes	characteristic
567	C₂²	C₇×#577	1	1	yes	characteristic
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₇×#551	1	1	yes	characteristic
582	C₄	C₇×#552	1	1	yes	characteristic
583	C₄	C₇×#553	1	1	yes	characteristic
584	C₄	C₇×#556	1	1	yes	characteristic
585	C₂	—	16	1	no	—
586	C₂	C₇×#2601	1	1	yes	characteristic
587	C₂	C₇×#3125	1	1	yes	characteristic
588	C₂	C₇×#3126	1	1	yes	characteristic
589	C₂	C₇×#3173	1	1	yes	characteristic
590	C₂	C₇×#3174	1	1	yes	characteristic
591	C₂	C₇×#3260	1	1	yes	characteristic
592	C₂	C₇×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2320	C₂	semidirect
3. C₇×#2088	C₂	semidirect
4. C₇×#2066	C₂	semidirect
8. C₇×#1941	C₂	semidirect
10. C₇×#1935	C₂	semidirect
12. C₇×#1920	C₂	semidirect
14. C₇×#1865	C₂	semidirect
15. C₇×#1768	C₂	semidirect
59. #29442	C₇	direct (N × H)
122. #2320	C₂×C₇	semidirect
123. #2088	C₂×C₇	semidirect
124. #2066	C₂×C₇	semidirect
128. #1941	C₂×C₇	semidirect
130. #1935	C₂×C₇	semidirect
132. #1920	C₂×C₇	semidirect
134. #1865	C₂×C₇	semidirect
135. #1768	C₂×C₇	semidirect
553. C₇	#29442	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×#2644	2
C₇×#2320	2
C₇×#2088	2
C₇×#2066	2
C₇×#2065	2
C₇×#2055	2
C₇×#1968	2
C₇×#1941	2
C₇×#1936	2
C₇×#1935	2
C₇×#1926	2
C₇×#1920	2
C₇×#1880	2
C₇×#1865	2
C₇×#1768	2
#29442	7

Subgroups — C7×#29442 #13206658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#29442 #13206658