Subgroups — C₇×#7929 #13185145

Order 1792.

1058 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#407	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1282	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₇×M₁₆	—	2	1	no	—
7	C₂²×C₇×M₁₆	C₄	1	2	yes	complemented
8	C₂²×C₇×C₂²⋊C₄	C₄	1	2	yes	—
9	C₂²×C₄²×C₇	—	2	1	no	—
10	C₇×#407	—	2	1	no	—
11	C₇×#407	—	2	1	no	—
12	C₇×#407	—	2	1	no	—
13	C₇×#407	—	2	1	no	—
14	C₇×#407	—	2	1	no	—
15	C₇×#407	—	2	1	no	—
16	C₇×#407	C₄	1	2	yes	complemented
17	C₇×#407	C₄	1	2	yes	complemented
18	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₇×C₂²⋊C₈	C₄	1	2	yes	complemented
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
23	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
24	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
25	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₇×#95	—	2	1	no	—
27	#7929	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂⁵×C₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₇	—	2	2	no	—
30	C₂³×C₄×C₇	—	4	4	no	—
31	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×M₁₆	—	2	2	no	—
46	C₂×C₇×M₁₆	—	2	2	no	—
47	C₂×C₇×M₁₆	—	2	2	no	—
48	C₂×C₇×M₁₆	—	2	2	no	—
49	C₂×C₇×M₁₆	—	4	4	no	—
50	C₂×C₇×M₁₆	—	4	4	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	C₂×C₄	1	4	yes	complemented
53	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
55	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₇	—	2	2	no	—
57	C₂×C₄²×C₇	—	2	2	no	—
58	C₂×C₄²×C₇	—	4	4	no	—
59	C₇×C₂²⋊C₈	—	2	2	no	—
60	C₇×C₂²⋊C₈	—	2	2	no	—
61	C₇×C₂²⋊C₈	—	2	2	no	—
62	C₇×C₂²⋊C₈	—	2	2	no	—
63	C₇×C₂²⋊C₈	—	2	2	no	—
64	C₇×C₂²⋊C₈	—	2	2	no	—
65	C₇×C₂²⋊C₈	—	2	2	no	—
66	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
67	C₇×#95	—	2	2	no	—
68	C₇×#95	—	2	2	no	—
69	C₂×#407	C₂×C₇	1	1	yes	characteristic
70	C₂×#407	C₂×C₇	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
72	#1282	C₂×C₇	1	4	yes	complemented
73	C₂⁴×C₇	—	2	4	no	—
74	C₂⁴×C₇	—	4	2	no	—
75	C₂⁴×C₇	—	4	2	no	—
76	C₂⁴×C₇	C₄²	1	1	yes	characteristic
77	C₂⁴×C₇	C₄²	1	1	yes	characteristic
78	C₂⁴×C₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	—	2	4	no	—
84	C₂²×C₄×C₇	—	2	4	no	—
85	C₂²×C₄×C₇	—	2	4	no	—
86	C₂²×C₄×C₇	—	2	8	no	—
87	C₂²×C₄×C₇	—	2	4	no	—
88	C₂²×C₄×C₇	—	4	2	no	—
89	C₂²×C₄×C₇	—	4	2	no	—
90	C₂²×C₄×C₇	—	4	2	no	—
91	C₂²×C₄×C₇	—	4	2	no	—
92	C₂²×C₄×C₇	—	4	2	no	—
93	C₂²×C₄×C₇	—	4	2	no	—
94	C₂²×C₄×C₇	—	4	2	no	—
95	C₂²×C₄×C₇	—	4	2	no	—
96	C₂²×C₄×C₇	—	4	2	no	—
97	C₂²×C₄×C₇	—	4	2	no	—
98	C₂²×C₄×C₇	—	4	2	no	—
99	C₂²×C₄×C₇	—	4	4	no	—
100	C₂²×C₄×C₇	—	4	4	no	—
101	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
129	C₇×M₁₆	—	4	4	no	—
130	C₇×M₁₆	—	4	4	no	—
131	C₇×M₁₆	—	4	4	no	—
132	C₇×M₁₆	—	4	4	no	—
133	C₂×C₇×C₈	—	2	4	no	—
134	C₂×C₇×C₈	—	2	4	no	—
135	C₂×C₇×C₈	—	4	4	no	—
136	C₂×C₇×C₈	—	4	4	no	—
137	C₇×C₂²⋊C₄	—	2	8	no	—
138	C₇×C₂²⋊C₄	—	2	4	no	—
139	C₇×C₂²⋊C₄	M₁₆	1	8	yes	complemented
140	C₄²×C₇	—	4	4	no	—
141	C₄²×C₇	—	4	4	no	—
142	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
143	C₂²×M₁₆	—	2	1	no	—
144	C₂²×M₁₆	C₄×C₇	1	2	yes	complemented
145	C₂²×C₂²⋊C₄	C₄×C₇	1	2	yes	—
146	C₂²×C₄²	—	2	1	no	—
147	#407	—	2	1	no	—
148	#407	—	2	1	no	—
149	#407	—	2	1	no	—
150	#407	—	2	1	no	—
151	#407	—	2	1	no	—
152	#407	—	2	1	no	—
153	#407	C₄×C₇	1	2	yes	complemented
154	#407	C₄×C₇	1	2	yes	complemented
155	C₂×C₂²⋊C₈	—	2	1	no	—
156	C₂×C₂²⋊C₈	C₄×C₇	1	2	yes	complemented
157	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
158	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
159	C₄×C₂²⋊C₄	—	2	1	no	—
160	C₄×C₂²⋊C₄	—	2	1	no	—
161	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
162	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
163	C₂×#95	—	2	1	no	—
164	C₂³×C₇	—	2	2	no	—
165	C₂³×C₇	—	2	2	no	—
166	C₂³×C₇	—	2	2	no	—
167	C₂³×C₇	—	2	2	no	—
168	C₂³×C₇	—	2	2	no	—
169	C₂³×C₇	—	2	2	no	—
170	C₂³×C₇	—	2	2	no	—
171	C₂³×C₇	—	2	2	no	—
172	C₂³×C₇	—	2	2	no	—
173	C₂³×C₇	—	2	2	no	—
174	C₂³×C₇	—	2	2	no	—
175	C₂³×C₇	—	2	2	no	—
176	C₂³×C₇	—	4	1	no	—
177	C₂³×C₇	—	4	1	no	—
178	C₂³×C₇	—	4	1	no	—
179	C₂³×C₇	—	4	1	no	—
180	C₂³×C₇	—	4	1	no	—
181	C₂³×C₇	—	4	1	no	—
182	C₂³×C₇	—	4	1	no	—
183	C₂³×C₇	—	4	1	no	—
184	C₂³×C₇	—	4	16	no	—
185	C₂³×C₇	#95	1	1	yes	characteristic
186	C₂³×C₇	#95	1	1	yes	characteristic
187	C₂³×C₇	#95	1	1	yes	characteristic
188	C₂³×C₇	#95	1	1	yes	characteristic
189	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
190	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂³×C₇	C₂×M₁₆	1	4	yes	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	8	no	—
209	C₂×C₄×C₇	—	4	1	no	—
210	C₂×C₄×C₇	—	4	1	no	—
211	C₂×C₄×C₇	—	4	1	no	—
212	C₂×C₄×C₇	—	4	1	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	1	no	—
220	C₂×C₄×C₇	—	4	1	no	—
221	C₂×C₄×C₇	—	4	4	no	—
222	C₂×C₄×C₇	—	4	16	no	—
223	C₂×C₄×C₇	—	4	4	no	—
224	C₂×C₄×C₇	#95	1	1	yes	characteristic
225	C₂×C₄×C₇	#95	1	1	yes	characteristic
226	C₂×C₄×C₇	#95	1	1	yes	characteristic
227	C₂×C₄×C₇	#95	1	1	yes	characteristic
228	C₂×C₄×C₇	#99	1	4	yes	—
229	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₇×C₈	—	4	4	no	—
234	C₇×C₈	—	4	4	no	—
235	C₂⁵	C₂×C₄×C₇	1	1	yes	characteristic
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	4	4	no	—
238	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
240	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
242	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
243	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
244	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
245	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
246	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
247	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
248	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
249	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
250	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	4	4	no	—
257	C₂×M₁₆	—	4	4	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	C₂×C₄×C₇	1	4	yes	complemented
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	4	4	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂²×C₇	—	2	8	no	—
277	C₂²×C₇	—	2	1	no	—
278	C₂²×C₇	—	2	1	no	—
279	C₂²×C₇	—	2	1	no	—
280	C₂²×C₇	—	2	1	no	—
281	C₂²×C₇	—	2	1	no	—
282	C₂²×C₇	—	2	1	no	—
283	C₂²×C₇	—	2	1	no	—
284	C₂²×C₇	—	2	1	no	—
285	C₂²×C₇	—	2	1	no	—
286	C₂²×C₇	—	2	1	no	—
287	C₂²×C₇	—	2	1	no	—
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	2	1	no	—
291	C₂²×C₇	—	2	1	no	—
292	C₂²×C₇	—	2	1	no	—
293	C₂²×C₇	—	4	4	no	—
294	C₂²×C₇	—	4	4	no	—
295	C₂²×C₇	—	4	4	no	—
296	C₂²×C₇	—	4	4	no	—
297	C₂²×C₇	—	4	4	no	—
298	C₂²×C₇	—	4	4	no	—
299	C₂²×C₇	#342	1	2	yes	—
300	C₂²×C₇	#344	1	2	yes	—
301	C₂²×C₇	C₂×#95	1	1	yes	characteristic
302	C₂²×C₇	C₄×M₁₆	1	2	yes	—
303	C₂²×C₇	#407	1	2	yes	—
304	C₂²×C₇	#423	1	2	yes	—
305	C₄×C₇	—	2	1	no	—
306	C₄×C₇	—	2	1	no	—
307	C₄×C₇	—	2	1	no	—
308	C₄×C₇	—	2	1	no	—
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	4	8	no	—
312	C₄×C₇	#342	1	2	yes	—
313	C₄×C₇	C₂×#99	1	2	yes	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	C₄²×C₇	1	1	yes	characteristic
318	C₂⁴	C₄²×C₇	1	1	yes	characteristic
319	C₂⁴	C₇×C₂²⋊C₄	1	1	yes	characteristic
320	C₂⁴	C₇×C₂²⋊C₄	1	1	yes	characteristic
321	C₂⁴	C₇×C₄⋊C₄	1	1	yes	characteristic
322	C₂⁴	C₇×C₄⋊C₄	1	1	yes	characteristic
323	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
343	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
344	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
345	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
346	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
350	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
361	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
362	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
370	M₁₆	—	4	4	no	—
371	M₁₆	—	4	4	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	—	4	4	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	4	4	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	C₇×M₁₆	1	8	yes	complemented
381	C₄²	—	4	4	no	—
382	C₄²	—	4	4	no	—
383	C₂×C₇	—	2	2	no	—
384	C₂×C₇	—	2	2	no	—
385	C₂×C₇	—	2	2	no	—
386	C₂×C₇	—	2	2	no	—
387	C₂×C₇	—	2	2	no	—
388	C₂×C₇	—	4	1	no	—
389	C₂×C₇	—	4	1	no	—
390	C₂×C₇	#1728	1	1	yes	characteristic
391	C₂×C₇	C₂×#342	1	1	yes	characteristic
392	C₂×C₇	C₂×#344	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	16	no	—
414	C₂³	C₇×#95	1	1	yes	characteristic
415	C₂³	C₇×#95	1	1	yes	characteristic
416	C₂³	C₇×#95	1	1	yes	characteristic
417	C₂³	C₇×#95	1	1	yes	characteristic
418	C₂³	C₂×C₄²×C₇	1	1	yes	characteristic
419	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
420	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
421	C₂³	C₂×C₇×M₁₆	1	4	yes	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	16	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	C₇×#95	1	1	yes	characteristic
454	C₂×C₄	C₇×#95	1	1	yes	characteristic
455	C₂×C₄	C₇×#95	1	1	yes	characteristic
456	C₂×C₄	C₇×#95	1	1	yes	characteristic
457	C₂×C₄	C₇×#99	1	4	yes	—
458	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
462	C₈	—	4	4	no	—
463	C₈	—	4	4	no	—
464	C₇	#7929	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²	—	2	8	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	C₇×#342	1	2	yes	—
489	C₂²	C₇×#344	1	2	yes	—
490	C₂²	C₂×C₇×#95	1	1	yes	characteristic
491	C₂²	C₄×C₇×M₁₆	1	2	yes	—
492	C₂²	C₇×#407	1	2	yes	—
493	C₂²	C₇×#423	1	2	yes	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	8	no	—
501	C₄	C₇×#342	1	2	yes	—
502	C₄	C₂×C₇×#99	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	2	2	no	—
508	C₂	—	4	1	no	—
509	C₂	—	4	1	no	—
510	C₂	C₇×#1728	1	1	yes	characteristic
511	C₂	C₂×C₇×#342	1	1	yes	characteristic
512	C₂	C₂×C₇×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₇
Frattini, cosocle	C₂³×C₄	C₂³×C₇
socle	C₂²×C₇	C₂×#95
prime radical	C₂⁵×C₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1282	C₂	semidirect
7. C₂²×C₇×M₁₆	C₄	semidirect
16. C₇×#407	C₄	semidirect
17. C₇×#407	C₄	semidirect
19. C₂×C₇×C₂²⋊C₈	C₄	semidirect
27. #7929	C₇	direct (N × H)
52. C₂²×C₇×C₈	C₂×C₄	semidirect
66. C₇×C₂²⋊C₈	C₂×C₄	semidirect
72. #1282	C₂×C₇	semidirect
139. C₇×C₂²⋊C₄	M₁₆	semidirect
144. C₂²×M₁₆	C₄×C₇	semidirect
153. #407	C₄×C₇	semidirect
154. #407	C₄×C₇	semidirect
156. C₂×C₂²⋊C₈	C₄×C₇	semidirect
259. C₂²×C₈	C₂×C₄×C₇	semidirect
273. C₂²⋊C₈	C₂×C₄×C₇	semidirect
380. C₂²⋊C₄	C₇×M₁₆	semidirect
464. C₇	#7929	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×#407	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₇×#1282	2
#7929	7

Subgroups — C7×#7929 #13185145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#7929 #13185145