Subgroups — C₇×#22651 #13199867

Order 1792.

992 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#424	C₂	1	2	yes	maximal, complemented
4	C₇×#2293	C₂	1	1	yes	maximal, characteristic
5	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1851	C₂	1	2	yes	maximal, complemented
8	C₇×#1850	C₂	1	2	yes	maximal, complemented
9	C₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1798	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	C₂²	1	2	yes	—
16	C₇×#436	—	2	4	no	—
17	C₇×C₈×D₄	—	2	4	no	—
18	C₇×#424	—	2	8	no	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#390	C₄	1	1	yes	characteristic
32	C₇×#390	C₄	1	1	yes	characteristic
33	C₇×#389	C₄	1	1	yes	characteristic
34	C₇×#389	C₄	1	1	yes	characteristic
35	C₇×#388	C₄	1	2	yes	—
36	C₇×#388	C₄	1	2	yes	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₄³×C₇	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	#22651	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂³	1	2	yes	—
47	C₂×C₇×M₁₆	—	2	4	no	—
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	—	4	2	no	—
50	C₂²×C₇×C₈	—	2	4	no	—
51	C₂²×C₇×C₈	—	2	4	no	—
52	C₂²×C₇×C₈	—	4	2	no	—
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₄×C₇×D₄	D₄	1	4	yes	—
60	C₄×C₇×D₄	Q₈	1	4	yes	—
61	C₇×#117	—	2	4	no	—
62	C₇×#117	—	2	4	no	—
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊C₈	—	2	4	no	—
82	C₇×C₄⋊C₈	—	2	4	no	—
83	C₇×C₄⋊C₈	—	2	4	no	—
84	C₇×C₄⋊C₈	—	2	2	no	—
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	4	2	no	—
88	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×C₂²⋊C₈	—	2	4	no	—
91	C₄×C₇×C₈	—	2	2	no	—
92	C₄×C₇×C₈	—	2	2	no	—
93	C₇×#95	C₂×C₄	1	2	yes	—
94	C₇×#95	C₂×C₄	1	2	yes	—
95	C₇×#95	C₂×C₄	1	2	yes	—
96	C₂×#436	C₂×C₇	1	1	yes	characteristic
97	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
98	C₂×#424	C₂×C₇	1	2	yes	complemented
99	#2293	C₂×C₇	1	1	yes	characteristic
100	#1939	C₂×C₇	1	1	yes	characteristic, complemented
101	#1939	C₂×C₇	1	1	yes	characteristic, complemented
102	#1851	C₂×C₇	1	2	yes	complemented
103	#1850	C₂×C₇	1	2	yes	complemented
104	#1842	C₂×C₇	1	1	yes	characteristic, complemented
105	#1798	C₂×C₇	1	2	yes	complemented
106	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
108	C₂×C₇×D₄	—	2	2	no	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
127	C₇×M₁₆	—	4	8	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	4	8	no	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
147	C₇×C₄⋊C₄	—	2	4	no	—
148	C₇×C₄⋊C₄	—	2	4	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
152	C₇×C₂²⋊C₄	—	2	4	no	—
153	C₇×C₂²⋊C₄	—	2	4	no	—
154	C₇×C₂²⋊C₄	—	2	4	no	—
155	C₇×C₂²⋊C₄	—	4	2	no	—
156	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	2	2	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	2	1	no	—
163	C₄²×C₇	—	2	1	no	—
164	C₄²×C₇	—	4	1	no	—
165	C₄²×C₇	C₂×D₄	1	2	yes	—
166	C₄²×C₇	C₂×D₄	1	2	yes	—
167	C₄²×C₇	C₂×Q₈	1	2	yes	—
168	C₄²×C₇	#41	1	2	yes	—
169	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
170	C₂³×C₈	C₂²×C₇	1	2	yes	—
171	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
172	C₂×#117	C₂²×C₇	1	2	yes	—
173	#436	—	2	4	no	—
174	C₈×D₄	—	2	4	no	—
175	#424	—	2	8	no	—
176	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
181	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
182	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
185	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
186	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
188	#390	C₄×C₇	1	1	yes	characteristic
189	#390	C₄×C₇	1	1	yes	characteristic
190	#389	C₄×C₇	1	1	yes	characteristic
191	#389	C₄×C₇	1	1	yes	characteristic
192	#388	C₄×C₇	1	2	yes	—
193	#388	C₄×C₇	1	2	yes	—
194	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
195	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
196	C₄³	C₂²×C₇	1	1	yes	characteristic
197	#336	C₂²×C₇	1	2	yes	—
198	#336	C₂²×C₇	1	2	yes	—
199	#336	C₂²×C₇	1	1	yes	characteristic
200	#336	C₂²×C₇	1	1	yes	characteristic
201	C₂³×C₇	—	2	2	no	—
202	C₂³×C₇	—	2	2	no	—
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	2	no	—
206	C₂³×C₇	—	2	2	no	—
207	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
208	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
209	C₇×D₄	—	2	8	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	4	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	2	4	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
234	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
235	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
236	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₇	#131	1	2	yes	—
239	C₂×C₄×C₇	#131	1	2	yes	—
240	C₂×C₄×C₇	#131	1	2	yes	—
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	2	2	no	—
249	C₇×C₈	—	4	2	no	—
250	C₇×C₈	—	4	2	no	—
251	C₇×C₈	—	4	1	no	—
252	C₇×C₈	—	4	1	no	—
253	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₇	1	2	yes	—
255	C₂×M₁₆	—	2	4	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	4	2	no	—
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	—	2	4	no	—
260	C₂²×C₈	—	4	2	no	—
261	C₂²×C₈	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	C₄×D₄	C₇×D₄	1	4	yes	—
268	C₄×D₄	C₇×Q₈	1	4	yes	—
269	#117	—	2	4	no	—
270	#117	—	2	4	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₇	1	2	yes	—
286	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
289	C₄⋊C₈	—	2	4	no	—
290	C₄⋊C₈	—	2	4	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	4	2	no	—
296	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
297	C₂²⋊C₈	—	2	4	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	C₂×C₄×C₇	1	2	yes	—
302	#95	C₂×C₄×C₇	1	2	yes	—
303	#95	C₂×C₄×C₇	1	2	yes	—
304	C₂²×C₇	—	2	4	no	—
305	C₂²×C₇	—	2	4	no	—
306	C₂²×C₇	—	2	4	no	—
307	C₂²×C₇	—	4	2	no	—
308	C₂²×C₇	—	4	2	no	—
309	C₂²×C₇	—	4	2	no	—
310	C₂²×C₇	—	4	2	no	—
311	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
312	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₇	#520	1	1	yes	characteristic
314	C₂²×C₇	C₂×#131	1	1	yes	characteristic
315	C₂²×C₇	C₂×#131	1	1	yes	characteristic
316	C₂²×C₇	C₂×#131	1	1	yes	characteristic
317	C₂²×C₇	#568	1	1	yes	characteristic
318	C₄×C₇	—	2	4	no	—
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	2	2	no	—
321	C₄×C₇	—	2	2	no	—
322	C₄×C₇	—	2	2	no	—
323	C₄×C₇	—	4	2	no	—
324	C₄×C₇	—	4	2	no	—
325	C₄×C₇	—	4	1	no	—
326	C₄×C₇	#424	1	4	yes	complemented
327	C₄×C₇	D₄²	1	1	yes	characteristic
328	C₄×C₇	#547	1	1	yes	characteristic
329	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
330	C₄×C₇	#554	1	1	yes	characteristic
331	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
349	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
351	M₁₆	—	4	8	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	8	no	—
369	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
370	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	C₂×C₇×D₄	1	2	yes	—
390	C₄²	C₂×C₇×D₄	1	2	yes	—
391	C₄²	C₂×C₇×Q₈	1	2	yes	—
392	C₄²	C₇×#41	1	2	yes	—
393	C₂×C₇	—	4	4	no	—
394	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
395	C₂×C₇	C₂×#424	1	1	yes	characteristic
396	C₂×C₇	#2906	1	1	yes	characteristic
397	C₂×C₇	#2931	1	1	yes	characteristic
398	C₂×C₇	#2935	1	1	yes	characteristic
399	C₂×C₇	#2993	1	1	yes	characteristic
400	C₂×C₇	#2994	1	1	yes	characteristic
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
408	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
409	D₄	—	2	8	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
434	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
435	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
436	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
437	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
438	C₂×C₄	C₇×#131	1	2	yes	—
439	C₂×C₄	C₇×#131	1	2	yes	—
440	C₂×C₄	C₇×#131	1	2	yes	—
441	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
444	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
445	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	—	4	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	1	no	—
453	C₇	#22651	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
462	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
463	C₂²	C₇×#520	1	1	yes	characteristic
464	C₂²	C₂×C₇×#131	1	1	yes	characteristic
465	C₂²	C₂×C₇×#131	1	1	yes	characteristic
466	C₂²	C₂×C₇×#131	1	1	yes	characteristic
467	C₂²	C₇×#568	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	C₇×#424	1	4	yes	complemented
477	C₄	C₇×D₄²	1	1	yes	characteristic
478	C₄	C₇×#547	1	1	yes	characteristic
479	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
480	C₄	C₇×#554	1	1	yes	characteristic
481	C₂	—	4	4	no	—
482	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
483	C₂	C₂×C₇×#424	1	1	yes	characteristic
484	C₂	C₇×#2906	1	1	yes	characteristic
485	C₂	C₇×#2931	1	1	yes	characteristic
486	C₂	C₇×#2935	1	1	yes	characteristic
487	C₂	C₇×#2993	1	1	yes	characteristic
488	C₂	C₇×#2994	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#424	C₂	semidirect
5. C₇×#1939	C₂	semidirect
6. C₇×#1939	C₂	semidirect
7. C₇×#1851	C₂	semidirect
8. C₇×#1850	C₂	semidirect
9. C₇×#1842	C₂	semidirect
10. C₇×#1798	C₂	semidirect
11. C₄×C₇×C₄⋊C₈	C₂	semidirect
44. #22651	C₇	direct (N × H)
88. C₇×C₄⋊C₈	D₄	semidirect
98. C₂×#424	C₂×C₇	semidirect
100. #1939	C₂×C₇	semidirect
101. #1939	C₂×C₇	semidirect
102. #1851	C₂×C₇	semidirect
103. #1850	C₂×C₇	semidirect
104. #1842	C₂×C₇	semidirect
105. #1798	C₂×C₇	semidirect
106. C₄×C₄⋊C₈	C₂×C₇	semidirect
296. C₄⋊C₈	C₇×D₄	semidirect
326. C₄×C₇	#424	semidirect
453. C₇	#22651	direct (N × H)
476. C₄	C₇×#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#436	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#424	2
C₇×#2293	2
C₇×#1939	2
C₇×#1851	2
C₇×#1850	2
C₇×#1842	2
C₇×#1798	2
C₄×C₇×C₄⋊C₈	2
#22651	7

Subgroups — C7×#22651 #13199867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22651 #13199867