Subgroups — C₇×#24766 #13201982

Order 1792.

960 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2621	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2324	C₂	1	1	yes	maximal, characteristic
7	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₇×#117	C₂²	1	1	yes	characteristic
26	C₇×#468	—	2	4	no	—
27	C₇×#465	—	2	4	no	—
28	C₇×#461	—	2	4	no	—
29	C₂×C₇×#107	C₂²	1	1	yes	characteristic
30	C₂×C₇×#106	C₂²	1	1	yes	characteristic
31	C₇×#424	—	2	4	no	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#103	C₂²	1	1	yes	characteristic
42	C₂×C₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₇×#102	C₂²	1	1	yes	characteristic
44	C₇×#398	—	2	1	no	—
45	C₇×#398	—	2	1	no	—
46	C₇×#397	—	2	1	no	—
47	C₇×#397	—	2	1	no	—
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#390	—	2	1	no	—
51	C₇×#390	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#388	—	2	1	no	—
54	C₇×#386	—	2	1	no	—
55	C₇×#385	—	2	1	no	—
56	C₇×#382	C₂²	1	1	yes	characteristic
57	C₇×#380	C₂²	1	1	yes	characteristic
58	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	C₇×#340	C₂²	1	1	yes	characteristic
63	#24766	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	—	2	1	no	—
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₇×SD₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	—	2	2	no	—
73	C₂×C₇×SD₁₆	—	2	2	no	—
74	C₂×C₇×SD₁₆	—	4	1	no	—
75	C₂×C₇×SD₁₆	—	4	1	no	—
76	C₂×C₇×M₁₆	—	2	2	no	—
77	C₂×C₇×M₁₆	—	2	2	no	—
78	C₂×C₇×M₁₆	—	4	1	no	—
79	C₂²×C₇×C₈	—	2	2	no	—
80	C₂²×C₇×C₈	—	2	2	no	—
81	C₂²×C₇×C₈	—	4	1	no	—
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₇×C₄⋊Q₈	—	2	2	no	—
87	C₇×C₄⋊Q₈	—	2	2	no	—
88	C₇×C₂²⋊Q₈	—	2	2	no	—
89	C₇×C₂²⋊Q₈	—	2	2	no	—
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₇×C₂²⋊Q₈	—	2	2	no	—
92	C₇×#121	—	2	2	no	—
93	C₇×#121	D₄	1	4	yes	—
94	C₄×C₇×D₄	—	2	2	no	—
95	C₄×C₇×D₄	—	2	2	no	—
96	C₇×#117	—	2	2	no	—
97	C₇×#117	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₇	—	2	1	no	—
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×#107	—	2	2	no	—
123	C₇×#106	—	2	2	no	—
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×C₄⋊C₈	—	2	2	no	—
127	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
128	C₇×#103	—	2	2	no	—
129	C₇×#103	—	2	2	no	—
130	C₇×#103	—	2	2	no	—
131	C₇×#103	—	2	2	no	—
132	C₇×#103	—	4	1	no	—
133	C₇×#103	—	4	1	no	—
134	C₇×#102	—	2	2	no	—
135	C₇×#102	—	2	2	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	—	2	1	no	—
143	C₇×#95	—	2	1	no	—
144	C₇×#95	—	2	1	no	—
145	C₂×#468	C₂×C₇	1	1	yes	characteristic
146	C₂×#465	C₂×C₇	1	1	yes	characteristic
147	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
149	#2621	C₂×C₇	1	1	yes	characteristic, complemented
150	#2324	C₂×C₇	1	1	yes	characteristic
151	#2068	C₂×C₇	1	1	yes	characteristic, complemented
152	#2066	C₂×C₇	1	1	yes	characteristic, complemented
153	#2055	C₂×C₇	1	1	yes	characteristic, complemented
154	#2055	C₂×C₇	1	1	yes	characteristic, complemented
155	#1981	C₂×C₇	1	1	yes	characteristic, complemented
156	#1949	C₂×C₇	1	1	yes	characteristic, complemented
157	#1894	C₂×C₇	1	1	yes	characteristic, complemented
158	#1892	C₂×C₇	1	1	yes	characteristic, complemented
159	#1804	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	—	2	1	no	—
161	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	2	1	no	—
172	C₂×C₇×Q₈	—	2	1	no	—
173	C₂×C₇×Q₈	—	2	1	no	—
174	C₂×C₇×D₄	—	2	4	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	2	1	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	—	2	1	no	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	—	8	1	no	—
181	C₂×C₇×D₄	—	8	1	no	—
182	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	1	no	—
194	C₂²×C₄×C₇	—	4	2	no	—
195	C₂²×C₄×C₇	—	8	1	no	—
196	C₂²×C₄×C₇	—	8	1	no	—
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇	#41	1	2	yes	—
204	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
205	C₇×SD₁₆	—	4	4	no	—
206	C₇×SD₁₆	—	4	4	no	—
207	C₇×M₁₆	—	4	4	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	4	4	no	—
219	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
220	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
221	C₇×C₄⋊C₄	—	2	2	no	—
222	C₇×C₄⋊C₄	—	2	2	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	4	2	no	—
233	C₇×C₄⋊C₄	—	4	2	no	—
234	C₇×C₄⋊C₄	—	4	2	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	—	8	1	no	—
237	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₇×C₂²⋊C₄	—	2	4	no	—
239	C₇×C₂²⋊C₄	—	2	2	no	—
240	C₇×C₂²⋊C₄	—	2	2	no	—
241	C₇×C₂²⋊C₄	—	4	2	no	—
242	C₇×C₂²⋊C₄	—	4	2	no	—
243	C₇×C₂²⋊C₄	—	4	2	no	—
244	C₇×C₂²⋊C₄	—	8	1	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₇×C₂²⋊C₄	—	8	1	no	—
247	C₄²×C₇	—	2	1	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	8	1	no	—
250	C₄²×C₇	C₂×D₄	1	2	yes	—
251	C₄²×C₇	#41	1	2	yes	—
252	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
253	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×#121	C₂²×C₇	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
261	C₂×#117	C₂²×C₇	1	1	yes	characteristic
262	#468	—	2	4	no	—
263	#465	—	2	4	no	—
264	#461	—	2	4	no	—
265	C₂×#107	C₂²×C₇	1	1	yes	characteristic
266	C₂×#106	C₂²×C₇	1	1	yes	characteristic
267	#424	—	2	4	no	—
268	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇	1	1	yes	characteristic
275	C₂×#103	C₂²×C₇	1	1	yes	characteristic
276	C₂×#103	C₂²×C₇	1	1	yes	characteristic
277	C₂×#103	C₂²×C₇	1	1	yes	characteristic
278	C₂×#102	C₂²×C₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₇	1	1	yes	characteristic
280	#398	—	2	1	no	—
281	#398	—	2	1	no	—
282	#397	—	2	1	no	—
283	#397	—	2	1	no	—
284	#391	C₂²×C₇	1	1	yes	characteristic
285	#391	C₂²×C₇	1	1	yes	characteristic
286	#390	—	2	1	no	—
287	#390	C₂²×C₇	1	1	yes	characteristic
288	#389	C₂²×C₇	1	1	yes	characteristic
289	#388	—	2	1	no	—
290	#386	—	2	1	no	—
291	#385	—	2	1	no	—
292	#382	C₂²×C₇	1	1	yes	characteristic
293	#380	C₂²×C₇	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
295	#340	C₂²×C₇	1	1	yes	characteristic
296	#340	C₂²×C₇	1	1	yes	characteristic
297	#340	C₂²×C₇	1	1	yes	characteristic
298	#340	C₂²×C₇	1	1	yes	characteristic
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	1	no	—
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	1	no	—
303	C₂³×C₇	—	2	1	no	—
304	C₂³×C₇	—	2	1	no	—
305	C₂³×C₇	—	2	2	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	—	4	1	no	—
308	C₂³×C₇	—	4	1	no	—
309	C₂³×C₇	—	4	1	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	#121	1	2	yes	—
313	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
314	C₇×Q₈	—	4	1	no	—
315	C₇×Q₈	—	4	1	no	—
316	C₇×Q₈	—	4	1	no	—
317	C₇×Q₈	—	4	1	no	—
318	C₇×Q₈	—	4	1	no	—
319	C₇×Q₈	—	4	1	no	—
320	C₇×Q₈	—	4	1	no	—
321	C₇×Q₈	—	4	1	no	—
322	C₇×D₄	—	2	2	no	—
323	C₇×D₄	—	2	2	no	—
324	C₇×D₄	—	4	1	no	—
325	C₇×D₄	—	4	1	no	—
326	C₇×D₄	—	8	4	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	2	1	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	4	1	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	8	4	no	—
365	C₂×C₄×C₇	#121	1	2	yes	—
366	C₂×C₄×C₇	#121	1	2	yes	—
367	C₂×C₄×C₇	#121	1	2	yes	—
368	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
374	C₇×C₈	—	2	2	no	—
375	C₇×C₈	—	2	2	no	—
376	C₇×C₈	—	4	1	no	—
377	C₇×C₈	—	4	1	no	—
378	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	4	1	no	—
389	C₂×SD₁₆	—	4	1	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	4	1	no	—
393	C₂²×C₈	—	2	2	no	—
394	C₂²×C₈	—	2	2	no	—
395	C₂²×C₈	—	4	1	no	—
396	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
400	C₄⋊Q₈	—	2	2	no	—
401	C₄⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	C₇×D₄	1	4	yes	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
436	#107	—	2	2	no	—
437	#106	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	2	2	no	—
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
442	#103	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	4	1	no	—
447	#103	—	4	1	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	C₂²×C₇	—	2	2	no	—
460	C₂²×C₇	—	2	2	no	—
461	C₂²×C₇	—	2	2	no	—
462	C₂²×C₇	—	4	1	no	—
463	C₂²×C₇	—	4	1	no	—
464	C₂²×C₇	—	4	1	no	—
465	C₂²×C₇	—	4	1	no	—
466	C₂²×C₇	—	4	2	no	—
467	C₂²×C₇	—	4	2	no	—
468	C₂²×C₇	—	4	2	no	—
469	C₂²×C₇	—	8	1	no	—
470	C₂²×C₇	—	8	1	no	—
471	C₂²×C₇	—	8	1	no	—
472	C₂²×C₇	—	8	1	no	—
473	C₂²×C₇	C₂×#121	1	1	yes	characteristic
474	C₂²×C₇	C₂×#121	1	1	yes	characteristic
475	C₂²×C₇	#537	1	1	yes	characteristic
476	C₂²×C₇	#577	1	1	yes	characteristic
477	C₂²×C₇	#577	1	1	yes	characteristic
478	C₂²×C₇	#577	1	1	yes	characteristic
479	C₂²×C₇	#578	1	1	yes	characteristic
480	C₄×C₇	—	2	2	no	—
481	C₄×C₇	—	2	2	no	—
482	C₄×C₇	—	2	2	no	—
483	C₄×C₇	—	4	2	no	—
484	C₄×C₇	—	4	1	no	—
485	C₄×C₇	—	4	1	no	—
486	C₄×C₇	—	8	1	no	—
487	C₄×C₇	—	8	1	no	—
488	C₄×C₇	—	8	1	no	—
489	C₄×C₇	—	8	1	no	—
490	C₄×C₇	—	8	1	no	—
491	C₄×C₇	—	8	1	no	—
492	C₄×C₇	D₄²	1	1	yes	characteristic
493	C₄×C₇	#547	1	1	yes	characteristic
494	C₄×C₇	#548	1	1	yes	characteristic
495	C₄×C₇	#553	1	1	yes	characteristic
496	C₂⁴	—	2	1	no	—
497	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	—	8	1	no	—
518	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
539	C₂²×C₄	C₇×#41	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
541	SD₁₆	—	4	4	no	—
542	SD₁₆	—	4	4	no	—
543	M₁₆	—	4	4	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	4	4	no	—
555	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
556	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	8	1	no	—
573	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	8	1	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	8	1	no	—
586	C₄²	C₂×C₇×D₄	1	2	yes	—
587	C₄²	C₇×#41	1	2	yes	—
588	C₂×C₇	—	4	2	no	—
589	C₂×C₇	—	8	2	no	—
590	C₂×C₇	#2416	1	1	yes	characteristic
591	C₂×C₇	#3042	1	1	yes	characteristic
592	C₂×C₇	#3046	1	1	yes	characteristic
593	C₂×C₇	#3057	1	1	yes	characteristic
594	C₂×C₇	#3063	1	1	yes	characteristic
595	C₂×C₇	#3258	1	1	yes	characteristic
596	C₂×C₇	#3260	1	1	yes	characteristic
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	C₇×#121	1	2	yes	—
611	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	C₇×#121	1	2	yes	—
664	C₂×C₄	C₇×#121	1	2	yes	—
665	C₂×C₄	C₇×#121	1	2	yes	—
666	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
667	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
668	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
669	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
670	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₇	#24766	1	1	yes	characteristic, direct product factor, Sylow
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×C₇×#121	1	1	yes	characteristic
692	C₂²	C₂×C₇×#121	1	1	yes	characteristic
693	C₂²	C₇×#537	1	1	yes	characteristic
694	C₂²	C₇×#577	1	1	yes	characteristic
695	C₂²	C₇×#577	1	1	yes	characteristic
696	C₂²	C₇×#577	1	1	yes	characteristic
697	C₂²	C₇×#578	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	C₇×D₄²	1	1	yes	characteristic
711	C₄	C₇×#547	1	1	yes	characteristic
712	C₄	C₇×#548	1	1	yes	characteristic
713	C₄	C₇×#553	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₇×#2416	1	1	yes	characteristic
717	C₂	C₇×#3042	1	1	yes	characteristic
718	C₂	C₇×#3046	1	1	yes	characteristic
719	C₂	C₇×#3057	1	1	yes	characteristic
720	C₂	C₇×#3063	1	1	yes	characteristic
721	C₂	C₇×#3258	1	1	yes	characteristic
722	C₂	C₇×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#461	C₂	semidirect
4. C₂×C₇×#424	C₂	semidirect
5. C₇×#2621	C₂	semidirect
7. C₇×#2068	C₂	semidirect
8. C₇×#2066	C₂	semidirect
9. C₇×#2055	C₂	semidirect
10. C₇×#2055	C₂	semidirect
11. C₇×#1981	C₂	semidirect
12. C₇×#1949	C₂	semidirect
13. C₇×#1894	C₂	semidirect
14. C₇×#1892	C₂	semidirect
15. C₇×#1804	C₂	semidirect
63. #24766	C₇	direct (N × H)
127. C₇×C₄⋊C₈	D₄	semidirect
147. C₂×#461	C₂×C₇	semidirect
148. C₂×#424	C₂×C₇	semidirect
149. #2621	C₂×C₇	semidirect
151. #2068	C₂×C₇	semidirect
152. #2066	C₂×C₇	semidirect
153. #2055	C₂×C₇	semidirect
154. #2055	C₂×C₇	semidirect
155. #1981	C₂×C₇	semidirect
156. #1949	C₂×C₇	semidirect
157. #1894	C₂×C₇	semidirect
158. #1892	C₂×C₇	semidirect
159. #1804	C₂×C₇	semidirect
441. C₄⋊C₈	C₇×D₄	semidirect
676. C₇	#24766	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×#468	2
C₂×C₇×#465	2
C₂×C₇×#461	2
C₂×C₇×#424	2
C₇×#2621	2
C₇×#2324	2
C₇×#2068	2
C₇×#2066	2
C₇×#2055	2
C₇×#1981	2
C₇×#1949	2
C₇×#1894	2
C₇×#1892	2
C₇×#1804	2
#24766	7

Subgroups — C7×#24766 #13201982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24766 #13201982