Subgroups — D₇×#918 #13059325

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×#239	C₂	1	1	yes	maximal, characteristic
2	D₃×Q₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#10621401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#918	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#10621086	C₂	1	1	yes	maximal, characteristic, complemented
7	#10621082	C₂	1	1	yes	maximal, characteristic, complemented
8	#10621074	C₂	1	1	yes	maximal, characteristic, complemented
9	#10621072	C₂	1	1	yes	maximal, characteristic, complemented
10	D₇×#216	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×#215	C₂	1	1	yes	maximal, characteristic, complemented
12	#10620842	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620825	C₂	1	1	yes	maximal, characteristic, complemented
14	D₇×#204	C₂	1	1	yes	maximal, characteristic, complemented
15	D₇×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₇×#137	—	3	1	no	maximal, Hall
17	#66732	C₂²	1	1	yes	characteristic
18	Q₈×D₂₁	C₂²	1	1	yes	characteristic, complemented
19	C₇×#239	C₂²	1	1	yes	characteristic
20	D₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×Q₈×D₇	C₂²	1	1	yes	characteristic
22	C₃×Q₈×D₇	C₂²	1	1	yes	characteristic
23	D₇×D₁₂	—	2	1	no	—
24	D₇×D₁₂	C₂²	1	1	yes	characteristic
25	C₄×D₃×D₇	—	2	1	no	—
26	C₄×D₃×D₇	—	2	1	no	—
27	C₄×D₃×D₇	C₂²	1	1	yes	characteristic
28	D₂₁⋊Q₈	—	2	1	no	—
29	D₂₁⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	#66673	—	2	1	no	—
31	#66673	C₂²	1	1	yes	characteristic
32	#66672	—	2	1	no	—
33	#66672	C₂²	1	1	yes	characteristic
34	D₃×Dic₁₄	—	2	1	no	—
35	D₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
36	D₇×Dic₆	—	2	1	no	—
37	D₇×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
39	#66635	C₂²	1	1	yes	characteristic, complemented
40	#66634	C₂²	1	1	yes	characteristic, complemented
41	#66623	C₂²	1	1	yes	characteristic, complemented
42	#66622	C₂²	1	1	yes	characteristic, complemented
43	C₇×#216	C₂²	1	1	yes	characteristic, complemented
44	C₇×#215	C₂²	1	1	yes	characteristic, complemented
45	C₇×#204	C₂²	1	1	yes	characteristic, complemented
46	C₇×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
47	C₃×#1144	C₂²	1	1	yes	characteristic, complemented
48	C₃×#1144	C₂²	1	1	yes	characteristic, complemented
49	C₃×Dic₂₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₈×D₇	C₂²	1	1	yes	characteristic
51	#66570	C₂²	1	1	yes	characteristic, complemented
52	#66569	C₂²	1	1	yes	characteristic, complemented
53	#66568	C₂²	1	1	yes	characteristic, complemented
54	#66567	C₂²	1	1	yes	characteristic, complemented
55	#66566	C₂²	1	1	yes	characteristic, complemented
56	#66564	C₂²	1	1	yes	characteristic, complemented
57	#66559	C₂²	1	1	yes	characteristic, complemented
58	#66558	C₂²	1	1	yes	characteristic, complemented
59	D₇×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	D₇×#41	—	3	1	no	—
61	C₂×Q₈×D₇	—	3	1	no	—
62	C₇×#137	—	3	1	no	—
63	#6514	—	3	1	no	—
64	#6505	—	3	1	no	—
65	#6481	—	3	1	no	—
66	#6481	—	3	1	no	—
67	D₇×Q₁₆	—	3	1	no	—
68	D₇×Q₁₆	D₃	1	1	yes	characteristic, complemented
69	#6478	—	3	1	no	—
70	#6478	—	3	1	no	—
71	D₇×SD₁₆	—	3	1	no	—
72	D₇×SD₁₆	—	3	1	no	—
73	#6472	—	3	1	no	—
74	D₇×M₁₆	—	3	1	no	—
75	C₂×#918	—	7	1	no	maximal, Hall
76	C₂×D₃×D₇	—	2	1	no	—
77	C₂×D₃×D₇	D₄	1	1	yes	characteristic
78	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
79	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
80	D₈₄	—	2	1	no	—
81	D₈₄	C₂³	1	1	yes	characteristic
82	C₄×D₂₁	—	2	1	no	—
83	C₄×D₂₁	—	2	1	no	—
84	C₄×D₂₁	C₂³	1	1	yes	characteristic
85	Dic₄₂	—	2	1	no	—
86	Dic₄₂	C₂³	1	1	yes	characteristic
87	C₇×D₁₂	—	2	1	no	—
88	C₇×D₁₂	C₂³	1	1	yes	characteristic
89	C₄×D₃×C₇	—	2	1	no	—
90	C₄×D₃×C₇	—	2	1	no	—
91	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
92	C₇×Dic₆	—	2	1	no	—
93	C₇×Dic₆	C₂³	1	1	yes	characteristic
94	C₃×C₄×D₇	—	2	1	no	—
95	C₃×C₄×D₇	—	2	1	no	—
96	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
97	C₃×Dic₁₄	—	2	1	no	—
98	C₃×Dic₁₄	—	2	1	no	—
99	C₃×Dic₁₄	C₂³	1	1	yes	characteristic
100	C₃×Dic₁₄	C₂³	1	1	yes	characteristic
101	#4248	—	2	1	no	—
102	#4248	—	2	1	no	—
103	#4248	—	2	1	no	—
104	#4247	—	2	1	no	—
105	#4247	—	2	1	no	—
106	#4247	—	2	1	no	—
107	D₂₁⋊C₄	—	2	1	no	—
108	D₂₁⋊C₄	—	2	1	no	—
109	D₂₁⋊C₄	D₄	1	1	yes	characteristic
110	D₃×Dic₇	—	2	1	no	—
111	D₃×Dic₇	—	2	1	no	—
112	D₃×Dic₇	D₄	1	1	yes	characteristic
113	Dic₃×D₇	—	2	1	no	—
114	Dic₃×D₇	D₄	1	1	yes	characteristic
115	C₃×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₃⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
117	C₃×C₇⋊C₈	C₂³	1	1	yes	characteristic
118	C₇×C₃⋊C₈	C₂³	1	1	yes	characteristic
119	C₇×#41	—	3	1	no	—
120	C₂×C₇×Q₈	—	3	1	no	—
121	#1161	—	3	1	no	—
122	Q₈×D₇	—	3	1	no	—
123	Q₈×D₇	—	3	1	no	—
124	Q₈×D₇	—	3	1	no	—
125	Q₈×D₇	—	6	1	no	—
126	Q₈×D₇	—	6	1	no	—
127	Q₈×D₇	C₂×D₃	1	1	yes	characteristic
128	Q₈×D₇	C₂×D₃	1	1	yes	characteristic
129	#1159	—	3	1	no	—
130	#1159	—	6	1	no	—
131	D₄×D₇	—	3	1	no	—
132	D₄×D₇	—	6	1	no	—
133	#1157	—	3	1	no	—
134	#1157	—	6	1	no	—
135	C₂×C₄×D₇	—	3	1	no	—
136	C₂×C₄×D₇	—	6	1	no	—
137	C₂×C₄×D₇	—	6	1	no	—
138	C₂×Dic₁₄	—	3	1	no	—
139	C₂×Dic₁₄	—	6	1	no	—
140	C₇×Q₁₆	—	3	1	no	—
141	C₇×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
142	C₇×SD₁₆	—	3	1	no	—
143	C₇×SD₁₆	—	3	1	no	—
144	C₇×M₁₆	—	3	1	no	—
145	#1144	—	3	1	no	—
146	#1144	—	3	1	no	—
147	#1144	C₂×D₃	1	1	yes	characteristic, complemented
148	#1144	C₂×D₃	1	1	yes	characteristic, complemented
149	#1143	—	3	1	no	—
150	#1143	—	3	1	no	—
151	#1142	—	3	1	no	—
152	#1142	—	3	1	no	—
153	#1136	—	3	1	no	—
154	Dic₂₈	—	3	1	no	—
155	Dic₂₈	C₂×D₃	1	1	yes	characteristic, complemented
156	#1132	—	3	1	no	—
157	#1132	—	3	1	no	—
158	#1131	—	3	1	no	—
159	#1131	—	3	1	no	—
160	C₈×D₇	—	3	1	no	—
161	C₈×D₇	C₂×D₃	1	1	yes	characteristic
162	C₂×#239	—	7	1	no	—
163	C₂×D₃×Q₈	—	7	1	no	—
164	C₂×C₃×Q₁₆	—	7	1	no	—
165	C₂×#216	—	7	1	no	—
166	C₂×#215	—	7	1	no	—
167	#918	—	7	1	no	—
168	#918	—	7	1	no	—
169	#918	—	7	1	no	—
170	#918	—	7	1	no	—
171	#918	—	7	1	no	—
172	#918	—	7	1	no	—
173	#918	—	7	1	no	—
174	#918	D₇	1	1	yes	characteristic, direct product factor
175	C₂×#204	—	7	1	no	—
176	C₂×ΓL(1,𝔽₂₅)	—	7	1	no	—
177	C₂×D₂₁	—	2	1	no	—
178	C₂×D₂₁	C₂×D₄	1	1	yes	characteristic
179	C₂×D₃×C₇	—	2	1	no	—
180	C₂×D₃×C₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
182	D₃×D₇	—	2	2	no	—
183	D₃×D₇	—	4	2	no	—
184	C₃×C₄×C₇	—	2	1	no	—
185	C₃×C₄×C₇	—	2	1	no	—
186	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
187	Dic₂₁	—	2	1	no	—
188	Dic₂₁	C₂×D₄	1	1	yes	characteristic
189	C₃×Dic₇	—	2	1	no	—
190	C₃×Dic₇	—	2	1	no	—
191	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
192	C₇×Dic₃	—	2	1	no	—
193	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
194	C₂×#137	—	21	1	no	Sylow
195	C₂²×D₇	—	3	1	no	—
196	C₂²×D₇	—	6	1	no	—
197	C₇×Q₈	—	3	1	no	—
198	C₇×Q₈	—	6	1	no	—
199	C₇×Q₈	C₂²×D₃	1	1	yes	characteristic
200	C₇×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₇×D₄	—	3	1	no	—
202	C₇×D₄	—	6	1	no	—
203	C₂×C₄×C₇	—	3	1	no	—
204	C₂×C₄×C₇	—	6	1	no	—
205	C₂×C₄×C₇	—	6	1	no	—
206	C₂²⋊D₇	—	6	1	no	—
207	C₂²⋊D₇	—	6	1	no	—
208	C₂²⋊D₇	—	6	1	no	—
209	C₂×Dic₇	—	3	1	no	—
210	C₂×Dic₇	—	6	1	no	—
211	C₂×Dic₇	—	6	1	no	—
212	D₂₈	—	3	1	no	—
213	D₂₈	—	6	1	no	—
214	C₄×D₇	—	2	1	no	—
215	C₄×D₇	—	2	1	no	—
216	C₄×D₇	—	3	1	no	—
217	C₄×D₇	—	3	1	no	—
218	C₄×D₇	—	3	1	no	—
219	C₄×D₇	—	6	1	no	—
220	C₄×D₇	—	6	1	no	—
221	C₄×D₇	—	6	1	no	—
222	C₄×D₇	—	6	1	no	—
223	C₄×D₇	—	6	1	no	—
224	C₄×D₇	C₂²×D₃	1	1	yes	characteristic
225	Dic₁₄	—	2	1	no	—
226	Dic₁₄	—	2	1	no	—
227	Dic₁₄	—	3	1	no	—
228	Dic₁₄	—	6	1	no	—
229	Dic₁₄	—	6	1	no	—
230	Dic₁₄	—	6	1	no	—
231	Dic₁₄	—	6	1	no	—
232	Dic₁₄	C₂²×D₃	1	1	yes	characteristic
233	Dic₁₄	C₂²×D₃	1	1	yes	characteristic
234	C₇×C₈	—	3	1	no	—
235	C₇×C₈	C₂²×D₃	1	1	yes	characteristic
236	C₇⋊C₈	—	3	1	no	—
237	C₇⋊C₈	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃×Q₈	—	7	1	no	—
239	C₂×C₃×Q₈	—	7	1	no	—
240	#239	—	7	1	no	—
241	#239	—	7	1	no	—
242	#239	—	7	1	no	—
243	#239	—	14	1	no	—
244	#239	—	14	1	no	—
245	#239	C₂×D₇	1	1	yes	characteristic
246	D₃×Q₈	—	7	1	no	—
247	D₃×Q₈	—	7	1	no	—
248	D₃×Q₈	—	7	1	no	—
249	D₃×Q₈	—	14	1	no	—
250	D₃×Q₈	—	14	1	no	—
251	D₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
252	C₂×D₁₂	—	7	1	no	—
253	C₂×D₁₂	—	14	1	no	—
254	C₂×C₄×D₃	—	7	1	no	—
255	C₂×C₄×D₃	—	14	1	no	—
256	C₂×C₄×D₃	—	14	1	no	—
257	C₂×Dic₆	—	7	1	no	—
258	C₂×Dic₆	—	14	1	no	—
259	C₃×Q₁₆	—	7	1	no	—
260	C₃×Q₁₆	—	7	1	no	—
261	C₃×Q₁₆	—	7	1	no	—
262	C₃×Q₁₆	C₂×D₇	1	1	yes	characteristic, complemented
263	C₂×C₃×C₈	—	7	1	no	—
264	#216	—	7	1	no	—
265	#216	—	7	1	no	—
266	#216	—	7	1	no	—
267	#216	C₂×D₇	1	1	yes	characteristic, complemented
268	#215	—	7	1	no	—
269	#215	—	7	1	no	—
270	#215	—	7	1	no	—
271	#215	C₂×D₇	1	1	yes	characteristic, complemented
272	C₂×C₃⋊C₈	—	7	1	no	—
273	#204	—	7	1	no	—
274	#204	—	7	1	no	—
275	#204	—	7	1	no	—
276	#204	C₂×D₇	1	1	yes	characteristic, complemented
277	ΓL(1,𝔽₂₅)	—	7	1	no	—
278	ΓL(1,𝔽₂₅)	—	7	1	no	—
279	ΓL(1,𝔽₂₅)	—	7	1	no	—
280	ΓL(1,𝔽₂₅)	C₂×D₇	1	1	yes	characteristic, complemented
281	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
282	D₂₁	—	2	1	no	—
283	D₂₁	—	4	1	no	—
284	C₃×D₇	#137	1	2	yes	complemented
285	D₃×C₇	—	2	1	no	—
286	D₃×C₇	—	4	1	no	—
287	C₂×#41	—	21	1	no	—
288	C₂²×Q₈	—	21	1	no	—
289	#137	—	3	1	no	—
290	#137	—	21	1	no	—
291	#137	—	21	1	no	—
292	#137	—	21	1	no	—
293	#137	—	21	1	no	—
294	#137	—	21	1	no	—
295	#137	—	21	1	no	—
296	#137	—	21	1	no	—
297	C₂×Q₁₆	—	7	1	no	—
298	C₂×Q₁₆	—	21	1	no	—
299	C₂×SD₁₆	—	21	1	no	—
300	C₂×SD₁₆	—	21	1	no	—
301	C₂×M₁₆	—	21	1	no	—
302	C₂²×C₇	—	3	1	no	—
303	C₂²×C₇	—	6	1	no	—
304	C₂×D₇	—	3	1	no	—
305	C₂×D₇	—	6	2	no	—
306	C₂×D₇	—	6	1	no	—
307	C₂×D₇	—	12	2	no	—
308	C₂×D₇	D₃×D₄	1	1	yes	characteristic
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	3	1	no	—
312	C₄×C₇	—	6	1	no	—
313	C₄×C₇	C₂³×D₃	1	1	yes	characteristic
314	Dic₇	—	2	1	no	—
315	Dic₇	—	2	1	no	—
316	Dic₇	—	3	1	no	—
317	Dic₇	—	6	1	no	—
318	Dic₇	D₃×D₄	1	1	yes	characteristic
319	C₂²×D₃	—	7	1	no	—
320	C₂²×D₃	—	14	1	no	—
321	C₃×Q₈	—	7	1	no	—
322	C₃×Q₈	—	7	1	no	—
323	C₃×Q₈	—	14	1	no	—
324	C₃×Q₈	—	14	1	no	—
325	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
326	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
327	C₂×C₃×C₄	—	7	1	no	—
328	C₂×C₃×C₄	—	14	1	no	—
329	C₂×C₃×C₄	—	14	1	no	—
330	C₂×Dic₃	—	7	1	no	—
331	C₂×Dic₃	—	14	1	no	—
332	D₁₂	—	2	1	no	—
333	D₁₂	—	7	1	no	—
334	D₁₂	—	14	1	no	—
335	D₁₂	—	14	1	no	—
336	D₁₂	—	14	1	no	—
337	D₁₂	—	14	1	no	—
338	D₁₂	C₂²×D₇	1	1	yes	characteristic
339	C₄×D₃	—	2	1	no	—
340	C₄×D₃	—	2	1	no	—
341	C₄×D₃	—	7	1	no	—
342	C₄×D₃	—	7	1	no	—
343	C₄×D₃	—	7	1	no	—
344	C₄×D₃	—	14	1	no	—
345	C₄×D₃	—	14	1	no	—
346	C₄×D₃	—	14	1	no	—
347	C₄×D₃	—	14	1	no	—
348	C₄×D₃	—	14	1	no	—
349	C₄×D₃	—	14	1	no	—
350	C₄×D₃	C₂²×D₇	1	1	yes	characteristic
351	Dic₆	—	2	1	no	—
352	Dic₆	—	7	1	no	—
353	Dic₆	—	14	1	no	—
354	Dic₆	—	14	1	no	—
355	Dic₆	—	14	1	no	—
356	Dic₆	—	14	1	no	—
357	Dic₆	C₂²×D₇	1	1	yes	characteristic
358	C₃×C₈	—	7	1	no	—
359	C₃×C₈	C₂²×D₇	1	1	yes	characteristic
360	C₃⋊C₈	—	7	1	no	—
361	C₃⋊C₈	C₂²×D₇	1	1	yes	characteristic
362	C₃×C₇	C₂×#137	1	1	yes	characteristic, complemented, Hall
363	#41	—	3	1	no	—
364	#41	—	21	1	no	—
365	#41	—	21	1	no	—
366	#41	—	21	1	no	—
367	#41	—	42	1	no	—
368	#41	—	42	1	no	—
369	C₂×Q₈	—	3	1	no	—
370	C₂×Q₈	—	7	1	no	—
371	C₂×Q₈	—	7	1	no	—
372	C₂×Q₈	—	21	1	no	—
373	C₂×Q₈	—	21	1	no	—
374	C₂×Q₈	—	21	1	no	—
375	C₂×Q₈	—	21	1	no	—
376	C₂×Q₈	—	42	1	no	—
377	C₂×Q₈	—	42	1	no	—
378	C₂×Q₈	—	42	1	no	—
379	C₂×D₄	—	21	1	no	—
380	C₂×D₄	—	42	1	no	—
381	C₂²×C₄	—	21	1	no	—
382	C₂²×C₄	—	42	1	no	—
383	C₂²×C₄	—	42	1	no	—
384	Q₁₆	—	3	1	no	—
385	Q₁₆	—	7	1	no	—
386	Q₁₆	—	7	1	no	—
387	Q₁₆	—	7	1	no	—
388	Q₁₆	—	21	1	no	—
389	Q₁₆	—	21	1	no	—
390	Q₁₆	—	21	1	no	—
391	Q₁₆	D₃×D₇	1	1	yes	characteristic, complemented
392	SD₁₆	—	3	1	no	—
393	SD₁₆	—	3	1	no	—
394	SD₁₆	—	21	1	no	—
395	SD₁₆	—	21	1	no	—
396	SD₁₆	—	21	1	no	—
397	SD₁₆	—	21	1	no	—
398	SD₁₆	—	21	1	no	—
399	SD₁₆	—	21	1	no	—
400	M₁₆	—	3	1	no	—
401	M₁₆	—	21	1	no	—
402	M₁₆	—	21	1	no	—
403	M₁₆	—	21	1	no	—
404	C₂×C₈	—	7	1	no	—
405	C₂×C₈	—	21	1	no	—
406	C₂×C₇	—	6	1	no	—
407	C₂×C₇	—	12	1	no	—
408	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
409	D₇	—	6	1	no	—
410	D₇	—	12	1	no	—
411	D₇	#918	1	2	yes	direct product factor
412	C₂²×C₃	—	7	1	no	—
413	C₂×D₃	—	2	1	no	—
414	C₂×D₃	—	7	1	no	—
415	C₂×D₃	—	14	2	no	—
416	C₂×D₃	—	14	1	no	—
417	C₂×D₃	—	28	2	no	—
418	C₂×D₃	D₄×D₇	1	1	yes	characteristic
419	C₃×C₄	—	2	1	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	7	1	no	—
422	C₃×C₄	—	14	1	no	—
423	C₃×C₄	—	14	1	no	—
424	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
425	Dic₃	—	2	1	no	—
426	Dic₃	—	7	1	no	—
427	Dic₃	—	14	1	no	—
428	Dic₃	D₄×D₇	1	1	yes	characteristic
429	C₂³	—	21	1	no	—
430	C₂³	—	42	1	no	—
431	Q₈	—	3	1	no	—
432	Q₈	—	6	1	no	—
433	Q₈	—	7	1	no	—
434	Q₈	—	7	1	no	—
435	Q₈	—	14	1	no	—
436	Q₈	—	14	1	no	—
437	Q₈	—	21	1	no	—
438	Q₈	—	42	1	no	—
439	Q₈	—	42	1	no	—
440	Q₈	—	42	1	no	—
441	Q₈	—	42	1	no	—
442	Q₈	C₂×D₃×D₇	1	1	yes	characteristic
443	Q₈	C₂×D₃×D₇	1	1	yes	characteristic
444	D₄	—	3	1	no	—
445	D₄	—	6	1	no	—
446	D₄	—	21	1	no	—
447	D₄	—	42	1	no	—
448	D₄	—	42	1	no	—
449	D₄	—	42	1	no	—
450	D₄	—	42	1	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	7	1	no	—
455	C₂×C₄	—	14	1	no	—
456	C₂×C₄	—	14	1	no	—
457	C₂×C₄	—	21	1	no	—
458	C₂×C₄	—	21	1	no	—
459	C₂×C₄	—	21	1	no	—
460	C₂×C₄	—	21	1	no	—
461	C₂×C₄	—	42	1	no	—
462	C₂×C₄	—	42	1	no	—
463	C₂×C₄	—	42	1	no	—
464	C₂×C₄	—	42	1	no	—
465	C₂×C₄	—	42	1	no	—
466	C₂×C₄	—	42	1	no	—
467	C₂×C₄	—	42	1	no	—
468	C₈	—	3	1	no	—
469	C₈	—	7	1	no	—
470	C₈	—	21	1	no	—
471	C₈	C₂×D₃×D₇	1	1	yes	characteristic
472	C₇	C₂×#918	1	1	yes	characteristic, complemented, Sylow
473	C₂×C₃	—	7	2	no	—
474	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
475	D₃	—	2	1	no	—
476	D₃	—	4	1	no	—
477	D₃	—	14	1	no	—
478	D₃	—	28	1	no	—
479	C₂²	—	3	1	no	—
480	C₂²	—	6	1	no	—
481	C₂²	—	7	1	no	—
482	C₂²	—	21	1	no	—
483	C₂²	—	42	2	no	—
484	C₂²	—	42	1	no	—
485	C₂²	—	84	2	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	3	1	no	—
489	C₄	—	6	1	no	—
490	C₄	—	7	1	no	—
491	C₄	—	14	1	no	—
492	C₄	—	14	1	no	—
493	C₄	—	21	1	no	—
494	C₄	—	42	1	no	—
495	C₄	C₂²×D₃×D₇	1	1	yes	characteristic
496	C₃	D₇×#137	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	6	1	no	—
498	C₂	—	7	2	no	—
499	C₂	—	12	1	no	—
500	C₂	—	42	1	no	—
501	C₂	—	84	1	no	—
502	C₂	D₃×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₄×D₇
commutator, cosocle	C₃×C₄×C₇	C₂⁴
Frattini	C₄	C₂²×D₃×D₇
Fitting	C₃×C₇×Q₁₆	C₂²
socle	C₂×C₃×C₇	C₂²×D₄
prime radical	D₇×#239	C₂
hypercenter	Q₁₆	D₃×D₇
hypocenter	C₃×C₇	C₂×#137
LCS	G ▷ C₃×C₄×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. D₃×Q₈×D₇	C₂	semidirect
3. #10621401	C₂	semidirect
4. C₇×#918	C₂	semidirect
5. C₃×D₇×Q₁₆	C₂	semidirect
6. #10621086	C₂	semidirect
7. #10621082	C₂	semidirect
8. #10621074	C₂	semidirect
9. #10621072	C₂	semidirect
10. D₇×#216	C₂	semidirect
11. D₇×#215	C₂	semidirect
12. #10620842	C₂	semidirect
13. #10620825	C₂	semidirect
14. D₇×#204	C₂	semidirect
15. D₇×ΓL(1,𝔽₂₅)	C₂	semidirect
18. Q₈×D₂₁	C₂²	semidirect
20. D₃×C₇×Q₈	C₂²	semidirect
29. D₂₁⋊Q₈	C₂²	semidirect
35. D₃×Dic₁₄	C₂²	semidirect
38. C₃×C₇×Q₁₆	C₂²	semidirect
39. #66635	C₂²	semidirect
40. #66634	C₂²	semidirect
41. #66623	C₂²	semidirect
42. #66622	C₂²	semidirect
43. C₇×#216	C₂²	semidirect
44. C₇×#215	C₂²	semidirect
45. C₇×#204	C₂²	semidirect
46. C₇×ΓL(1,𝔽₂₅)	C₂²	semidirect
47. C₃×#1144	C₂²	semidirect
48. C₃×#1144	C₂²	semidirect
49. C₃×Dic₂₈	C₂²	semidirect
51. #66570	C₂²	semidirect
52. #66569	C₂²	semidirect
53. #66568	C₂²	semidirect
54. #66567	C₂²	semidirect
55. #66566	C₂²	semidirect
56. #66564	C₂²	semidirect
57. #66559	C₂²	semidirect
58. #66558	C₂²	semidirect
68. D₇×Q₁₆	D₃	semidirect
141. C₇×Q₁₆	C₂×D₃	semidirect
147. #1144	C₂×D₃	semidirect
148. #1144	C₂×D₃	semidirect
155. Dic₂₈	C₂×D₃	semidirect
174. #918	D₇	direct (N × H)
251. D₃×Q₈	C₂×D₇	semidirect
262. C₃×Q₁₆	C₂×D₇	semidirect
267. #216	C₂×D₇	semidirect
271. #215	C₂×D₇	semidirect
276. #204	C₂×D₇	semidirect
280. ΓL(1,𝔽₂₅)	C₂×D₇	semidirect
284. C₃×D₇	#137	semidirect
362. C₃×C₇	C₂×#137	semidirect
391. Q₁₆	D₃×D₇	semidirect
411. D₇	#918	direct (N × H)
472. C₇	C₂×#918	semidirect
496. C₃	D₇×#137	semidirect

Maximal subgroups

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

subgroup	index
D₇×#239	2
D₃×Q₈×D₇	2
#10621401	2
C₇×#918	2
C₃×D₇×Q₁₆	2
#10621086	2
#10621082	2
#10621074	2
#10621072	2
D₇×#216	2
D₇×#215	2
#10620842	2
#10620825	2
D₇×#204	2
D₇×ΓL(1,𝔽₂₅)	2
D₇×#137	3
C₂×#918	7

Subgroups — D7×#918 #13059325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#918 #13059325