Subgroups — #13059342

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10621582	C₂	1	1	yes	maximal, characteristic, complemented
2	#10621575	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×#6482	C₂	1	1	yes	maximal, characteristic, complemented
6	#10621083	C₂	1	1	yes	maximal, characteristic, complemented
7	#10621079	C₂	1	1	yes	maximal, characteristic, complemented
8	#10621070	C₂	1	1	yes	maximal, characteristic, complemented
9	#10621067	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×#1143	C₂	1	1	yes	maximal, characteristic, complemented
11	#10621064	C₂	1	1	yes	maximal, characteristic, complemented
12	#10620828	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620820	C₂	1	1	yes	maximal, characteristic, complemented
14	#10620816	C₂	1	1	yes	maximal, characteristic, complemented
15	D₇×#204	C₂	1	1	yes	maximal, characteristic, complemented
16	#90469	—	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×#1161	C₂²	1	1	yes	characteristic
22	C₃×#1161	C₂²	1	1	yes	characteristic, complemented
23	#66681	—	2	1	no	—
24	#66681	C₂²	1	1	yes	characteristic
25	D₃×D₂₈	—	2	1	no	—
26	D₃×D₂₈	C₂²	1	1	yes	characteristic
27	D₇×D₁₂	—	2	1	no	—
28	D₇×D₁₂	C₂²	1	1	yes	characteristic
29	#66675	—	2	1	no	—
30	#66675	—	2	1	no	—
31	#66675	C₂²	1	1	yes	characteristic
32	#66670	—	2	1	no	—
33	#66670	C₂²	1	1	yes	characteristic, complemented
34	#66669	—	2	1	no	—
35	#66669	C₂²	1	1	yes	characteristic, complemented
36	D₇×Dic₆	—	2	1	no	—
37	D₇×Dic₆	C₂²	1	1	yes	characteristic, complemented
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×#1143	C₂²	1	1	yes	characteristic, complemented
48	C₃×#1143	C₂²	1	1	yes	characteristic, complemented
49	C₃×D₅₆	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₈×D₇	C₂²	1	1	yes	characteristic, complemented
51	#66568	C₂²	1	1	yes	characteristic, complemented
52	#66567	C₂²	1	1	yes	characteristic, complemented
53	#66565	C₂²	1	1	yes	characteristic, complemented
54	#66563	C₂²	1	1	yes	characteristic, complemented
55	#66561	C₂²	1	1	yes	characteristic, complemented
56	#66560	C₂²	1	1	yes	characteristic, complemented
57	#66557	C₂²	1	1	yes	characteristic, complemented
58	D₂₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	D₃×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#6553	—	3	1	no	—
61	#6551	—	3	1	no	—
62	C₇×#137	—	3	1	no	—
63	#6513	—	3	1	no	—
64	C₂×#1143	—	3	1	no	—
65	#6482	—	3	1	no	—
66	#6482	D₃	1	1	yes	characteristic, complemented
67	#6481	—	3	1	no	—
68	#6481	—	3	1	no	—
69	#6477	—	3	1	no	—
70	#6477	—	3	1	no	—
71	D₇×SD₁₆	—	3	1	no	—
72	D₇×SD₁₆	—	3	1	no	—
73	#6471	—	3	1	no	—
74	#6470	—	3	1	no	—
75	#5770	—	7	1	no	maximal, Hall
76	C₂×D₃×D₇	—	2	1	no	—
77	C₂×D₃×D₇	—	2	1	no	—
78	C₂×D₃×D₇	—	2	1	no	—
79	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
80	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
81	D₈₄	—	2	1	no	—
82	D₈₄	C₂³	1	1	yes	characteristic
83	C₄×D₂₁	—	2	1	no	—
84	C₄×D₂₁	—	2	1	no	—
85	C₄×D₂₁	C₂³	1	1	yes	characteristic
86	Dic₄₂	—	2	1	no	—
87	Dic₄₂	C₂³	1	1	yes	characteristic
88	C₇×D₁₂	—	2	1	no	—
89	C₇×D₁₂	C₂³	1	1	yes	characteristic
90	C₄×D₃×C₇	—	2	1	no	—
91	C₄×D₃×C₇	—	2	1	no	—
92	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
93	C₇×Dic₆	—	2	1	no	—
94	C₇×Dic₆	C₂³	1	1	yes	characteristic
95	C₃×D₂₈	—	2	1	no	—
96	C₃×D₂₈	—	2	1	no	—
97	C₃×D₂₈	C₂³	1	1	yes	characteristic
98	C₃×D₂₈	C₂³	1	1	yes	characteristic
99	C₃×C₄×D₇	—	2	1	no	—
100	C₃×C₄×D₇	—	2	1	no	—
101	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
102	#4248	—	2	1	no	—
103	#4248	D₄	1	1	yes	characteristic
104	#4247	—	2	1	no	—
105	#4247	D₄	1	1	yes	characteristic
106	#4246	—	2	1	no	—
107	#4246	—	2	1	no	—
108	#4246	D₄	1	1	yes	characteristic
109	#4245	—	2	1	no	—
110	#4245	—	2	1	no	—
111	#4245	D₄	1	1	yes	characteristic
112	Dic₃×D₇	—	2	1	no	—
113	Dic₃×D₇	—	2	1	no	—
114	Dic₃×D₇	—	2	1	no	—
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	#1161	—	3	1	no	—
123	#1161	—	6	1	no	—
124	#1161	C₂×D₃	1	1	yes	characteristic
125	#1161	C₂×D₃	1	1	yes	characteristic, complemented
126	Q₈×D₇	—	3	1	no	—
127	Q₈×D₇	—	3	1	no	—
128	Q₈×D₇	—	6	1	no	—
129	D₄×D₇	—	3	1	no	—
130	D₄×D₇	—	3	1	no	—
131	D₄×D₇	—	6	1	no	—
132	D₄×D₇	—	6	1	no	—
133	#1157	—	3	1	no	—
134	#1157	—	3	1	no	—
135	#1157	—	6	1	no	—
136	#1157	—	6	1	no	—
137	#1157	—	6	1	no	—
138	C₂×D₂₈	—	3	1	no	—
139	C₂×D₂₈	—	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	#1143	—	3	1	no	—
147	#1143	—	3	1	no	—
148	#1143	—	3	1	no	—
149	#1143	C₂×D₃	1	1	yes	characteristic, complemented
150	#1143	C₂×D₃	1	1	yes	characteristic, complemented
151	#1142	—	3	1	no	—
152	#1141	—	3	1	no	—
153	C₂×C₇⋊C₈	—	3	1	no	—
154	D₅₆	—	3	1	no	—
155	D₅₆	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, complemented
162	#1010	—	7	1	no	—
163	#1009	—	7	1	no	—
164	C₃×#135	—	7	1	no	—
165	#951	—	7	1	no	—
166	#949	—	7	1	no	—
167	#918	—	7	1	no	—
168	#918	D₇	1	1	yes	characteristic, complemented
169	#916	—	7	1	no	—
170	#916	—	7	1	no	—
171	D₃×SD₁₆	—	7	1	no	—
172	D₃×SD₁₆	—	7	1	no	—
173	#911	—	7	1	no	—
174	#911	—	7	1	no	—
175	C₂×#204	—	7	1	no	—
176	#901	—	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	—	2	1	no	—
182	C₂×C₃×D₇	—	2	1	no	—
183	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
184	D₃×D₇	—	8	1	no	—
185	D₃×D₇	—	8	1	no	—
186	D₃×D₇	—	8	1	no	—
187	C₃×C₄×C₇	—	2	1	no	—
188	C₃×C₄×C₇	—	2	1	no	—
189	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	Dic₂₁	—	2	1	no	—
191	Dic₂₁	C₂×D₄	1	1	yes	characteristic
192	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
193	C₇×Dic₃	—	2	1	no	—
194	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
195	#577	—	21	1	no	Sylow
196	C₂²×D₇	—	6	1	no	—
197	C₂²×D₇	—	6	1	no	—
198	C₂²×D₇	—	6	1	no	—
199	C₇×Q₈	—	3	1	no	—
200	C₇×Q₈	—	6	1	no	—
201	C₇×Q₈	C₂²×D₃	1	1	yes	characteristic
202	C₇×Q₈	C₂²×D₃	1	1	yes	characteristic
203	C₇×D₄	—	3	1	no	—
204	C₇×D₄	—	6	1	no	—
205	C₂×C₄×C₇	—	3	1	no	—
206	C₂×C₄×C₇	—	6	1	no	—
207	C₂×C₄×C₇	—	6	1	no	—
208	C₂²⋊D₇	—	3	1	no	—
209	C₂²⋊D₇	—	3	1	no	—
210	C₂²⋊D₇	—	6	1	no	—
211	C₂²⋊D₇	—	6	1	no	—
212	C₂²⋊D₇	—	6	1	no	—
213	D₂₈	—	2	1	no	—
214	D₂₈	—	2	1	no	—
215	D₂₈	—	3	1	no	—
216	D₂₈	—	3	1	no	—
217	D₂₈	—	6	1	no	—
218	D₂₈	—	6	1	no	—
219	D₂₈	—	6	1	no	—
220	D₂₈	C₂²×D₃	1	1	yes	characteristic
221	D₂₈	C₂²×D₃	1	1	yes	characteristic
222	C₄×D₇	—	2	1	no	—
223	C₄×D₇	—	2	1	no	—
224	C₄×D₇	—	3	1	no	—
225	C₄×D₇	—	6	1	no	—
226	C₄×D₇	—	6	1	no	—
227	C₄×D₇	—	6	1	no	—
228	C₄×D₇	—	6	1	no	—
229	C₄×D₇	—	6	1	no	—
230	C₄×D₇	C₂²×D₃	1	1	yes	characteristic
231	Dic₁₄	—	3	1	no	—
232	Dic₁₄	—	3	1	no	—
233	Dic₁₄	—	6	1	no	—
234	Dic₁₄	—	6	1	no	—
235	C₇×C₈	—	3	1	no	—
236	C₇×C₈	C₂²×D₃	1	1	yes	characteristic
237	C₇⋊C₈	—	3	1	no	—
238	C₇⋊C₈	C₂²×D₃	1	1	yes	characteristic
239	C₃×#41	—	7	1	no	—
240	C₃×#41	—	7	1	no	—
241	#239	—	7	1	no	—
242	#239	C₂×D₇	1	1	yes	characteristic
243	D₃×Q₈	—	7	1	no	—
244	D₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
245	#237	—	7	1	no	—
246	#237	—	7	1	no	—
247	#237	—	14	1	no	—
248	#237	—	14	1	no	—
249	D₃×D₄	—	7	1	no	—
250	D₃×D₄	—	7	1	no	—
251	D₃×D₄	—	14	1	no	—
252	D₃×D₄	—	14	1	no	—
253	#235	—	7	1	no	—
254	#235	—	14	1	no	—
255	#235	—	14	1	no	—
256	C₂×D₁₂	—	7	1	no	—
257	C₂×D₁₂	—	14	1	no	—
258	C₂×Dic₆	—	7	1	no	—
259	C₂×Dic₆	—	14	1	no	—
260	C₃×Q₁₆	C₂×D₇	1	1	yes	characteristic, complemented
261	C₃×SD₁₆	—	7	1	no	—
262	C₃×SD₁₆	—	7	1	no	—
263	C₃×D₈	—	7	1	no	—
264	C₂×C₃×C₈	—	7	1	no	—
265	#216	—	7	1	no	—
266	#216	C₂×D₇	1	1	yes	characteristic, complemented
267	#215	—	7	1	no	—
268	#215	C₂×D₇	1	1	yes	characteristic, complemented
269	#214	—	7	1	no	—
270	#214	—	7	1	no	—
271	#213	—	7	1	no	—
272	#213	—	7	1	no	—
273	#208	—	7	1	no	—
274	#204	—	7	1	no	—
275	#204	—	7	1	no	—
276	#204	—	7	1	no	—
277	#204	C₂×D₇	1	1	yes	characteristic, complemented
278	ΓL(1,𝔽₂₅)	—	7	1	no	—
279	ΓL(1,𝔽₂₅)	C₂×D₇	1	1	yes	characteristic, complemented
280	D₃×C₈	—	7	1	no	—
281	D₃×C₈	—	7	1	no	—
282	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
283	D₂₁	—	2	1	no	—
284	D₂₁	—	4	1	no	—
285	C₃×D₇	—	2	1	no	—
286	C₃×D₇	—	4	1	no	—
287	C₃×D₇	—	4	1	no	—
288	D₃×C₇	—	2	1	no	—
289	D₃×C₇	—	4	1	no	—
290	2₋¹⁺⁴	—	21	1	no	—
291	H(5,𝔽₂)	—	21	1	no	—
292	#137	—	3	1	no	—
293	#137	—	21	1	no	—
294	#137	—	21	1	no	—
295	AGL(1,ℤ/8)	—	21	1	no	—
296	AGL(1,ℤ/8)	—	21	1	no	—
297	AGL(1,ℤ/8)	—	21	1	no	—
298	#135	—	7	1	no	—
299	#135	—	21	1	no	—
300	#135	—	21	1	no	—
301	C₂×SD₁₆	—	21	1	no	—
302	C₂×SD₁₆	—	21	1	no	—
303	C₂×SD₁₆	—	21	1	no	—
304	#131	—	21	1	no	—
305	C₂²×C₇	—	3	1	no	—
306	C₂²×C₇	—	6	1	no	—
307	C₂×D₇	—	2	1	no	—
308	C₂×D₇	—	2	1	no	—
309	C₂×D₇	—	3	1	no	—
310	C₂×D₇	—	6	1	no	—
311	C₂×D₇	—	24	1	no	—
312	C₂×D₇	—	24	1	no	—
313	C₂×D₇	—	24	1	no	—
314	C₂×D₇	D₃×D₄	1	1	yes	characteristic
315	C₄×C₇	—	2	1	no	—
316	C₄×C₇	—	2	1	no	—
317	C₄×C₇	—	3	1	no	—
318	C₄×C₇	—	6	1	no	—
319	C₄×C₇	C₂³×D₃	1	1	yes	characteristic
320	Dic₇	—	3	1	no	—
321	Dic₇	—	6	1	no	—
322	Dic₇	D₃×D₄	1	1	yes	characteristic
323	C₂²×D₃	—	14	1	no	—
324	C₂²×D₃	—	14	1	no	—
325	C₂²×D₃	—	14	1	no	—
326	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
327	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
328	C₃×D₄	—	7	1	no	—
329	C₃×D₄	—	7	1	no	—
330	C₃×D₄	—	14	1	no	—
331	C₃×D₄	—	14	1	no	—
332	C₂×C₃×C₄	—	7	1	no	—
333	C₂×C₃×C₄	—	14	1	no	—
334	C₂×C₃×C₄	—	14	1	no	—
335	#67	—	7	1	no	—
336	#67	—	7	1	no	—
337	#67	—	14	1	no	—
338	#67	—	14	1	no	—
339	#67	—	14	1	no	—
340	#67	—	14	1	no	—
341	C₂×Dic₃	—	14	1	no	—
342	C₂×Dic₃	—	14	1	no	—
343	C₂×Dic₃	—	14	1	no	—
344	D₁₂	—	2	1	no	—
345	D₁₂	—	7	1	no	—
346	D₁₂	—	7	1	no	—
347	D₁₂	—	14	1	no	—
348	D₁₂	—	14	1	no	—
349	D₁₂	C₂²×D₇	1	1	yes	characteristic
350	C₄×D₃	—	2	1	no	—
351	C₄×D₃	—	2	1	no	—
352	C₄×D₃	—	7	1	no	—
353	C₄×D₃	—	14	1	no	—
354	C₄×D₃	—	14	1	no	—
355	C₄×D₃	C₂²×D₇	1	1	yes	characteristic
356	Dic₆	—	2	1	no	—
357	Dic₆	—	7	1	no	—
358	Dic₆	—	7	1	no	—
359	Dic₆	—	14	1	no	—
360	Dic₆	—	14	1	no	—
361	Dic₆	C₂²×D₇	1	1	yes	characteristic
362	C₃×C₈	—	7	1	no	—
363	C₃×C₈	C₂²×D₇	1	1	yes	characteristic
364	C₃⋊C₈	—	7	1	no	—
365	C₃⋊C₈	C₂²×D₇	1	1	yes	characteristic
366	C₃×C₇	#577	1	1	yes	characteristic, complemented, Hall
367	#41	—	3	1	no	—
368	#41	—	7	1	no	—
369	#41	—	7	1	no	—
370	#41	—	21	1	no	—
371	#41	—	21	1	no	—
372	#41	—	21	1	no	—
373	#41	—	21	1	no	—
374	#41	—	42	1	no	—
375	#41	—	42	1	no	—
376	#41	—	42	1	no	—
377	#41	—	42	1	no	—
378	C₂×Q₈	—	3	1	no	—
379	C₂×Q₈	—	21	1	no	—
380	C₂×Q₈	—	21	1	no	—
381	C₂×Q₈	—	42	1	no	—
382	C₂×D₄	—	21	1	no	—
383	C₂×D₄	—	21	1	no	—
384	C₂×D₄	—	21	1	no	—
385	C₂×D₄	—	42	1	no	—
386	C₂×D₄	—	42	1	no	—
387	C₂×D₄	—	42	1	no	—
388	Q₁₆	—	3	1	no	—
389	Q₁₆	—	21	1	no	—
390	Q₁₆	D₃×D₇	1	1	yes	characteristic, complemented
391	SD₁₆	—	3	1	no	—
392	SD₁₆	—	3	1	no	—
393	SD₁₆	—	7	1	no	—
394	SD₁₆	—	7	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	SD₁₆	—	21	1	no	—
401	D₈	—	7	1	no	—
402	D₈	—	21	1	no	—
403	D₈	—	21	1	no	—
404	M₁₆	—	3	1	no	—
405	M₁₆	—	21	1	no	—
406	M₁₆	—	21	1	no	—
407	C₂×C₈	—	7	1	no	—
408	C₂×C₈	—	21	1	no	—
409	C₂×C₈	—	21	1	no	—
410	C₂×C₇	—	6	1	no	—
411	C₂×C₇	—	12	1	no	—
412	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
413	D₇	—	2	1	no	—
414	D₇	—	4	1	no	—
415	D₇	—	4	1	no	—
416	D₇	—	6	1	no	—
417	D₇	—	12	1	no	—
418	C₂²×C₃	—	7	1	no	—
419	C₂²×C₃	—	14	1	no	—
420	C₂²×C₃	—	14	1	no	—
421	C₂×D₃	—	2	1	no	—
422	C₂×D₃	—	7	1	no	—
423	C₂×D₃	—	14	1	no	—
424	C₂×D₃	—	56	1	no	—
425	C₂×D₃	—	56	1	no	—
426	C₂×D₃	—	56	1	no	—
427	C₂×D₃	D₄×D₇	1	1	yes	characteristic
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	7	1	no	—
431	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
432	Dic₃	—	2	1	no	—
433	Dic₃	—	7	1	no	—
434	Dic₃	—	14	1	no	—
435	Dic₃	D₄×D₇	1	1	yes	characteristic
436	C₂³	—	42	1	no	—
437	C₂³	—	42	1	no	—
438	C₂³	—	42	1	no	—
439	Q₈	—	3	1	no	—
440	Q₈	—	6	1	no	—
441	Q₈	—	21	1	no	—
442	Q₈	—	21	1	no	—
443	Q₈	—	42	1	no	—
444	Q₈	—	42	1	no	—
445	Q₈	C₂×D₃×D₇	1	1	yes	characteristic
446	Q₈	C₂×D₃×D₇	1	1	yes	characteristic
447	D₄	—	3	1	no	—
448	D₄	—	6	1	no	—
449	D₄	—	7	1	no	—
450	D₄	—	7	1	no	—
451	D₄	—	14	1	no	—
452	D₄	—	14	1	no	—
453	D₄	—	21	1	no	—
454	D₄	—	21	1	no	—
455	D₄	—	21	1	no	—
456	D₄	—	21	1	no	—
457	D₄	—	42	1	no	—
458	D₄	—	42	1	no	—
459	D₄	—	42	1	no	—
460	D₄	—	42	1	no	—
461	D₄	—	42	1	no	—
462	D₄	—	42	1	no	—
463	C₂×C₄	—	3	1	no	—
464	C₂×C₄	—	6	1	no	—
465	C₂×C₄	—	6	1	no	—
466	C₂×C₄	—	7	1	no	—
467	C₂×C₄	—	14	1	no	—
468	C₂×C₄	—	14	1	no	—
469	C₂×C₄	—	21	1	no	—
470	C₂×C₄	—	42	1	no	—
471	C₂×C₄	—	42	1	no	—
472	C₂×C₄	—	42	1	no	—
473	C₂×C₄	—	42	1	no	—
474	C₂×C₄	—	42	1	no	—
475	C₈	—	3	1	no	—
476	C₈	—	7	1	no	—
477	C₈	—	21	1	no	—
478	C₈	C₂×D₃×D₇	1	1	yes	characteristic
479	C₇	#5770	1	1	yes	characteristic, complemented, Sylow
480	C₂×C₃	—	14	1	no	—
481	C₂×C₃	—	28	1	no	—
482	C₂×C₃	—	28	1	no	—
483	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
484	D₃	—	2	1	no	—
485	D₃	—	4	1	no	—
486	D₃	—	14	1	no	—
487	D₃	—	28	1	no	—
488	C₂²	—	3	1	no	—
489	C₂²	—	6	1	no	—
490	C₂²	—	7	1	no	—
491	C₂²	—	14	1	no	—
492	C₂²	—	14	1	no	—
493	C₂²	—	21	1	no	—
494	C₂²	—	42	1	no	—
495	C₂²	—	168	1	no	—
496	C₂²	—	168	1	no	—
497	C₂²	—	168	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	3	1	no	—
501	C₄	—	6	1	no	—
502	C₄	—	7	1	no	—
503	C₄	—	21	1	no	—
504	C₄	—	42	1	no	—
505	C₄	C₂²×D₃×D₇	1	1	yes	characteristic
506	C₃	#90469	1	1	yes	characteristic, complemented, Sylow
507	C₂	—	6	1	no	—
508	C₂	—	12	1	no	—
509	C₂	—	14	1	no	—
510	C₂	—	28	1	no	—
511	C₂	—	28	1	no	—
512	C₂	—	42	1	no	—
513	C₂	—	84	1	no	—
514	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
hypercenter	Q₁₆	D₃×D₇
hypocenter	C₃×C₇	#577
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
1. #10621582	C₂	semidirect
2. #10621575	C₂	semidirect
3. #10621401	C₂	semidirect
4. C₇×#918	C₂	semidirect
5. C₃×#6482	C₂	semidirect
6. #10621083	C₂	semidirect
7. #10621079	C₂	semidirect
8. #10621070	C₂	semidirect
9. #10621067	C₂	semidirect
10. D₃×#1143	C₂	semidirect
11. #10621064	C₂	semidirect
12. #10620828	C₂	semidirect
13. #10620820	C₂	semidirect
14. #10620816	C₂	semidirect
15. D₇×#204	C₂	semidirect
18. Q₈×D₂₁	C₂²	semidirect
20. D₃×C₇×Q₈	C₂²	semidirect
22. C₃×#1161	C₂²	semidirect
33. #66670	C₂²	semidirect
35. #66669	C₂²	semidirect
37. D₇×Dic₆	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×#1143	C₂²	semidirect
48. C₃×#1143	C₂²	semidirect
49. C₃×D₅₆	C₂²	semidirect
50. C₃×C₈×D₇	C₂²	semidirect
51. #66568	C₂²	semidirect
52. #66567	C₂²	semidirect
53. #66565	C₂²	semidirect
54. #66563	C₂²	semidirect
55. #66561	C₂²	semidirect
56. #66560	C₂²	semidirect
57. #66557	C₂²	semidirect
58. D₂₁⋊C₈	C₂²	semidirect
59. D₃×C₇⋊C₈	C₂²	semidirect
66. #6482	D₃	semidirect
125. #1161	C₂×D₃	semidirect
141. C₇×Q₁₆	C₂×D₃	semidirect
149. #1143	C₂×D₃	semidirect
150. #1143	C₂×D₃	semidirect
155. D₅₆	C₂×D₃	semidirect
161. C₈×D₇	C₂×D₃	semidirect
168. #918	D₇	semidirect
244. D₃×Q₈	C₂×D₇	semidirect
260. C₃×Q₁₆	C₂×D₇	semidirect
266. #216	C₂×D₇	semidirect
268. #215	C₂×D₇	semidirect
277. #204	C₂×D₇	semidirect
279. ΓL(1,𝔽₂₅)	C₂×D₇	semidirect
366. C₃×C₇	#577	semidirect
390. Q₁₆	D₃×D₇	semidirect
479. C₇	#5770	semidirect
506. C₃	#90469	semidirect

Maximal subgroups

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

subgroup	index
#10621582	2
#10621575	2
#10621401	2
C₇×#918	2
C₃×#6482	2
#10621083	2
#10621079	2
#10621070	2
#10621067	2
D₃×#1143	2
#10621064	2
#10620828	2
#10620820	2
#10620816	2
D₇×#204	2
#90469	3
#5770	7