Subgroups — #13360729

Order 1792.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
2	#11741373	C₂	1	1	yes	maximal, characteristic
3	#11741237	C₂	1	2	yes	maximal, complemented
4	C₄×#6464	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729840	C₂	1	1	yes	maximal, characteristic, complemented
6	#11729765	C₂	1	2	yes	maximal, complemented
7	#11728473	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728460	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728145	C₂	1	2	yes	maximal, complemented
10	#11728132	C₂	1	2	yes	maximal, complemented
11	#11727533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₂²	1	1	yes	characteristic
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	#90513	C₂²	1	2	yes	—
15	C₂×#6464	C₂²	1	1	yes	characteristic
16	C₂×#6464	C₂²	1	1	yes	characteristic
17	C₄×#1157	C₂²	1	1	yes	characteristic
18	C₇×#443	—	2	1	no	—
19	C₇×#443	—	2	1	no	—
20	C₇×#443	—	2	1	no	—
21	C₇×#443	—	2	1	no	—
22	C₂×C₇×#108	C₂²	1	1	yes	characteristic
23	C₂×C₇×#104	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	#90012	C₂²	1	2	yes	—
26	#90009	C₂²	1	2	yes	—
27	#90008	C₂²	1	2	yes	—
28	#89964	C₄	1	2	yes	complemented
29	#89949	C₄	1	4	yes	complemented
30	#89932	C₄	1	2	yes	complemented
31	#89917	—	2	4	no	—
32	#89916	—	2	4	no	—
33	#89911	C₂²	1	2	yes	—
34	#89896	C₂²	1	2	yes	—
35	C₂×#6393	C₂²	1	1	yes	characteristic
36	#89878	C₂²	1	1	yes	characteristic
37	#89873	C₂²	1	2	yes	—
38	#89873	C₂²	1	1	yes	characteristic
39	#89873	C₂²	1	1	yes	characteristic
40	C₄×#1136	C₂²	1	1	yes	characteristic
41	#89461	—	2	1	no	—
42	#89461	—	2	1	no	—
43	C₄×#1131	—	2	1	no	—
44	C₄×C₈×D₇	—	2	1	no	—
45	#89351	C₂²	1	2	yes	—
46	#89351	C₂²	1	2	yes	—
47	#89318	C₂²	1	2	yes	—
48	#21558	—	7	1	no	maximal, Sylow
49	C₂×C₇×#41	C₂³	1	2	yes	—
50	C₂×#1157	C₂³	1	1	yes	characteristic
51	C₇×#135	—	2	1	no	—
52	C₇×#135	—	2	1	no	—
53	C₇×#135	—	2	1	no	—
54	C₇×#135	—	2	1	no	—
55	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	complemented
57	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic, complemented
58	C₇×#131	—	2	2	no	—
59	C₇×#131	—	2	2	no	—
60	C₇×#131	—	2	2	no	—
61	C₇×#131	—	2	2	no	—
62	C₂×C₇×M₁₆	—	2	2	no	—
63	C₂×C₇×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	—	2	2	no	—
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	#6514	—	2	2	no	—
69	#6513	—	2	4	no	—
70	#6512	—	2	2	no	—
71	#6505	C₂×C₄	1	4	yes	—
72	#6495	C₂×C₄	1	4	yes	—
73	C₄×C₂²⋊D₇	—	2	2	no	—
74	#6489	C₂³	1	2	yes	—
75	#6489	C₂³	1	1	yes	characteristic
76	C₂×#1136	C₂³	1	1	yes	characteristic
77	C₂×#1136	C₂³	1	2	yes	—
78	C₂×#1136	C₂³	1	1	yes	characteristic
79	#6464	—	2	1	no	—
80	#6464	—	2	1	no	—
81	#6464	—	2	1	no	—
82	#6464	—	2	1	no	—
83	#6464	C₂×C₄	1	2	yes	—
84	#6464	C₂×C₄	1	2	yes	—
85	#6464	D₄	1	2	yes	—
86	#6464	D₄	1	2	yes	—
87	C₂×#1131	—	2	1	no	—
88	C₂×#1131	—	2	1	no	—
89	C₂×C₈×D₇	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	C₄×D₂₈	—	2	1	no	—
92	#6435	—	2	1	no	—
93	C₄²×D₇	—	2	1	no	—
94	C₄×Dic₁₄	—	2	1	no	—
95	C₇×#108	—	2	1	no	—
96	C₇×#108	—	2	1	no	—
97	C₇×#104	—	2	2	no	—
98	C₇×#104	—	2	2	no	—
99	C₄×C₇×C₈	D₄	1	1	yes	characteristic
100	C₄×C₇×C₈	D₄	1	1	yes	characteristic
101	C₄×C₇×C₈	D₄	1	1	yes	characteristic
102	C₄×C₇×C₈	D₄	1	1	yes	characteristic
103	#6411	—	2	4	no	—
104	#6410	C₂×C₄	1	4	yes	complemented
105	#6408	—	2	4	no	—
106	#6407	C₂×C₄	1	4	yes	complemented
107	#6399	—	2	4	no	—
108	#6396	—	2	4	no	—
109	#6393	C₂×C₄	1	2	yes	complemented
110	#6393	C₂×C₄	1	2	yes	complemented
111	#6392	—	2	1	no	—
112	#6391	—	2	1	no	—
113	#6389	—	2	2	no	—
114	#6389	—	2	1	no	—
115	#6389	—	2	1	no	—
116	C₈×Dic₇	—	2	2	no	—
117	C₈×Dic₇	—	2	1	no	—
118	C₈×Dic₇	—	2	1	no	—
119	#6377	—	2	1	no	—
120	C₄×C₇⋊C₈	—	2	1	no	—
121	#3067	—	7	1	no	—
122	#2955	—	7	2	no	—
123	C₂×#443	D₇	1	1	yes	characteristic, complemented
124	C₄×#131	—	7	1	no	—
125	#1976	—	7	1	no	—
126	#1953	—	7	1	no	—
127	#1932	—	7	2	no	—
128	#1906	—	7	2	no	—
129	#1814	—	7	1	no	—
130	#1772	—	7	1	no	—
131	#1757	—	7	2	no	—
132	C₇×#41	—	2	2	no	—
133	C₇×#41	—	2	2	no	—
134	C₇×#41	—	2	2	no	—
135	C₇×#41	—	2	2	no	—
136	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
137	C₂×C₇×D₄	—	2	2	no	—
138	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
142	C₂×C₂²⋊D₇	—	2	1	no	—
143	#1157	—	2	1	no	—
144	#1157	—	2	1	no	—
145	#1157	C₂²×C₄	1	2	yes	—
146	#1157	C₂×D₄	1	2	yes	—
147	C₂×D₂₈	#41	1	1	yes	characteristic
148	C₂×C₄×D₇	—	2	1	no	—
149	C₂×C₄×D₇	—	2	2	no	—
150	C₂×Dic₁₄	#41	1	1	yes	characteristic
151	C₇×Q₁₆	—	2	1	no	—
152	C₇×Q₁₆	—	2	1	no	—
153	C₇×SD₁₆	—	2	2	no	—
154	C₇×SD₁₆	—	2	2	no	—
155	C₇×D₈	—	2	1	no	—
156	C₇×D₈	—	2	1	no	—
157	C₇×M₁₆	—	2	2	no	—
158	C₇×M₁₆	—	2	2	no	—
159	C₇×M₁₆	—	4	2	no	—
160	C₇×M₁₆	—	4	2	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	4	2	no	—
163	C₂×C₇×C₈	—	4	2	no	—
164	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₇×C₈	#41	1	1	yes	characteristic
173	C₂×C₇×C₈	#41	1	1	yes	characteristic
174	C₂×C₇×C₈	#41	1	1	yes	characteristic
175	C₂×C₇×C₈	#41	1	1	yes	characteristic
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
179	C₂²⋊Dic₇	—	2	2	no	—
180	C₂²⋊Dic₇	#41	1	2	yes	—
181	#1144	—	2	4	no	—
182	#1143	—	2	4	no	—
183	#1142	—	2	4	no	—
184	#1141	—	2	4	no	—
185	(C₂×D₇)⋊C₄	—	2	2	no	—
186	C₄⋊Dic₇	—	2	1	no	—
187	C₄⋊Dic₇	—	2	2	no	—
188	Dic₇⋊C₄	—	2	2	no	—
189	C₄×Dic₇	—	2	2	no	—
190	C₄×Dic₇	—	2	1	no	—
191	C₄×Dic₇	—	2	2	no	—
192	#1136	—	2	1	no	—
193	#1136	—	2	1	no	—
194	#1136	—	2	2	no	—
195	#1136	C₂²×C₄	1	2	yes	—
196	#1136	C₂²×C₄	1	4	yes	—
197	#1136	C₂×D₄	1	2	yes	—
198	C₂×C₇⋊C₈	—	2	1	no	—
199	C₂×C₇⋊C₈	—	2	1	no	—
200	C₂×C₇⋊C₈	—	2	2	no	—
201	#1131	—	2	2	no	—
202	#1131	—	2	2	no	—
203	#1131	—	2	2	no	—
204	#1131	—	2	2	no	—
205	C₈×D₇	—	2	2	no	—
206	C₈×D₇	—	2	2	no	—
207	C₈×D₇	—	2	2	no	—
208	C₈×D₇	—	2	2	no	—
209	#575	—	7	2	no	—
210	C₂×#135	C₂×D₇	1	1	yes	characteristic
211	C₂×#131	—	7	1	no	—
212	C₂×#131	—	7	1	no	—
213	C₂×#131	C₂×D₇	1	2	yes	—
214	C₄×#41	—	7	1	no	—
215	#473	—	7	2	no	—
216	#472	—	7	2	no	—
217	#471	—	7	4	no	—
218	#444	—	14	4	no	—
219	#443	—	2	1	no	—
220	#443	—	2	1	no	—
221	#443	—	2	1	no	—
222	#443	—	2	1	no	—
223	#443	—	14	4	no	—
224	#430	—	7	2	no	—
225	C₂×#108	—	7	1	no	—
226	C₂×#108	C₂×D₇	1	1	yes	characteristic
227	#427	—	7	1	no	—
228	#421	—	7	2	no	—
229	#421	—	7	2	no	—
230	C₂×#104	C₂×D₇	1	2	yes	—
231	#413	—	7	2	no	—
232	#410	—	7	2	no	—
233	#405	—	7	1	no	—
234	#405	—	7	1	no	—
235	#405	—	7	2	no	—
236	#405	—	14	1	no	—
237	#405	—	14	1	no	—
238	C₄×M₁₆	—	7	1	no	—
239	C₄×M₁₆	—	14	1	no	—
240	C₂×C₄×C₈	—	14	1	no	—
241	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
242	#344	—	7	2	no	—
243	#344	—	7	2	no	—
244	#339	—	7	2	no	—
245	C₂³×C₇	—	2	2	no	—
246	C₂³×C₇	C₂×#41	1	1	yes	characteristic
247	C₂²×D₇	—	2	1	no	—
248	C₇×Q₈	—	2	2	no	—
249	C₇×Q₈	—	2	2	no	—
250	C₇×D₄	—	2	2	no	—
251	C₇×D₄	—	2	2	no	—
252	C₇×D₄	—	4	2	no	—
253	C₇×D₄	—	4	2	no	—
254	C₂×C₄×C₇	—	2	1	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	1	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	—	4	2	no	—
259	C₂×C₄×C₇	—	4	2	no	—
260	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂²⋊D₇	—	2	2	no	—
267	C₂²⋊D₇	—	2	2	no	—
268	C₂×Dic₇	—	2	1	no	—
269	C₂×Dic₇	—	2	2	no	—
270	C₂×Dic₇	—	4	2	no	—
271	D₂₈	—	2	1	no	—
272	D₂₈	C₄×D₄	1	2	yes	—
273	C₄×D₇	—	2	2	no	—
274	C₄×D₇	—	2	2	no	—
275	C₄×D₇	—	4	4	no	—
276	Dic₁₄	—	2	1	no	—
277	Dic₁₄	C₄×D₄	1	2	yes	—
278	C₇×C₈	—	4	2	no	—
279	C₇×C₈	C₄×D₄	1	1	yes	characteristic
280	C₇×C₈	C₄×D₄	1	1	yes	characteristic
281	C₇×C₈	C₄×D₄	1	1	yes	characteristic
282	C₇×C₈	C₄×D₄	1	1	yes	characteristic
283	C₇×C₈	#121	1	1	yes	characteristic
284	C₇×C₈	#121	1	1	yes	characteristic
285	C₇×C₈	#121	1	1	yes	characteristic
286	C₇×C₈	#121	1	1	yes	characteristic
287	C₇⋊C₈	—	2	2	no	—
288	C₇⋊C₈	—	2	4	no	—
289	C₇⋊C₈	—	2	2	no	—
290	C₂×#41	—	7	1	no	—
291	C₂×#41	C₂²×D₇	1	2	yes	—
292	#137	—	7	4	no	—
293	#137	—	14	2	no	—
294	AGL(1,ℤ/8)	—	7	4	no	—
295	AGL(1,ℤ/8)	—	14	2	no	—
296	#135	—	2	1	no	—
297	#135	—	2	1	no	—
298	#135	—	2	1	no	—
299	#135	—	2	1	no	—
300	#135	—	14	4	no	—
301	C₂×Q₁₆	C₄×D₇	1	1	yes	characteristic, complemented
302	C₂×SD₁₆	C₄×D₇	1	2	yes	complemented
303	C₂×D₈	C₄×D₇	1	1	yes	characteristic, complemented
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	#131	—	2	2	no	—
308	#131	—	7	2	no	—
309	#131	—	7	2	no	—
310	#131	—	7	2	no	—
311	#131	—	7	2	no	—
312	#131	—	14	1	no	—
313	#131	—	14	1	no	—
314	#131	—	14	1	no	—
315	#131	—	14	1	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	7	1	no	—
318	C₂×M₁₆	—	7	1	no	—
319	C₂×M₁₆	—	7	2	no	—
320	C₂×M₁₆	—	14	1	no	—
321	C₂×M₁₆	—	14	1	no	—
322	C₂×M₁₆	C₂²×D₇	1	2	yes	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	14	1	no	—
325	C₂²×C₈	—	14	1	no	—
326	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
328	C₄×Q₈	—	14	1	no	—
329	C₄×D₄	—	14	1	no	—
330	C₄×D₄	—	14	2	no	—
331	#117	—	7	1	no	—
332	#117	—	7	2	no	—
333	#117	—	14	1	no	—
334	C₂×C₄²	—	14	1	no	—
335	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
336	#108	—	2	1	no	—
337	#108	—	2	1	no	—
338	#108	—	7	2	no	—
339	#108	—	7	2	no	—
340	#108	—	14	4	no	—
341	#107	—	14	1	no	—
342	#106	—	14	1	no	—
343	#104	—	2	2	no	—
344	#104	—	2	2	no	—
345	#104	—	14	4	no	—
346	#104	—	14	4	no	—
347	#101	—	7	4	no	—
348	#100	—	7	4	no	—
349	#99	—	14	4	no	—
350	#97	—	14	2	no	—
351	#97	—	14	1	no	—
352	#97	—	14	1	no	—
353	#97	—	14	1	no	—
354	C₄×C₈	—	14	2	no	—
355	C₄×C₈	—	14	1	no	—
356	C₄×C₈	—	14	1	no	—
357	C₄×C₈	—	14	1	no	—
358	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
359	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
360	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
361	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
362	C₂²×C₇	—	4	1	no	—
363	C₂²×C₇	—	4	2	no	—
364	C₂²×C₇	—	8	2	no	—
365	C₂²×C₇	C₄×#41	1	1	yes	characteristic
366	C₂²×C₇	#525	1	1	yes	characteristic
367	C₂²×C₇	#532	1	1	yes	characteristic
368	C₂×D₇	—	2	2	no	—
369	C₂×D₇	—	4	2	no	—
370	C₄×C₇	—	2	2	no	—
371	C₄×C₇	—	4	1	no	—
372	C₄×C₇	—	4	2	no	—
373	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
374	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
375	C₄×C₇	C₂×#121	1	1	yes	characteristic
376	C₄×C₇	#529	1	1	yes	characteristic
377	Dic₇	—	2	2	no	—
378	Dic₇	—	4	2	no	—
379	Dic₇	—	8	2	no	—
380	#41	—	2	2	no	—
381	#41	—	2	2	no	—
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	7	2	no	—
385	#41	—	7	2	no	—
386	#41	—	14	1	no	—
387	#41	—	14	1	no	—
388	C₂×Q₈	—	7	1	no	—
389	C₂×Q₈	C₂×C₄×D₇	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	7	1	no	—
392	C₂×D₄	—	14	1	no	—
393	C₂×D₄	C₂×C₄×D₇	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	14	2	no	—
397	C₂²×C₄	—	14	1	no	—
398	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
399	Q₁₆	—	2	1	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	—	14	4	no	—
402	SD₁₆	—	2	2	no	—
403	SD₁₆	—	2	2	no	—
404	SD₁₆	—	14	4	no	—
405	SD₁₆	—	14	4	no	—
406	D₈	—	2	1	no	—
407	D₈	—	2	1	no	—
408	D₈	—	14	4	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	4	2	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	—	7	2	no	—
414	M₁₆	—	7	4	no	—
415	M₁₆	—	7	2	no	—
416	M₁₆	—	14	1	no	—
417	M₁₆	—	14	1	no	—
418	M₁₆	—	14	2	no	—
419	M₁₆	—	14	2	no	—
420	M₁₆	—	14	2	no	—
421	M₁₆	—	14	2	no	—
422	M₁₆	—	14	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₂×C₈	—	14	2	no	—
427	C₂×C₈	—	14	1	no	—
428	C₂×C₈	—	14	1	no	—
429	C₂×C₈	—	14	2	no	—
430	C₂×C₈	—	14	2	no	—
431	C₂×C₈	—	14	2	no	—
432	C₂×C₈	—	14	2	no	—
433	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
434	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
435	C₂×C₈	#1157	1	1	yes	characteristic
436	C₂×C₈	#1157	1	1	yes	characteristic
437	C₂×C₈	D₄×D₇	1	1	yes	characteristic
438	C₂×C₈	D₄×D₇	1	1	yes	characteristic
439	C₂×C₈	#1159	1	1	yes	characteristic
440	C₂×C₈	#1159	1	1	yes	characteristic
441	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
442	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
443	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
444	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
445	C₄⋊C₄	—	14	2	no	—
446	C₄⋊C₄	—	14	1	no	—
447	C₄⋊C₄	—	14	2	no	—
448	C₂²⋊C₄	—	7	2	no	—
449	C₂²⋊C₄	—	14	2	no	—
450	C₂²⋊C₄	—	14	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	14	2	no	—
453	C₄²	—	14	1	no	—
454	C₄²	—	14	2	no	—
455	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
456	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
457	C₂×C₇	—	2	1	no	—
458	C₂×C₇	—	2	1	no	—
459	C₂×C₇	—	2	1	no	—
460	C₂×C₇	—	8	2	no	—
461	C₂×C₇	C₄×#121	1	1	yes	characteristic
462	D₇	—	4	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	14	1	no	—
465	C₂³	D₇×#41	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	7	2	no	—
469	Q₈	—	14	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	7	2	no	—
475	D₄	—	14	2	no	—
476	D₄	—	14	2	no	—
477	D₄	—	14	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	14	1	no	—
485	C₂×C₄	—	14	2	no	—
486	C₂×C₄	—	14	2	no	—
487	C₂×C₄	—	14	2	no	—
488	C₂×C₄	—	28	4	no	—
489	C₂×C₄	—	28	2	no	—
490	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
491	C₂×C₄	C₂×#1157	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
493	C₂×C₄	C₂×#1159	1	1	yes	characteristic
494	C₂×C₄	D₇×#41	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
496	C₈	—	4	2	no	—
497	C₈	—	14	2	no	—
498	C₈	—	14	4	no	—
499	C₈	—	14	2	no	—
500	C₈	C₄×C₂²⋊D₇	1	1	yes	characteristic
501	C₈	C₄×C₂²⋊D₇	1	1	yes	characteristic
502	C₈	C₄×C₂²⋊D₇	1	1	yes	characteristic
503	C₈	C₄×C₂²⋊D₇	1	1	yes	characteristic
504	C₈	#6501	1	1	yes	characteristic
505	C₈	#6501	1	1	yes	characteristic
506	C₈	#6501	1	1	yes	characteristic
507	C₈	#6501	1	1	yes	characteristic
508	C₇	#21558	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	14	2	no	—
513	C₂²	—	28	2	no	—
514	C₂²	C₄×#1159	1	1	yes	characteristic
515	C₂²	#90239	1	1	yes	characteristic
516	C₂²	#90519	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	14	2	no	—
521	C₄	—	28	2	no	—
522	C₄	—	56	2	no	—
523	C₄	C₄×D₄×D₇	1	1	yes	characteristic
524	C₄	#90248	1	1	yes	characteristic
525	C₄	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
526	C₄	C₂×#6501	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	2	no	—
531	C₂	—	28	2	no	—
532	C₂	C₄×#6501	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#6501
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₂×C₇×#443	C₂
socle	C₂×C₇	C₄×#121
prime radical	#11741373	C₂
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	C₂×#443	D₇
hypocenter	C₇	#21558
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#443	C₂	semidirect
3. #11741237	C₂	semidirect
4. C₄×#6464	C₂	semidirect
5. #11729840	C₂	semidirect
6. #11729765	C₂	semidirect
7. #11728473	C₂	semidirect
8. #11728460	C₂	semidirect
9. #11728145	C₂	semidirect
10. #11728132	C₂	semidirect
11. #11727533	C₂	semidirect
28. #89964	C₄	semidirect
29. #89949	C₄	semidirect
30. #89932	C₄	semidirect
55. C₂×C₇×Q₁₆	C₂×C₄	semidirect
56. C₂×C₇×SD₁₆	C₂×C₄	semidirect
57. C₂×C₇×D₈	C₂×C₄	semidirect
104. #6410	C₂×C₄	semidirect
106. #6407	C₂×C₄	semidirect
109. #6393	C₂×C₄	semidirect
110. #6393	C₂×C₄	semidirect
123. C₂×#443	D₇	semidirect
301. C₂×Q₁₆	C₄×D₇	semidirect
302. C₂×SD₁₆	C₄×D₇	semidirect
303. C₂×D₈	C₄×D₇	semidirect
508. C₇	#21558	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#443	2
#11741373	2
#11741237	2
C₄×#6464	2
#11729840	2
#11729765	2
#11728473	2
#11728460	2
#11728145	2
#11728132	2
#11727533	2
#21558	7