Subgroups — #32004385

Order 18176.

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	#22598056	C₂	1	1	yes	maximal, characteristic
2	#22597241	C₂	1	2	yes	maximal, complemented
3	C₄×#14556134	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589239	C₂	1	1	yes	maximal, characteristic, complemented
5	#22589128	C₂	1	1	yes	maximal, characteristic, complemented
6	#22589006	C₂	1	2	yes	maximal, complemented
7	#22588844	C₂	1	2	yes	maximal, complemented
8	#22588395	C₂	1	1	yes	maximal, characteristic, complemented
9	#22588219	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588140	C₂	1	2	yes	maximal, complemented
11	C₂×#443×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#17986797	C₂²	1	2	yes	—
13	C₂×#14556134	C₂²	1	1	yes	characteristic
14	C₂×#14556134	C₂²	1	1	yes	characteristic
15	C₄×#11765865	C₂²	1	1	yes	characteristic
16	#17986271	C₄	1	2	yes	complemented
17	#17986266	C₄	1	2	yes	complemented
18	#17986259	C₄	1	4	yes	complemented
19	#17986119	—	2	4	no	—
20	#17986114	—	2	4	no	—
21	#17986047	C₂²	1	2	yes	—
22	C₂×#14556064	C₂²	1	1	yes	characteristic
23	#17986037	C₂²	1	1	yes	characteristic
24	#17986016	C₂²	1	2	yes	—
25	#17986015	C₂²	1	2	yes	—
26	#17985983	C₂²	1	2	yes	—
27	#17985973	C₂²	1	2	yes	—
28	#17985954	C₂²	1	1	yes	characteristic
29	#17985954	C₂²	1	2	yes	—
30	#17985954	C₂²	1	1	yes	characteristic
31	#17985953	—	2	1	no	—
32	#17985953	—	2	1	no	—
33	C₄×#11765849	C₂²	1	1	yes	characteristic
34	C₄×#11765848	—	2	1	no	—
35	C₄×C₈×D₇₁	—	2	1	no	—
36	#17985770	C₂²	1	2	yes	—
37	#17985770	C₂²	1	2	yes	—
38	#17985759	C₂²	1	2	yes	—
39	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
40	C₂×#131×C₇₁	C₂²	1	2	yes	—
41	#443×C₇₁	—	2	1	no	—
42	#443×C₇₁	—	2	1	no	—
43	#443×C₇₁	—	2	1	no	—
44	#443×C₇₁	—	2	1	no	—
45	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
46	C₂×#104×C₇₁	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×#11765865	C₂³	1	1	yes	characteristic
49	#14556159	C₂×C₄	1	4	yes	—
50	#14556158	—	2	2	no	—
51	#14556154	C₂×C₄	1	4	yes	—
52	#14556153	—	2	2	no	—
53	#14556148	—	2	4	no	—
54	#14556134	—	2	1	no	—
55	#14556134	—	2	1	no	—
56	#14556134	—	2	1	no	—
57	#14556134	—	2	1	no	—
58	#14556134	C₂×C₄	1	2	yes	—
59	#14556134	C₂×C₄	1	2	yes	—
60	#14556134	D₄	1	2	yes	—
61	#14556134	D₄	1	2	yes	—
62	C₂×#11765849	C₂³	1	1	yes	characteristic
63	C₂×#11765849	C₂³	1	2	yes	—
64	C₂×#11765849	C₂³	1	1	yes	characteristic
65	C₂×#11765848	—	2	1	no	—
66	C₂×#11765848	—	2	1	no	—
67	C₂×C₈×D₇₁	—	2	1	no	—
68	C₂×C₈×D₇₁	—	2	1	no	—
69	C₄×Dic₁₄₂	—	2	1	no	—
70	C₄×D₂₈₄	—	2	1	no	—
71	C₄×C₂²⋊D₇₁	—	2	2	no	—
72	#14556087	C₂³	1	2	yes	—
73	#14556087	C₂³	1	1	yes	characteristic
74	#14556085	—	2	1	no	—
75	C₄²×D₇₁	—	2	1	no	—
76	#14556064	C₂×C₄	1	2	yes	complemented
77	#14556064	C₂×C₄	1	2	yes	complemented
78	#14556063	—	2	4	no	—
79	#14556062	—	2	1	no	—
80	#14556060	—	2	1	no	—
81	#14556055	—	2	4	no	—
82	#14556054	—	2	4	no	—
83	#14556047	C₂×C₄	1	4	yes	complemented
84	#14556045	C₂×C₄	1	4	yes	complemented
85	#14556043	—	2	4	no	—
86	#14556039	—	2	1	no	—
87	#14556038	—	2	2	no	—
88	#14556038	—	2	1	no	—
89	#14556038	—	2	1	no	—
90	C₄×C₇₁⋊C₈	—	2	1	no	—
91	C₈×Dic₇₁	—	2	2	no	—
92	C₈×Dic₇₁	—	2	1	no	—
93	C₈×Dic₇₁	—	2	1	no	—
94	C₂×#41×C₇₁	C₂³	1	2	yes	—
95	#135×C₇₁	—	2	1	no	—
96	#135×C₇₁	—	2	1	no	—
97	#135×C₇₁	—	2	1	no	—
98	#135×C₇₁	—	2	1	no	—
99	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
101	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
102	#131×C₇₁	—	2	2	no	—
103	#131×C₇₁	—	2	2	no	—
104	#131×C₇₁	—	2	2	no	—
105	#131×C₇₁	—	2	2	no	—
106	C₂×M₁₆×C₇₁	—	2	2	no	—
107	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
108	C₂²×C₈×C₇₁	—	2	2	no	—
109	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
112	#108×C₇₁	—	2	1	no	—
113	#108×C₇₁	—	2	1	no	—
114	#104×C₇₁	—	2	2	no	—
115	#104×C₇₁	—	2	2	no	—
116	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
117	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
118	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
119	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
120	#11765865	—	2	1	no	—
121	#11765865	—	2	1	no	—
122	#11765865	C₂²×C₄	1	2	yes	—
123	#11765865	C₂×D₄	1	2	yes	—
124	C₂×Dic₁₄₂	#41	1	1	yes	characteristic
125	C₂×D₂₈₄	#41	1	1	yes	characteristic
126	C₂×C₂²⋊D₇₁	—	2	1	no	—
127	C₂×C₄×D₇₁	—	2	1	no	—
128	C₂×C₄×D₇₁	—	2	2	no	—
129	#11765855	—	2	4	no	—
130	#11765853	—	2	4	no	—
131	#11765852	—	2	4	no	—
132	#11765850	—	2	4	no	—
133	#11765849	—	2	1	no	—
134	#11765849	—	2	1	no	—
135	#11765849	—	2	2	no	—
136	#11765849	C₂²×C₄	1	2	yes	—
137	#11765849	C₂²×C₄	1	4	yes	—
138	#11765849	C₂×D₄	1	2	yes	—
139	#11765848	—	2	2	no	—
140	#11765848	—	2	2	no	—
141	#11765848	—	2	2	no	—
142	#11765848	—	2	2	no	—
143	C₂×C₇₁⋊C₈	—	2	1	no	—
144	C₂×C₇₁⋊C₈	—	2	1	no	—
145	C₂×C₇₁⋊C₈	—	2	2	no	—
146	C₈×D₇₁	—	2	2	no	—
147	C₈×D₇₁	—	2	2	no	—
148	C₈×D₇₁	—	2	2	no	—
149	C₈×D₇₁	—	2	2	no	—
150	C₄⋊Dic₇₁	—	2	1	no	—
151	C₄⋊Dic₇₁	—	2	2	no	—
152	Dic₇₁⋊C₄	—	2	2	no	—
153	C₂²⋊Dic₇₁	—	2	2	no	—
154	C₂²⋊Dic₇₁	#41	1	2	yes	—
155	(C₂×D₇₁)⋊C₄	—	2	2	no	—
156	C₄×Dic₇₁	—	2	2	no	—
157	C₄×Dic₇₁	—	2	1	no	—
158	C₄×Dic₇₁	—	2	2	no	—
159	#41×C₇₁	—	2	2	no	—
160	#41×C₇₁	—	2	2	no	—
161	#41×C₇₁	—	2	2	no	—
162	#41×C₇₁	—	2	2	no	—
163	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₇₁	—	2	2	no	—
165	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₇₁	—	2	1	no	—
167	C₂²×C₄×C₇₁	—	2	2	no	—
168	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₇₁	—	2	1	no	—
170	Q₁₆×C₇₁	—	2	1	no	—
171	SD₁₆×C₇₁	—	2	2	no	—
172	SD₁₆×C₇₁	—	2	2	no	—
173	D₈×C₇₁	—	2	1	no	—
174	D₈×C₇₁	—	2	1	no	—
175	M₁₆×C₇₁	—	2	2	no	—
176	M₁₆×C₇₁	—	2	2	no	—
177	M₁₆×C₇₁	—	4	2	no	—
178	M₁₆×C₇₁	—	4	2	no	—
179	C₂×C₈×C₇₁	—	2	2	no	—
180	C₂×C₈×C₇₁	—	4	2	no	—
181	C₂×C₈×C₇₁	—	4	2	no	—
182	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
191	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
192	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
193	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
194	C₄²×C₇₁	—	2	1	no	—
195	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₇₁	—	2	2	no	—
198	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
199	C₂²×D₇₁	—	2	1	no	—
200	Q₈×C₇₁	—	2	2	no	—
201	Q₈×C₇₁	—	2	2	no	—
202	D₄×C₇₁	—	2	2	no	—
203	D₄×C₇₁	—	2	2	no	—
204	D₄×C₇₁	—	4	2	no	—
205	D₄×C₇₁	—	4	2	no	—
206	C₂×C₄×C₇₁	—	2	1	no	—
207	C₂×C₄×C₇₁	—	2	2	no	—
208	C₂×C₄×C₇₁	—	2	1	no	—
209	C₂×C₄×C₇₁	—	4	2	no	—
210	C₂×C₄×C₇₁	—	4	2	no	—
211	C₂×C₄×C₇₁	—	4	2	no	—
212	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
218	C₂²⋊D₇₁	—	2	2	no	—
219	C₂²⋊D₇₁	—	2	2	no	—
220	C₂×Dic₇₁	—	2	1	no	—
221	C₂×Dic₇₁	—	2	2	no	—
222	C₂×Dic₇₁	—	4	2	no	—
223	D₂₈₄	—	2	1	no	—
224	D₂₈₄	C₄×D₄	1	2	yes	—
225	C₄×D₇₁	—	2	2	no	—
226	C₄×D₇₁	—	2	2	no	—
227	C₄×D₇₁	—	4	4	no	—
228	Dic₁₄₂	—	2	1	no	—
229	Dic₁₄₂	C₄×D₄	1	2	yes	—
230	C₈×C₇₁	—	4	2	no	—
231	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
232	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
233	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
234	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
235	C₈×C₇₁	#121	1	1	yes	characteristic
236	C₈×C₇₁	#121	1	1	yes	characteristic
237	C₈×C₇₁	#121	1	1	yes	characteristic
238	C₈×C₇₁	#121	1	1	yes	characteristic
239	C₇₁⋊C₈	—	2	2	no	—
240	C₇₁⋊C₈	—	2	4	no	—
241	C₇₁⋊C₈	—	2	2	no	—
242	C₂²×C₇₁	—	4	1	no	—
243	C₂²×C₇₁	—	4	2	no	—
244	C₂²×C₇₁	—	8	2	no	—
245	C₂²×C₇₁	C₄×#41	1	1	yes	characteristic
246	C₂²×C₇₁	#525	1	1	yes	characteristic
247	C₂²×C₇₁	#532	1	1	yes	characteristic
248	C₂×D₇₁	—	2	2	no	—
249	C₂×D₇₁	—	4	2	no	—
250	C₄×C₇₁	—	2	2	no	—
251	C₄×C₇₁	—	4	1	no	—
252	C₄×C₇₁	—	4	2	no	—
253	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₇₁	C₂×#121	1	1	yes	characteristic
256	C₄×C₇₁	#529	1	1	yes	characteristic
257	Dic₇₁	—	2	2	no	—
258	Dic₇₁	—	4	2	no	—
259	Dic₇₁	—	8	2	no	—
260	#21558	—	71	1	no	maximal, Sylow
261	C₂×C₇₁	—	2	1	no	—
262	C₂×C₇₁	—	2	1	no	—
263	C₂×C₇₁	—	2	1	no	—
264	C₂×C₇₁	—	8	2	no	—
265	C₂×C₇₁	C₄×#121	1	1	yes	characteristic
266	D₇₁	—	4	2	no	—
267	#3067	—	71	1	no	—
268	#2955	—	71	2	no	—
269	C₂×#443	D₇₁	1	1	yes	characteristic, complemented
270	C₄×#131	—	71	1	no	—
271	#1976	—	71	1	no	—
272	#1953	—	71	1	no	—
273	#1932	—	71	2	no	—
274	#1906	—	71	2	no	—
275	#1814	—	71	1	no	—
276	#1772	—	71	1	no	—
277	#1757	—	71	2	no	—
278	C₇₁	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	—	71	2	no	—
280	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
281	C₂×#131	—	71	1	no	—
282	C₂×#131	—	71	1	no	—
283	C₂×#131	C₂×D₇₁	1	2	yes	—
284	C₄×#41	—	71	1	no	—
285	#473	—	71	2	no	—
286	#472	—	71	2	no	—
287	#471	—	71	4	no	—
288	#444	—	142	4	no	—
289	#443	—	2	1	no	—
290	#443	—	2	1	no	—
291	#443	—	2	1	no	—
292	#443	—	2	1	no	—
293	#443	—	142	4	no	—
294	#430	—	71	2	no	—
295	C₂×#108	—	71	1	no	—
296	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
297	#427	—	71	1	no	—
298	#421	—	71	2	no	—
299	#421	—	71	2	no	—
300	C₂×#104	C₂×D₇₁	1	2	yes	—
301	#413	—	71	2	no	—
302	#410	—	71	2	no	—
303	#405	—	71	1	no	—
304	#405	—	71	1	no	—
305	#405	—	71	2	no	—
306	#405	—	142	1	no	—
307	#405	—	142	1	no	—
308	C₄×M₁₆	—	71	1	no	—
309	C₄×M₁₆	—	142	1	no	—
310	C₂×C₄×C₈	—	142	1	no	—
311	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
312	#344	—	71	2	no	—
313	#344	—	71	2	no	—
314	#339	—	71	2	no	—
315	C₂×#41	—	71	1	no	—
316	C₂×#41	C₂²×D₇₁	1	2	yes	—
317	#137	—	71	4	no	—
318	#137	—	142	2	no	—
319	AGL(1,ℤ/8)	—	71	4	no	—
320	AGL(1,ℤ/8)	—	142	2	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	#135	—	142	4	no	—
326	C₂×Q₁₆	C₄×D₇₁	1	1	yes	characteristic, complemented
327	C₂×SD₁₆	C₄×D₇₁	1	2	yes	complemented
328	C₂×D₈	C₄×D₇₁	1	1	yes	characteristic, complemented
329	#131	—	2	2	no	—
330	#131	—	2	2	no	—
331	#131	—	2	2	no	—
332	#131	—	2	2	no	—
333	#131	—	71	2	no	—
334	#131	—	71	2	no	—
335	#131	—	71	2	no	—
336	#131	—	71	2	no	—
337	#131	—	142	1	no	—
338	#131	—	142	1	no	—
339	#131	—	142	1	no	—
340	#131	—	142	1	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	71	1	no	—
343	C₂×M₁₆	—	71	1	no	—
344	C₂×M₁₆	—	71	2	no	—
345	C₂×M₁₆	—	142	1	no	—
346	C₂×M₁₆	—	142	1	no	—
347	C₂×M₁₆	C₂²×D₇₁	1	2	yes	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	—	142	1	no	—
350	C₂²×C₈	—	142	1	no	—
351	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
353	C₄×Q₈	—	142	1	no	—
354	C₄×D₄	—	142	1	no	—
355	C₄×D₄	—	142	2	no	—
356	#117	—	71	1	no	—
357	#117	—	71	2	no	—
358	#117	—	142	1	no	—
359	C₂×C₄²	—	142	1	no	—
360	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
361	#108	—	2	1	no	—
362	#108	—	2	1	no	—
363	#108	—	71	2	no	—
364	#108	—	71	2	no	—
365	#108	—	142	4	no	—
366	#107	—	142	1	no	—
367	#106	—	142	1	no	—
368	#104	—	2	2	no	—
369	#104	—	2	2	no	—
370	#104	—	142	4	no	—
371	#104	—	142	4	no	—
372	#101	—	71	4	no	—
373	#100	—	71	4	no	—
374	#99	—	142	4	no	—
375	#97	—	142	2	no	—
376	#97	—	142	1	no	—
377	#97	—	142	1	no	—
378	#97	—	142	1	no	—
379	C₄×C₈	—	142	2	no	—
380	C₄×C₈	—	142	1	no	—
381	C₄×C₈	—	142	1	no	—
382	C₄×C₈	—	142	1	no	—
383	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
384	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
385	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
386	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	71	2	no	—
392	#41	—	71	2	no	—
393	#41	—	142	1	no	—
394	#41	—	142	1	no	—
395	C₂×Q₈	—	71	1	no	—
396	C₂×Q₈	C₂×C₄×D₇₁	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	71	1	no	—
399	C₂×D₄	—	142	1	no	—
400	C₂×D₄	C₂×C₄×D₇₁	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	142	2	no	—
404	C₂²×C₄	—	142	1	no	—
405	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
406	Q₁₆	—	2	1	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	142	4	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	142	4	no	—
412	SD₁₆	—	142	4	no	—
413	D₈	—	2	1	no	—
414	D₈	—	2	1	no	—
415	D₈	—	142	4	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	4	2	no	—
419	M₁₆	—	4	2	no	—
420	M₁₆	—	71	2	no	—
421	M₁₆	—	71	4	no	—
422	M₁₆	—	71	2	no	—
423	M₁₆	—	142	2	no	—
424	M₁₆	—	142	1	no	—
425	M₁₆	—	142	1	no	—
426	M₁₆	—	142	2	no	—
427	M₁₆	—	142	2	no	—
428	M₁₆	—	142	2	no	—
429	M₁₆	—	142	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	4	2	no	—
432	C₂×C₈	—	4	2	no	—
433	C₂×C₈	—	142	2	no	—
434	C₂×C₈	—	142	1	no	—
435	C₂×C₈	—	142	1	no	—
436	C₂×C₈	—	142	2	no	—
437	C₂×C₈	—	142	2	no	—
438	C₂×C₈	—	142	2	no	—
439	C₂×C₈	—	142	2	no	—
440	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
441	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
442	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
443	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
444	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
445	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
446	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
447	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
448	C₂×C₈	#11765864	1	1	yes	characteristic
449	C₂×C₈	#11765864	1	1	yes	characteristic
450	C₂×C₈	#11765865	1	1	yes	characteristic
451	C₂×C₈	#11765865	1	1	yes	characteristic
452	C₄⋊C₄	—	142	2	no	—
453	C₄⋊C₄	—	142	2	no	—
454	C₄⋊C₄	—	142	1	no	—
455	C₂²⋊C₄	—	71	2	no	—
456	C₂²⋊C₄	—	142	2	no	—
457	C₂²⋊C₄	—	142	2	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	142	2	no	—
460	C₄²	—	142	2	no	—
461	C₄²	—	142	1	no	—
462	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
463	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
464	C₂³	—	2	2	no	—
465	C₂³	—	142	1	no	—
466	C₂³	#41×D₇₁	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	71	2	no	—
470	Q₈	—	142	1	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	71	2	no	—
476	D₄	—	142	2	no	—
477	D₄	—	142	2	no	—
478	D₄	—	142	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	284	4	no	—
486	C₂×C₄	—	284	2	no	—
487	C₂×C₄	—	142	2	no	—
488	C₂×C₄	—	142	1	no	—
489	C₂×C₄	—	142	2	no	—
490	C₂×C₄	—	142	2	no	—
491	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
494	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
496	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
497	C₈	—	4	2	no	—
498	C₈	—	142	4	no	—
499	C₈	—	142	2	no	—
500	C₈	—	142	2	no	—
501	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
502	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
503	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
504	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
505	C₈	#14556099	1	1	yes	characteristic
506	C₈	#14556099	1	1	yes	characteristic
507	C₈	#14556099	1	1	yes	characteristic
508	C₈	#14556099	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	284	2	no	—
513	C₂²	—	142	2	no	—
514	C₂²	C₄×#11765864	1	1	yes	characteristic
515	C₂²	#17986506	1	1	yes	characteristic
516	C₂²	#17986546	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	284	2	no	—
521	C₄	—	568	2	no	—
522	C₄	—	142	2	no	—
523	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
524	C₄	C₂×C₄×C₂²⋊D₇₁	1	1	yes	characteristic
525	C₄	C₂×#14556099	1	1	yes	characteristic
526	C₄	#17986531	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	—	284	2	no	—
532	C₂	C₄×#14556099	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14556099
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₂×#443×C₇₁	C₂
socle	C₂×C₇₁	C₄×#121
prime radical	#22598056	C₂
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	C₂×#443	D₇₁
hypocenter	C₇₁	#21558
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. #22597241	C₂	semidirect
3. C₄×#14556134	C₂	semidirect
4. #22589239	C₂	semidirect
5. #22589128	C₂	semidirect
6. #22589006	C₂	semidirect
7. #22588844	C₂	semidirect
8. #22588395	C₂	semidirect
9. #22588219	C₂	semidirect
10. #22588140	C₂	semidirect
11. C₂×#443×C₇₁	C₂	semidirect
16. #17986271	C₄	semidirect
17. #17986266	C₄	semidirect
18. #17986259	C₄	semidirect
76. #14556064	C₂×C₄	semidirect
77. #14556064	C₂×C₄	semidirect
83. #14556047	C₂×C₄	semidirect
84. #14556045	C₂×C₄	semidirect
99. C₂×Q₁₆×C₇₁	C₂×C₄	semidirect
100. C₂×SD₁₆×C₇₁	C₂×C₄	semidirect
101. C₂×D₈×C₇₁	C₂×C₄	semidirect
269. C₂×#443	D₇₁	semidirect
278. C₇₁	#21558	semidirect
326. C₂×Q₁₆	C₄×D₇₁	semidirect
327. C₂×SD₁₆	C₄×D₇₁	semidirect
328. C₂×D₈	C₄×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22598056	2
#22597241	2
C₄×#14556134	2
#22589239	2
#22589128	2
#22589006	2
#22588844	2
#22588395	2
#22588219	2
#22588140	2
C₂×#443×C₇₁	2
#21558	71