Subgroups — #72343240

Order 4096.

At least 6559 conjugacy classes of subgroups; only the 1479 normal subgroups are shown.

The subgroup lattice has 776 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72343227	C₂	1	1	yes	maximal, characteristic, complemented
2	#72343221	C₂	1	2	yes	maximal, complemented
3	#72343212	C₂	1	2	yes	maximal, complemented
4	#72343205	C₂	1	2	yes	maximal, complemented
5	#72343192	C₂	1	2	yes	maximal, complemented
6	#72343189	C₂²	1	2	yes	—
7	#72343172	C₂	1	2	yes	maximal, complemented
8	#72343170	C₂	1	2	yes	maximal, complemented
9	#72343163	C₂	1	4	yes	maximal, complemented
10	#72343161	C₂²	1	4	yes	—
11	#72343157	C₂	1	4	yes	maximal, complemented
12	#72343154	C₂²	1	4	yes	—
13	#72343154	C₂²	1	2	yes	—
14	#72343150	C₂²	1	4	yes	—
15	#72343148	C₂²	1	4	yes	complemented
16	#72343148	C₂²	1	4	yes	complemented
17	#72343148	C₂²	1	4	yes	complemented
18	#72343010	C₂	1	1	yes	maximal, characteristic
19	#72343007	C₂²	1	2	yes	—
20	#72343002	C₄	1	4	yes	—
21	#72343000	C₂²	1	2	yes	—
22	#72342994	C₄	1	2	yes	—
23	#72342991	C₂²	1	4	yes	—
24	#72342989	C₄	1	2	yes	—
25	#72342959	C₄	1	2	yes	—
26	#72342931	C₄	1	2	yes	—
27	#72342902	C₄	1	1	yes	characteristic
28	#72321514	C₄	1	1	yes	characteristic
29	#72321074	C₄	1	1	yes	characteristic
30	#72320761	C₄	1	1	yes	characteristic
31	#72319792	C₂	1	1	yes	maximal, characteristic, complemented
32	#72319723	C₂²	1	1	yes	characteristic
33	#72319611	C₂²	1	1	yes	characteristic
34	#72319506	C₂²	1	1	yes	characteristic
35	#72319283	C₂	1	1	yes	maximal, characteristic, complemented
36	#72319273	C₂²	1	2	yes	—
37	#72319258	C₂²	1	2	yes	—
38	#72319258	C₂²	1	4	yes	—
39	#72319246	C₂²	1	2	yes	complemented
40	#72319246	C₂²	1	4	yes	complemented
41	#72319240	C₂²	1	2	yes	complemented
42	#72319240	C₂²	1	4	yes	complemented
43	#72287831	C₂	1	1	yes	maximal, characteristic, complemented
44	#72287825	C₂²	1	2	yes	—
45	#72287821	C₂²	1	2	yes	—
46	#72287815	C₂²	1	4	yes	—
47	#72287764	C₂²	1	1	yes	characteristic
48	#72287764	C₂²	1	1	yes	characteristic
49	#72287633	C₂²	1	1	yes	characteristic
50	#72287622	C₂²	1	2	yes	—
51	#72287536	C₂²	1	2	yes	—
52	#72287462	C₂	1	1	yes	maximal, characteristic, complemented
53	#72287460	C₂	1	2	yes	maximal, complemented
54	#72287454	C₂²	1	4	yes	—
55	#72287453	C₂²	1	2	yes	—
56	#72287450	C₂²	1	4	yes	—
57	#72287450	C₂²	1	2	yes	—
58	#72287445	C₂²	1	4	yes	complemented
59	#72287445	C₂²	1	4	yes	complemented
60	#72287445	C₂²	1	4	yes	complemented
61	#72287362	C₂²	1	1	yes	characteristic
62	#72287291	C₂²	1	2	yes	—
63	#72287156	C₂²	1	1	yes	characteristic
64	#72287154	C₂²	1	2	yes	—
65	#72287154	C₂²	1	2	yes	—
66	#72286336	C₂²	1	2	yes	complemented
67	#72286336	C₂²	1	2	yes	complemented
68	#72286336	C₂²	1	2	yes	complemented
69	#72224969	C₂	1	2	yes	maximal, complemented
70	#72224968	C₂	1	1	yes	maximal, characteristic, complemented
71	#72224963	C₂²	1	2	yes	complemented
72	#72224963	C₂²	1	4	yes	complemented
73	#72224962	C₂²	1	2	yes	—
74	#72224961	C₂²	1	4	yes	—
75	#72224958	C₂²	1	2	yes	complemented
76	#72224958	C₂²	1	4	yes	complemented
77	#72224957	C₂²	1	4	yes	—
78	#72224957	C₂²	1	2	yes	—
79	#72224956	C₂²	1	1	yes	characteristic, complemented
80	#72224956	C₂²	1	2	yes	complemented
81	#72224955	C₂²	1	2	yes	complemented
82	#72224955	C₂²	1	1	yes	characteristic, complemented
83	#72224951	C₂²	1	1	yes	characteristic, complemented
84	#72224951	C₂²	1	2	yes	complemented
85	#72224948	C₂²	1	1	yes	characteristic, complemented
86	#72217290	C₂²	1	1	yes	characteristic
87	#72217287	C₂²	1	2	yes	—
88	#72217274	C₂²	1	2	yes	—
89	#72217272	C₂²	1	1	yes	characteristic
90	#72216670	C₂²	1	1	yes	characteristic
91	#72216668	C₂²	1	2	yes	—
92	#10574593	C₂³	1	1	yes	characteristic
93	#7622779	C₂×C₄	1	2	yes	—
94	#7622779	C₂×C₄	1	2	yes	—
95	#7622779	D₄	1	4	yes	—
96	#7622775	C₂×C₄	1	1	yes	characteristic
97	#7622775	C₂×C₄	1	1	yes	characteristic
98	#7622775	D₄	1	2	yes	—
99	#7622758	C₂×C₄	1	1	yes	characteristic
100	#7622758	C₂×C₄	1	1	yes	characteristic
101	#7622758	D₄	1	2	yes	—
102	#7622739	C₂³	1	1	yes	characteristic
103	#7622739	C₂³	1	1	yes	characteristic
104	#7622738	C₂³	1	2	yes	—
105	#7622738	C₂³	1	2	yes	—
106	#7622661	C₂³	1	1	yes	characteristic
107	#7622661	C₂³	1	1	yes	characteristic
108	#7622660	C₂³	1	2	yes	—
109	#7622660	C₂³	1	2	yes	—
110	#7622628	C₂³	1	1	yes	characteristic
111	#7622588	C₂³	1	2	yes	—
112	#6469078	C₂³	1	4	yes	—
113	#6469078	C₂³	1	2	yes	—
114	#6342500	C₂³	1	1	yes	characteristic
115	#6342500	C₂³	1	2	yes	—
116	#6342482	C₂³	1	2	yes	—
117	#6342482	C₂³	1	1	yes	characteristic
118	#512043	C₂×C₄	1	2	yes	—
119	#512038	C₂×C₄	1	4	yes	—
120	#512038	C₂×C₄	1	2	yes	—
121	#511935	C₂×C₄	1	2	yes	—
122	#511930	C₂×C₄	1	2	yes	—
123	#511930	C₂×C₄	1	4	yes	—
124	#506210	C₂×C₄	1	4	yes	—
125	#506209	C₂×C₄	1	2	yes	—
126	#506208	C₂×C₄	1	2	yes	—
127	#506207	C₂×C₄	1	4	yes	—
128	#505707	C₂×C₄	1	2	yes	—
129	#505706	C₂×C₄	1	1	yes	characteristic
130	#505705	C₂×C₄	1	1	yes	characteristic
131	#505704	C₂×C₄	1	2	yes	—
132	#500853	C₂×C₄	1	2	yes	—
133	#500852	C₂×C₄	1	1	yes	characteristic
134	#500851	C₂×C₄	1	1	yes	characteristic
135	#500850	C₂×C₄	1	2	yes	—
136	#496723	C₂³	1	4	yes	—
137	#496723	C₂³	1	2	yes	—
138	#496469	C₂³	1	4	yes	—
139	#496469	C₂³	1	2	yes	—
140	#496303	C₂³	1	2	yes	—
141	#496303	C₂³	1	4	yes	—
142	#494212	C₂³	1	1	yes	characteristic
143	#494212	C₂³	1	2	yes	—
144	#494051	C₂³	1	4	yes	—
145	#494051	C₂³	1	2	yes	—
146	#494015	C₂³	1	2	yes	—
147	#494015	C₂³	1	4	yes	—
148	#493203	C₂³	1	4	yes	—
149	#493203	C₂³	1	2	yes	—
150	#483414	C₂³	1	1	yes	characteristic
151	#483414	C₂³	1	2	yes	—
152	#483327	C₂³	1	1	yes	characteristic
153	#481290	C₂³	1	4	yes	—
154	#481290	C₂³	1	2	yes	—
155	#481073	C₂³	1	2	yes	—
156	#480436	C₂³	1	2	yes	—
157	#480436	C₂³	1	4	yes	—
158	#479976	C₂³	1	2	yes	—
159	#479976	C₂³	1	2	yes	—
160	#479976	C₂³	1	2	yes	—
161	#479968	D₄	1	2	yes	complemented
162	#479968	D₄	1	1	yes	characteristic, complemented
163	#479968	C₂³	1	1	yes	characteristic
164	#479968	C₂³	1	2	yes	—
165	#479966	D₄	1	2	yes	complemented
166	#479966	D₄	1	1	yes	characteristic, complemented
167	#479961	D₄	1	2	yes	complemented
168	#479961	D₄	1	1	yes	characteristic, complemented
169	#479961	C₂³	1	2	yes	—
170	#479961	C₂³	1	1	yes	characteristic
171	#479960	D₄	1	2	yes	complemented
172	#479960	D₄	1	1	yes	characteristic, complemented
173	#479960	C₂³	1	2	yes	—
174	#479960	C₂³	1	1	yes	characteristic
175	#479959	D₄	1	1	yes	characteristic, complemented
176	#479959	D₄	1	1	yes	characteristic, complemented
177	#479958	D₄	1	2	yes	complemented
178	#479958	D₄	1	2	yes	complemented
179	#479908	D₄	1	1	yes	characteristic, complemented
180	#479908	D₄	1	2	yes	complemented
181	#479908	C₂³	1	1	yes	characteristic
182	C₂×#11404	D₄	1	1	yes	characteristic, complemented
183	C₂²×#1313	D₄	1	2	yes	complemented
184	#139582	C₂×C₄	1	4	yes	—
185	#139581	C₂×C₄	1	2	yes	—
186	#139580	C₂×C₄	1	4	yes	—
187	#139579	C₂×C₄	1	2	yes	—
188	#139578	C₂×C₄	1	4	yes	—
189	#139577	C₂×C₄	1	4	yes	—
190	#139577	C₂×C₄	1	4	yes	—
191	#139576	C₂×C₄	1	4	yes	—
192	#139575	C₂×C₄	1	2	yes	—
193	#139574	C₂×C₄	1	4	yes	—
194	#139573	C₂×C₄	1	2	yes	—
195	#139572	C₂×C₄	1	4	yes	—
196	#139571	C₂×C₄	1	4	yes	—
197	#139571	C₂×C₄	1	4	yes	—
198	#134778	C₂×C₄	1	2	yes	—
199	#134777	C₂×C₄	1	1	yes	characteristic
200	#134776	C₂×C₄	1	2	yes	—
201	#134775	C₂×C₄	1	1	yes	characteristic
202	#134774	C₂×C₄	1	2	yes	—
203	#134773	C₂×C₄	1	2	yes	—
204	#134773	C₂×C₄	1	2	yes	—
205	#134750	C₂×C₄	1	2	yes	—
206	#134749	C₂×C₄	1	4	yes	—
207	#134748	C₂×C₄	1	2	yes	—
208	#134747	C₂×C₄	1	4	yes	—
209	#127410	C₂³	1	2	yes	—
210	#127410	C₂³	1	4	yes	—
211	#127356	C₂³	1	4	yes	—
212	#127356	C₂³	1	2	yes	—
213	#127316	C₂³	1	4	yes	—
214	#127316	C₂³	1	4	yes	—
215	#127316	C₂³	1	4	yes	—
216	#127134	C₂³	1	4	yes	—
217	#127134	C₂³	1	4	yes	—
218	#127134	C₂³	1	4	yes	—
219	#126873	C₂³	1	4	yes	—
220	#126873	C₂³	1	2	yes	—
221	#126851	C₂³	1	2	yes	—
222	#126851	C₂³	1	4	yes	—
223	#126723	C₂³	1	2	yes	—
224	#126723	C₂³	1	4	yes	—
225	#41²	#41	1	1	yes	characteristic
226	#62635	C₂²×C₄	1	1	yes	characteristic
227	#60308	C₂²×C₄	1	1	yes	characteristic
228	#60308	C₂×D₄	1	1	yes	characteristic
229	#60305	C₂²×C₄	1	1	yes	characteristic
230	#60305	C₂²×C₄	1	2	yes	—
231	#60305	C₂×D₄	1	1	yes	characteristic
232	#60305	C₂×D₄	1	2	yes	—
233	#60280	#41	1	1	yes	characteristic
234	#60280	#41	1	2	yes	—
235	#60204	C₂⁴	1	2	yes	—
236	#60204	C₂⁴	1	1	yes	characteristic
237	#60183	C₂⁴	1	2	yes	—
238	#33494	C₂²×C₄	1	2	yes	—
239	#33494	C₂²×C₄	1	2	yes	—
240	#33494	C₂×D₄	1	4	yes	—
241	#33493	C₂²×C₄	1	1	yes	characteristic
242	#33493	C₂²×C₄	1	1	yes	characteristic
243	#33493	C₂×D₄	1	2	yes	—
244	#33492	C₂²×C₄	1	2	yes	—
245	#33492	C₂×D₄	1	2	yes	—
246	#33491	C₂²×C₄	1	2	yes	—
247	#33491	C₂²×C₄	1	2	yes	—
248	#33491	C₂×D₄	1	4	yes	—
249	#33475	#41	1	2	yes	—
250	#33475	#41	1	2	yes	—
251	#33475	#41	1	4	yes	—
252	#33474	#41	1	1	yes	characteristic
253	#33474	#41	1	1	yes	characteristic
254	#33474	#41	1	2	yes	—
255	#33435	C₂²×C₄	1	2	yes	—
256	#33435	C₂²×C₄	1	2	yes	—
257	#33435	C₂×D₄	1	4	yes	—
258	#33434	C₂²×C₄	1	1	yes	characteristic
259	#33434	C₂²×C₄	1	1	yes	characteristic
260	#33434	C₂×D₄	1	2	yes	—
261	#33433	C₂²×C₄	1	1	yes	characteristic
262	#33433	C₂²×C₄	1	1	yes	characteristic
263	#33433	C₂×D₄	1	2	yes	—
264	#33433	#41	1	1	yes	characteristic
265	#33433	#41	1	1	yes	characteristic
266	#33433	#41	1	2	yes	—
267	#33432	C₂²×C₄	1	2	yes	—
268	#33432	C₂²×C₄	1	2	yes	—
269	#33432	C₂×D₄	1	4	yes	—
270	#33432	#41	1	2	yes	—
271	#33432	#41	1	2	yes	—
272	#33432	#41	1	4	yes	—
273	#33428	C₂⁴	1	2	yes	—
274	#33428	C₂⁴	1	4	yes	—
275	#33421	C₂×D₄	1	2	yes	—
276	#33421	C₂×D₄	1	1	yes	characteristic
277	#33421	C₂×D₄	1	2	yes	—
278	#33421	C₂×D₄	1	1	yes	characteristic
279	#33421	C₂⁴	1	2	yes	—
280	#33421	C₂⁴	1	1	yes	characteristic
281	#33421	C₂⁴	1	2	yes	—
282	#33421	C₂⁴	1	1	yes	characteristic
283	#33418	C₂×D₄	1	2	yes	—
284	#33418	C₂×D₄	1	1	yes	characteristic
285	#33418	C₂×D₄	1	2	yes	—
286	#33418	C₂×D₄	1	1	yes	characteristic
287	#33414	C₂²×C₄	1	1	yes	characteristic
288	#33401	C₂⁴	1	2	yes	—
289	#33385	C₂²×C₄	1	2	yes	—
290	#33326	C₂×D₄	1	1	yes	characteristic
291	#33326	C₂×D₄	1	2	yes	—
292	#33326	C₂×D₄	1	1	yes	characteristic
293	#33326	C₂×D₄	1	2	yes	—
294	#33326	C₂⁴	1	1	yes	characteristic
295	#33326	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×M₃₂	C₂×D₄	1	1	yes	characteristic
297	C₂×C₄×M₃₂	C₂×D₄	1	1	yes	characteristic
298	C₂²×#346	C₂×D₄	1	2	yes	—
299	C₂²×#346	C₂×D₄	1	2	yes	—
300	#27693	C₂²×C₄	1	2	yes	—
301	#27693	C₂²×C₄	1	4	yes	—
302	#27691	C₂²×C₄	1	4	yes	—
303	#27691	C₂²×C₄	1	2	yes	—
304	#24287	C₂²×C₄	1	2	yes	—
305	#24287	C₂²×C₄	1	4	yes	—
306	#24285	C₂²×C₄	1	4	yes	—
307	#24285	C₂²×C₄	1	2	yes	—
308	#20787	C₂⁴	1	4	yes	—
309	#20787	C₂⁴	1	2	yes	—
310	#17342	#41	1	2	yes	—
311	#17342	#41	1	2	yes	—
312	#17342	#41	1	2	yes	—
313	#17336	C₂×D₄	1	2	yes	—
314	#17336	C₂×D₄	1	1	yes	characteristic
315	#17336	C₂⁴	1	2	yes	—
316	#17336	C₂⁴	1	1	yes	characteristic
317	M₁₆²	#41	1	1	yes	characteristic
318	M₁₆²	#41	1	2	yes	—
319	#17325	#41	1	1	yes	characteristic
320	#17325	#41	1	2	yes	—
321	#17323	C₂×D₄	1	2	yes	—
322	#17323	C₂×D₄	1	1	yes	characteristic
323	#17316	C₂×D₄	1	2	yes	—
324	#17316	C₂×D₄	1	1	yes	characteristic
325	#17316	C₂⁴	1	1	yes	characteristic
326	C₂²×#322	C₂×D₄	1	2	yes	—
327	C₂²×#322	C₂×D₄	1	1	yes	characteristic
328	#12878	C₂²×C₄	1	2	yes	—
329	#12878	C₂²×C₄	1	4	yes	—
330	#12877	C₂²×C₄	1	2	yes	—
331	#12877	C₂²×C₄	1	4	yes	—
332	#12840	C₂²×C₄	1	2	yes	—
333	#12840	C₂²×C₄	1	1	yes	characteristic
334	#12839	C₂²×C₄	1	1	yes	characteristic
335	#12839	C₂²×C₄	1	2	yes	—
336	#12832	C₂²×C₄	1	2	yes	—
337	#12832	C₂²×C₄	1	4	yes	—
338	#12809	C₂²×C₄	1	2	yes	—
339	#12809	C₂²×C₄	1	4	yes	—
340	#12807	C₂²×C₄	1	2	yes	—
341	#12807	C₂²×C₄	1	4	yes	—
342	#12805	C₂²×C₄	1	4	yes	—
343	#12805	C₂²×C₄	1	4	yes	—
344	#12805	C₂²×C₄	1	4	yes	—
345	#12746	C₂²×C₄	1	2	yes	—
346	#12746	C₂²×C₄	1	4	yes	—
347	#12745	C₂²×C₄	1	2	yes	—
348	#12745	C₂²×C₄	1	4	yes	—
349	#11406	C₂×D₄	1	2	yes	—
350	#11406	C₂×D₄	1	1	yes	characteristic
351	#11406	C₂×D₄	1	2	yes	—
352	#11406	C₂×D₄	1	1	yes	characteristic
353	#11406	C₂×D₄	1	2	yes	—
354	#11406	C₂×D₄	1	1	yes	characteristic
355	#11406	C₂×D₄	1	2	yes	—
356	#11406	C₂×D₄	1	1	yes	characteristic
357	#11405	C₂×D₄	1	2	yes	—
358	#11405	C₂×D₄	1	1	yes	characteristic
359	#11405	C₂×D₄	1	2	yes	—
360	#11405	C₂×D₄	1	1	yes	characteristic
361	#11405	C₂×D₄	1	2	yes	—
362	#11405	C₂×D₄	1	1	yes	characteristic
363	#11405	C₂×D₄	1	2	yes	—
364	#11405	C₂×D₄	1	1	yes	characteristic
365	#11404	C₂×D₄	1	1	yes	characteristic
366	#11404	C₂×D₄	1	2	yes	—
367	#11404	C₂×D₄	1	1	yes	characteristic
368	#11404	C₂×D₄	1	2	yes	—
369	#11404	C₂×D₄	1	1	yes	characteristic
370	#11404	C₂×D₄	1	2	yes	—
371	#11404	C₂×D₄	1	1	yes	characteristic
372	#11404	C₂×D₄	1	2	yes	—
373	C₂×#1313	C₂×D₄	1	2	yes	—
374	C₂×#1313	C₂×D₄	1	1	yes	characteristic
375	C₂×#1313	C₂×D₄	1	2	yes	—
376	C₂×#1313	C₂×D₄	1	1	yes	characteristic
377	C₂×#1313	C₂×D₄	1	2	yes	—
378	C₂×#1313	C₂×D₄	1	1	yes	characteristic
379	C₂×#1313	C₂×D₄	1	2	yes	—
380	C₂×#1313	C₂×D₄	1	1	yes	characteristic
381	#7229	C₂²×C₄	1	4	yes	—
382	#7229	C₂²×C₄	1	2	yes	—
383	#7228	C₂²×C₄	1	2	yes	—
384	#7228	C₂²×C₄	1	4	yes	—
385	#7227	C₂²×C₄	1	4	yes	—
386	#7227	C₂²×C₄	1	4	yes	—
387	#7227	C₂²×C₄	1	4	yes	—
388	#3584	C₂³×C₄	1	2	yes	—
389	#3483	C₄×D₄	1	1	yes	characteristic
390	#3481	C₄×D₄	1	1	yes	characteristic
391	#3481	C₄×D₄	1	2	yes	—
392	#3444	C₂×#41	1	2	yes	—
393	#3444	C₂×#41	1	1	yes	characteristic
394	C₂×#504	C₄×D₄	1	1	yes	characteristic
395	C₂×#504	C₄×D₄	1	2	yes	—
396	C₂×#504	C₄×D₄	1	1	yes	characteristic
397	C₂×#504	C₄×D₄	1	2	yes	—
398	C₂×#504	#121	1	2	yes	—
399	C₂×#504	#121	1	4	yes	—
400	C₂×#504	C₂³×C₄	1	1	yes	characteristic
401	C₂×#504	C₂³×C₄	1	1	yes	characteristic
402	C₂×#504	C₂²×D₄	1	2	yes	—
403	C₂²×M₃₂	C₄×D₄	1	1	yes	characteristic
404	C₂²×M₃₂	C₄×D₄	1	1	yes	characteristic
405	C₂²×M₃₂	#121	1	2	yes	—
406	C₂³×C₁₆	C₄×D₄	1	2	yes	—
407	C₂³×C₁₆	C₄×D₄	1	2	yes	—
408	C₂³×C₁₆	#121	1	4	yes	—
409	#2979	C₄×D₄	1	1	yes	characteristic
410	#2979	C₄×D₄	1	2	yes	—
411	#2979	C₄×D₄	1	1	yes	characteristic
412	#2979	C₄×D₄	1	2	yes	—
413	#2977	C₄×D₄	1	2	yes	—
414	#2977	C₄×D₄	1	2	yes	—
415	#2977	C₄×D₄	1	2	yes	—
416	#2960	C₂×#41	1	1	yes	characteristic
417	#2960	C₂×#41	1	2	yes	—
418	#2960	C₂×#41	1	1	yes	characteristic
419	#2960	C₂×#41	1	2	yes	—
420	#2931	C₂³×C₄	1	1	yes	characteristic
421	#2931	C₂³×C₄	1	2	yes	—
422	#2931	C₂²×D₄	1	1	yes	characteristic
423	#2931	C₂²×D₄	1	2	yes	—
424	#2929	C₂³×C₄	1	2	yes	—
425	#2929	C₂³×C₄	1	1	yes	characteristic
426	#2929	C₂²×D₄	1	2	yes	—
427	#2929	C₂²×D₄	1	1	yes	characteristic
428	#2929	C₂×#41	1	2	yes	—
429	#2929	C₂×#41	1	1	yes	characteristic
430	#2929	C₂×#41	1	2	yes	—
431	#2929	C₂×#41	1	1	yes	characteristic
432	#2922	C₂×#41	1	2	yes	—
433	#2922	C₂×#41	1	1	yes	characteristic
434	#2922	C₂×#41	1	2	yes	—
435	#2922	C₂×#41	1	1	yes	characteristic
436	#2920	C₂×#41	1	2	yes	—
437	#2920	C₂×#41	1	1	yes	characteristic
438	#2916	C₂³×C₄	1	2	yes	—
439	C₄×#131	C₂²×D₄	1	1	yes	characteristic
440	C₄×#131	C₂²×D₄	1	2	yes	—
441	C₄×#131	C₂⁵	1	1	yes	characteristic
442	C₂²×C₄×C₈	C₂²×D₄	1	2	yes	—
443	C₂²×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
444	#2151	C₄×D₄	1	2	yes	—
445	#2151	C₄×D₄	1	1	yes	characteristic
446	#2151	C₄×D₄	1	2	yes	—
447	#2151	C₄×D₄	1	1	yes	characteristic
448	#2151	#121	1	4	yes	—
449	#2151	#121	1	2	yes	—
450	#2151	C₂×#41	1	2	yes	—
451	#2151	C₂×#41	1	1	yes	characteristic
452	#2151	C₂×#41	1	2	yes	—
453	#2151	C₂×#41	1	1	yes	characteristic
454	#2151	C₂×#41	1	4	yes	—
455	#2151	C₂×#41	1	2	yes	—
456	#2150	C₄×D₄	1	1	yes	characteristic
457	#2150	C₄×D₄	1	2	yes	—
458	#2150	C₄×D₄	1	1	yes	characteristic
459	#2150	C₄×D₄	1	2	yes	—
460	#2150	#121	1	2	yes	—
461	#2150	#121	1	4	yes	—
462	#2113	C₄×D₄	1	2	yes	—
463	#2113	C₄×D₄	1	1	yes	characteristic
464	#2113	C₄×D₄	1	2	yes	—
465	#2113	C₄×D₄	1	1	yes	characteristic
466	#2113	#121	1	4	yes	—
467	#2113	#121	1	2	yes	—
468	#2113	C₂³×C₄	1	2	yes	—
469	#2113	C₂³×C₄	1	1	yes	characteristic
470	#2113	C₂³×C₄	1	2	yes	—
471	#2113	C₂³×C₄	1	1	yes	characteristic
472	#2113	C₂²×D₄	1	4	yes	—
473	#2113	C₂²×D₄	1	2	yes	—
474	#2112	C₄×D₄	1	2	yes	—
475	#2112	C₄×D₄	1	1	yes	characteristic
476	#2112	C₄×D₄	1	2	yes	—
477	#2112	C₄×D₄	1	1	yes	characteristic
478	#2112	#121	1	4	yes	—
479	#2112	#121	1	2	yes	—
480	#2108	C₄×D₄	1	2	yes	—
481	#2108	C₄×D₄	1	1	yes	characteristic
482	#2108	C₄×D₄	1	2	yes	—
483	#2108	C₄×D₄	1	1	yes	characteristic
484	#2108	#121	1	4	yes	—
485	#2108	#121	1	2	yes	—
486	#2108	C₂×#41	1	2	yes	—
487	#2108	C₂×#41	1	1	yes	characteristic
488	#2108	C₂×#41	1	2	yes	—
489	#2108	C₂×#41	1	1	yes	characteristic
490	#2108	C₂×#41	1	4	yes	—
491	#2108	C₂×#41	1	2	yes	—
492	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
493	C₄×M₃₂	C₂²×D₄	1	2	yes	—
494	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
495	C₄×M₃₂	C₂²×D₄	1	2	yes	—
496	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
497	C₄×M₃₂	C₂²×D₄	1	2	yes	—
498	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
499	C₄×M₃₂	C₂²×D₄	1	2	yes	—
500	C₂×#346	C₄×D₄	1	2	yes	—
501	C₂×#346	C₄×D₄	1	2	yes	—
502	C₂×#346	#121	1	4	yes	—
503	C₂×#346	C₂²×D₄	1	2	yes	—
504	C₂×#346	C₂²×D₄	1	1	yes	characteristic
505	C₂×#346	C₂²×D₄	1	2	yes	—
506	C₂×#346	C₂²×D₄	1	1	yes	characteristic
507	C₂×#346	C₂²×D₄	1	2	yes	—
508	C₂×#346	C₂²×D₄	1	1	yes	characteristic
509	C₂×#346	C₂²×D₄	1	2	yes	—
510	C₂×#346	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₁₆	C₄×D₄	1	1	yes	characteristic
512	C₂×C₄×C₁₆	C₄×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₆	#121	1	2	yes	—
514	#1813	C₂³×C₄	1	2	yes	—
515	#1813	C₂³×C₄	1	4	yes	—
516	#1812	C₂³×C₄	1	2	yes	—
517	#1812	C₂³×C₄	1	4	yes	—
518	#1455	C₂×#41	1	2	yes	—
519	#1455	C₂×#41	1	2	yes	—
520	#1455	C₂×#41	1	2	yes	—
521	#1453	C₂×#41	1	2	yes	—
522	#1453	C₂×#41	1	2	yes	—
523	#1453	C₂×#41	1	2	yes	—
524	#1450	C₂²×D₄	1	2	yes	—
525	#1450	C₂²×D₄	1	1	yes	characteristic
526	#1450	C₂²×D₄	1	2	yes	—
527	#1450	C₂²×D₄	1	1	yes	characteristic
528	C₂×#322	C₂²×D₄	1	2	yes	—
529	C₂×#322	C₂²×D₄	1	1	yes	characteristic
530	C₂×#322	C₂²×D₄	1	2	yes	—
531	C₂×#322	C₂²×D₄	1	1	yes	characteristic
532	#1313	#120	1	1	yes	characteristic
533	#1313	#120	1	2	yes	—
534	#1313	#120	1	2	yes	—
535	#1313	#120	1	2	yes	—
536	#1313	#120	1	1	yes	characteristic
537	#1313	#120	1	1	yes	characteristic
538	#1313	#120	1	1	yes	characteristic
539	#1313	#120	1	2	yes	—
540	#1313	#120	1	2	yes	—
541	#1313	#120	1	2	yes	—
542	C₂×#131	C₂×C₄×D₄	1	1	yes	characteristic
543	C₂×#131	C₂×C₄×D₄	1	2	yes	—
544	C₂×#131	C₂×#121	1	1	yes	characteristic
545	C₂×#131	C₂×#121	1	2	yes	—
546	C₂×#131	C₂⁴×C₄	1	1	yes	characteristic
547	C₂×#131	C₂³×D₄	1	1	yes	characteristic
548	C₂³×C₈	C₂×C₄×D₄	1	2	yes	—
549	C₂³×C₈	C₂×C₄×D₄	1	1	yes	characteristic
550	C₂³×C₈	C₂×#121	1	2	yes	—
551	C₂³×C₈	C₂×#121	1	1	yes	characteristic
552	#559	#444	1	1	yes	characteristic
553	#559	#444	1	2	yes	—
554	Q₈²	#444	1	1	yes	characteristic
555	#555	#444	1	1	yes	characteristic
556	#555	#444	1	2	yes	—
557	#551	#444	1	2	yes	—
558	#551	#444	1	2	yes	—
559	#551	#444	1	2	yes	—
560	D₄²	#444	1	1	yes	characteristic
561	D₄²	#444	1	2	yes	—
562	#533	#529	1	1	yes	characteristic
563	#533	#529	1	2	yes	—
564	#532	C₂×C₄×D₄	1	1	yes	characteristic
565	#532	C₂×C₄×D₄	1	2	yes	—
566	#525	C₂×C₄×D₄	1	2	yes	—
567	#525	C₂×C₄×D₄	1	1	yes	characteristic
568	#525	#529	1	2	yes	—
569	#525	#529	1	1	yes	characteristic
570	C₄×#41	#525	1	1	yes	characteristic
571	C₄×#41	#525	1	2	yes	—
572	C₄×#41	C₂²×#41	1	1	yes	characteristic
573	C₂²×C₄²	#525	1	2	yes	—
574	C₂²×C₄²	#525	1	1	yes	characteristic
575	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
576	C₂×M₃₂	C₂×C₄×D₄	1	2	yes	—
577	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
578	C₂×M₃₂	C₂×C₄×D₄	1	2	yes	—
579	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
580	C₂×M₃₂	C₂×C₄×D₄	1	2	yes	—
581	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
582	C₂×M₃₂	C₂×C₄×D₄	1	2	yes	—
583	C₂×M₃₂	C₂×#121	1	2	yes	—
584	C₂×M₃₂	C₂×#121	1	4	yes	—
585	C₂×M₃₂	C₂×#121	1	2	yes	—
586	C₂×M₃₂	C₂×#121	1	4	yes	—
587	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
588	C₂²×C₁₆	C₂×C₄×D₄	1	2	yes	—
589	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
590	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
591	C₂²×C₁₆	C₂×C₄×D₄	1	2	yes	—
592	C₂²×C₁₆	C₂×C₄×D₄	1	2	yes	—
593	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
594	C₂²×C₁₆	C₂×C₄×D₄	1	2	yes	—
595	C₂²×C₁₆	C₂×#121	1	2	yes	—
596	C₂²×C₁₆	C₂×#121	1	4	yes	—
597	C₂²×C₁₆	C₂×#121	1	2	yes	—
598	C₂²×C₁₆	C₂×#121	1	4	yes	—
599	#424	C₄×#41	1	2	yes	—
600	#424	C₄×#41	1	1	yes	characteristic
601	#424	#529	1	2	yes	—
602	#424	#529	1	1	yes	characteristic
603	#424	#529	1	2	yes	—
604	#424	#529	1	1	yes	characteristic
605	#424	#532	1	2	yes	—
606	#424	#532	1	1	yes	characteristic
607	#423	C₄×#41	1	1	yes	characteristic
608	#423	C₄×#41	1	2	yes	—
609	#423	#532	1	1	yes	characteristic
610	#423	#532	1	2	yes	—
611	#408	C₂×C₄×D₄	1	2	yes	—
612	#408	C₂×C₄×D₄	1	1	yes	characteristic
613	#408	C₂×C₄×D₄	1	2	yes	—
614	#408	C₂×C₄×D₄	1	1	yes	characteristic
615	#408	C₄×#41	1	2	yes	—
616	#408	C₄×#41	1	1	yes	characteristic
617	#408	#532	1	2	yes	—
618	#408	#532	1	1	yes	characteristic
619	#407	C₄×#41	1	2	yes	—
620	#407	C₄×#41	1	1	yes	characteristic
621	#407	#532	1	2	yes	—
622	#407	#532	1	1	yes	characteristic
623	#405	C₂×C₄×D₄	1	2	yes	—
624	#405	C₂×C₄×D₄	1	1	yes	characteristic
625	#405	C₂×#121	1	2	yes	—
626	#405	C₂×#121	1	1	yes	characteristic
627	#405	C₂²×#41	1	2	yes	—
628	#405	C₂²×#41	1	1	yes	characteristic
629	#405	C₂²×#41	1	2	yes	—
630	#405	C₂²×#41	1	1	yes	characteristic
631	C₄×M₁₆	#525	1	1	yes	characteristic
632	C₄×M₁₆	#525	1	2	yes	—
633	C₄×M₁₆	C₂²×#41	1	2	yes	—
634	C₄×M₁₆	C₂²×#41	1	1	yes	characteristic
635	C₂×C₄×C₈	C₂×C₄×D₄	1	1	yes	characteristic
636	C₂×C₄×C₈	C₂×C₄×D₄	1	2	yes	—
637	C₂×C₄×C₈	C₂×#121	1	1	yes	characteristic
638	C₂×C₄×C₈	C₂×#121	1	2	yes	—
639	C₂×C₄×C₈	#525	1	2	yes	—
640	C₂×C₄×C₈	#525	1	1	yes	characteristic
641	C₂×C₄×C₈	C₂³×D₄	1	2	yes	—
642	C₂×C₄×C₈	C₂³×D₄	1	1	yes	characteristic
643	#346	C₂×#120	1	1	yes	characteristic
644	#346	C₂×#120	1	2	yes	—
645	#346	C₂×#120	1	1	yes	characteristic
646	#346	C₂×#120	1	1	yes	characteristic
647	#346	C₂×#120	1	2	yes	—
648	#346	C₂×#120	1	1	yes	characteristic
649	#346	#525	1	4	yes	—
650	#346	#525	1	2	yes	—
651	#346	#525	1	2	yes	—
652	#346	#525	1	2	yes	—
653	#346	#525	1	1	yes	characteristic
654	#346	#525	1	1	yes	characteristic
655	C₄×C₁₆	#525	1	2	yes	—
656	C₄×C₁₆	#525	1	4	yes	—
657	C₄×C₁₆	#525	1	2	yes	—
658	C₄×C₁₆	#525	1	2	yes	—
659	C₄×C₁₆	#525	1	2	yes	—
660	#322	C₂×#120	1	1	yes	characteristic
661	#322	C₂×#120	1	2	yes	—
662	#322	C₂×#120	1	1	yes	characteristic
663	#322	#525	1	2	yes	—
664	#322	#525	1	1	yes	characteristic
665	#322	#525	1	2	yes	—
666	#322	#525	1	1	yes	characteristic
667	C₈²	#525	1	2	yes	—
668	C₈²	#525	1	2	yes	—
669	C₈²	#525	1	2	yes	—
670	C₂×#41	C₄×#121	1	1	yes	characteristic
671	C₂×#41	C₄×#121	1	2	yes	—
672	C₂×#41	C₂²×C₄×D₄	1	1	yes	characteristic
673	C₂³×C₄	C₄×#121	1	2	yes	—
674	C₂³×C₄	C₄×#121	1	1	yes	characteristic
675	C₂×M₁₆	C₄×#121	1	1	yes	characteristic
676	C₂×M₁₆	C₄×#121	1	2	yes	—
677	C₂×M₁₆	C₄×#121	1	1	yes	characteristic
678	C₂×M₁₆	C₄×#121	1	2	yes	—
679	C₂×M₁₆	C₂×C₄×#41	1	2	yes	—
680	C₂×M₁₆	C₂×C₄×#41	1	1	yes	characteristic
681	C₂×M₁₆	C₂×#532	1	2	yes	—
682	C₂×M₁₆	C₂×#532	1	1	yes	characteristic
683	C₂²×C₈	C₄×#121	1	2	yes	—
684	C₂²×C₈	C₄×#121	1	1	yes	characteristic
685	C₂²×C₈	C₄×#121	1	2	yes	—
686	C₂²×C₈	C₄×#121	1	1	yes	characteristic
687	C₂²×C₈	C₂²×C₄×D₄	1	2	yes	—
688	C₂²×C₈	C₂²×C₄×D₄	1	1	yes	characteristic
689	C₂²×C₈	C₂²×#121	1	2	yes	—
690	C₂²×C₈	C₂²×#121	1	1	yes	characteristic
691	C₄⋊Q₈	C₂×#444	1	1	yes	characteristic
692	C₄⋊Q₈	C₂×#444	1	2	yes	—
693	#127	C₂×#444	1	1	yes	characteristic
694	#127	C₂×#444	1	2	yes	—
695	#124	C₂×#444	1	1	yes	characteristic
696	#124	C₂×#444	1	2	yes	—
697	#124	C₂×#444	1	1	yes	characteristic
698	#124	C₂×#444	1	2	yes	—
699	#123	C₂×#444	1	2	yes	—
700	#123	C₂×#444	1	2	yes	—
701	#123	C₂×#444	1	2	yes	—
702	#120	C₂×#444	1	2	yes	—
703	#120	C₂×#444	1	2	yes	—
704	#120	C₂×#444	1	2	yes	—
705	#117	C₄×#121	1	2	yes	—
706	#117	C₄×#121	1	1	yes	characteristic
707	#117	C₂×#529	1	2	yes	—
708	#117	C₂×#529	1	1	yes	characteristic
709	C₂×C₄²	C₄×#121	1	1	yes	characteristic
710	C₂×C₄²	C₄×#121	1	2	yes	—
711	C₂×C₄²	C₂×#525	1	1	yes	characteristic
712	C₂×C₄²	C₂×#525	1	2	yes	—
713	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
714	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
715	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
716	C₂×C₁₆	C₄×#120	1	2	yes	—
717	C₂×C₁₆	C₄×#120	1	2	yes	—
718	C₂×C₁₆	C₄×#120	1	1	yes	characteristic
719	C₂×C₁₆	#2847	1	2	yes	—
720	C₂×C₁₆	#2847	1	2	yes	—
721	C₂×C₁₆	#2847	1	4	yes	—
722	#97	#3444	1	2	yes	—
723	#97	#3444	1	2	yes	—
724	#97	#3444	1	2	yes	—
725	C₄×C₈	C₂²×#120	1	1	yes	characteristic
726	C₄×C₈	C₂×#525	1	2	yes	—
727	C₄×C₈	C₂×#525	1	1	yes	characteristic
728	C₄×C₈	C₂×#525	1	1	yes	characteristic
729	C₄×C₈	C₂×#525	1	2	yes	—
730	C₄×C₈	C₂×#525	1	1	yes	characteristic
731	C₄×C₈	C₂×#525	1	2	yes	—
732	C₂⁴	#21546	1	2	yes	—
733	C₂⁴	#21546	1	1	yes	characteristic
734	C₂×Q₈	#21546	1	2	yes	—
735	C₂×Q₈	#21546	1	1	yes	characteristic
736	C₂×Q₈	C₂²×#444	1	1	yes	characteristic
737	C₂×D₄	#21546	1	2	yes	—
738	C₂×D₄	#21546	1	1	yes	characteristic
739	C₂×D₄	C₂²×#444	1	2	yes	—
740	C₂×D₄	C₂²×#444	1	1	yes	characteristic
741	C₂²×C₄	#21546	1	1	yes	characteristic
742	C₂²×C₄	#21546	1	2	yes	—
743	C₂²×C₄	C₂×C₄×#121	1	1	yes	characteristic
744	C₂²×C₄	C₂×C₄×#121	1	2	yes	—
745	C₂×C₈	C₂×C₄×#120	1	1	yes	characteristic
746	C₂×C₈	C₄×#525	1	2	yes	—
747	C₂×C₈	C₄×#525	1	1	yes	characteristic
748	C₂×C₈	C₂×#2847	1	1	yes	characteristic
749	C₂×C₈	#36624	1	2	yes	—
750	C₂×C₈	#36624	1	1	yes	characteristic
751	C₂²⋊C₄	#21546	1	2	yes	—
752	C₂²⋊C₄	#21546	1	2	yes	—
753	C₂²⋊C₄	#21546	1	2	yes	—
754	C₄²	#21546	1	2	yes	—
755	C₄²	#21546	1	1	yes	characteristic
756	C₄²	#21546	1	1	yes	characteristic
757	C₄²	#21546	1	2	yes	—
758	C₄²	#36614	1	1	yes	characteristic
759	C₄²	#36621	1	1	yes	characteristic
760	C₄²	#36621	1	2	yes	—
761	C₁₆	#21483	1	1	yes	characteristic
762	C₁₆	#21483	1	1	yes	characteristic
763	C₂³	C₂×#21546	1	1	yes	characteristic
764	C₂³	C₂×#21546	1	2	yes	—
765	C₂×C₄	C₄×#2847	1	1	yes	characteristic
766	C₂×C₄	C₂×#21546	1	1	yes	characteristic
767	C₂×C₄	C₂×#21546	1	2	yes	—
768	C₈	C₂×#21483	1	1	yes	characteristic
769	C₈	#6372742	1	1	yes	characteristic
770	C₈	#6629045	1	2	yes	—
771	C₂²	#72231444	1	1	yes	characteristic
772	C₄	#72281182	1	1	yes	characteristic
773	C₄	#72342948	1	1	yes	characteristic
774	C₂	#72343145	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#72281182
commutator	C₂×#131	C₂⁴×C₄
Frattini, cosocle	C₄×#131	C₂⁵
socle	C₂	#72343145
prime radical	#72343010	C₂
LCS	G ▷ C₂×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #33326 ◁ G
LECS	G ▷ C₄×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72343227	C₂	semidirect
2. #72343221	C₂	semidirect
3. #72343212	C₂	semidirect
4. #72343205	C₂	semidirect
5. #72343192	C₂	semidirect
7. #72343172	C₂	semidirect
8. #72343170	C₂	semidirect
9. #72343163	C₂	semidirect
11. #72343157	C₂	semidirect
15. #72343148	C₂²	semidirect
16. #72343148	C₂²	semidirect
17. #72343148	C₂²	semidirect
31. #72319792	C₂	semidirect
35. #72319283	C₂	semidirect
39. #72319246	C₂²	semidirect
40. #72319246	C₂²	semidirect
41. #72319240	C₂²	semidirect
42. #72319240	C₂²	semidirect
43. #72287831	C₂	semidirect
52. #72287462	C₂	semidirect
53. #72287460	C₂	semidirect
58. #72287445	C₂²	semidirect
59. #72287445	C₂²	semidirect
60. #72287445	C₂²	semidirect
66. #72286336	C₂²	semidirect
67. #72286336	C₂²	semidirect
68. #72286336	C₂²	semidirect
69. #72224969	C₂	semidirect
70. #72224968	C₂	semidirect
71. #72224963	C₂²	semidirect
72. #72224963	C₂²	semidirect
75. #72224958	C₂²	semidirect
76. #72224958	C₂²	semidirect
79. #72224956	C₂²	semidirect
80. #72224956	C₂²	semidirect
81. #72224955	C₂²	semidirect
82. #72224955	C₂²	semidirect
83. #72224951	C₂²	semidirect
84. #72224951	C₂²	semidirect
85. #72224948	C₂²	semidirect
161. #479968	D₄	semidirect
162. #479968	D₄	semidirect
165. #479966	D₄	semidirect
166. #479966	D₄	semidirect
167. #479961	D₄	semidirect
168. #479961	D₄	semidirect
171. #479960	D₄	semidirect
172. #479960	D₄	semidirect
175. #479959	D₄	semidirect
176. #479959	D₄	semidirect
177. #479958	D₄	semidirect
178. #479958	D₄	semidirect
179. #479908	D₄	semidirect
180. #479908	D₄	semidirect
182. C₂×#11404	D₄	semidirect
183. C₂²×#1313	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72343227	2
#72343221	2
#72343212	2
#72343205	2
#72343192	2
#72343172	2
#72343170	2
#72343163	2
#72343157	2
#72343010	2
#72319792	2
#72319283	2
#72287831	2
#72287462	2
#72287460	2
#72224969	2
#72224968	2