Subgroups — #72231730

Order 2048.

At least 17547 conjugacy classes of subgroups; only the 1026 normal subgroups are shown.

The subgroup lattice has 657 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72231719	C₂	1	1	yes	maximal, characteristic, complemented
2	#72231715	C₂	1	1	yes	maximal, characteristic, complemented
3	#72231714	C₂	1	1	yes	maximal, characteristic, complemented
4	#72231712	C₂	1	1	yes	maximal, characteristic, complemented
5	#72231710	C₂	1	2	yes	maximal, complemented
6	#72231708	C₂	1	1	yes	maximal, characteristic, complemented
7	#72231705	C₂	1	1	yes	maximal, characteristic, complemented
8	#72231704	C₂	1	2	yes	maximal, complemented
9	#72231703	C₂	1	1	yes	maximal, characteristic, complemented
10	#72231701	C₂	1	2	yes	maximal, complemented
11	#72231700	C₂	1	2	yes	maximal, complemented
12	#72231699	C₂	1	1	yes	maximal, characteristic, complemented
13	#72231624	C₂	1	1	yes	maximal, characteristic, complemented
14	#72231620	C₂	1	1	yes	maximal, characteristic, complemented
15	#72231615	C₂	1	2	yes	maximal, complemented
16	#72231612	C₂	1	1	yes	maximal, characteristic, complemented
17	#72231607	C₂	1	1	yes	maximal, characteristic, complemented
18	#72231603	C₂	1	2	yes	maximal, complemented
19	#72231599	C₂	1	1	yes	maximal, characteristic, complemented
20	#72231596	C₂	1	2	yes	maximal, complemented
21	#72231593	C₂	1	1	yes	maximal, characteristic, complemented
22	#72213945	C₂	1	1	yes	maximal, characteristic, complemented
23	#72213937	C₂	1	2	yes	maximal, complemented
24	#10584532	C₂²	1	1	yes	characteristic
25	#10584288	C₂²	1	2	yes	—
26	#10584270	C₂²	1	1	yes	characteristic
27	#10583460	C₂²	1	1	yes	characteristic
28	#10583240	C₂²	1	2	yes	—
29	#10583198	C₂²	1	1	yes	characteristic
30	#10580981	C₂²	1	1	yes	characteristic
31	#10580978	C₂²	1	2	yes	—
32	#10576942	C₂²	1	1	yes	characteristic
33	#10576928	C₂²	1	2	yes	—
34	#10574651	C₂²	1	1	yes	characteristic
35	#7623148	C₂²	1	1	yes	characteristic, complemented
36	#7623148	C₂²	1	2	yes	complemented
37	#7622637	C₂²	1	1	yes	characteristic, complemented
38	#6469085	C₂²	1	2	yes	complemented
39	#6469080	C₂²	1	1	yes	characteristic, complemented
40	#512046	C₂²	1	2	yes	complemented
41	#512045	C₂²	1	1	yes	characteristic, complemented
42	#512038	C₂²	1	1	yes	characteristic, complemented
43	#511946	C₂²	1	2	yes	complemented
44	#511937	C₂²	1	1	yes	characteristic, complemented
45	#511930	C₂²	1	1	yes	characteristic, complemented
46	#500355	C₂²	1	1	yes	characteristic, complemented
47	#500353	C₂²	1	1	yes	characteristic, complemented
48	#500351	C₂²	1	2	yes	complemented
49	#500349	C₂²	1	2	yes	complemented
50	#500168	C₂²	1	2	yes	complemented
51	#500164	C₂²	1	2	yes	complemented
52	#500160	C₂²	1	1	yes	characteristic, complemented
53	#500158	C₂²	1	1	yes	characteristic, complemented
54	#500007	C₂²	1	1	yes	characteristic, complemented
55	#500005	C₂²	1	1	yes	characteristic, complemented
56	#500003	C₂²	1	2	yes	complemented
57	#500001	C₂²	1	2	yes	complemented
58	#499752	C₂²	1	2	yes	complemented
59	#499750	C₂²	1	1	yes	characteristic, complemented
60	#499746	C₂²	1	1	yes	characteristic, complemented
61	#499742	C₂²	1	2	yes	complemented
62	#495573	C₂²	1	2	yes	complemented
63	#495573	C₂²	1	1	yes	characteristic, complemented
64	#495507	C₂²	1	1	yes	characteristic, complemented
65	#495505	C₂²	1	2	yes	complemented
66	#494058	C₂²	1	1	yes	characteristic, complemented
67	#494058	C₂²	1	2	yes	complemented
68	#494018	C₂²	1	1	yes	characteristic, complemented
69	#494016	C₂²	1	2	yes	complemented
70	#486701	C₂²	1	2	yes	complemented
71	#486701	C₂²	1	2	yes	complemented
72	#486698	C₂²	1	1	yes	characteristic, complemented
73	#486697	C₂²	1	1	yes	characteristic, complemented
74	#486694	C₂²	1	2	yes	complemented
75	#486691	C₂²	1	2	yes	complemented
76	#486689	C₂²	1	2	yes	complemented
77	#486345	C₂²	1	2	yes	complemented
78	#486345	C₂²	1	2	yes	complemented
79	#486342	C₂²	1	1	yes	characteristic, complemented
80	#486341	C₂²	1	1	yes	characteristic, complemented
81	#486338	C₂²	1	2	yes	complemented
82	#486335	C₂²	1	2	yes	complemented
83	#486333	C₂²	1	2	yes	complemented
84	#482709	C₂²	1	2	yes	complemented
85	#482709	C₂²	1	2	yes	complemented
86	#482709	C₂²	1	2	yes	complemented
87	#480442	C₂²	1	1	yes	characteristic, complemented
88	#480440	C₂²	1	2	yes	complemented
89	#130854	C₂²	1	2	yes	complemented
90	#130854	C₂²	1	2	yes	complemented
91	#130852	C₂²	1	2	yes	complemented
92	#130850	C₂²	1	2	yes	complemented
93	#130848	C₂²	1	2	yes	complemented
94	#130847	C₂²	1	1	yes	characteristic, complemented
95	#130845	C₂²	1	1	yes	characteristic, complemented
96	#130791	C₂²	1	1	yes	characteristic, complemented
97	#130786	C₂²	1	1	yes	characteristic, complemented
98	#130785	C₂²	1	2	yes	complemented
99	#130782	C₂²	1	2	yes	complemented
100	#130780	C₂²	1	2	yes	complemented
101	#130776	C₂²	1	2	yes	complemented
102	#130776	C₂²	1	2	yes	complemented
103	#130296	C₂²	1	2	yes	complemented
104	#130296	C₂²	1	2	yes	complemented
105	#130294	C₂²	1	2	yes	complemented
106	#130294	C₂²	1	2	yes	complemented
107	#130292	C₂²	1	2	yes	complemented
108	#130290	C₂²	1	2	yes	complemented
109	#130288	C₂²	1	2	yes	complemented
110	#130288	C₂²	1	2	yes	complemented
111	#130284	C₂²	1	2	yes	complemented
112	#130284	C₂²	1	2	yes	complemented
113	#130241	C₂²	1	1	yes	characteristic, complemented
114	#130237	C₂²	1	1	yes	characteristic, complemented
115	#130234	C₂²	1	1	yes	characteristic, complemented
116	#130233	C₂²	1	1	yes	characteristic, complemented
117	#129615	C₂²	1	1	yes	characteristic, complemented
118	#129615	C₂²	1	1	yes	characteristic, complemented
119	#129613	C₂²	1	2	yes	complemented
120	#129613	C₂²	1	2	yes	complemented
121	#129596	C₂²	1	1	yes	characteristic, complemented
122	#129596	C₂²	1	1	yes	characteristic, complemented
123	#41²	D₄	1	1	yes	characteristic
124	#62636	C₂³	1	1	yes	characteristic
125	#62392	D₄	1	2	yes	complemented
126	#62392	D₄	1	2	yes	complemented
127	#62373	D₄	1	1	yes	characteristic, complemented
128	#62372	D₄	1	1	yes	characteristic, complemented
129	#62334	C₂³	1	2	yes	—
130	#62334	C₂³	1	2	yes	—
131	#62331	C₂³	1	1	yes	characteristic
132	#62328	C₂³	1	1	yes	characteristic
133	#62290	D₄	1	2	yes	complemented
134	#62283	C₂³	1	2	yes	—
135	#62270	D₄	1	2	yes	complemented
136	#62270	C₂³	1	2	yes	—
137	#62269	D₄	1	2	yes	complemented
138	#62269	C₂³	1	2	yes	—
139	#61414	D₄	1	2	yes	complemented
140	#61409	D₄	1	1	yes	characteristic, complemented
141	#61378	D₄	1	2	yes	complemented
142	#61374	D₄	1	1	yes	characteristic, complemented
143	#61293	C₂³	1	2	yes	—
144	#61288	C₂³	1	1	yes	characteristic
145	#61267	D₄	1	1	yes	characteristic, complemented
146	#61267	C₂³	1	1	yes	characteristic
147	#61259	D₄	1	2	yes	complemented
148	#61259	C₂³	1	2	yes	—
149	#61089	C₂³	1	1	yes	characteristic
150	#61079	C₂³	1	2	yes	—
151	#61063	D₄	1	1	yes	characteristic, complemented
152	#61063	C₂³	1	1	yes	characteristic
153	#61049	D₄	1	2	yes	complemented
154	#61049	C₂³	1	2	yes	—
155	#60974	D₄	1	2	yes	complemented
156	#60974	D₄	1	2	yes	complemented
157	#60974	D₄	1	2	yes	complemented
158	#60968	D₄	1	1	yes	characteristic, complemented
159	#60968	D₄	1	2	yes	complemented
160	#60967	D₄	1	1	yes	characteristic, complemented
161	#60964	D₄	1	2	yes	complemented
162	#60698	D₄	1	2	yes	complemented
163	#60698	D₄	1	1	yes	characteristic, complemented
164	#60698	C₂³	1	2	yes	—
165	#60698	C₂³	1	1	yes	characteristic
166	C₂×#3184	D₄	1	1	yes	characteristic, complemented
167	#60688	D₄	1	2	yes	complemented
168	#60320	D₄	1	1	yes	characteristic
169	#60320	C₂³	1	1	yes	characteristic
170	#60314	D₄	1	2	yes	—
171	#60314	C₂³	1	2	yes	—
172	#60305	D₄	1	1	yes	characteristic
173	#60305	C₂³	1	1	yes	characteristic
174	#60287	D₄	1	1	yes	characteristic
175	#60286	D₄	1	2	yes	—
176	#60208	C₂³	1	1	yes	characteristic
177	#60207	C₂³	1	2	yes	—
178	#60184	C₂³	1	1	yes	characteristic, complemented
179	#60176	D₄	1	1	yes	characteristic, complemented
180	#60176	D₄	1	2	yes	complemented
181	#60176	C₂³	1	1	yes	characteristic
182	C₄×#575	D₄	1	1	yes	characteristic, complemented
183	C₂²×#442	D₄	1	2	yes	complemented
184	#33659	C₂³	1	1	yes	characteristic, complemented
185	#33659	C₂³	1	2	yes	complemented
186	#33657	C₂³	1	1	yes	characteristic, complemented
187	#33657	C₂³	1	2	yes	complemented
188	#33533	C₂³	1	2	yes	complemented
189	#33533	C₂³	1	1	yes	characteristic, complemented
190	#33531	C₂³	1	2	yes	complemented
191	#33531	C₂³	1	1	yes	characteristic, complemented
192	#33426	C₂³	1	2	yes	complemented
193	#33426	C₂³	1	1	yes	characteristic, complemented
194	#33404	C₂³	1	1	yes	characteristic, complemented
195	#33392	C₂³	1	1	yes	characteristic
196	#33388	C₂³	1	1	yes	characteristic, complemented
197	#33329	C₂³	1	1	yes	characteristic, complemented
198	#27694	C₂³	1	2	yes	complemented
199	#27693	C₂³	1	1	yes	characteristic, complemented
200	#27692	C₂³	1	1	yes	characteristic, complemented
201	#27691	C₂³	1	2	yes	complemented
202	#24288	C₂³	1	2	yes	complemented
203	#24287	C₂³	1	1	yes	characteristic, complemented
204	#24286	C₂³	1	1	yes	characteristic, complemented
205	#24285	C₂³	1	2	yes	complemented
206	#20788	C₂³	1	1	yes	characteristic, complemented
207	#20788	C₂³	1	2	yes	complemented
208	#13079	C₂³	1	2	yes	complemented
209	#13079	C₂³	1	1	yes	characteristic, complemented
210	#13077	C₂³	1	2	yes	complemented
211	#13077	C₂³	1	1	yes	characteristic, complemented
212	#13076	C₂³	1	1	yes	characteristic, complemented
213	#13076	C₂³	1	2	yes	complemented
214	#13074	C₂³	1	2	yes	complemented
215	#13074	C₂³	1	1	yes	characteristic, complemented
216	#12989	C₂³	1	1	yes	characteristic, complemented
217	#12989	C₂³	1	1	yes	characteristic, complemented
218	#12988	C₂³	1	2	yes	complemented
219	#12988	C₂³	1	2	yes	complemented
220	#12982	C₂³	1	1	yes	characteristic, complemented
221	#12982	C₂³	1	1	yes	characteristic, complemented
222	#12981	C₂³	1	2	yes	complemented
223	#12981	C₂³	1	2	yes	complemented
224	#12874	C₂³	1	2	yes	complemented
225	#12874	C₂³	1	1	yes	characteristic, complemented
226	#12873	C₂³	1	2	yes	complemented
227	#12873	C₂³	1	1	yes	characteristic, complemented
228	#12810	C₂³	1	2	yes	complemented
229	#12809	C₂³	1	1	yes	characteristic, complemented
230	#12808	C₂³	1	2	yes	complemented
231	#12807	C₂³	1	1	yes	characteristic, complemented
232	#12806	C₂³	1	2	yes	complemented
233	#12805	C₂³	1	2	yes	complemented
234	#12805	C₂³	1	2	yes	complemented
235	#12743	C₂³	1	1	yes	characteristic
236	#12743	C₂³	1	2	yes	—
237	#12741	C₂³	1	2	yes	—
238	#12741	C₂³	1	1	yes	characteristic
239	#11872	C₂³	1	2	yes	complemented
240	#11872	C₂³	1	2	yes	complemented
241	#11872	C₂³	1	2	yes	complemented
242	#11870	C₂³	1	2	yes	complemented
243	#11870	C₂³	1	2	yes	complemented
244	#11870	C₂³	1	2	yes	complemented
245	#11868	C₂³	1	2	yes	complemented
246	#11868	C₂³	1	2	yes	complemented
247	#11868	C₂³	1	2	yes	complemented
248	#11867	C₂³	1	2	yes	complemented
249	#11867	C₂³	1	2	yes	complemented
250	#11867	C₂³	1	2	yes	complemented
251	#11486	C₂³	1	2	yes	complemented
252	#11486	C₂³	1	2	yes	complemented
253	#11485	C₂³	1	1	yes	characteristic, complemented
254	#11485	C₂³	1	1	yes	characteristic, complemented
255	#11484	C₂³	1	2	yes	complemented
256	#11483	C₂³	1	2	yes	complemented
257	#11483	C₂³	1	2	yes	complemented
258	#3584	C₂⁴	1	1	yes	characteristic
259	C₂×#576	C₂×D₄	1	1	yes	characteristic
260	C₂×#576	C₂×D₄	1	2	yes	—
261	C₂×#576	C₂⁴	1	1	yes	characteristic
262	C₂×#575	C₂×D₄	1	1	yes	characteristic
263	C₂³×D₈	C₂×D₄	1	2	yes	—
264	#3483	C₂×D₄	1	1	yes	characteristic
265	#3481	C₂×D₄	1	1	yes	characteristic
266	#3481	C₂×D₄	1	2	yes	—
267	#3444	C₂×D₄	1	2	yes	—
268	#3444	C₂×D₄	1	1	yes	characteristic
269	#3407	C₂⁴	1	1	yes	characteristic
270	#3407	C₂⁴	1	1	yes	characteristic
271	#3263	C₂×D₄	1	2	yes	—
272	#3263	C₂×D₄	1	2	yes	—
273	#3263	C₂×D₄	1	2	yes	—
274	#3259	C₂×D₄	1	2	yes	—
275	#3259	C₂×D₄	1	2	yes	—
276	#3259	C₂×D₄	1	2	yes	—
277	#3256	C₂×D₄	1	2	yes	—
278	#3256	C₂×D₄	1	2	yes	—
279	#3255	C₂×D₄	1	1	yes	characteristic
280	#3253	C₂×D₄	1	2	yes	—
281	#3253	C₂×D₄	1	2	yes	—
282	#3253	C₂×D₄	1	1	yes	characteristic
283	#3253	C₂×D₄	1	1	yes	characteristic
284	#3253	C₂×D₄	1	1	yes	characteristic
285	#3204	C₂×D₄	1	2	yes	—
286	#3204	C₂×D₄	1	2	yes	—
287	#3204	C₂×D₄	1	2	yes	—
288	#3199	C₂×D₄	1	2	yes	—
289	#3199	C₂×D₄	1	2	yes	—
290	#3199	C₂×D₄	1	2	yes	—
291	#3197	C₂×D₄	1	2	yes	—
292	#3195	C₂×D₄	1	2	yes	—
293	#3192	C₂×D₄	1	2	yes	—
294	#3192	C₂×D₄	1	2	yes	—
295	#3192	C₂×D₄	1	2	yes	—
296	#3192	C₂×D₄	1	2	yes	—
297	#3184	C₂×D₄	1	2	yes	—
298	#3184	C₂×D₄	1	2	yes	—
299	#3184	C₂×D₄	1	2	yes	—
300	#3183	C₂×D₄	1	2	yes	—
301	#3183	C₂×D₄	1	2	yes	—
302	#3183	C₂×D₄	1	2	yes	—
303	#3176	C₂×D₄	1	2	yes	—
304	#3176	C₂×D₄	1	2	yes	—
305	#3176	C₂×D₄	1	2	yes	—
306	#3173	C₂×D₄	1	2	yes	—
307	#3173	C₂×D₄	1	2	yes	—
308	#3173	C₂×D₄	1	2	yes	—
309	#3163	C₂×D₄	1	2	yes	—
310	#3163	C₂×D₄	1	1	yes	characteristic
311	#3163	C₂×D₄	1	1	yes	characteristic
312	#3163	C₂×D₄	1	2	yes	—
313	#3162	C₂×D₄	1	2	yes	—
314	C₂×#498	C₂×D₄	1	1	yes	characteristic
315	#3155	C₂×D₄	1	2	yes	—
316	#3155	C₂×D₄	1	1	yes	characteristic
317	#3155	C₂×D₄	1	2	yes	—
318	#3155	C₂×D₄	1	1	yes	characteristic
319	#3150	C₂×D₄	1	2	yes	—
320	C₂×#493	C₂×D₄	1	1	yes	characteristic
321	#3060	C₂×D₄	1	1	yes	characteristic
322	#3060	C₂×D₄	1	2	yes	—
323	#3060	C₂⁴	1	1	yes	characteristic
324	#3060	C₂⁴	1	2	yes	—
325	#3058	C₂×D₄	1	1	yes	characteristic
326	#3058	C₂×D₄	1	2	yes	—
327	#3058	C₂⁴	1	1	yes	characteristic
328	#3058	C₂⁴	1	2	yes	—
329	C₂×#469	C₂×D₄	1	1	yes	characteristic
330	C₂×#469	C₂×D₄	1	1	yes	characteristic
331	#3050	C₂×D₄	1	2	yes	—
332	#3050	C₂×D₄	1	2	yes	—
333	#2980	C₂×D₄	1	2	yes	—
334	#2980	C₂×D₄	1	2	yes	—
335	#2979	C₂×D₄	1	1	yes	characteristic
336	#2979	C₂×D₄	1	1	yes	characteristic
337	#2978	C₂×D₄	1	2	yes	—
338	#2977	C₂×D₄	1	2	yes	—
339	#2977	C₂×D₄	1	2	yes	—
340	#2961	C₂×D₄	1	2	yes	—
341	#2961	C₂×D₄	1	2	yes	—
342	#2960	C₂×D₄	1	1	yes	characteristic
343	#2960	C₂×D₄	1	1	yes	characteristic
344	#2952	C₂×D₄	1	2	yes	—
345	#2952	C₂×D₄	1	1	yes	characteristic
346	#2952	C₂×D₄	1	2	yes	—
347	#2952	C₂×D₄	1	1	yes	characteristic
348	#2948	C₂×D₄	1	2	yes	—
349	#2948	C₂×D₄	1	1	yes	characteristic
350	#2948	C₂×D₄	1	1	yes	characteristic
351	#2948	C₂×D₄	1	2	yes	—
352	#2943	C₂×D₄	1	1	yes	characteristic
353	#2943	C₂×D₄	1	2	yes	—
354	#2943	C₂×D₄	1	2	yes	—
355	#2943	C₂×D₄	1	1	yes	characteristic
356	C₂×#442	C₂×D₄	1	2	yes	—
357	C₂×#442	C₂×D₄	1	2	yes	—
358	C₂×#442	C₂×D₄	1	2	yes	—
359	C₂×#442	C₂×D₄	1	1	yes	characteristic
360	C₂×#442	C₂×D₄	1	1	yes	characteristic
361	C₂×#442	C₂×D₄	1	2	yes	—
362	C₄×#135	C₂×D₄	1	1	yes	characteristic
363	C₄×#135	C₂×D₄	1	1	yes	characteristic
364	#2932	C₂×D₄	1	2	yes	—
365	#2932	C₂⁴	1	2	yes	—
366	#2931	C₂×D₄	1	1	yes	characteristic
367	#2931	C₂⁴	1	1	yes	characteristic
368	#2930	C₂×D₄	1	1	yes	characteristic
369	#2930	C₂×D₄	1	1	yes	characteristic
370	#2930	C₂×D₄	1	1	yes	characteristic
371	#2930	C₂⁴	1	1	yes	characteristic
372	#2929	C₂×D₄	1	2	yes	—
373	#2929	C₂×D₄	1	2	yes	—
374	#2929	C₂×D₄	1	2	yes	—
375	#2929	C₂⁴	1	2	yes	—
376	#2923	C₂×D₄	1	2	yes	—
377	#2923	C₂×D₄	1	1	yes	characteristic
378	#2923	C₂×D₄	1	2	yes	—
379	#2923	C₂×D₄	1	1	yes	characteristic
380	#2920	C₂×D₄	1	2	yes	—
381	#2920	C₂×D₄	1	1	yes	characteristic
382	#2916	C₂⁴	1	1	yes	characteristic
383	#2912	C₂×D₄	1	1	yes	characteristic
384	#2912	C₂×D₄	1	2	yes	—
385	#2912	C₂⁴	1	1	yes	characteristic
386	#2911	C₂×D₄	1	1	yes	characteristic
387	C₂²×#106	C₂×D₄	1	2	yes	—
388	#2875	C₂×D₄	1	1	yes	characteristic
389	#2875	C₂×D₄	1	2	yes	—
390	#2875	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
392	C₂²×#97	C₂×D₄	1	2	yes	—
393	#2115	C₂⁴	1	2	yes	—
394	#2115	C₂⁴	1	1	yes	characteristic
395	#2115	C₂⁴	1	1	yes	characteristic
396	#2115	C₂⁴	1	2	yes	—
397	#1813	C₂⁴	1	1	yes	characteristic
398	#1813	C₂⁴	1	2	yes	—
399	#1812	C₂⁴	1	1	yes	characteristic
400	#1812	C₂⁴	1	2	yes	—
401	C₂×#135	C₂²×D₄	1	1	yes	characteristic
402	C₂×#135	C₂²×D₄	1	2	yes	—
403	C₂×#135	C₂²×D₄	1	2	yes	—
404	C₂×#135	C₂²×D₄	1	1	yes	characteristic
405	C₂²×D₈	C₂²×D₄	1	2	yes	—
406	C₂²×D₈	C₂²×D₄	1	1	yes	characteristic
407	C₂²×D₈	C₂²×D₄	1	1	yes	characteristic
408	C₂²×D₈	C₂²×D₄	1	2	yes	—
409	C₂×#131	#120	1	1	yes	characteristic
410	C₂×#131	#120	1	2	yes	—
411	C₂×#131	C₂²×D₄	1	1	yes	characteristic
412	C₂×#131	C₂²×D₄	1	2	yes	—
413	C₂×#131	C₂²×D₄	1	1	yes	characteristic
414	C₂×#131	C₂⁵	1	1	yes	characteristic
415	C₂²×M₁₆	#120	1	1	yes	characteristic
416	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
417	C₂³×C₈	#120	1	2	yes	—
418	C₂³×C₈	C₂²×D₄	1	2	yes	—
419	#559	AGL(1,ℤ/8)	1	1	yes	characteristic
420	#559	AGL(1,ℤ/8)	1	2	yes	—
421	Q₈²	AGL(1,ℤ/8)	1	1	yes	characteristic
422	#555	AGL(1,ℤ/8)	1	1	yes	characteristic
423	#555	AGL(1,ℤ/8)	1	2	yes	—
424	#551	AGL(1,ℤ/8)	1	2	yes	—
425	#551	AGL(1,ℤ/8)	1	2	yes	—
426	#551	AGL(1,ℤ/8)	1	2	yes	—
427	D₄²	AGL(1,ℤ/8)	1	1	yes	characteristic
428	D₄²	AGL(1,ℤ/8)	1	2	yes	—
429	#533	#120	1	1	yes	characteristic
430	#533	#120	1	2	yes	—
431	#532	C₂²×D₄	1	1	yes	characteristic
432	#532	C₂²×D₄	1	2	yes	—
433	#525	#120	1	2	yes	—
434	#525	#120	1	1	yes	characteristic
435	#525	C₂²×D₄	1	2	yes	—
436	#525	C₂²×D₄	1	1	yes	characteristic
437	C₄×#41	#120	1	1	yes	characteristic
438	C₄×#41	#120	1	2	yes	—
439	C₄×#41	C₂²×D₄	1	1	yes	characteristic
440	C₂²×C₄²	#120	1	2	yes	—
441	C₂²×C₄²	#120	1	1	yes	characteristic
442	#499	#120	1	2	yes	—
443	#499	#120	1	2	yes	—
444	#499	#120	1	2	yes	—
445	#498	#120	1	2	yes	—
446	#498	#120	1	2	yes	—
447	#498	#120	1	2	yes	—
448	#495	#120	1	2	yes	—
449	#495	#120	1	2	yes	—
450	#495	#120	1	2	yes	—
451	#493	#120	1	2	yes	—
452	#493	#120	1	2	yes	—
453	#493	#120	1	2	yes	—
454	#470	C₂²×D₄	1	2	yes	—
455	#470	C₂²×D₄	1	2	yes	—
456	#470	C₂²×D₄	1	2	yes	—
457	#469	C₂²×D₄	1	2	yes	—
458	#469	C₂²×D₄	1	2	yes	—
459	#469	C₂²×D₄	1	2	yes	—
460	#469	C₂²×D₄	1	2	yes	—
461	#469	C₂²×D₄	1	2	yes	—
462	#469	C₂²×D₄	1	2	yes	—
463	#469	C₂²×D₄	1	2	yes	—
464	#469	C₂²×D₄	1	2	yes	—
465	#469	C₂²×D₄	1	2	yes	—
466	#442	#120	1	2	yes	—
467	#442	#120	1	2	yes	—
468	#442	#120	1	2	yes	—
469	#442	#120	1	2	yes	—
470	#442	#120	1	1	yes	characteristic
471	#442	#120	1	2	yes	—
472	#442	#120	1	2	yes	—
473	#442	#120	1	2	yes	—
474	#442	#120	1	2	yes	—
475	#442	#120	1	2	yes	—
476	#442	#120	1	2	yes	—
477	#442	#120	1	1	yes	characteristic
478	#442	#120	1	2	yes	—
479	#442	#120	1	2	yes	—
480	#442	#120	1	1	yes	characteristic
481	#442	#120	1	2	yes	—
482	#442	#120	1	1	yes	characteristic
483	#441	#120	1	1	yes	characteristic
484	#441	#120	1	2	yes	—
485	#441	#120	1	2	yes	—
486	#441	#120	1	1	yes	characteristic
487	#441	#120	1	2	yes	—
488	#441	#120	1	1	yes	characteristic
489	#441	#120	1	1	yes	characteristic
490	#427	C₂²×D₄	1	1	yes	characteristic
491	#427	C₂²×D₄	1	2	yes	—
492	#427	C₂²×D₄	1	1	yes	characteristic
493	#427	C₂²×D₄	1	2	yes	—
494	C₂×#106	C₂²×D₄	1	1	yes	characteristic
495	C₂×#106	C₂²×D₄	1	1	yes	characteristic
496	C₂×#106	C₂²×D₄	1	2	yes	—
497	C₂×#106	C₂²×D₄	1	2	yes	—
498	#424	#120	1	1	yes	characteristic
499	#424	#120	1	2	yes	—
500	#424	#120	1	2	yes	—
501	#424	#120	1	2	yes	—
502	#424	#120	1	1	yes	characteristic
503	#424	#120	1	1	yes	characteristic
504	#424	C₂²×D₄	1	1	yes	characteristic
505	#424	C₂²×D₄	1	2	yes	—
506	#423	#120	1	2	yes	—
507	#423	#120	1	1	yes	characteristic
508	#423	C₂²×D₄	1	2	yes	—
509	#423	C₂²×D₄	1	1	yes	characteristic
510	#408	#120	1	1	yes	characteristic
511	#408	#120	1	2	yes	—
512	#408	C₂²×D₄	1	1	yes	characteristic
513	#408	C₂²×D₄	1	2	yes	—
514	#408	C₂²×D₄	1	2	yes	—
515	#408	C₂²×D₄	1	1	yes	characteristic
516	#408	C₂²×D₄	1	2	yes	—
517	#408	C₂²×D₄	1	1	yes	characteristic
518	#407	#120	1	2	yes	—
519	#407	#120	1	1	yes	characteristic
520	#407	C₂²×D₄	1	2	yes	—
521	#407	C₂²×D₄	1	1	yes	characteristic
522	#405	#120	1	1	yes	characteristic
523	#405	#120	1	2	yes	—
524	#405	C₂²×D₄	1	2	yes	—
525	#405	C₂²×D₄	1	1	yes	characteristic
526	#405	C₂²×D₄	1	2	yes	—
527	#405	C₂²×D₄	1	1	yes	characteristic
528	#405	C₂²×D₄	1	2	yes	—
529	#405	C₂²×D₄	1	1	yes	characteristic
530	C₄×M₁₆	#120	1	1	yes	characteristic
531	C₄×M₁₆	#120	1	2	yes	—
532	C₄×M₁₆	C₂²×D₄	1	1	yes	characteristic
533	C₄×M₁₆	C₂²×D₄	1	2	yes	—
534	C₂×#97	#120	1	2	yes	—
535	C₂×#97	#120	1	2	yes	—
536	C₂×#97	#120	1	1	yes	characteristic
537	C₂×#97	C₂²×D₄	1	2	yes	—
538	C₂×#97	C₂²×D₄	1	2	yes	—
539	C₂×#97	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₈	#120	1	1	yes	characteristic
541	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
542	C₂×#41	C₂×#120	1	1	yes	characteristic
543	C₂×#41	C₂×#120	1	2	yes	—
544	C₂×#41	C₂³×D₄	1	1	yes	characteristic
545	C₂³×C₄	C₂×#120	1	2	yes	—
546	C₂³×C₄	C₂×#120	1	1	yes	characteristic
547	C₂×Q₁₆	C₂×#120	1	1	yes	characteristic
548	C₂×Q₁₆	C₂×#120	1	2	yes	—
549	C₂×Q₁₆	C₂×#120	1	1	yes	characteristic
550	C₂×D₈	C₂×#120	1	2	yes	—
551	C₂×D₈	C₂×#120	1	1	yes	characteristic
552	C₂×D₈	C₂×#120	1	2	yes	—
553	C₂×D₈	C₂×#120	1	2	yes	—
554	C₂×D₈	C₂×#120	1	2	yes	—
555	C₂×D₈	C₂×#120	1	2	yes	—
556	C₂×D₈	C₂×#120	1	1	yes	characteristic
557	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
558	C₂×M₁₆	C₂×#120	1	2	yes	—
559	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
560	C₂×M₁₆	C₂×#120	1	2	yes	—
561	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
562	C₂×M₁₆	C₂×#120	1	2	yes	—
563	C₂×M₁₆	C₂³×D₄	1	1	yes	characteristic
564	C₂×M₁₆	C₂³×D₄	1	2	yes	—
565	C₂²×C₈	C₂×#120	1	2	yes	—
566	C₂²×C₈	C₂×#120	1	2	yes	—
567	C₂²×C₈	C₂×#120	1	1	yes	characteristic
568	C₂²×C₈	C₂×#120	1	1	yes	characteristic
569	C₂²×C₈	C₂×#120	1	2	yes	—
570	C₂²×C₈	C₂×#120	1	1	yes	characteristic
571	C₂²×C₈	C₂³×D₄	1	2	yes	—
572	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
573	C₄⋊Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₄⋊Q₈	C₂×AGL(1,ℤ/8)	1	2	yes	—
575	#127	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
576	#127	C₂×AGL(1,ℤ/8)	1	2	yes	—
577	#124	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
578	#124	C₂×AGL(1,ℤ/8)	1	2	yes	—
579	#124	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
580	#124	C₂×AGL(1,ℤ/8)	1	2	yes	—
581	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
582	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
583	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
584	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
585	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
586	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
587	#117	C₂×#120	1	2	yes	—
588	#117	C₂×#120	1	1	yes	characteristic
589	#117	C₂×#120	1	2	yes	—
590	#117	C₂×#120	1	1	yes	characteristic
591	C₂×C₄²	C₂×#120	1	2	yes	—
592	C₂×C₄²	C₂×#120	1	1	yes	characteristic
593	C₂×C₄²	C₂×#120	1	2	yes	—
594	C₂×C₄²	C₂×#120	1	1	yes	characteristic
595	#106	C₂×#120	1	1	yes	characteristic
596	#106	C₂×#120	1	2	yes	—
597	#106	C₂×#120	1	2	yes	—
598	#106	C₂×#120	1	2	yes	—
599	#106	C₂×#120	1	2	yes	—
600	#106	C₂×#120	1	2	yes	—
601	#106	C₂×#120	1	1	yes	characteristic
602	#106	C₂×#120	1	2	yes	—
603	#106	C₂×#120	1	1	yes	characteristic
604	#106	C₂×#120	1	1	yes	characteristic
605	#97	C₂×#120	1	1	yes	characteristic
606	#97	C₂×#120	1	2	yes	—
607	#97	C₂×#120	1	2	yes	—
608	#97	C₂×#120	1	2	yes	—
609	#97	C₂×#120	1	1	yes	characteristic
610	#97	C₂×#120	1	1	yes	characteristic
611	#97	C₂×#120	1	1	yes	characteristic
612	C₄×C₈	C₂×#120	1	2	yes	—
613	C₄×C₈	C₂×#120	1	2	yes	—
614	C₄×C₈	C₂×#120	1	2	yes	—
615	C₂⁴	#3003	1	2	yes	—
616	C₂⁴	#3003	1	1	yes	characteristic
617	C₂×Q₈	#3003	1	2	yes	—
618	C₂×Q₈	#3003	1	1	yes	characteristic
619	C₂×Q₈	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₂×D₄	#3003	1	1	yes	characteristic
621	C₂×D₄	#3003	1	2	yes	—
622	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
623	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	2	yes	—
624	C₂²×C₄	#3003	1	1	yes	characteristic
625	C₂²×C₄	#3003	1	2	yes	—
626	C₂²×C₄	C₂²×#120	1	2	yes	—
627	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
628	D₈	#3025	1	2	yes	—
629	C₂×C₈	#2846	1	1	yes	characteristic
630	C₂×C₈	#2846	1	1	yes	characteristic
631	C₂×C₈	#2846	1	2	yes	—
632	C₂×C₈	C₂²×#120	1	1	yes	characteristic
633	C₂×C₈	C₂²×#120	1	2	yes	—
634	C₂×C₈	C₂²×#120	1	1	yes	characteristic
635	C₂²⋊C₄	#3003	1	2	yes	—
636	C₂²⋊C₄	#3003	1	2	yes	—
637	C₂²⋊C₄	#3003	1	2	yes	—
638	C₄²	#2846	1	1	yes	characteristic
639	C₄²	#2846	1	2	yes	—
640	C₄²	#2846	1	1	yes	characteristic
641	C₄²	#3003	1	1	yes	characteristic
642	C₄²	#3003	1	1	yes	characteristic
643	C₄²	#3003	1	2	yes	—
644	C₄²	#3003	1	2	yes	—
645	C₂³	C₂×#3003	1	1	yes	characteristic
646	C₂³	C₂×#3003	1	2	yes	—
647	C₂×C₄	C₂×#2846	1	1	yes	characteristic
648	C₂×C₄	C₂×#3003	1	1	yes	characteristic
649	C₂×C₄	C₂×#3003	1	2	yes	—
650	C₈	C₂×#3025	1	1	yes	characteristic
651	C₈	#60398	1	1	yes	characteristic
652	C₂²	#6628842	1	1	yes	characteristic
653	C₄	#6628885	1	1	yes	characteristic
654	C₄	#6628891	1	1	yes	characteristic
655	C₂	#72231727	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72231727
commutator, Frattini, cosocle	C₂×#131	C₂⁵
LCS	G ▷ C₂×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #2875 ◁ G
LECS	G ▷ C₂×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72231719	C₂	semidirect
2. #72231715	C₂	semidirect
3. #72231714	C₂	semidirect
4. #72231712	C₂	semidirect
5. #72231710	C₂	semidirect
6. #72231708	C₂	semidirect
7. #72231705	C₂	semidirect
8. #72231704	C₂	semidirect
9. #72231703	C₂	semidirect
10. #72231701	C₂	semidirect
11. #72231700	C₂	semidirect
12. #72231699	C₂	semidirect
13. #72231624	C₂	semidirect
14. #72231620	C₂	semidirect
15. #72231615	C₂	semidirect
16. #72231612	C₂	semidirect
17. #72231607	C₂	semidirect
18. #72231603	C₂	semidirect
19. #72231599	C₂	semidirect
20. #72231596	C₂	semidirect
21. #72231593	C₂	semidirect
22. #72213945	C₂	semidirect
23. #72213937	C₂	semidirect
35. #7623148	C₂²	semidirect
36. #7623148	C₂²	semidirect
37. #7622637	C₂²	semidirect
38. #6469085	C₂²	semidirect
39. #6469080	C₂²	semidirect
40. #512046	C₂²	semidirect
41. #512045	C₂²	semidirect
42. #512038	C₂²	semidirect
43. #511946	C₂²	semidirect
44. #511937	C₂²	semidirect
45. #511930	C₂²	semidirect
46. #500355	C₂²	semidirect
47. #500353	C₂²	semidirect
48. #500351	C₂²	semidirect
49. #500349	C₂²	semidirect
50. #500168	C₂²	semidirect
51. #500164	C₂²	semidirect
52. #500160	C₂²	semidirect
53. #500158	C₂²	semidirect
54. #500007	C₂²	semidirect
55. #500005	C₂²	semidirect
56. #500003	C₂²	semidirect
57. #500001	C₂²	semidirect
58. #499752	C₂²	semidirect
59. #499750	C₂²	semidirect
60. #499746	C₂²	semidirect
61. #499742	C₂²	semidirect
62. #495573	C₂²	semidirect
63. #495573	C₂²	semidirect
64. #495507	C₂²	semidirect
65. #495505	C₂²	semidirect
66. #494058	C₂²	semidirect
67. #494058	C₂²	semidirect
68. #494018	C₂²	semidirect
69. #494016	C₂²	semidirect
70. #486701	C₂²	semidirect
71. #486701	C₂²	semidirect
72. #486698	C₂²	semidirect
73. #486697	C₂²	semidirect
74. #486694	C₂²	semidirect
75. #486691	C₂²	semidirect
76. #486689	C₂²	semidirect
77. #486345	C₂²	semidirect
78. #486345	C₂²	semidirect
79. #486342	C₂²	semidirect
80. #486341	C₂²	semidirect
81. #486338	C₂²	semidirect
82. #486335	C₂²	semidirect
83. #486333	C₂²	semidirect
84. #482709	C₂²	semidirect
85. #482709	C₂²	semidirect
86. #482709	C₂²	semidirect
87. #480442	C₂²	semidirect
88. #480440	C₂²	semidirect
89. #130854	C₂²	semidirect
90. #130854	C₂²	semidirect
91. #130852	C₂²	semidirect
92. #130850	C₂²	semidirect
93. #130848	C₂²	semidirect
94. #130847	C₂²	semidirect
95. #130845	C₂²	semidirect
96. #130791	C₂²	semidirect
97. #130786	C₂²	semidirect
98. #130785	C₂²	semidirect
99. #130782	C₂²	semidirect
100. #130780	C₂²	semidirect
101. #130776	C₂²	semidirect
102. #130776	C₂²	semidirect
103. #130296	C₂²	semidirect
104. #130296	C₂²	semidirect
105. #130294	C₂²	semidirect
106. #130294	C₂²	semidirect
107. #130292	C₂²	semidirect
108. #130290	C₂²	semidirect
109. #130288	C₂²	semidirect
110. #130288	C₂²	semidirect
111. #130284	C₂²	semidirect
112. #130284	C₂²	semidirect
113. #130241	C₂²	semidirect
114. #130237	C₂²	semidirect
115. #130234	C₂²	semidirect
116. #130233	C₂²	semidirect
117. #129615	C₂²	semidirect
118. #129615	C₂²	semidirect
119. #129613	C₂²	semidirect
120. #129613	C₂²	semidirect
121. #129596	C₂²	semidirect
122. #129596	C₂²	semidirect
125. #62392	D₄	semidirect
126. #62392	D₄	semidirect
127. #62373	D₄	semidirect
128. #62372	D₄	semidirect
133. #62290	D₄	semidirect
135. #62270	D₄	semidirect
137. #62269	D₄	semidirect
139. #61414	D₄	semidirect
140. #61409	D₄	semidirect
141. #61378	D₄	semidirect
142. #61374	D₄	semidirect
145. #61267	D₄	semidirect
147. #61259	D₄	semidirect
151. #61063	D₄	semidirect
153. #61049	D₄	semidirect
155. #60974	D₄	semidirect
156. #60974	D₄	semidirect
157. #60974	D₄	semidirect
158. #60968	D₄	semidirect
159. #60968	D₄	semidirect
160. #60967	D₄	semidirect
161. #60964	D₄	semidirect
162. #60698	D₄	semidirect
163. #60698	D₄	semidirect
166. C₂×#3184	D₄	semidirect
167. #60688	D₄	semidirect
178. #60184	C₂³	semidirect
179. #60176	D₄	semidirect
180. #60176	D₄	semidirect
182. C₄×#575	D₄	semidirect
183. C₂²×#442	D₄	semidirect
184. #33659	C₂³	semidirect
185. #33659	C₂³	semidirect
186. #33657	C₂³	semidirect
187. #33657	C₂³	semidirect
188. #33533	C₂³	semidirect
189. #33533	C₂³	semidirect
190. #33531	C₂³	semidirect
191. #33531	C₂³	semidirect
192. #33426	C₂³	semidirect
193. #33426	C₂³	semidirect
194. #33404	C₂³	semidirect
196. #33388	C₂³	semidirect
197. #33329	C₂³	semidirect
198. #27694	C₂³	semidirect
199. #27693	C₂³	semidirect
200. #27692	C₂³	semidirect
201. #27691	C₂³	semidirect
202. #24288	C₂³	semidirect
203. #24287	C₂³	semidirect
204. #24286	C₂³	semidirect
205. #24285	C₂³	semidirect
206. #20788	C₂³	semidirect
207. #20788	C₂³	semidirect
208. #13079	C₂³	semidirect
209. #13079	C₂³	semidirect
210. #13077	C₂³	semidirect
211. #13077	C₂³	semidirect
212. #13076	C₂³	semidirect
213. #13076	C₂³	semidirect
214. #13074	C₂³	semidirect
215. #13074	C₂³	semidirect
216. #12989	C₂³	semidirect
217. #12989	C₂³	semidirect
218. #12988	C₂³	semidirect
219. #12988	C₂³	semidirect
220. #12982	C₂³	semidirect
221. #12982	C₂³	semidirect
222. #12981	C₂³	semidirect
223. #12981	C₂³	semidirect
224. #12874	C₂³	semidirect
225. #12874	C₂³	semidirect
226. #12873	C₂³	semidirect
227. #12873	C₂³	semidirect
228. #12810	C₂³	semidirect
229. #12809	C₂³	semidirect
230. #12808	C₂³	semidirect
231. #12807	C₂³	semidirect
232. #12806	C₂³	semidirect
233. #12805	C₂³	semidirect
234. #12805	C₂³	semidirect
239. #11872	C₂³	semidirect
240. #11872	C₂³	semidirect
241. #11872	C₂³	semidirect
242. #11870	C₂³	semidirect
243. #11870	C₂³	semidirect
244. #11870	C₂³	semidirect
245. #11868	C₂³	semidirect
246. #11868	C₂³	semidirect
247. #11868	C₂³	semidirect
248. #11867	C₂³	semidirect
249. #11867	C₂³	semidirect
250. #11867	C₂³	semidirect
251. #11486	C₂³	semidirect
252. #11486	C₂³	semidirect
253. #11485	C₂³	semidirect
254. #11485	C₂³	semidirect
255. #11484	C₂³	semidirect
256. #11483	C₂³	semidirect
257. #11483	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72231719	2
#72231715	2
#72231714	2
#72231712	2
#72231710	2
#72231708	2
#72231705	2
#72231704	2
#72231703	2
#72231701	2
#72231700	2
#72231699	2
#72231624	2
#72231620	2
#72231615	2
#72231612	2
#72231607	2
#72231603	2
#72231599	2
#72231596	2
#72231593	2
#72213945	2
#72213937	2