Subgroups — #72318794

Order 2048.

At least 13820 conjugacy classes of subgroups; only the 976 normal subgroups are shown.

The subgroup lattice has 625 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72318784	C₂	1	1	yes	maximal, characteristic, complemented
2	#72318775	C₂	1	1	yes	maximal, characteristic, complemented
3	#72318768	C₂	1	1	yes	maximal, characteristic, complemented
4	#72318763	C₂	1	1	yes	maximal, characteristic, complemented
5	#72318757	C₂	1	2	yes	maximal, complemented
6	#72318749	C₂	1	2	yes	maximal, complemented
7	#72318739	C₂	1	2	yes	maximal, complemented
8	#72318733	C₂	1	2	yes	maximal, complemented
9	#72318727	C₂	1	2	yes	maximal, complemented
10	#72318719	C₂	1	2	yes	maximal, complemented
11	#72318542	C₂	1	1	yes	maximal, characteristic, complemented
12	#72318458	C₂	1	1	yes	maximal, characteristic, complemented
13	#72318439	C₂	1	1	yes	maximal, characteristic, complemented
14	#72318347	C₂	1	1	yes	maximal, characteristic, complemented
15	#72318212	C₂	1	1	yes	maximal, characteristic, complemented
16	#72317868	C₂	1	1	yes	maximal, characteristic, complemented
17	#72317711	C₂	1	1	yes	maximal, characteristic, complemented
18	#72285763	C₂	1	1	yes	maximal, characteristic, complemented
19	#72285670	C₂	1	1	yes	maximal, characteristic, complemented
20	#72278795	C₂	1	1	yes	maximal, characteristic, complemented
21	#72278427	C₂	1	2	yes	maximal, complemented
22	#72278396	C₂	1	2	yes	maximal, complemented
23	#72213224	C₂	1	1	yes	maximal, characteristic, complemented
24	#10575560	C₂²	1	1	yes	characteristic, complemented
25	#9015670	C₂²	1	2	yes	—
26	#8934366	C₂²	1	1	yes	characteristic
27	#8926850	C₂²	1	1	yes	characteristic
28	#8807309	C₂²	1	2	yes	—
29	#8756105	C₂²	1	1	yes	characteristic
30	#8193898	C₂²	1	1	yes	characteristic
31	#8122973	C₂²	1	2	yes	—
32	#7783287	C₂²	1	2	yes	—
33	#7743196	C₂²	1	1	yes	characteristic
34	#7737411	C₂²	1	1	yes	characteristic
35	#7674604	C₂²	1	1	yes	characteristic
36	#6435072	C₂²	1	1	yes	characteristic, complemented
37	#6432082	C₂²	1	1	yes	characteristic, complemented
38	#6347140	C₂²	1	2	yes	complemented
39	#6346414	C₂²	1	2	yes	complemented
40	#485870	C₂²	1	2	yes	complemented
41	#485864	C₂²	1	2	yes	complemented
42	#485798	C₂²	1	2	yes	complemented
43	#485792	C₂²	1	2	yes	complemented
44	#485740	C₂²	1	2	yes	complemented
45	#485720	C₂²	1	2	yes	complemented
46	#485709	C₂²	1	2	yes	complemented
47	#485708	C₂²	1	2	yes	complemented
48	#485690	C₂²	1	2	yes	complemented
49	#485688	C₂²	1	2	yes	complemented
50	#485660	C₂²	1	2	yes	complemented
51	#485640	C₂²	1	2	yes	complemented
52	#485629	C₂²	1	2	yes	complemented
53	#485628	C₂²	1	2	yes	complemented
54	#485610	C₂²	1	2	yes	complemented
55	#485608	C₂²	1	2	yes	complemented
56	#482640	C₂²	1	2	yes	complemented
57	#482633	C₂²	1	2	yes	complemented
58	#481774	C₂²	1	2	yes	complemented
59	#481756	C₂²	1	2	yes	complemented
60	#480716	C₂²	1	2	yes	complemented
61	#480405	C₂²	1	2	yes	complemented
62	#441116	C₂²	1	1	yes	characteristic, complemented
63	#441113	C₂²	1	1	yes	characteristic, complemented
64	#422773	C₂²	1	1	yes	characteristic, complemented
65	#422772	C₂²	1	1	yes	characteristic, complemented
66	#417936	C₂²	1	1	yes	characteristic, complemented
67	#417934	C₂²	1	1	yes	characteristic, complemented
68	#417799	C₂²	1	1	yes	characteristic, complemented
69	#417798	C₂²	1	1	yes	characteristic, complemented
70	#374262	C₂²	1	1	yes	characteristic, complemented
71	#361634	C₂²	1	1	yes	characteristic, complemented
72	#360028	C₂²	1	1	yes	characteristic, complemented
73	#246939	C₂²	1	2	yes	complemented
74	#246936	C₂²	1	2	yes	complemented
75	#246931	C₂²	1	1	yes	characteristic, complemented
76	#246930	C₂²	1	1	yes	characteristic
77	#246930	C₂²	1	2	yes	complemented
78	#246930	C₂²	1	1	yes	characteristic, complemented
79	#246930	C₂²	1	1	yes	characteristic, complemented
80	#246928	C₂²	1	1	yes	characteristic, complemented
81	#246927	C₂²	1	1	yes	characteristic
82	#246927	C₂²	1	2	yes	complemented
83	#246927	C₂²	1	1	yes	characteristic, complemented
84	#246927	C₂²	1	1	yes	characteristic, complemented
85	#201638	C₂²	1	2	yes	complemented
86	#201614	C₂²	1	2	yes	complemented
87	#187836	C₂²	1	1	yes	characteristic, complemented
88	#187836	C₂²	1	1	yes	characteristic, complemented
89	#134094	C₂²	1	2	yes	complemented
90	#134093	C₂²	1	1	yes	characteristic, complemented
91	#134093	C₂²	1	1	yes	characteristic, complemented
92	#134056	C₂²	1	1	yes	characteristic, complemented
93	#134056	C₂²	1	1	yes	characteristic, complemented
94	#134055	C₂²	1	2	yes	complemented
95	#131982	C₂²	1	2	yes	complemented
96	#131982	C₂²	1	2	yes	complemented
97	#131980	C₂²	1	1	yes	characteristic, complemented
98	#131980	C₂²	1	1	yes	characteristic, complemented
99	#131979	C₂²	1	1	yes	characteristic
100	#131979	C₂²	1	1	yes	characteristic
101	#131979	C₂²	1	1	yes	characteristic, complemented
102	#131979	C₂²	1	1	yes	characteristic, complemented
103	#131979	C₂²	1	1	yes	characteristic, complemented
104	#131979	C₂²	1	1	yes	characteristic, complemented
105	#131979	C₂²	1	2	yes	complemented
106	#131979	C₂²	1	2	yes	complemented
107	#130145	C₂²	1	2	yes	complemented
108	#130145	C₂²	1	2	yes	complemented
109	#130142	C₂²	1	2	yes	complemented
110	#130142	C₂²	1	2	yes	complemented
111	#130089	C₂²	1	2	yes	complemented
112	#130089	C₂²	1	2	yes	complemented
113	#130086	C₂²	1	2	yes	complemented
114	#130086	C₂²	1	2	yes	complemented
115	#130072	C₂²	1	2	yes	complemented
116	#130072	C₂²	1	2	yes	complemented
117	#130071	C₂²	1	2	yes	complemented
118	#130071	C₂²	1	2	yes	complemented
119	#130070	C₂²	1	2	yes	complemented
120	#130070	C₂²	1	2	yes	complemented
121	#130068	C₂²	1	2	yes	complemented
122	#130068	C₂²	1	2	yes	complemented
123	C₂×#3500	D₄	1	1	yes	characteristic
124	C₂×#3500	D₄	1	1	yes	characteristic
125	C₂×#3498	D₄	1	1	yes	characteristic
126	C₂×#3498	C₂³	1	1	yes	characteristic
127	C₂×#3543	D₄	1	1	yes	characteristic, complemented
128	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
129	#62686	C₂³	1	1	yes	characteristic, complemented
130	#60644	C₂³	1	1	yes	characteristic
131	#60644	C₂³	1	1	yes	characteristic, complemented
132	#60619	C₂³	1	1	yes	characteristic
133	#60619	C₂³	1	1	yes	characteristic, complemented
134	#60125	C₂³	1	1	yes	characteristic, complemented
135	#60045	C₂³	1	2	yes	—
136	#59362	C₂³	1	2	yes	—
137	#58197	D₄	1	2	yes	—
138	#57971	D₄	1	2	yes	—
139	#54678	D₄	1	2	yes	—
140	#54174	D₄	1	2	yes	—
141	#52673	D₄	1	2	yes	—
142	#52662	D₄	1	2	yes	—
143	#52054	D₄	1	1	yes	characteristic, complemented
144	#52054	C₂³	1	1	yes	characteristic
145	#52005	D₄	1	2	yes	complemented
146	#52005	C₂³	1	2	yes	—
147	#52004	D₄	1	1	yes	characteristic, complemented
148	#52004	D₄	1	1	yes	characteristic, complemented
149	#52004	D₄	1	2	yes	complemented
150	#52004	D₄	1	1	yes	characteristic, complemented
151	#52004	C₂³	1	1	yes	characteristic
152	#52004	C₂³	1	2	yes	—
153	#52004	C₂³	1	1	yes	characteristic
154	#52004	C₂³	1	1	yes	characteristic
155	#47818	D₄	1	2	yes	complemented
156	#47794	D₄	1	2	yes	complemented
157	#47545	D₄	1	2	yes	complemented
158	#47036	C₂³	1	2	yes	—
159	#47003	C₂³	1	2	yes	—
160	#46965	D₄	1	2	yes	complemented
161	#46458	C₂³	1	2	yes	—
162	#46384	C₂³	1	2	yes	—
163	#46270	C₂³	1	2	yes	—
164	#46232	C₂³	1	2	yes	—
165	#43361	D₄	1	2	yes	—
166	#43360	D₄	1	2	yes	—
167	#42414	D₄	1	2	yes	complemented
168	#42410	D₄	1	2	yes	complemented
169	#42405	D₄	1	2	yes	complemented
170	#42404	D₄	1	2	yes	complemented
171	#37556	D₄	1	2	yes	complemented
172	#35676	C₂³	1	1	yes	characteristic
173	#35616	D₄	1	1	yes	characteristic
174	#35527	D₄	1	1	yes	characteristic
175	#35527	C₂³	1	1	yes	characteristic
176	#35327	C₂³	1	1	yes	characteristic
177	#35327	C₂³	1	1	yes	characteristic
178	#35272	D₄	1	1	yes	characteristic
179	#35272	C₂³	1	1	yes	characteristic
180	#35237	D₄	1	2	yes	complemented
181	#35144	C₂³	1	2	yes	—
182	#34963	C₂³	1	2	yes	—
183	C₂×#2657	D₄	1	1	yes	characteristic
184	#34364	D₄	1	1	yes	characteristic, complemented
185	C₂×#2380	D₄	1	1	yes	characteristic, complemented
186	#34070	D₄	1	1	yes	characteristic
187	#34070	C₂³	1	1	yes	characteristic
188	#23560	C₂³	1	1	yes	characteristic, complemented
189	#23498	C₂³	1	1	yes	characteristic, complemented
190	#23470	C₂³	1	1	yes	characteristic, complemented
191	#23469	C₂³	1	1	yes	characteristic, complemented
192	#23461	C₂³	1	1	yes	characteristic, complemented
193	#23446	C₂³	1	1	yes	characteristic, complemented
194	#23445	C₂³	1	1	yes	characteristic, complemented
195	#23406	C₂³	1	1	yes	characteristic, complemented
196	#20632	C₂³	1	1	yes	characteristic, complemented
197	C₄×#413	C₂³	1	1	yes	characteristic, complemented
198	#18155	C₂³	1	2	yes	complemented
199	#18154	C₂³	1	2	yes	—
200	#18154	C₂³	1	2	yes	complemented
201	#18154	C₂³	1	2	yes	complemented
202	#18153	C₂³	1	2	yes	complemented
203	#18152	C₂³	1	2	yes	—
204	#18152	C₂³	1	2	yes	complemented
205	#18152	C₂³	1	2	yes	complemented
206	#17366	C₂³	1	2	yes	complemented
207	#17366	C₂³	1	2	yes	complemented
208	#11763	C₂³	1	2	yes	complemented
209	#11763	C₂³	1	2	yes	complemented
210	#11761	C₂³	1	2	yes	—
211	#11761	C₂³	1	2	yes	—
212	#11761	C₂³	1	2	yes	complemented
213	#11761	C₂³	1	2	yes	complemented
214	#11761	C₂³	1	2	yes	complemented
215	#11761	C₂³	1	2	yes	complemented
216	#11756	C₂³	1	2	yes	complemented
217	#11756	C₂³	1	2	yes	complemented
218	#11754	C₂³	1	2	yes	—
219	#11754	C₂³	1	2	yes	—
220	#11754	C₂³	1	2	yes	complemented
221	#11754	C₂³	1	2	yes	complemented
222	#11754	C₂³	1	2	yes	complemented
223	#11754	C₂³	1	2	yes	complemented
224	#11513	C₂³	1	2	yes	complemented
225	#11513	C₂³	1	2	yes	complemented
226	#11507	C₂³	1	2	yes	complemented
227	#11507	C₂³	1	2	yes	complemented
228	#11504	C₂³	1	2	yes	complemented
229	#11504	C₂³	1	2	yes	complemented
230	#11503	C₂³	1	2	yes	complemented
231	#11503	C₂³	1	2	yes	complemented
232	#11006	C₂³	1	1	yes	characteristic
233	#11006	C₂³	1	1	yes	characteristic
234	#11006	C₂³	1	1	yes	characteristic, complemented
235	#11006	C₂³	1	1	yes	characteristic, complemented
236	#10959	C₂³	1	1	yes	characteristic, complemented
237	#10959	C₂³	1	1	yes	characteristic, complemented
238	#10940	C₂³	1	1	yes	characteristic, complemented
239	#10940	C₂³	1	1	yes	characteristic, complemented
240	#10939	C₂³	1	1	yes	characteristic, complemented
241	#10939	C₂³	1	1	yes	characteristic, complemented
242	#10893	C₂³	1	1	yes	characteristic, complemented
243	#10893	C₂³	1	1	yes	characteristic, complemented
244	#9492	C₂³	1	2	yes	—
245	#9492	C₂³	1	2	yes	—
246	#9492	C₂³	1	2	yes	complemented
247	#9492	C₂³	1	2	yes	complemented
248	#9492	C₂³	1	2	yes	complemented
249	#9492	C₂³	1	2	yes	complemented
250	#9491	C₂³	1	2	yes	complemented
251	#9491	C₂³	1	2	yes	complemented
252	#8522	C₂³	1	1	yes	characteristic
253	#8522	C₂³	1	1	yes	characteristic
254	#8522	C₂³	1	1	yes	characteristic
255	#8522	C₂³	1	1	yes	characteristic
256	#8522	C₂³	1	2	yes	complemented
257	#8522	C₂³	1	2	yes	complemented
258	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
259	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
260	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
261	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
262	C₂×#559	C₂×D₄	1	1	yes	characteristic
263	C₂×#550	C₂×D₄	1	2	yes	—
264	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄²	C₂×D₄	1	2	yes	—
267	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
268	#3458	C₂⁴	1	1	yes	characteristic
269	#3449	C₂⁴	1	1	yes	characteristic
270	C₂×#536	C₂×D₄	1	1	yes	characteristic
271	C₂×#536	C₂×D₄	1	1	yes	characteristic
272	C₂×#535	C₂×D₄	1	1	yes	characteristic
273	C₂×#535	C₂×D₄	1	1	yes	characteristic
274	C₂×#535	C₂×D₄	1	1	yes	characteristic
275	C₂×#535	C₂×D₄	1	1	yes	characteristic
276	C₂×#535	C₂×D₄	1	1	yes	characteristic
277	C₂×#535	C₂×D₄	1	1	yes	characteristic
278	C₂×#535	C₂×D₄	1	1	yes	characteristic
279	C₂×#535	C₂×D₄	1	1	yes	characteristic
280	C₂×#535	C₂⁴	1	1	yes	characteristic
281	C₂×#535	C₂⁴	1	1	yes	characteristic
282	C₂×#532	C₂×D₄	1	1	yes	characteristic
283	C₂×#532	C₂×D₄	1	1	yes	characteristic
284	C₂×#532	C₂×D₄	1	1	yes	characteristic
285	C₂×#532	C₂×D₄	1	1	yes	characteristic
286	C₂²×#127	C₂×D₄	1	1	yes	characteristic
287	C₂²×#127	C₂×D₄	1	1	yes	characteristic
288	C₂²×#127	C₂×D₄	1	1	yes	characteristic
289	C₂²×#127	C₂×D₄	1	1	yes	characteristic
290	C₂²×#127	C₂×D₄	1	1	yes	characteristic
291	C₂×#529	C₂×D₄	1	2	yes	—
292	C₂²×#124	C₂×D₄	1	1	yes	characteristic
293	C₂²×#124	C₂×D₄	1	1	yes	characteristic
294	C₂²×#124	C₂×D₄	1	1	yes	characteristic
295	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
296	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
297	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
298	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
300	#2873	C₂⁴	1	1	yes	characteristic
301	#2873	C₂⁴	1	1	yes	characteristic
302	#2844	C₂×D₄	1	2	yes	—
303	#2842	C₂×D₄	1	2	yes	—
304	#2841	C₂×D₄	1	2	yes	—
305	#2833	C₂×D₄	1	2	yes	—
306	#2832	C₂×D₄	1	2	yes	—
307	#2819	C₂×D₄	1	2	yes	—
308	#2815	C₂×D₄	1	2	yes	—
309	#2812	C₂×D₄	1	2	yes	—
310	#2804	C₂×D₄	1	2	yes	—
311	#2795	C₂×D₄	1	2	yes	—
312	#2795	C₂×D₄	1	2	yes	—
313	#2794	C₂×D₄	1	2	yes	—
314	#2784	C₂×D₄	1	2	yes	—
315	#2771	C₂×D₄	1	2	yes	—
316	#2760	C₂×D₄	1	2	yes	—
317	#2752	C₂×D₄	1	2	yes	—
318	#2752	C₂×D₄	1	2	yes	—
319	#2735	C₂×D₄	1	2	yes	—
320	#2699	C₂×D₄	1	2	yes	—
321	#2680	C₂×D₄	1	2	yes	—
322	#2679	C₂×D₄	1	2	yes	—
323	#2670	C₂×D₄	1	2	yes	—
324	#2668	C₂×D₄	1	2	yes	—
325	#2668	C₂×D₄	1	2	yes	—
326	#2634	C₂×D₄	1	2	yes	—
327	#2633	C₂×D₄	1	2	yes	—
328	#2632	C₂×D₄	1	2	yes	—
329	#2632	C₂×D₄	1	2	yes	—
330	#2632	C₂×D₄	1	2	yes	—
331	#2631	C₂×D₄	1	2	yes	—
332	#2631	C₂×D₄	1	2	yes	—
333	#2631	C₂×D₄	1	2	yes	—
334	#2631	C₂×D₄	1	2	yes	—
335	#2631	C₂×D₄	1	2	yes	—
336	#2631	C₂×D₄	1	2	yes	—
337	#2631	C₂×D₄	1	2	yes	—
338	#2612	C₂×D₄	1	2	yes	—
339	#2609	C₂×D₄	1	2	yes	—
340	#2607	C₂×D₄	1	2	yes	—
341	#2600	C₂×D₄	1	2	yes	—
342	#2599	C₂×D₄	1	2	yes	—
343	#2599	C₂⁴	1	2	yes	—
344	#2598	C₂×D₄	1	2	yes	—
345	#2598	C₂×D₄	1	2	yes	—
346	#2598	C₂×D₄	1	2	yes	—
347	#2598	C₂⁴	1	2	yes	—
348	#2598	C₂⁴	1	2	yes	—
349	#2598	C₂⁴	1	2	yes	—
350	#2572	C₂×D₄	1	2	yes	—
351	#2572	C₂×D₄	1	2	yes	—
352	#2564	C₂×D₄	1	2	yes	—
353	#2564	C₂×D₄	1	2	yes	—
354	#2543	C₂×D₄	1	2	yes	—
355	#2543	C₂×D₄	1	2	yes	—
356	#2534	C₂×D₄	1	2	yes	—
357	#2534	C₂×D₄	1	2	yes	—
358	#2534	C₂×D₄	1	2	yes	—
359	#2534	C₂×D₄	1	2	yes	—
360	#2487	C₂×D₄	1	2	yes	—
361	#2487	C₂×D₄	1	2	yes	—
362	#2437	C₂×D₄	1	2	yes	—
363	#2408	C₂×D₄	1	2	yes	—
364	#2408	C₂×D₄	1	2	yes	—
365	#2403	C₂×D₄	1	2	yes	—
366	#2398	C₂×D₄	1	2	yes	—
367	#2398	C₂×D₄	1	2	yes	—
368	#2397	C₂×D₄	1	2	yes	—
369	#2397	C₂×D₄	1	2	yes	—
370	#2380	C₂×D₄	1	2	yes	—
371	#2380	C₂×D₄	1	1	yes	characteristic
372	#2380	C₂×D₄	1	1	yes	characteristic
373	#2380	C₂×D₄	1	1	yes	characteristic
374	#2380	C₂×D₄	1	1	yes	characteristic
375	#2380	C₂×D₄	1	2	yes	—
376	#2328	C₂×D₄	1	2	yes	—
377	#2327	C₂×D₄	1	2	yes	—
378	#2326	C₂×D₄	1	2	yes	—
379	#2326	C₂×D₄	1	2	yes	—
380	#2310	C₂⁴	1	1	yes	characteristic
381	#2309	C₂×D₄	1	1	yes	characteristic
382	#2309	C₂×D₄	1	1	yes	characteristic
383	#2309	C₂⁴	1	1	yes	characteristic
384	#2297	C₂×D₄	1	1	yes	characteristic
385	#2297	C₂×D₄	1	1	yes	characteristic
386	#2297	C₂×D₄	1	1	yes	characteristic
387	#2297	C₂⁴	1	1	yes	characteristic
388	#2285	C₂×D₄	1	1	yes	characteristic
389	#2285	C₂⁴	1	1	yes	characteristic
390	#2283	C₂×D₄	1	2	yes	—
391	C₂×#383	C₂×D₄	1	2	yes	—
392	C₂×#376	C₂×D₄	1	1	yes	characteristic
393	#1742	C₂⁴	1	1	yes	characteristic
394	#1742	C₂⁴	1	1	yes	characteristic
395	#1740	C₂⁴	1	1	yes	characteristic
396	#1740	C₂⁴	1	1	yes	characteristic
397	#1464	C₂⁴	1	2	yes	—
398	#1464	C₂⁴	1	2	yes	—
399	#1464	C₂⁴	1	2	yes	—
400	#1464	C₂⁴	1	2	yes	—
401	C₂²×#41	#120	1	1	yes	characteristic
402	C₂²×#41	#120	1	1	yes	characteristic
403	C₂²×#41	#120	1	1	yes	characteristic
404	C₂²×#41	#120	1	1	yes	characteristic
405	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
406	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
407	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
408	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
409	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
410	C₂³×D₄	#120	1	1	yes	characteristic
411	C₂³×D₄	#120	1	1	yes	characteristic
412	C₂³×D₄	#120	1	1	yes	characteristic
413	C₂³×D₄	#120	1	1	yes	characteristic
414	C₂³×D₄	#120	1	2	yes	—
415	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
416	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
417	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
419	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
420	C₂×#127	#120	1	1	yes	characteristic
421	C₂×#127	#120	1	1	yes	characteristic
422	C₂×#127	#120	1	1	yes	characteristic
423	C₂×#127	#120	1	1	yes	characteristic
424	C₂×#127	#120	1	1	yes	characteristic
425	C₂×#127	#120	1	1	yes	characteristic
426	C₂×#127	C₂²×D₄	1	1	yes	characteristic
427	C₂×#127	C₂²×D₄	1	1	yes	characteristic
428	C₂×#127	C₂²×D₄	1	1	yes	characteristic
429	C₂×#127	C₂²×D₄	1	1	yes	characteristic
430	C₂×#125	#120	1	2	yes	—
431	C₂×#124	#120	1	1	yes	characteristic
432	C₂×#124	#120	1	1	yes	characteristic
433	C₂×#124	#120	1	1	yes	characteristic
434	C₂×#124	#120	1	1	yes	characteristic
435	C₂×#124	#120	1	2	yes	—
436	C₂×#124	C₂²×D₄	1	1	yes	characteristic
437	C₂×#124	C₂²×D₄	1	1	yes	characteristic
438	C₂×#124	C₂²×D₄	1	1	yes	characteristic
439	C₂×#124	C₂²×D₄	1	1	yes	characteristic
440	C₂×#123	#120	1	2	yes	—
441	C₂×#123	#120	1	2	yes	—
442	C₂×C₂²⋊Q₈	#120	1	2	yes	—
443	C₂×#121	#120	1	2	yes	—
444	C₂×#120	#120	1	1	yes	characteristic
445	C₂×#120	#120	1	1	yes	characteristic
446	C₂×#120	#120	1	1	yes	characteristic
447	C₂×#120	#120	1	1	yes	characteristic
448	C₂×C₄×Q₈	#120	1	2	yes	—
449	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
450	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
451	C₂×C₄×D₄	#120	1	2	yes	—
452	C₂×C₄×D₄	#120	1	2	yes	—
453	C₂×C₄×D₄	#120	1	2	yes	—
454	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
455	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
456	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
457	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
458	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
459	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
460	C₂×#117	C₂²×D₄	1	1	yes	characteristic
461	C₂×#117	C₂²×D₄	1	1	yes	characteristic
462	C₂×#117	C₂²×D₄	1	1	yes	characteristic
463	C₂×#117	C₂²×D₄	1	1	yes	characteristic
464	C₂×#117	C₂²×D₄	1	1	yes	characteristic
465	C₂×#117	C₂⁵	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	#120	1	2	yes	—
467	C₂²×C₂²⋊C₄	#120	1	2	yes	—
468	C₂²×C₂²⋊C₄	#120	1	2	yes	—
469	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
470	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
471	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
472	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
474	#400	#120	1	2	yes	—
475	#400	#120	1	2	yes	—
476	#400	#120	1	2	yes	—
477	#400	C₂²×D₄	1	2	yes	—
478	#400	C₂²×D₄	1	2	yes	—
479	#400	C₂²×D₄	1	2	yes	—
480	#399	#120	1	2	yes	—
481	#399	#120	1	2	yes	—
482	#399	#120	1	2	yes	—
483	#399	C₂²×D₄	1	2	yes	—
484	#399	C₂²×D₄	1	2	yes	—
485	#399	C₂²×D₄	1	2	yes	—
486	#398	#120	1	2	yes	—
487	#398	C₂²×D₄	1	2	yes	—
488	#397	#120	1	2	yes	—
489	#397	C₂²×D₄	1	2	yes	—
490	#395	#120	1	2	yes	—
491	#395	C₂²×D₄	1	2	yes	—
492	#394	#120	1	2	yes	—
493	#394	#120	1	2	yes	—
494	#394	#120	1	2	yes	—
495	#394	C₂²×D₄	1	2	yes	—
496	#394	C₂²×D₄	1	2	yes	—
497	#394	C₂²×D₄	1	2	yes	—
498	#393	#120	1	2	yes	—
499	#393	C₂²×D₄	1	2	yes	—
500	#392	#120	1	2	yes	—
501	#392	#120	1	2	yes	—
502	#392	#120	1	2	yes	—
503	#392	C₂²×D₄	1	2	yes	—
504	#392	C₂²×D₄	1	2	yes	—
505	#392	C₂²×D₄	1	2	yes	—
506	#391	#120	1	2	yes	—
507	#391	C₂²×D₄	1	2	yes	—
508	#390	#120	1	2	yes	—
509	#390	C₂²×D₄	1	2	yes	—
510	#384	C₂²×D₄	1	2	yes	—
511	#383	#120	1	2	yes	—
512	#383	#120	1	2	yes	—
513	#383	C₂²×D₄	1	2	yes	—
514	#383	C₂²×D₄	1	2	yes	—
515	#383	C₂²×D₄	1	2	yes	—
516	#383	C₂²×D₄	1	2	yes	—
517	#382	C₂²×D₄	1	2	yes	—
518	#381	C₂²×D₄	1	2	yes	—
519	#381	C₂²×D₄	1	2	yes	—
520	#380	#120	1	2	yes	—
521	#380	#120	1	2	yes	—
522	#380	#120	1	2	yes	—
523	#380	#120	1	2	yes	—
524	#379	C₂²×D₄	1	2	yes	—
525	#379	C₂²×D₄	1	2	yes	—
526	#376	#120	1	2	yes	—
527	#376	#120	1	2	yes	—
528	#376	#120	1	2	yes	—
529	#376	#120	1	2	yes	—
530	C₂×#95	#120	1	2	yes	—
531	C₂×#95	#120	1	2	yes	—
532	C₂⁵	C₂×#120	1	1	yes	characteristic
533	C₂⁵	C₂×#120	1	1	yes	characteristic
534	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
535	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
536	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
537	C₂²×Q₈	C₂×#120	1	2	yes	—
538	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
539	C₂²×D₄	C₂×#120	1	1	yes	characteristic
540	C₂²×D₄	C₂×#120	1	1	yes	characteristic
541	C₂²×D₄	C₂×#120	1	1	yes	characteristic
542	C₂²×D₄	C₂×#120	1	1	yes	characteristic
543	C₂²×D₄	C₂×#120	1	1	yes	characteristic
544	C₂²×D₄	C₂×#120	1	1	yes	characteristic
545	C₂²×D₄	C₂×#120	1	1	yes	characteristic
546	C₂²×D₄	C₂×#120	1	1	yes	characteristic
547	C₂²×D₄	C₂×#120	1	1	yes	characteristic
548	C₂²×D₄	C₂×#120	1	1	yes	characteristic
549	C₂²×D₄	C₂×#120	1	2	yes	—
550	C₂²×D₄	C₂×#120	1	2	yes	—
551	C₂²×D₄	C₂×#120	1	2	yes	—
552	C₂³×C₄	C₂×#120	1	2	yes	—
553	C₂³×C₄	C₂×#120	1	1	yes	characteristic
554	C₂³×C₄	C₂×#120	1	1	yes	characteristic
555	C₂³×C₄	C₂×#120	1	2	yes	—
556	C₂³×C₄	C₂×#120	1	2	yes	—
557	C₂³×C₄	C₂×#120	1	2	yes	—
558	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
559	#127	B(4,𝔽₂)	1	4	yes	—
560	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
561	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
562	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
563	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
564	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
565	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
566	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
574	C₂×C₄²	C₂×#120	1	1	yes	characteristic
575	C₂×C₄²	C₂×#120	1	2	yes	—
576	C₂×C₄²	C₂×#120	1	1	yes	characteristic
577	C₂×C₄²	C₂×#120	1	2	yes	—
578	C₂×C₄²	C₂×#120	1	2	yes	—
579	C₂×C₄²	C₂×#120	1	1	yes	characteristic
580	C₂×C₄²	C₂×#120	1	2	yes	—
581	C₂×C₄²	C₂×#120	1	1	yes	characteristic
582	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
583	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
584	#95	C₂×#120	1	2	yes	—
585	#95	C₂×#120	1	2	yes	—
586	#95	C₂×#120	1	2	yes	—
587	#95	C₂×#120	1	2	yes	—
588	#95	C₂×#120	1	2	yes	—
589	#95	C₂×#120	1	2	yes	—
590	#95	C₂×#120	1	2	yes	—
591	#95	C₂×#120	1	2	yes	—
592	C₂⁴	#2846	1	1	yes	characteristic
593	C₂⁴	#2846	1	1	yes	characteristic
594	C₂⁴	C₂²×#120	1	1	yes	characteristic
595	C₂×D₄	#3019	1	2	yes	—
596	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
597	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
598	C₂²×C₄	#2846	1	1	yes	characteristic
599	C₂²×C₄	#2846	1	1	yes	characteristic
600	C₂²×C₄	#2846	1	2	yes	—
601	C₂²×C₄	#2846	1	2	yes	—
602	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
603	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
604	C₂²×C₄	C₂²×#120	1	2	yes	—
605	C₂²×C₄	C₂²×#120	1	2	yes	—
606	C₄²	#3019	1	2	yes	—
607	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
608	C₄²	#3026	1	1	yes	characteristic
609	C₄²	#3026	1	1	yes	characteristic
610	C₂³	C₂×#2846	1	1	yes	characteristic
611	C₂³	#60388	1	1	yes	characteristic
612	C₂³	#60389	1	1	yes	characteristic
613	C₂×C₄	#32898	1	2	yes	—
614	C₂×C₄	#32898	1	2	yes	—
615	C₂×C₄	C₂×#3019	1	1	yes	characteristic
616	C₂×C₄	C₂×#3019	1	1	yes	characteristic
617	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
618	C₂×C₄	C₂×#3026	1	1	yes	characteristic
619	C₂²	#6628867	1	1	yes	characteristic
620	C₂²	#6628876	1	1	yes	characteristic
621	C₂²	C₂×#32898	1	1	yes	characteristic
622	C₂	#72234211	1	2	yes	—
623	C₂	#72234687	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂×#117	C₂⁵
LCS	G ▷ C₂×#117 ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#3498 ◁ G
LECS	G ▷ C₂×#117 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72318784	C₂	semidirect
2. #72318775	C₂	semidirect
3. #72318768	C₂	semidirect
4. #72318763	C₂	semidirect
5. #72318757	C₂	semidirect
6. #72318749	C₂	semidirect
7. #72318739	C₂	semidirect
8. #72318733	C₂	semidirect
9. #72318727	C₂	semidirect
10. #72318719	C₂	semidirect
11. #72318542	C₂	semidirect
12. #72318458	C₂	semidirect
13. #72318439	C₂	semidirect
14. #72318347	C₂	semidirect
15. #72318212	C₂	semidirect
16. #72317868	C₂	semidirect
17. #72317711	C₂	semidirect
18. #72285763	C₂	semidirect
19. #72285670	C₂	semidirect
20. #72278795	C₂	semidirect
21. #72278427	C₂	semidirect
22. #72278396	C₂	semidirect
23. #72213224	C₂	semidirect
24. #10575560	C₂²	semidirect
36. #6435072	C₂²	semidirect
37. #6432082	C₂²	semidirect
38. #6347140	C₂²	semidirect
39. #6346414	C₂²	semidirect
40. #485870	C₂²	semidirect
41. #485864	C₂²	semidirect
42. #485798	C₂²	semidirect
43. #485792	C₂²	semidirect
44. #485740	C₂²	semidirect
45. #485720	C₂²	semidirect
46. #485709	C₂²	semidirect
47. #485708	C₂²	semidirect
48. #485690	C₂²	semidirect
49. #485688	C₂²	semidirect
50. #485660	C₂²	semidirect
51. #485640	C₂²	semidirect
52. #485629	C₂²	semidirect
53. #485628	C₂²	semidirect
54. #485610	C₂²	semidirect
55. #485608	C₂²	semidirect
56. #482640	C₂²	semidirect
57. #482633	C₂²	semidirect
58. #481774	C₂²	semidirect
59. #481756	C₂²	semidirect
60. #480716	C₂²	semidirect
61. #480405	C₂²	semidirect
62. #441116	C₂²	semidirect
63. #441113	C₂²	semidirect
64. #422773	C₂²	semidirect
65. #422772	C₂²	semidirect
66. #417936	C₂²	semidirect
67. #417934	C₂²	semidirect
68. #417799	C₂²	semidirect
69. #417798	C₂²	semidirect
70. #374262	C₂²	semidirect
71. #361634	C₂²	semidirect
72. #360028	C₂²	semidirect
73. #246939	C₂²	semidirect
74. #246936	C₂²	semidirect
75. #246931	C₂²	semidirect
77. #246930	C₂²	semidirect
78. #246930	C₂²	semidirect
79. #246930	C₂²	semidirect
80. #246928	C₂²	semidirect
82. #246927	C₂²	semidirect
83. #246927	C₂²	semidirect
84. #246927	C₂²	semidirect
85. #201638	C₂²	semidirect
86. #201614	C₂²	semidirect
87. #187836	C₂²	semidirect
88. #187836	C₂²	semidirect
89. #134094	C₂²	semidirect
90. #134093	C₂²	semidirect
91. #134093	C₂²	semidirect
92. #134056	C₂²	semidirect
93. #134056	C₂²	semidirect
94. #134055	C₂²	semidirect
95. #131982	C₂²	semidirect
96. #131982	C₂²	semidirect
97. #131980	C₂²	semidirect
98. #131980	C₂²	semidirect
101. #131979	C₂²	semidirect
102. #131979	C₂²	semidirect
103. #131979	C₂²	semidirect
104. #131979	C₂²	semidirect
105. #131979	C₂²	semidirect
106. #131979	C₂²	semidirect
107. #130145	C₂²	semidirect
108. #130145	C₂²	semidirect
109. #130142	C₂²	semidirect
110. #130142	C₂²	semidirect
111. #130089	C₂²	semidirect
112. #130089	C₂²	semidirect
113. #130086	C₂²	semidirect
114. #130086	C₂²	semidirect
115. #130072	C₂²	semidirect
116. #130072	C₂²	semidirect
117. #130071	C₂²	semidirect
118. #130071	C₂²	semidirect
119. #130070	C₂²	semidirect
120. #130070	C₂²	semidirect
121. #130068	C₂²	semidirect
122. #130068	C₂²	semidirect
127. C₂×#3543	D₄	semidirect
128. C₂²×D₄²	D₄	semidirect
129. #62686	C₂³	semidirect
131. #60644	C₂³	semidirect
133. #60619	C₂³	semidirect
134. #60125	C₂³	semidirect
143. #52054	D₄	semidirect
145. #52005	D₄	semidirect
147. #52004	D₄	semidirect
148. #52004	D₄	semidirect
149. #52004	D₄	semidirect
150. #52004	D₄	semidirect
155. #47818	D₄	semidirect
156. #47794	D₄	semidirect
157. #47545	D₄	semidirect
160. #46965	D₄	semidirect
167. #42414	D₄	semidirect
168. #42410	D₄	semidirect
169. #42405	D₄	semidirect
170. #42404	D₄	semidirect
171. #37556	D₄	semidirect
180. #35237	D₄	semidirect
184. #34364	D₄	semidirect
185. C₂×#2380	D₄	semidirect
188. #23560	C₂³	semidirect
189. #23498	C₂³	semidirect
190. #23470	C₂³	semidirect
191. #23469	C₂³	semidirect
192. #23461	C₂³	semidirect
193. #23446	C₂³	semidirect
194. #23445	C₂³	semidirect
195. #23406	C₂³	semidirect
196. #20632	C₂³	semidirect
197. C₄×#413	C₂³	semidirect
198. #18155	C₂³	semidirect
200. #18154	C₂³	semidirect
201. #18154	C₂³	semidirect
202. #18153	C₂³	semidirect
204. #18152	C₂³	semidirect
205. #18152	C₂³	semidirect
206. #17366	C₂³	semidirect
207. #17366	C₂³	semidirect
208. #11763	C₂³	semidirect
209. #11763	C₂³	semidirect
212. #11761	C₂³	semidirect
213. #11761	C₂³	semidirect
214. #11761	C₂³	semidirect
215. #11761	C₂³	semidirect
216. #11756	C₂³	semidirect
217. #11756	C₂³	semidirect
220. #11754	C₂³	semidirect
221. #11754	C₂³	semidirect
222. #11754	C₂³	semidirect
223. #11754	C₂³	semidirect
224. #11513	C₂³	semidirect
225. #11513	C₂³	semidirect
226. #11507	C₂³	semidirect
227. #11507	C₂³	semidirect
228. #11504	C₂³	semidirect
229. #11504	C₂³	semidirect
230. #11503	C₂³	semidirect
231. #11503	C₂³	semidirect
234. #11006	C₂³	semidirect
235. #11006	C₂³	semidirect
236. #10959	C₂³	semidirect
237. #10959	C₂³	semidirect
238. #10940	C₂³	semidirect
239. #10940	C₂³	semidirect
240. #10939	C₂³	semidirect
241. #10939	C₂³	semidirect
242. #10893	C₂³	semidirect
243. #10893	C₂³	semidirect
246. #9492	C₂³	semidirect
247. #9492	C₂³	semidirect
248. #9492	C₂³	semidirect
249. #9492	C₂³	semidirect
250. #9491	C₂³	semidirect
251. #9491	C₂³	semidirect
256. #8522	C₂³	semidirect
257. #8522	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72318784	2
#72318775	2
#72318768	2
#72318763	2
#72318757	2
#72318749	2
#72318739	2
#72318733	2
#72318727	2
#72318719	2
#72318542	2
#72318458	2
#72318439	2
#72318347	2
#72318212	2
#72317868	2
#72317711	2
#72285763	2
#72285670	2
#72278795	2
#72278427	2
#72278396	2
#72213224	2