Subgroups — D₃×#511825 #72253904

Order 3072.

At least 15866 conjugacy classes of subgroups; only the 1151 normal subgroups are shown.

The subgroup lattice has 688 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72253895	C₂	1	1	yes	maximal, characteristic, complemented
2	#72253893	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×#63045	C₂	1	1	yes	maximal, characteristic, complemented
4	#72253847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#511825	C₂	1	1	yes	maximal, characteristic, complemented
6	#72253837	C₂	1	2	yes	maximal, complemented
7	D₃×#12758	C₂	1	2	yes	maximal, complemented
8	#72253833	C₂	1	2	yes	maximal, complemented
9	D₃×#23874	C₂	1	1	yes	maximal, characteristic, complemented
10	#72253828	C₂	1	1	yes	maximal, characteristic, complemented
11	#72253821	C₂	1	1	yes	maximal, characteristic, complemented
12	#72253818	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#12716	C₂	1	1	yes	maximal, characteristic, complemented
14	#72253803	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#33556	C₂	1	2	yes	maximal, complemented
16	#72253790	C₂	1	2	yes	maximal, complemented
17	#72253777	C₂	1	2	yes	maximal, complemented
18	D₃×#12766	C₂	1	1	yes	maximal, characteristic, complemented
19	D₃×#33550	C₂	1	1	yes	maximal, characteristic, complemented
20	D₃×#33570	C₂	1	1	yes	maximal, characteristic, complemented
21	D₃×#12778	C₂	1	1	yes	maximal, characteristic, complemented
22	D₃×#12711	C₂	1	2	yes	maximal, complemented
23	D₃×#23882	C₂	1	2	yes	maximal, complemented
24	D₃×#3585	C₂²	1	1	yes	characteristic, complemented
25	#11708420	C₂²	1	1	yes	characteristic, complemented
26	#11708418	C₂²	1	1	yes	characteristic, complemented
27	#11708417	C₂²	1	2	yes	complemented
28	#11708415	C₂²	1	2	yes	complemented
29	#11708411	C₂²	1	1	yes	characteristic, complemented
30	D₃×#3500	C₂²	1	1	yes	characteristic
31	D₃×#3484	C₂²	1	2	yes	—
32	D₃×#3549	C₂²	1	1	yes	characteristic
33	D₃×#3540	C₂²	1	2	yes	—
34	D₃×#3529	C₂²	1	1	yes	characteristic
35	D₃×#3028	C₂²	1	1	yes	characteristic, complemented
36	D₃×#3025	C₂²	1	2	yes	complemented
37	D₃×#3021	C₂²	1	2	yes	complemented
38	D₃×#3018	C₂²	1	1	yes	characteristic, complemented
39	#10949390	C₂²	1	1	yes	characteristic, complemented
40	#10949389	C₂²	1	2	yes	complemented
41	#10949388	C₂²	1	1	yes	characteristic, complemented
42	#10949387	C₂²	1	1	yes	characteristic, complemented
43	#10949385	C₂²	1	2	yes	complemented
44	#10949298	C₂²	1	2	yes	complemented
45	#10949297	C₂²	1	2	yes	complemented
46	#10949296	C₂²	1	2	yes	complemented
47	#10949295	C₂²	1	2	yes	complemented
48	#10949294	C₂²	1	2	yes	complemented
49	#10949293	C₂²	1	2	yes	complemented
50	#10949291	C₂²	1	2	yes	complemented
51	#10949240	C₂²	1	1	yes	characteristic, complemented
52	#10949239	C₂²	1	2	yes	complemented
53	#10949238	C₂²	1	1	yes	characteristic, complemented
54	#10949236	C₂²	1	1	yes	characteristic, complemented
55	#10949234	C₂²	1	2	yes	complemented
56	D₃×#2134	C₂²	1	2	yes	complemented
57	D₃×#2132	C₂²	1	1	yes	characteristic, complemented
58	D₃×#2128	C₂²	1	2	yes	complemented
59	D₃×#2126	C₂²	1	1	yes	characteristic, complemented
60	D₃×#2123	C₂²	1	2	yes	complemented
61	D₃×#2120	C₂²	1	2	yes	complemented
62	D₃×#2120	C₂²	1	2	yes	complemented
63	#10826602	C₂²	1	2	yes	complemented
64	#10826601	C₂²	1	2	yes	complemented
65	#10826600	C₂²	1	2	yes	complemented
66	#10826599	C₂²	1	2	yes	complemented
67	#10826598	C₂²	1	2	yes	complemented
68	#10826596	C₂²	1	2	yes	complemented
69	#10826593	C₂²	1	2	yes	complemented
70	#10826506	C₂²	1	1	yes	characteristic, complemented
71	#10826505	C₂²	1	1	yes	characteristic, complemented
72	#10826504	C₂²	1	1	yes	characteristic, complemented
73	#10826503	C₂²	1	1	yes	characteristic, complemented
74	#10826502	C₂²	1	1	yes	characteristic, complemented
75	#10826500	C₂²	1	1	yes	characteristic, complemented
76	#10826497	C₂²	1	1	yes	characteristic, complemented
77	D₃×#1915	C₂²	1	1	yes	characteristic, complemented
78	D₃×#1910	C₂²	1	2	yes	complemented
79	D₃×#1891	C₂²	1	2	yes	complemented
80	D₃×#1884	C₂²	1	1	yes	characteristic, complemented
81	D₃×#1795	C₂²	1	2	yes	complemented
82	D₃×#1795	C₂²	1	1	yes	characteristic, complemented
83	#10711082	C₂²	1	1	yes	characteristic, complemented
84	#10711081	C₂²	1	2	yes	complemented
85	#10711080	C₂²	1	1	yes	characteristic, complemented
86	#10711079	C₂²	1	1	yes	characteristic, complemented
87	#10711078	C₂²	1	2	yes	complemented
88	#10711028	C₂²	1	1	yes	characteristic, complemented
89	#10711027	C₂²	1	1	yes	characteristic, complemented
90	#10711026	C₂²	1	2	yes	complemented
91	#10711025	C₂²	1	2	yes	complemented
92	#10711024	C₂²	1	1	yes	characteristic, complemented
93	#10710984	C₂²	1	2	yes	complemented
94	#10710983	C₂²	1	2	yes	complemented
95	#10710982	C₂²	1	2	yes	complemented
96	#10710981	C₂²	1	2	yes	complemented
97	#10710980	C₂²	1	2	yes	complemented
98	#10710979	C₂²	1	2	yes	complemented
99	#10710978	C₂²	1	2	yes	complemented
100	#10710760	C₂²	1	1	yes	characteristic, complemented
101	#10710759	C₂²	1	1	yes	characteristic, complemented
102	#10710758	C₂²	1	2	yes	complemented
103	#10710757	C₂²	1	2	yes	complemented
104	#10710756	C₂²	1	1	yes	characteristic, complemented
105	#10710735	C₂²	1	2	yes	complemented
106	#10710734	C₂²	1	2	yes	complemented
107	#10710733	C₂²	1	2	yes	complemented
108	#10710732	C₂²	1	2	yes	complemented
109	#10710732	C₂²	1	2	yes	complemented
110	#10710731	C₂²	1	2	yes	complemented
111	#10710731	C₂²	1	2	yes	complemented
112	C₃×#63045	C₂²	1	1	yes	characteristic, complemented
113	C₃×#33570	C₂²	1	1	yes	characteristic, complemented
114	C₃×#33556	C₂²	1	2	yes	complemented
115	C₃×#33550	C₂²	1	1	yes	characteristic, complemented
116	C₃×#23882	C₂²	1	2	yes	complemented
117	C₃×#23874	C₂²	1	1	yes	characteristic, complemented
118	C₃×#12778	C₂²	1	1	yes	characteristic, complemented
119	C₃×#12766	C₂²	1	1	yes	characteristic, complemented
120	C₃×#12758	C₂²	1	2	yes	complemented
121	C₃×#12716	C₂²	1	1	yes	characteristic, complemented
122	C₃×#12711	C₂²	1	2	yes	complemented
123	#511825	D₃	1	1	yes	characteristic, direct product factor
124	D₃×#585	C₂³	1	1	yes	characteristic
125	C₂×D₃×2₋¹⁺⁴	D₄	1	1	yes	characteristic, complemented
126	C₂×D₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
127	C₂³×D₃×D₄	D₄	1	2	yes	complemented
128	C₃×#3585	C₂³	1	1	yes	characteristic, complemented
129	C₃×#3549	C₂³	1	1	yes	characteristic
130	C₃×#3540	C₂³	1	2	yes	—
131	C₃×#3529	C₂³	1	1	yes	characteristic
132	C₃×#3500	C₂³	1	1	yes	characteristic
133	C₃×#3484	C₂³	1	2	yes	—
134	#87298	C₂³	1	1	yes	characteristic, complemented
135	#87293	D₄	1	1	yes	characteristic, complemented
136	#87284	C₂³	1	2	yes	—
137	#87283	C₂³	1	1	yes	characteristic
138	#87277	C₂³	1	1	yes	characteristic, complemented
139	#87239	D₄	1	2	yes	complemented
140	#87167	C₂³	1	1	yes	characteristic, complemented
141	D₃×#568	C₂³	1	1	yes	characteristic
142	D₃×#563	D₄	1	1	yes	characteristic
143	#87115	D₄	1	1	yes	characteristic
144	D₃×H(3,𝔽₄)	D₄	1	1	yes	characteristic
145	D₃×H(3,𝔽₄)	D₄	1	2	yes	complemented
146	#87087	D₄	1	2	yes	complemented
147	#87085	D₄	1	1	yes	characteristic
148	D₃×#560	D₄	1	2	yes	—
149	D₃×#560	D₄	1	4	yes	complemented
150	#87073	D₄	1	4	yes	complemented
151	#87070	D₄	1	2	yes	—
152	D₃×#559	D₄	1	4	yes	complemented
153	#87057	D₄	1	4	yes	complemented
154	D₃×#555	D₄	1	2	yes	complemented
155	#86968	D₄	1	2	yes	complemented
156	D₃×#536	C₂³	1	1	yes	characteristic
157	#86345	C₂³	1	2	yes	—
158	#86341	C₂³	1	1	yes	characteristic
159	#86330	D₄	1	2	yes	complemented
160	#86330	C₂³	1	2	yes	—
161	D₃×#535	D₄	1	2	yes	complemented
162	D₃×#535	D₄	1	1	yes	characteristic, complemented
163	D₃×#535	C₂³	1	2	yes	—
164	#86326	C₂³	1	2	yes	—
165	#86322	C₂³	1	2	yes	—
166	#86317	D₄	1	1	yes	characteristic, complemented
167	#86252	C₂³	1	1	yes	characteristic
168	#86248	C₂³	1	1	yes	characteristic
169	#86244	C₂³	1	1	yes	characteristic
170	D₃×#532	C₂³	1	1	yes	characteristic
171	#86076	D₄	1	1	yes	characteristic, complemented
172	C₂×D₃×#124	D₄	1	1	yes	characteristic, complemented
173	#86055	C₂³	1	2	yes	—
174	#86048	C₂³	1	2	yes	—
175	#86039	D₄	1	2	yes	complemented
176	#86039	C₂³	1	2	yes	—
177	D₃×#525	D₄	1	2	yes	complemented
178	D₃×#525	C₂³	1	2	yes	—
179	#85867	D₄	1	2	yes	complemented
180	D₃×#518	D₄	1	2	yes	complemented
181	#85847	D₄	1	1	yes	characteristic, complemented
182	C₄×D₃×#41	D₄	1	1	yes	characteristic, complemented
183	C₃×#3028	C₂³	1	1	yes	characteristic, complemented
184	C₃×#3025	C₂³	1	2	yes	complemented
185	C₃×#3021	C₂³	1	2	yes	complemented
186	C₃×#3018	C₂³	1	1	yes	characteristic, complemented
187	#84125	C₂³	1	2	yes	complemented
188	#84124	C₂³	1	1	yes	characteristic, complemented
189	#84122	C₂³	1	2	yes	complemented
190	#84121	C₂³	1	1	yes	characteristic, complemented
191	#83417	C₂³	1	1	yes	characteristic, complemented
192	#83395	C₂³	1	2	yes	complemented
193	#83322	C₂³	1	1	yes	characteristic, complemented
194	#82936	C₂³	1	2	yes	complemented
195	#78717	C₂³	1	2	yes	complemented
196	#78716	C₂³	1	1	yes	characteristic, complemented
197	D₃×#413	C₂³	1	2	yes	—
198	D₃×#413	C₂³	1	1	yes	characteristic
199	D₃×#410	C₂³	1	1	yes	characteristic
200	D₃×#410	C₂³	1	2	yes	—
201	#78692	C₂³	1	1	yes	characteristic, complemented
202	#78690	C₂³	1	2	yes	complemented
203	C₃×#2134	C₂³	1	2	yes	complemented
204	C₃×#2132	C₂³	1	1	yes	characteristic, complemented
205	C₃×#2128	C₂³	1	2	yes	complemented
206	C₃×#2126	C₂³	1	1	yes	characteristic, complemented
207	C₃×#2123	C₂³	1	2	yes	complemented
208	C₃×#2120	C₂³	1	2	yes	complemented
209	C₃×#2120	C₂³	1	2	yes	complemented
210	C₃×#1915	C₂³	1	1	yes	characteristic, complemented
211	C₃×#1910	C₂³	1	2	yes	complemented
212	C₃×#1891	C₂³	1	2	yes	complemented
213	C₃×#1884	C₂³	1	1	yes	characteristic, complemented
214	C₃×#1795	C₂³	1	1	yes	characteristic, complemented
215	C₃×#1795	C₂³	1	2	yes	complemented
216	#72141	C₂³	1	1	yes	characteristic, complemented
217	#72141	C₂³	1	2	yes	complemented
218	#72031	C₂³	1	1	yes	characteristic, complemented
219	#72029	C₂³	1	2	yes	complemented
220	#72025	C₂³	1	2	yes	complemented
221	#72021	C₂³	1	1	yes	characteristic, complemented
222	#71870	C₂³	1	2	yes	complemented
223	#71866	C₂³	1	1	yes	characteristic, complemented
224	#71862	C₂³	1	2	yes	complemented
225	#71861	C₂³	1	2	yes	complemented
226	#71854	C₂³	1	2	yes	complemented
227	#71820	C₂³	1	1	yes	characteristic, complemented
228	#71819	C₂³	1	1	yes	characteristic, complemented
229	#71817	C₂³	1	1	yes	characteristic, complemented
230	#71716	C₂³	1	2	yes	complemented
231	#71716	C₂³	1	2	yes	complemented
232	#71714	C₂³	1	2	yes	complemented
233	#70149	C₂³	1	2	yes	complemented
234	#70149	C₂³	1	2	yes	complemented
235	#70148	C₂³	1	2	yes	complemented
236	#70147	C₂³	1	2	yes	complemented
237	#70145	C₂³	1	2	yes	complemented
238	#70145	C₂³	1	2	yes	complemented
239	#70139	C₂³	1	1	yes	characteristic, complemented
240	#70139	C₂³	1	2	yes	complemented
241	#70138	C₂³	1	1	yes	characteristic, complemented
242	#70136	C₂³	1	2	yes	complemented
243	#70061	C₂³	1	2	yes	complemented
244	#70061	C₂³	1	2	yes	complemented
245	#70060	C₂³	1	2	yes	complemented
246	#70058	C₂³	1	2	yes	complemented
247	#70056	C₂³	1	2	yes	complemented
248	#70056	C₂³	1	2	yes	complemented
249	#70048	C₂³	1	1	yes	characteristic, complemented
250	#70048	C₂³	1	2	yes	complemented
251	#70047	C₂³	1	2	yes	complemented
252	#70045	C₂³	1	1	yes	characteristic, complemented
253	#63045	C₂×D₃	1	1	yes	characteristic, complemented
254	#33570	C₂×D₃	1	1	yes	characteristic, complemented
255	#33556	C₂×D₃	1	2	yes	complemented
256	#33550	C₂×D₃	1	1	yes	characteristic, complemented
257	#23882	C₂×D₃	1	2	yes	complemented
258	#23874	C₂×D₃	1	1	yes	characteristic, complemented
259	#12778	C₂×D₃	1	1	yes	characteristic, complemented
260	#12766	C₂×D₃	1	1	yes	characteristic, complemented
261	#12758	C₂×D₃	1	2	yes	complemented
262	#12716	C₂×D₃	1	1	yes	characteristic, complemented
263	#12711	C₂×D₃	1	2	yes	complemented
264	C₃×#585	C₂⁴	1	1	yes	characteristic
265	C₂×C₃×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
266	C₂×C₃×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
267	C₂³×C₃×D₄	C₂×D₄	1	2	yes	complemented
268	#5964	C₂⁴	1	1	yes	characteristic
269	C₂×#1010	C₂×D₄	1	1	yes	characteristic, complemented
270	C₂×#1010	C₂×D₄	1	1	yes	characteristic, complemented
271	C₂×#1009	C₂×D₄	1	2	yes	—
272	C₂×#1009	C₂×D₄	1	1	yes	characteristic
273	C₂×#1009	C₂⁴	1	1	yes	characteristic
274	C₂×D₃×#41	C₂×D₄	1	1	yes	characteristic
275	C₂×D₃×#41	C₂×D₄	1	2	yes	—
276	C₂×D₃×#41	C₂×D₄	1	1	yes	characteristic
277	C₂×D₃×#41	C₂⁴	1	1	yes	characteristic
278	C₂×#1007	C₂×D₄	1	1	yes	characteristic, complemented
279	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic
280	C₂×#1004	C₂×D₄	1	1	yes	characteristic
281	C₂×#1004	C₂×D₄	1	2	yes	—
282	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
283	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
284	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
285	C₂²×D₃×D₄	C₂×D₄	1	2	yes	complemented
286	C₂²×D₃×D₄	C₂×D₄	1	2	yes	complemented
287	C₂³×D₁₂	C₂×D₄	1	2	yes	complemented
288	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
289	C₃×#568	C₂⁴	1	1	yes	characteristic
290	C₃×#563	C₂×D₄	1	1	yes	characteristic
291	C₃×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
292	C₃×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
293	C₃×#560	C₂×D₄	1	2	yes	—
294	C₃×#560	C₂×D₄	1	4	yes	complemented
295	C₃×#559	C₂×D₄	1	4	yes	complemented
296	C₃×#555	C₂×D₄	1	2	yes	complemented
297	C₃×#536	C₂⁴	1	1	yes	characteristic
298	C₃×#535	C₂×D₄	1	1	yes	characteristic, complemented
299	C₃×#535	C₂×D₄	1	2	yes	complemented
300	C₃×#535	C₂⁴	1	2	yes	—
301	C₃×#532	C₂⁴	1	1	yes	characteristic
302	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic, complemented
303	C₃×#525	C₂×D₄	1	2	yes	complemented
304	C₃×#525	C₂⁴	1	2	yes	—
305	C₃×#518	C₂×D₄	1	2	yes	complemented
306	C₃×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
307	#5832	C₂×D₄	1	1	yes	characteristic
308	#5832	C₂⁴	1	1	yes	characteristic
309	#5830	C₂×D₄	1	2	yes	complemented
310	#5830	C₂×D₄	1	1	yes	characteristic, complemented
311	#5830	C₂⁴	1	2	yes	—
312	#5828	C₂×D₄	1	2	yes	complemented
313	#5828	C₂⁴	1	2	yes	—
314	Dic₃×#41	C₂×D₄	1	1	yes	characteristic, complemented
315	#5825	C₂⁴	1	1	yes	characteristic
316	#5819	C₂⁴	1	1	yes	characteristic
317	#5816	C₂×D₄	1	1	yes	characteristic
318	C₂×#947	C₂×D₄	1	1	yes	characteristic, complemented
319	#5805	C₂×D₄	1	2	yes	—
320	#5805	C₂×D₄	1	2	yes	complemented
321	#5805	C₂×D₄	1	1	yes	characteristic, complemented
322	#5798	C₂×D₄	1	2	yes	complemented
323	C₂×#936	C₂×D₄	1	1	yes	characteristic, complemented
324	#5791	C₂×D₄	1	2	yes	—
325	#5791	C₂×D₄	1	2	yes	complemented
326	#5734	C₂×D₄	1	2	yes	complemented
327	#5725	C₂×D₄	1	1	yes	characteristic
328	D₃×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
329	#5720	C₂×D₄	1	2	yes	—
330	#5720	C₂×D₄	1	4	yes	complemented
331	#5716	C₂×D₄	1	1	yes	characteristic
332	#5715	C₂×D₄	1	4	yes	—
333	D₃×#127	C₂×D₄	1	4	yes	—
334	D₃×#127	C₂×D₄	1	1	yes	characteristic
335	#5713	C₂×D₄	1	4	yes	complemented
336	#5683	C₂×D₄	1	1	yes	characteristic
337	#5683	C₂×D₄	1	4	yes	complemented
338	#5683	C₂×D₄	1	2	yes	complemented
339	#5674	C₂×D₄	1	4	yes	—
340	D₃×#124	C₂×D₄	1	4	yes	—
341	D₃×#124	C₂×D₄	1	1	yes	characteristic
342	D₃×#124	C₂×D₄	1	1	yes	characteristic
343	#5672	C₂×D₄	1	1	yes	characteristic
344	#5670	C₂×D₄	1	4	yes	complemented
345	#5668	C₂×D₄	1	1	yes	characteristic
346	#5668	C₂×D₄	1	1	yes	characteristic
347	#5666	C₂×D₄	1	2	yes	—
348	#5666	C₂×D₄	1	4	yes	complemented
349	#5664	C₂×D₄	1	4	yes	complemented
350	#5664	C₂×D₄	1	4	yes	complemented
351	#5656	C₂×D₄	1	2	yes	—
352	#5656	C₂×D₄	1	2	yes	—
353	D₃×#123	C₂×D₄	1	2	yes	—
354	D₃×#123	C₂×D₄	1	2	yes	—
355	D₃×#123	C₂×D₄	1	4	yes	—
356	#5651	C₂×D₄	1	2	yes	—
357	#5648	C₂×D₄	1	4	yes	—
358	#5595	C₂×D₄	1	2	yes	—
359	#5595	C₂×D₄	1	4	yes	complemented
360	#5594	C₂×D₄	1	2	yes	—
361	D₃×#120	C₂×D₄	1	2	yes	—
362	D₃×#120	C₂×D₄	1	2	yes	—
363	#5586	C₂×D₄	1	2	yes	—
364	#5586	C₂×D₄	1	2	yes	—
365	#5526	C₂×D₄	1	1	yes	characteristic
366	#5525	C₂×D₄	1	2	yes	—
367	#5525	C₂×D₄	1	2	yes	complemented
368	#5525	C₂×D₄	1	1	yes	characteristic, complemented
369	#5524	C₂×D₄	1	2	yes	—
370	#5524	C₂×D₄	1	2	yes	complemented
371	#5522	C₂×D₄	1	1	yes	characteristic, complemented
372	#5521	C₂×D₄	1	2	yes	complemented
373	#5521	C₂×D₄	1	2	yes	complemented
374	D₃×#117	C₂×D₄	1	2	yes	—
375	D₃×#117	C₂×D₄	1	1	yes	characteristic
376	D₃×#117	C₂×D₄	1	2	yes	—
377	#5477	C₂×D₄	1	1	yes	characteristic
378	C₂×#875	C₂×D₄	1	1	yes	characteristic, complemented
379	C₄×#235	C₂×D₄	1	1	yes	characteristic, complemented
380	C₂×C₄²×D₃	C₂×D₄	1	1	yes	characteristic
381	C₃×#413	C₂⁴	1	1	yes	characteristic
382	C₃×#413	C₂⁴	1	2	yes	—
383	C₃×#410	C₂⁴	1	2	yes	—
384	C₃×#410	C₂⁴	1	1	yes	characteristic
385	#5240	C₂⁴	1	1	yes	characteristic
386	#5240	C₂⁴	1	2	yes	—
387	#5237	C₂⁴	1	2	yes	—
388	#5237	C₂⁴	1	1	yes	characteristic
389	#3585	C₂²×D₃	1	1	yes	characteristic, complemented
390	#3549	C₂²×D₃	1	1	yes	characteristic
391	#3540	C₂²×D₃	1	2	yes	—
392	#3529	C₂²×D₃	1	1	yes	characteristic
393	#3500	C₂²×D₃	1	1	yes	characteristic
394	#3484	C₂²×D₃	1	2	yes	—
395	#3028	C₂²×D₃	1	1	yes	characteristic, complemented
396	#3025	C₂²×D₃	1	2	yes	complemented
397	#3021	C₂²×D₃	1	2	yes	complemented
398	#3018	C₂²×D₃	1	1	yes	characteristic, complemented
399	#2134	C₂²×D₃	1	2	yes	complemented
400	#2132	C₂²×D₃	1	1	yes	characteristic, complemented
401	#2128	C₂²×D₃	1	2	yes	complemented
402	#2126	C₂²×D₃	1	1	yes	characteristic, complemented
403	#2123	C₂²×D₃	1	2	yes	complemented
404	#2120	C₂²×D₃	1	2	yes	complemented
405	#2120	C₂²×D₃	1	2	yes	complemented
406	#1915	C₂²×D₃	1	1	yes	characteristic, complemented
407	#1910	C₂²×D₃	1	2	yes	complemented
408	#1891	C₂²×D₃	1	2	yes	complemented
409	#1884	C₂²×D₃	1	1	yes	characteristic, complemented
410	#1795	C₂²×D₃	1	1	yes	characteristic, complemented
411	#1795	C₂²×D₃	1	2	yes	complemented
412	C₂⁴×D₃	#120	1	2	yes	—
413	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
415	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₃×#41	C₂⁵	1	1	yes	characteristic
417	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
419	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
420	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
421	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
422	C₂³×Dic₃	#120	1	2	yes	—
423	C₂×#239	#120	1	1	yes	characteristic
424	C₂×#239	#120	1	1	yes	characteristic
425	C₂×#239	#120	1	2	yes	—
426	C₂×#239	C₂²×D₄	1	1	yes	characteristic
427	C₂×D₃×Q₈	#120	1	1	yes	characteristic
428	C₂×D₃×Q₈	#120	1	1	yes	characteristic
429	C₂×D₃×Q₈	C₂²×D₄	1	1	yes	characteristic
430	C₂×#237	#120	1	1	yes	characteristic
431	C₂×#237	#120	1	1	yes	characteristic
432	C₂×#237	#120	1	2	yes	—
433	C₂×#237	C₂²×D₄	1	2	yes	—
434	C₂×#237	C₂²×D₄	1	1	yes	characteristic
435	C₂×D₃×D₄	#120	1	2	yes	—
436	C₂×D₃×D₄	#120	1	2	yes	—
437	C₂×D₃×D₄	#120	1	2	yes	—
438	C₂×D₃×D₄	#120	1	1	yes	characteristic
439	C₂×D₃×D₄	#120	1	4	yes	—
440	C₂×D₃×D₄	#120	1	4	yes	—
441	C₂×D₃×D₄	#120	1	2	yes	—
442	C₂×D₃×D₄	#120	1	1	yes	characteristic
443	C₂×D₃×D₄	C₂²×D₄	1	2	yes	—
444	C₂×D₃×D₄	C₂²×D₄	1	1	yes	characteristic
445	C₂×#235	C₂²×D₄	1	1	yes	characteristic
446	C₂×#235	C₂²×D₄	1	2	yes	—
447	C₂×#235	C₂²×D₄	1	1	yes	characteristic
448	C₂×#235	C₂²×D₄	1	1	yes	characteristic
449	C₂×#235	C₂²×D₄	1	2	yes	—
450	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
451	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
452	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic
453	C₂²×C₄×D₃	#120	1	2	yes	—
454	C₂²×C₄×D₃	#120	1	2	yes	—
455	C₂²×C₄×D₃	#120	1	2	yes	—
456	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
457	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
458	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
459	C₂²×Dic₆	#120	1	2	yes	—
460	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic
461	C₃×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
462	C₃×#127	C₂²×D₄	1	4	yes	—
463	C₃×#127	C₂²×D₄	1	1	yes	characteristic
464	C₃×#124	C₂²×D₄	1	1	yes	characteristic
465	C₃×#124	C₂²×D₄	1	4	yes	—
466	C₃×#124	C₂²×D₄	1	1	yes	characteristic
467	C₃×#123	C₂²×D₄	1	2	yes	—
468	C₃×#123	C₂²×D₄	1	4	yes	—
469	C₃×#123	C₂²×D₄	1	2	yes	—
470	C₃×#120	C₂²×D₄	1	2	yes	—
471	C₃×#120	C₂²×D₄	1	2	yes	—
472	C₃×#117	C₂²×D₄	1	2	yes	—
473	C₃×#117	C₂²×D₄	1	1	yes	characteristic
474	C₃×#117	C₂²×D₄	1	2	yes	—
475	C₂×C₃×C₄²	C₂²×D₄	1	1	yes	characteristic
476	#953	#120	1	2	yes	—
477	#953	#120	1	2	yes	—
478	#947	#120	1	1	yes	characteristic
479	#947	C₂²×D₄	1	4	yes	—
480	#947	C₂²×D₄	1	1	yes	characteristic
481	#944	#120	1	1	yes	characteristic
482	#944	C₂²×D₄	1	1	yes	characteristic
483	#940	#120	1	4	yes	—
484	#940	#120	1	1	yes	characteristic
485	#940	C₂²×D₄	1	4	yes	—
486	#940	C₂²×D₄	1	1	yes	characteristic
487	#937	C₂²×D₄	1	2	yes	—
488	#937	C₂²×D₄	1	2	yes	—
489	#936	#120	1	4	yes	—
490	#936	#120	1	1	yes	characteristic
491	#936	C₂²×D₄	1	1	yes	characteristic
492	#935	C₂²×D₄	1	4	yes	—
493	#935	C₂²×D₄	1	2	yes	—
494	#935	C₂²×D₄	1	2	yes	—
495	#929	#120	1	2	yes	—
496	#929	#120	1	2	yes	—
497	#929	#120	1	4	yes	—
498	#926	C₂²×D₄	1	2	yes	—
499	#926	C₂²×D₄	1	1	yes	characteristic
500	#926	C₂²×D₄	1	2	yes	—
501	C₂×C₄×Dic₃	C₂²×D₄	1	1	yes	characteristic
502	#886	#120	1	4	yes	—
503	#886	#120	1	2	yes	—
504	#886	#120	1	2	yes	—
505	#882	#120	1	2	yes	—
506	#882	#120	1	2	yes	—
507	D₃×C₂²⋊C₄	#120	1	2	yes	—
508	D₃×C₂²⋊C₄	#120	1	2	yes	—
509	D₃×C₂²⋊C₄	#120	1	2	yes	—
510	#877	#120	1	2	yes	—
511	#877	#120	1	2	yes	—
512	#877	#120	1	2	yes	—
513	#875	#120	1	1	yes	characteristic
514	#875	#120	1	1	yes	characteristic
515	#875	#120	1	4	yes	—
516	#874	#120	1	4	yes	—
517	#874	#120	1	1	yes	characteristic
518	#872	#120	1	4	yes	—
519	C₄²×D₃	#120	1	1	yes	characteristic
520	C₄²×D₃	#120	1	1	yes	characteristic
521	C₄²×D₃	#120	1	4	yes	—
522	C₄²×D₃	#120	1	1	yes	characteristic
523	C₄²×D₃	#120	1	1	yes	characteristic
524	#869	#120	1	1	yes	characteristic
525	#585	C₂³×D₃	1	1	yes	characteristic
526	C₂×2₋¹⁺⁴	D₃×D₄	1	1	yes	characteristic, complemented
527	C₂×H(5,𝔽₂)	C₂³×D₃	1	1	yes	characteristic
528	C₂³×D₄	D₃×D₄	1	2	yes	complemented
529	#568	C₂³×D₃	1	1	yes	characteristic
530	#563	D₃×D₄	1	1	yes	characteristic
531	H(3,𝔽₄)	D₃×D₄	1	1	yes	characteristic
532	H(3,𝔽₄)	D₃×D₄	1	2	yes	complemented
533	#560	D₃×D₄	1	2	yes	—
534	#560	D₃×D₄	1	4	yes	complemented
535	#559	D₃×D₄	1	4	yes	complemented
536	#555	D₃×D₄	1	2	yes	complemented
537	#536	C₂³×D₃	1	1	yes	characteristic
538	#535	D₃×D₄	1	2	yes	complemented
539	#535	D₃×D₄	1	1	yes	characteristic, complemented
540	#535	C₂³×D₃	1	2	yes	—
541	#532	C₂³×D₃	1	1	yes	characteristic
542	C₂×#124	D₃×D₄	1	1	yes	characteristic, complemented
543	#525	D₃×D₄	1	2	yes	complemented
544	#525	C₂³×D₃	1	2	yes	—
545	#518	D₃×D₄	1	2	yes	complemented
546	C₄×#41	D₃×D₄	1	1	yes	characteristic, complemented
547	#413	C₂³×D₃	1	1	yes	characteristic
548	#413	C₂³×D₃	1	2	yes	—
549	#410	C₂³×D₃	1	1	yes	characteristic
550	#410	C₂³×D₃	1	2	yes	—
551	C₂⁴×C₃	C₂×#120	1	2	yes	—
552	C₂³×D₃	C₂×#120	1	2	yes	—
553	C₂³×D₃	C₂×#120	1	1	yes	characteristic
554	C₂³×D₃	C₂×#120	1	2	yes	—
555	C₂×C₃×Q₈	C₂×#120	1	1	yes	characteristic
556	C₂×C₃×Q₈	C₂×#120	1	1	yes	characteristic
557	C₂×C₃×Q₈	C₂³×D₄	1	1	yes	characteristic
558	C₂×C₃×D₄	C₂×#120	1	2	yes	—
559	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
560	C₂×C₃×D₄	C₂×#120	1	4	yes	—
561	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
562	C₂×C₃×D₄	C₂³×D₄	1	2	yes	—
563	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
564	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
565	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
566	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
567	C₂²×C₃×C₄	C₂³×D₄	1	2	yes	—
568	C₂×#67	C₂×#120	1	2	yes	—
569	C₂×#67	C₂×#120	1	2	yes	—
570	C₂×#67	C₂×#120	1	2	yes	—
571	C₂²×Dic₃	C₂×#120	1	2	yes	—
572	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
573	C₂²×Dic₃	C₂×#120	1	2	yes	—
574	C₂²×Dic₃	C₂×#120	1	2	yes	—
575	D₃×D₄	B(4,𝔽₂)	1	2	yes	—
576	D₃×D₄	B(4,𝔽₂)	1	2	yes	—
577	C₂×D₁₂	C₂×#120	1	2	yes	—
578	C₂×D₁₂	C₂×#120	1	1	yes	characteristic
579	C₂×D₁₂	C₂×#120	1	1	yes	characteristic
580	C₂×D₁₂	C₂×#120	1	4	yes	—
581	C₂×D₁₂	C₂×#120	1	2	yes	—
582	C₂×D₁₂	C₂×#120	1	1	yes	characteristic
583	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
584	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
585	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
586	C₂×C₄×D₃	C₂×#120	1	2	yes	—
587	C₂×C₄×D₃	C₂×#120	1	2	yes	—
588	C₂×C₄×D₃	C₂×#120	1	2	yes	—
589	C₂×C₄×D₃	C₂×#120	1	1	yes	characteristic
590	C₂×Dic₆	C₂×#120	1	1	yes	characteristic
591	C₂×Dic₆	C₂×#120	1	1	yes	characteristic
592	C₂×Dic₆	C₂×#120	1	1	yes	characteristic
593	C₂×Dic₆	C₂×#120	1	2	yes	—
594	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	—
595	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	—
596	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	—
597	C₃×C₄²	C₂×#120	1	4	yes	—
598	C₃×C₄²	C₂×#120	1	1	yes	characteristic
599	C₃×C₄²	C₂×#120	1	1	yes	characteristic
600	#217	C₂×#120	1	2	yes	—
601	#217	C₂×#120	1	2	yes	—
602	#217	C₂×#120	1	2	yes	—
603	C₄×Dic₃	C₂×#120	1	1	yes	characteristic
604	C₄×Dic₃	C₂×#120	1	1	yes	characteristic
605	C₄×Dic₃	C₂×#120	1	4	yes	—
606	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
607	C₂×#41	C₂×D₃×D₄	1	2	yes	—
608	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
609	C₂×#41	C₂⁴×D₃	1	1	yes	characteristic
610	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
611	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
612	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
613	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
614	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
615	C₄⋊Q₈	C₂×D₃×D₄	1	1	yes	characteristic
616	#127	C₂×D₃×D₄	1	1	yes	characteristic
617	#127	C₂×D₃×D₄	1	4	yes	—
618	#124	C₂×D₃×D₄	1	1	yes	characteristic
619	#124	C₂×D₃×D₄	1	1	yes	characteristic
620	#124	C₂×D₃×D₄	1	4	yes	—
621	#123	C₂×D₃×D₄	1	2	yes	—
622	#123	C₂×D₃×D₄	1	2	yes	—
623	#123	C₂×D₃×D₄	1	4	yes	—
624	#120	C₂×D₃×D₄	1	2	yes	—
625	#120	C₂×D₃×D₄	1	2	yes	—
626	#117	C₂×D₃×D₄	1	1	yes	characteristic
627	#117	C₂×D₃×D₄	1	2	yes	—
628	#117	C₂×D₃×D₄	1	2	yes	—
629	C₂×C₄²	C₂×D₃×D₄	1	1	yes	characteristic
630	C₂³×C₃	C₂²×#120	1	2	yes	—
631	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
632	C₂²×D₃	#2846	1	1	yes	characteristic
633	C₂²×D₃	#2846	1	2	yes	—
634	C₂²×D₃	#2846	1	1	yes	characteristic
635	C₃×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
636	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
637	C₂×C₃×C₄	C₂²×#120	1	2	yes	—
638	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
639	C₂×Dic₃	#2846	1	1	yes	characteristic
640	C₂×Dic₃	#2846	1	2	yes	—
641	C₂×Dic₃	#2846	1	1	yes	characteristic
642	D₁₂	C₂×B(4,𝔽₂)	1	2	yes	—
643	C₄×D₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
644	C₄×D₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
645	C₄×D₃	#3026	1	1	yes	characteristic
646	C₄×D₃	#3026	1	1	yes	characteristic
647	C₂⁴	D₃×#120	1	2	yes	—
648	C₂×Q₈	D₃×#120	1	1	yes	characteristic
649	C₂×Q₈	D₃×#120	1	1	yes	characteristic
650	C₂×Q₈	C₂²×D₃×D₄	1	1	yes	characteristic
651	C₂×D₄	D₃×#120	1	1	yes	characteristic
652	C₂×D₄	D₃×#120	1	4	yes	—
653	C₂×D₄	D₃×#120	1	2	yes	—
654	C₂×D₄	D₃×#120	1	1	yes	characteristic
655	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
656	C₂×D₄	C₂²×D₃×D₄	1	2	yes	—
657	C₂²×C₄	D₃×#120	1	2	yes	—
658	C₂²×C₄	D₃×#120	1	2	yes	—
659	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂²×D₃×D₄	1	2	yes	—
661	C₂²⋊C₄	D₃×#120	1	2	yes	—
662	C₂²⋊C₄	D₃×#120	1	2	yes	—
663	C₂²⋊C₄	D₃×#120	1	2	yes	—
664	C₄²	D₃×#120	1	1	yes	characteristic
665	C₄²	D₃×#120	1	1	yes	characteristic
666	C₄²	D₃×#120	1	4	yes	—
667	C₂²×C₃	C₂×#2846	1	1	yes	characteristic
668	C₂×D₃	#32898	1	1	yes	characteristic
669	C₂×D₃	#32898	1	1	yes	characteristic
670	C₃×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
671	C₃×C₄	C₂×#3026	1	1	yes	characteristic
672	Dic₃	#32898	1	1	yes	characteristic
673	Dic₃	#32898	1	1	yes	characteristic
674	C₂³	C₂×D₃×#120	1	2	yes	—
675	C₂³	C₂×D₃×#120	1	1	yes	characteristic
676	D₄	D₃×B(4,𝔽₂)	1	2	yes	—
677	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
678	C₂×C₄	C₂×D₃×#120	1	2	yes	—
679	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
680	C₂×C₃	C₂×#32898	1	1	yes	characteristic
681	D₃	#511825	1	2	yes	direct product factor
682	C₂²	D₃×#2846	1	1	yes	characteristic
683	C₄	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
684	C₄	D₃×#3026	1	1	yes	characteristic
685	C₃	C₂×#511825	1	1	yes	characteristic, complemented, Sylow
686	C₂	D₃×#32898	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×#32898
commutator, cosocle	C₂×C₃×#41	C₂⁵
Frattini	C₂×#41	C₂⁴×D₃
Fitting	C₃×#511825	C₂
socle	C₂×C₃	C₂×#32898
hypercenter	#511825	D₃
hypocenter	C₃	C₂×#511825
LCS	G ▷ C₂×C₃×#41 ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×H(5,𝔽₂) ◁ #511825

Complements

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

N	H ≅ G/N	type
1. #72253895	C₂	semidirect
2. #72253893	C₂	semidirect
3. D₃×#63045	C₂	semidirect
4. #72253847	C₂	semidirect
5. C₃×#511825	C₂	semidirect
6. #72253837	C₂	semidirect
7. D₃×#12758	C₂	semidirect
8. #72253833	C₂	semidirect
9. D₃×#23874	C₂	semidirect
10. #72253828	C₂	semidirect
11. #72253821	C₂	semidirect
12. #72253818	C₂	semidirect
13. D₃×#12716	C₂	semidirect
14. #72253803	C₂	semidirect
15. D₃×#33556	C₂	semidirect
16. #72253790	C₂	semidirect
17. #72253777	C₂	semidirect
18. D₃×#12766	C₂	semidirect
19. D₃×#33550	C₂	semidirect
20. D₃×#33570	C₂	semidirect
21. D₃×#12778	C₂	semidirect
22. D₃×#12711	C₂	semidirect
23. D₃×#23882	C₂	semidirect
24. D₃×#3585	C₂²	semidirect
25. #11708420	C₂²	semidirect
26. #11708418	C₂²	semidirect
27. #11708417	C₂²	semidirect
28. #11708415	C₂²	semidirect
29. #11708411	C₂²	semidirect
35. D₃×#3028	C₂²	semidirect
36. D₃×#3025	C₂²	semidirect
37. D₃×#3021	C₂²	semidirect
38. D₃×#3018	C₂²	semidirect
39. #10949390	C₂²	semidirect
40. #10949389	C₂²	semidirect
41. #10949388	C₂²	semidirect
42. #10949387	C₂²	semidirect
43. #10949385	C₂²	semidirect
44. #10949298	C₂²	semidirect
45. #10949297	C₂²	semidirect
46. #10949296	C₂²	semidirect
47. #10949295	C₂²	semidirect
48. #10949294	C₂²	semidirect
49. #10949293	C₂²	semidirect
50. #10949291	C₂²	semidirect
51. #10949240	C₂²	semidirect
52. #10949239	C₂²	semidirect
53. #10949238	C₂²	semidirect
54. #10949236	C₂²	semidirect
55. #10949234	C₂²	semidirect
56. D₃×#2134	C₂²	semidirect
57. D₃×#2132	C₂²	semidirect
58. D₃×#2128	C₂²	semidirect
59. D₃×#2126	C₂²	semidirect
60. D₃×#2123	C₂²	semidirect
61. D₃×#2120	C₂²	semidirect
62. D₃×#2120	C₂²	semidirect
63. #10826602	C₂²	semidirect
64. #10826601	C₂²	semidirect
65. #10826600	C₂²	semidirect
66. #10826599	C₂²	semidirect
67. #10826598	C₂²	semidirect
68. #10826596	C₂²	semidirect
69. #10826593	C₂²	semidirect
70. #10826506	C₂²	semidirect
71. #10826505	C₂²	semidirect
72. #10826504	C₂²	semidirect
73. #10826503	C₂²	semidirect
74. #10826502	C₂²	semidirect
75. #10826500	C₂²	semidirect
76. #10826497	C₂²	semidirect
77. D₃×#1915	C₂²	semidirect
78. D₃×#1910	C₂²	semidirect
79. D₃×#1891	C₂²	semidirect
80. D₃×#1884	C₂²	semidirect
81. D₃×#1795	C₂²	semidirect
82. D₃×#1795	C₂²	semidirect
83. #10711082	C₂²	semidirect
84. #10711081	C₂²	semidirect
85. #10711080	C₂²	semidirect
86. #10711079	C₂²	semidirect
87. #10711078	C₂²	semidirect
88. #10711028	C₂²	semidirect
89. #10711027	C₂²	semidirect
90. #10711026	C₂²	semidirect
91. #10711025	C₂²	semidirect
92. #10711024	C₂²	semidirect
93. #10710984	C₂²	semidirect
94. #10710983	C₂²	semidirect
95. #10710982	C₂²	semidirect
96. #10710981	C₂²	semidirect
97. #10710980	C₂²	semidirect
98. #10710979	C₂²	semidirect
99. #10710978	C₂²	semidirect
100. #10710760	C₂²	semidirect
101. #10710759	C₂²	semidirect
102. #10710758	C₂²	semidirect
103. #10710757	C₂²	semidirect
104. #10710756	C₂²	semidirect
105. #10710735	C₂²	semidirect
106. #10710734	C₂²	semidirect
107. #10710733	C₂²	semidirect
108. #10710732	C₂²	semidirect
109. #10710732	C₂²	semidirect
110. #10710731	C₂²	semidirect
111. #10710731	C₂²	semidirect
112. C₃×#63045	C₂²	semidirect
113. C₃×#33570	C₂²	semidirect
114. C₃×#33556	C₂²	semidirect
115. C₃×#33550	C₂²	semidirect
116. C₃×#23882	C₂²	semidirect
117. C₃×#23874	C₂²	semidirect
118. C₃×#12778	C₂²	semidirect
119. C₃×#12766	C₂²	semidirect
120. C₃×#12758	C₂²	semidirect
121. C₃×#12716	C₂²	semidirect
122. C₃×#12711	C₂²	semidirect
123. #511825	D₃	direct (N × H)
125. C₂×D₃×2₋¹⁺⁴	D₄	semidirect
127. C₂³×D₃×D₄	D₄	semidirect
128. C₃×#3585	C₂³	semidirect
134. #87298	C₂³	semidirect
135. #87293	D₄	semidirect
138. #87277	C₂³	semidirect
139. #87239	D₄	semidirect
140. #87167	C₂³	semidirect
145. D₃×H(3,𝔽₄)	D₄	semidirect
146. #87087	D₄	semidirect
149. D₃×#560	D₄	semidirect
150. #87073	D₄	semidirect
152. D₃×#559	D₄	semidirect
153. #87057	D₄	semidirect
154. D₃×#555	D₄	semidirect
155. #86968	D₄	semidirect
159. #86330	D₄	semidirect
161. D₃×#535	D₄	semidirect
162. D₃×#535	D₄	semidirect
166. #86317	D₄	semidirect
171. #86076	D₄	semidirect
172. C₂×D₃×#124	D₄	semidirect
175. #86039	D₄	semidirect
177. D₃×#525	D₄	semidirect
179. #85867	D₄	semidirect
180. D₃×#518	D₄	semidirect
181. #85847	D₄	semidirect
182. C₄×D₃×#41	D₄	semidirect
183. C₃×#3028	C₂³	semidirect
184. C₃×#3025	C₂³	semidirect
185. C₃×#3021	C₂³	semidirect
186. C₃×#3018	C₂³	semidirect
187. #84125	C₂³	semidirect
188. #84124	C₂³	semidirect
189. #84122	C₂³	semidirect
190. #84121	C₂³	semidirect
191. #83417	C₂³	semidirect
192. #83395	C₂³	semidirect
193. #83322	C₂³	semidirect
194. #82936	C₂³	semidirect
195. #78717	C₂³	semidirect
196. #78716	C₂³	semidirect
201. #78692	C₂³	semidirect
202. #78690	C₂³	semidirect
203. C₃×#2134	C₂³	semidirect
204. C₃×#2132	C₂³	semidirect
205. C₃×#2128	C₂³	semidirect
206. C₃×#2126	C₂³	semidirect
207. C₃×#2123	C₂³	semidirect
208. C₃×#2120	C₂³	semidirect
209. C₃×#2120	C₂³	semidirect
210. C₃×#1915	C₂³	semidirect
211. C₃×#1910	C₂³	semidirect
212. C₃×#1891	C₂³	semidirect
213. C₃×#1884	C₂³	semidirect
214. C₃×#1795	C₂³	semidirect
215. C₃×#1795	C₂³	semidirect
216. #72141	C₂³	semidirect
217. #72141	C₂³	semidirect
218. #72031	C₂³	semidirect
219. #72029	C₂³	semidirect
220. #72025	C₂³	semidirect
221. #72021	C₂³	semidirect
222. #71870	C₂³	semidirect
223. #71866	C₂³	semidirect
224. #71862	C₂³	semidirect
225. #71861	C₂³	semidirect
226. #71854	C₂³	semidirect
227. #71820	C₂³	semidirect
228. #71819	C₂³	semidirect
229. #71817	C₂³	semidirect
230. #71716	C₂³	semidirect
231. #71716	C₂³	semidirect
232. #71714	C₂³	semidirect
233. #70149	C₂³	semidirect
234. #70149	C₂³	semidirect
235. #70148	C₂³	semidirect
236. #70147	C₂³	semidirect
237. #70145	C₂³	semidirect
238. #70145	C₂³	semidirect
239. #70139	C₂³	semidirect
240. #70139	C₂³	semidirect
241. #70138	C₂³	semidirect
242. #70136	C₂³	semidirect
243. #70061	C₂³	semidirect
244. #70061	C₂³	semidirect
245. #70060	C₂³	semidirect
246. #70058	C₂³	semidirect
247. #70056	C₂³	semidirect
248. #70056	C₂³	semidirect
249. #70048	C₂³	semidirect
250. #70048	C₂³	semidirect
251. #70047	C₂³	semidirect
252. #70045	C₂³	semidirect
253. #63045	C₂×D₃	semidirect
254. #33570	C₂×D₃	semidirect
255. #33556	C₂×D₃	semidirect
256. #33550	C₂×D₃	semidirect
257. #23882	C₂×D₃	semidirect
258. #23874	C₂×D₃	semidirect
259. #12778	C₂×D₃	semidirect
260. #12766	C₂×D₃	semidirect
261. #12758	C₂×D₃	semidirect
262. #12716	C₂×D₃	semidirect
263. #12711	C₂×D₃	semidirect
265. C₂×C₃×2₋¹⁺⁴	C₂×D₄	semidirect
267. C₂³×C₃×D₄	C₂×D₄	semidirect
269. C₂×#1010	C₂×D₄	semidirect
270. C₂×#1010	C₂×D₄	semidirect
278. C₂×#1007	C₂×D₄	semidirect
285. C₂²×D₃×D₄	C₂×D₄	semidirect
286. C₂²×D₃×D₄	C₂×D₄	semidirect
287. C₂³×D₁₂	C₂×D₄	semidirect
292. C₃×H(3,𝔽₄)	C₂×D₄	semidirect
294. C₃×#560	C₂×D₄	semidirect
295. C₃×#559	C₂×D₄	semidirect
296. C₃×#555	C₂×D₄	semidirect
298. C₃×#535	C₂×D₄	semidirect
299. C₃×#535	C₂×D₄	semidirect
302. C₂×C₃×#124	C₂×D₄	semidirect
303. C₃×#525	C₂×D₄	semidirect
305. C₃×#518	C₂×D₄	semidirect
306. C₃×C₄×#41	C₂×D₄	semidirect
309. #5830	C₂×D₄	semidirect
310. #5830	C₂×D₄	semidirect
312. #5828	C₂×D₄	semidirect
314. Dic₃×#41	C₂×D₄	semidirect
318. C₂×#947	C₂×D₄	semidirect
320. #5805	C₂×D₄	semidirect
321. #5805	C₂×D₄	semidirect
322. #5798	C₂×D₄	semidirect
323. C₂×#936	C₂×D₄	semidirect
325. #5791	C₂×D₄	semidirect
326. #5734	C₂×D₄	semidirect
330. #5720	C₂×D₄	semidirect
335. #5713	C₂×D₄	semidirect
337. #5683	C₂×D₄	semidirect
338. #5683	C₂×D₄	semidirect
344. #5670	C₂×D₄	semidirect
348. #5666	C₂×D₄	semidirect
349. #5664	C₂×D₄	semidirect
350. #5664	C₂×D₄	semidirect
359. #5595	C₂×D₄	semidirect
367. #5525	C₂×D₄	semidirect
368. #5525	C₂×D₄	semidirect
370. #5524	C₂×D₄	semidirect
371. #5522	C₂×D₄	semidirect
372. #5521	C₂×D₄	semidirect
373. #5521	C₂×D₄	semidirect
378. C₂×#875	C₂×D₄	semidirect
379. C₄×#235	C₂×D₄	semidirect
389. #3585	C₂²×D₃	semidirect
395. #3028	C₂²×D₃	semidirect
396. #3025	C₂²×D₃	semidirect
397. #3021	C₂²×D₃	semidirect
398. #3018	C₂²×D₃	semidirect
399. #2134	C₂²×D₃	semidirect
400. #2132	C₂²×D₃	semidirect
401. #2128	C₂²×D₃	semidirect
402. #2126	C₂²×D₃	semidirect
403. #2123	C₂²×D₃	semidirect
404. #2120	C₂²×D₃	semidirect
405. #2120	C₂²×D₃	semidirect
406. #1915	C₂²×D₃	semidirect
407. #1910	C₂²×D₃	semidirect
408. #1891	C₂²×D₃	semidirect
409. #1884	C₂²×D₃	semidirect
410. #1795	C₂²×D₃	semidirect
411. #1795	C₂²×D₃	semidirect
526. C₂×2₋¹⁺⁴	D₃×D₄	semidirect
528. C₂³×D₄	D₃×D₄	semidirect
532. H(3,𝔽₄)	D₃×D₄	semidirect
534. #560	D₃×D₄	semidirect
535. #559	D₃×D₄	semidirect
536. #555	D₃×D₄	semidirect
538. #535	D₃×D₄	semidirect
539. #535	D₃×D₄	semidirect
542. C₂×#124	D₃×D₄	semidirect
543. #525	D₃×D₄	semidirect
545. #518	D₃×D₄	semidirect
546. C₄×#41	D₃×D₄	semidirect
681. D₃	#511825	direct (N × H)
685. C₃	C₂×#511825	semidirect

Maximal subgroups

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

subgroup	index
#72253895	2
#72253893	2
D₃×#63045	2
#72253847	2
C₃×#511825	2
#72253837	2
D₃×#12758	2
#72253833	2
D₃×#23874	2
#72253828	2
#72253821	2
#72253818	2
D₃×#12716	2
#72253803	2
D₃×#33556	2
#72253790	2
#72253777	2
C₂×#511825	3
D₃×#12766	2
D₃×#33550	2
D₃×#33570	2
D₃×#12778	2
D₃×#12711	2
D₃×#23882	2

Subgroups — D3×#511825 #72253904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#511825 #72253904