Subgroups — D₃×#529 #86145

Order 384.

1232 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5706	C₂	1	2	yes	maximal, complemented
3	D₃×#126	C₂	1	2	yes	maximal, complemented
4	#5691	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#123	C₂	1	2	yes	maximal, complemented
9	#5649	C₂	1	2	yes	maximal, complemented
10	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#5624	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#121	C₂	1	1	yes	maximal, characteristic
13	#5600	C₂	1	1	yes	maximal, characteristic, complemented
14	#5580	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#5557	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₃×D₄	C₂	1	2	yes	maximal, complemented
19	#5538	C₂	1	2	yes	maximal, complemented
20	#5528	C₂	1	2	yes	maximal, complemented
21	D₃×#117	C₂	1	2	yes	maximal, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#529	—	3	1	no	maximal, Sylow
25	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	2	yes	—
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₃	C₂²	1	2	yes	—
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#125	C₂²	1	1	yes	characteristic, complemented
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#121	C₂²	1	1	yes	characteristic
38	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×D₄	C₂²	1	2	yes	complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	2	yes	complemented
42	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
43	#947	C₂²	1	1	yes	characteristic, complemented
44	#946	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	#939	C₂²	1	2	yes	—
47	#938	C₂²	1	1	yes	characteristic
48	#936	C₂²	1	1	yes	characteristic, complemented
49	#935	C₂²	1	2	yes	complemented
50	D₄×Dic₃	C₂²	1	2	yes	complemented
51	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	#930	C₂²	1	1	yes	characteristic
53	#929	C₂²	1	2	yes	complemented
54	C₄×#67	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	#926	C₂²	1	2	yes	complemented
58	#924	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
62	#898	C₂²	1	2	yes	complemented
63	#898	C₂²	1	2	yes	complemented
64	#898	C₂²	1	2	yes	complemented
65	#897	C₂²	1	1	yes	characteristic, complemented
66	#896	C₂²	1	2	yes	complemented
67	#895	C₂²	1	1	yes	characteristic
68	#894	C₂²	1	2	yes	complemented
69	#894	C₂²	1	2	yes	complemented
70	#893	C₂²	1	2	yes	complemented
71	#893	C₂²	1	1	yes	characteristic, complemented
72	#892	C₂²	1	2	yes	complemented
73	#892	C₂²	1	2	yes	complemented
74	D₃×C₄⋊C₄	C₂²	1	2	yes	—
75	D₃×C₄⋊C₄	C₂²	1	2	yes	—
76	D₃×C₄⋊C₄	C₂²	1	2	yes	—
77	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	D₃×C₄⋊C₄	C₂²	1	2	yes	—
80	#890	C₂²	1	1	yes	characteristic, complemented
81	#890	C₂²	1	1	yes	characteristic, complemented
82	#889	C₂²	1	2	yes	complemented
83	#889	C₂²	1	2	yes	complemented
84	#887	C₂²	1	2	yes	complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#886	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#884	C₂²	1	2	yes	—
90	#883	C₂²	1	2	yes	complemented
91	#883	C₂²	1	2	yes	complemented
92	#67⋊C₄	C₂²	1	2	yes	complemented
93	#67⋊C₄	C₂²	1	2	yes	complemented
94	#67⋊C₄	C₂²	1	2	yes	complemented
95	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	#879	C₂²	1	2	yes	complemented
101	#879	C₂²	1	2	yes	complemented
102	#879	C₂²	1	2	yes	complemented
103	#878	C₂²	1	2	yes	complemented
104	#877	C₂²	1	2	yes	complemented
105	#877	C₂²	1	2	yes	complemented
106	#876	C₂²	1	2	yes	complemented
107	#875	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₁₂	C₂²	1	2	yes	complemented
110	#872	C₂²	1	2	yes	complemented
111	#872	C₂²	1	2	yes	complemented
112	C₄²×D₃	C₂²	1	1	yes	characteristic
113	C₄²×D₃	C₂²	1	1	yes	characteristic
114	C₄²×D₃	C₂²	1	1	yes	characteristic
115	C₄²×D₃	C₂²	1	1	yes	characteristic
116	C₄²×D₃	C₂²	1	2	yes	—
117	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	#870	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	2	yes	complemented
124	#529	—	3	2	no	—
125	#529	—	3	1	no	—
126	#529	—	3	1	no	—
127	#529	—	3	2	no	—
128	#529	—	3	1	no	—
129	#529	—	3	1	no	—
130	#529	—	3	1	no	—
131	#529	—	3	2	no	—
132	#529	—	3	1	no	—
133	#529	—	3	2	no	—
134	#529	—	3	1	no	—
135	#529	D₃	1	1	yes	characteristic, direct product factor
136	C₂×#126	—	3	2	no	—
137	C₂×#125	—	3	1	no	—
138	C₂×#124	—	3	1	no	—
139	C₂×#123	—	3	2	no	—
140	C₂×C₂²⋊Q₈	—	3	1	no	—
141	C₂×#121	—	3	1	no	—
142	C₂×C₄×Q₈	—	3	1	no	—
143	C₂×C₄×D₄	—	3	2	no	—
144	C₂×C₄×D₄	—	3	1	no	—
145	C₂×#117	—	3	2	no	—
146	C₂²×C₄²	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂²×Dic₃	C₂³	1	2	yes	—
160	C₂²×Dic₃	C₂³	1	1	yes	characteristic
161	C₂²×Dic₃	C₂³	1	1	yes	characteristic
162	C₂²×Dic₃	C₂³	1	1	yes	characteristic
163	D₃×Q₈	—	2	4	no	—
164	D₃×D₄	—	2	8	no	—
165	D₃×D₄	—	2	4	no	—
166	C₂×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₁₂	C₂³	1	2	yes	—
168	C₂×C₄×D₃	—	2	4	no	—
169	C₂×C₄×D₃	—	2	4	no	—
170	C₂×C₄×D₃	—	2	8	no	—
171	C₂×C₄×D₃	—	2	4	no	—
172	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
189	C₂×Dic₆	C₂³	1	1	yes	characteristic
190	C₂×Dic₆	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	2	yes	—
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₃×C₄²	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₄×Dic₃	C₂³	1	1	yes	characteristic
239	C₄×Dic₃	C₂³	1	2	yes	—
240	C₄×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₃	C₂³	1	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₄×Dic₃	C₂³	1	2	yes	—
253	C₂²×Q₈	—	3	1	no	—
254	C₂²×D₄	—	3	2	no	—
255	C₂²×D₄	—	3	1	no	—
256	C₂³×C₄	—	3	2	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₂³×C₄	—	3	1	no	—
259	C₂³×C₄	—	3	1	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	C₂×D₃	1	2	yes	complemented
268	#125	—	3	2	no	—
269	#125	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	—	3	1	no	—
272	#125	—	3	1	no	—
273	#125	C₂×D₃	1	1	yes	characteristic, complemented
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	1	no	—
279	#124	C₂×D₃	1	1	yes	characteristic, complemented
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	C₂×D₃	1	2	yes	complemented
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
294	#121	—	3	1	no	—
295	#121	—	3	2	no	—
296	#121	—	3	1	no	—
297	#121	—	3	1	no	—
298	#121	—	3	2	no	—
299	#121	C₂×D₃	1	1	yes	characteristic
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	2	no	—
302	C₄×Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
306	C₄×D₄	—	3	1	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	2	no	—
309	C₄×D₄	—	3	2	no	—
310	C₄×D₄	—	3	2	no	—
311	C₄×D₄	—	3	1	no	—
312	C₄×D₄	—	3	2	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	1	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
319	C₄×D₄	C₂×D₃	1	2	yes	complemented
320	#117	—	3	2	no	—
321	#117	—	3	2	no	—
322	#117	—	3	2	no	—
323	#117	—	3	2	no	—
324	#117	—	3	2	no	—
325	#117	—	3	2	no	—
326	#117	—	3	2	no	—
327	#117	C₂×D₃	1	2	yes	complemented
328	C₂×C₄⋊C₄	—	3	2	no	—
329	C₂×C₄⋊C₄	—	3	2	no	—
330	C₂×C₄⋊C₄	—	3	1	no	—
331	C₂×C₄⋊C₄	—	3	2	no	—
332	C₂×C₄⋊C₄	—	3	1	no	—
333	C₂×C₄⋊C₄	—	3	2	no	—
334	C₂×C₂²⋊C₄	—	3	2	no	—
335	C₂×C₂²⋊C₄	—	3	2	no	—
336	C₂×C₂²⋊C₄	—	3	2	no	—
337	C₂×C₂²⋊C₄	—	3	2	no	—
338	C₂×C₂²⋊C₄	—	3	2	no	—
339	C₂×C₄²	—	3	1	no	—
340	C₂×C₄²	—	3	1	no	—
341	C₂×C₄²	—	3	1	no	—
342	C₂×C₄²	—	3	1	no	—
343	C₂×C₄²	—	3	2	no	—
344	C₂×C₄²	—	3	1	no	—
345	C₂×C₄²	—	3	1	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	2	4	no	—
358	C₂²×D₃	—	2	4	no	—
359	C₂²×D₃	#41	1	4	yes	—
360	C₂²×D₃	C₂⁴	1	2	yes	—
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₃×Q₈	—	2	2	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	#67	—	2	4	no	—
380	#67	—	2	4	no	—
381	#67	—	2	4	no	—
382	C₂×Dic₃	—	2	2	no	—
383	C₂×Dic₃	—	2	2	no	—
384	C₂×Dic₃	—	2	2	no	—
385	C₂×Dic₃	—	2	4	no	—
386	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	2	yes	—
391	C₂×Dic₃	C₂⁴	1	2	yes	—
392	C₂×Dic₃	C₂⁴	1	2	yes	—
393	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	D₁₂	—	2	4	no	—
396	D₁₂	—	2	2	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	4	no	—
404	C₄×D₃	—	2	4	no	—
405	C₄×D₃	—	2	4	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	4	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	4	no	—
412	C₄×D₃	#41	1	4	yes	—
413	C₄×D₃	#41	1	4	yes	—
414	Dic₆	—	2	2	no	—
415	Dic₆	—	2	4	no	—
416	C₂⁴	—	3	1	no	—
417	C₂⁴	—	3	2	no	—
418	C₂×Q₈	—	3	2	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×Q₈	—	6	4	no	—
421	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	6	4	no	—
428	C₂×D₄	—	6	8	no	—
429	C₂×D₄	C₂²×D₃	1	2	yes	—
430	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	6	4	no	—
453	C₂²×C₄	—	6	8	no	—
454	C₂²×C₄	—	6	4	no	—
455	C₂²×C₄	—	6	4	no	—
456	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₃	1	2	yes	—
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₃	1	2	yes	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₄²	—	3	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	1	no	—
508	C₄²	—	3	1	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	2	no	—
513	C₄²	—	3	2	no	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	1	no	—
516	C₄²	—	3	2	no	—
517	C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₄²	C₂²×D₃	1	1	yes	characteristic
520	C₄²	C₂²×D₃	1	1	yes	characteristic
521	C₄²	C₂²×D₃	1	2	yes	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	C₂×#41	1	2	yes	—
528	C₂²×C₃	C₂⁵	1	1	yes	characteristic
529	C₂×D₃	—	2	1	no	—
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	8	no	—
532	C₂×D₃	—	2	2	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	4	8	no	—
536	C₂×D₃	C₂×#41	1	2	yes	—
537	C₂×D₃	C₂×#41	1	2	yes	—
538	C₂×D₃	C₂×#41	1	2	yes	—
539	C₂×D₃	C₂×#41	1	2	yes	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	C₂×#41	1	2	yes	—
548	C₃×C₄	C₂×#41	1	2	yes	—
549	Dic₃	—	2	2	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	2	no	—
555	Dic₃	—	2	2	no	—
556	Dic₃	C₂×#41	1	2	yes	—
557	Dic₃	C₂×#41	1	2	yes	—
558	C₂³	—	3	1	no	—
559	C₂³	—	3	4	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	3	2	no	—
562	C₂³	—	6	2	no	—
563	C₂³	—	6	2	no	—
564	C₂³	—	6	4	no	—
565	C₂³	—	6	4	no	—
566	C₂³	—	6	4	no	—
567	C₂³	C₂³×D₃	1	2	yes	—
568	C₂³	C₂³×D₃	1	1	yes	characteristic
569	Q₈	—	2	2	no	—
570	Q₈	—	6	4	no	—
571	Q₈	—	6	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	2	no	—
574	D₄	—	6	4	no	—
575	D₄	—	6	4	no	—
576	D₄	—	6	4	no	—
577	D₄	—	6	4	no	—
578	D₄	—	6	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	3	4	no	—
586	C₂×C₄	—	3	4	no	—
587	C₂×C₄	—	3	1	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	2	no	—
594	C₂×C₄	—	6	2	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	2	no	—
598	C₂×C₄	—	6	2	no	—
599	C₂×C₄	—	6	4	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	2	no	—
604	C₂×C₄	—	6	4	no	—
605	C₂×C₄	—	6	4	no	—
606	C₂×C₄	—	6	2	no	—
607	C₂×C₄	—	6	4	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	4	no	—
612	C₂×C₄	—	6	2	no	—
613	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	2	yes	—
618	C₂×C₄	C₂³×D₃	1	2	yes	—
619	C₂×C₄	C₂³×D₃	1	2	yes	—
620	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₃	—	2	2	no	—
623	C₂×C₃	—	4	2	no	—
624	C₂×C₃	C₂²×#41	1	1	yes	characteristic
625	C₂×C₃	C₂²×#41	1	1	yes	characteristic
626	C₂×C₃	C₂²×#41	1	1	yes	characteristic
627	D₃	—	2	2	no	—
628	D₃	—	4	2	no	—
629	D₃	#529	1	4	yes	direct product factor
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	3	2	no	—
636	C₂²	—	3	2	no	—
637	C₂²	—	3	2	no	—
638	C₂²	—	3	2	no	—
639	C₂²	—	6	8	no	—
640	C₂²	—	6	1	no	—
641	C₂²	—	6	1	no	—
642	C₂²	—	6	2	no	—
643	C₂²	—	6	2	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	12	8	no	—
646	C₂²	D₃×#41	1	2	yes	—
647	C₂²	C₂⁴×D₃	1	1	yes	characteristic
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	3	2	no	—
656	C₄	—	3	2	no	—
657	C₄	—	6	1	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	1	no	—
660	C₄	—	6	1	no	—
661	C₄	—	6	2	no	—
662	C₄	—	6	2	no	—
663	C₄	—	6	2	no	—
664	C₄	D₃×#41	1	2	yes	—
665	C₄	D₃×#41	1	2	yes	—
666	C₃	C₂×#529	1	1	yes	characteristic, complemented, Sylow
667	C₂	—	2	2	no	—
668	C₂	—	3	4	no	—
669	C₂	—	4	2	no	—
670	C₂	—	6	2	no	—
671	C₂	—	12	2	no	—
672	C₂	C₂×D₃×#41	1	1	yes	characteristic
673	C₂	C₂×D₃×#41	1	1	yes	characteristic
674	C₂	C₂×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Frattini	C₂²	C₂⁴×D₃
Fitting	C₃×#529	C₂
prime radical	D₃×#121	C₂
hypercenter	#529	D₃
hypocenter	C₃	C₂×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5706	C₂	semidirect
3. D₃×#126	C₂	semidirect
4. #5691	C₂	semidirect
5. D₃×#125	C₂	semidirect
6. #5680	C₂	semidirect
7. D₃×#124	C₂	semidirect
8. D₃×#123	C₂	semidirect
9. #5649	C₂	semidirect
10. D₃×C₂²⋊Q₈	C₂	semidirect
11. #5624	C₂	semidirect
13. #5600	C₂	semidirect
14. #5580	C₂	semidirect
15. C₄×D₃×Q₈	C₂	semidirect
16. #5557	C₂	semidirect
17. C₄×D₃×D₄	C₂	semidirect
18. C₄×D₃×D₄	C₂	semidirect
19. #5538	C₂	semidirect
20. #5528	C₂	semidirect
21. D₃×#117	C₂	semidirect
22. #5479	C₂	semidirect
23. C₂×C₄²×D₃	C₂	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#125	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×C₄×Q₈	C₂²	semidirect
39. C₃×C₄×D₄	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. C₂×C₃×C₄²	C₂²	semidirect
43. #947	C₂²	semidirect
44. #946	C₂²	semidirect
45. Q₈×Dic₃	C₂²	semidirect
48. #936	C₂²	semidirect
49. #935	C₂²	semidirect
50. D₄×Dic₃	C₂²	semidirect
51. D₄×Dic₃	C₂²	semidirect
53. #929	C₂²	semidirect
54. C₄×#67	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
57. #926	C₂²	semidirect
58. #924	C₂²	semidirect
59. C₂×C₄×Dic₃	C₂²	semidirect
60. C₂×C₄×Dic₃	C₂²	semidirect
61. C₂×C₄×Dic₃	C₂²	semidirect
62. #898	C₂²	semidirect
63. #898	C₂²	semidirect
64. #898	C₂²	semidirect
65. #897	C₂²	semidirect
66. #896	C₂²	semidirect
68. #894	C₂²	semidirect
69. #894	C₂²	semidirect
70. #893	C₂²	semidirect
71. #893	C₂²	semidirect
72. #892	C₂²	semidirect
73. #892	C₂²	semidirect
80. #890	C₂²	semidirect
81. #890	C₂²	semidirect
82. #889	C₂²	semidirect
83. #889	C₂²	semidirect
84. #887	C₂²	semidirect
85. #887	C₂²	semidirect
86. #886	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
90. #883	C₂²	semidirect
91. #883	C₂²	semidirect
92. #67⋊C₄	C₂²	semidirect
93. #67⋊C₄	C₂²	semidirect
94. #67⋊C₄	C₂²	semidirect
100. #879	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #878	C₂²	semidirect
104. #877	C₂²	semidirect
105. #877	C₂²	semidirect
106. #876	C₂²	semidirect
107. #875	C₂²	semidirect
108. C₄×D₁₂	C₂²	semidirect
109. C₄×D₁₂	C₂²	semidirect
110. #872	C₂²	semidirect
111. #872	C₂²	semidirect
117. C₄²×D₃	C₂²	semidirect
118. C₄²×D₃	C₂²	semidirect
119. C₄²×D₃	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. #870	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #529	D₃	direct (N × H)
267. #126	C₂×D₃	semidirect
273. #125	C₂×D₃	semidirect
279. #124	C₂×D₃	semidirect
287. #123	C₂×D₃	semidirect
293. C₂²⋊Q₈	C₂×D₃	semidirect
305. C₄×Q₈	C₂×D₃	semidirect
318. C₄×D₄	C₂×D₃	semidirect
319. C₄×D₄	C₂×D₃	semidirect
327. #117	C₂×D₃	semidirect
351. C₂×C₄²	C₂×D₃	semidirect
629. D₃	#529	direct (N × H)
666. C₃	C₂×#529	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5706	2
D₃×#126	2
#5691	2
D₃×#125	2
#5680	2
D₃×#124	2
D₃×#123	2
#5649	2
D₃×C₂²⋊Q₈	2
#5624	2
D₃×#121	2
#5600	2
#5580	2
C₄×D₃×Q₈	2
#5557	2
C₄×D₃×D₄	2
#5538	2
#5528	2
D₃×#117	2
#5479	2
C₂×C₄²×D₃	2
C₂×#529	3

Subgroups — D3×#529 #86145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#529 #86145