Subgroups — C₃×#60516 #10679123

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3449	C₂	1	1	yes	maximal, characteristic
2	C₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3099	C₂	1	4	yes	maximal, complemented
4	C₃×#3098	C₂	1	4	yes	maximal, complemented
5	C₃×#3097	C₂	1	4	yes	maximal, complemented
6	C₃×#3096	C₂	1	4	yes	maximal, complemented
7	C₃×#3091	C₂	1	8	yes	maximal, complemented
8	C₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
13	#60516	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
18	C₃×#537	C₂²	1	4	yes	—
19	C₃×#536	—	2	1	no	—
20	C₃×#536	C₂²	1	2	yes	—
21	C₃×#535	—	2	1	no	—
22	C₃×#535	C₂²	1	2	yes	—
23	C₃×#534	—	2	2	no	—
24	C₃×#532	—	2	2	no	—
25	C₃×#525	—	2	2	no	—
26	C₃×#525	C₂²	1	4	yes	—
27	C₃×#520	C₂²	1	4	yes	—
28	C₃×#520	C₂²	1	4	yes	complemented
29	C₃×#519	—	2	1	no	—
30	C₃×#518	—	2	2	no	—
31	C₃×#518	—	2	1	no	—
32	C₃×C₄×#41	—	2	2	no	—
33	C₃×C₄×#41	—	2	2	no	—
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃×#117	C₂²	1	4	yes	complemented
38	C₃×#485	C₂²	1	8	yes	complemented
39	C₃×#485	C₂²	1	8	yes	complemented
40	C₃×#484	C₂²	1	8	yes	complemented
41	C₃×#483	C₂²	1	8	yes	complemented
42	C₃×#482	C₂²	1	8	yes	complemented
43	C₃×#482	C₂²	1	8	yes	complemented
44	C₃×#481	C₂²	1	8	yes	complemented
45	C₃×#480	C₂²	1	8	yes	complemented
46	C₃×#428	C₂²	1	4	yes	complemented
47	C₃×#428	C₂²	1	4	yes	complemented
48	C₃×#427	C₂²	1	4	yes	complemented
49	C₃×#427	C₂²	1	4	yes	complemented
50	C₃×#427	C₂²	1	4	yes	complemented
51	C₂×C₃×#107	C₂²	1	2	yes	complemented
52	C₂×C₃×#106	C₂²	1	2	yes	complemented
53	C₃×#419	C₂²	1	2	yes	complemented
54	C₃×#418	C₂²	1	2	yes	complemented
55	C₃×#417	C₂²	1	4	yes	complemented
56	C₃×#416	C₂²	1	4	yes	—
57	C₃×#416	C₂²	1	4	yes	—
58	C₃×#416	C₂²	1	2	yes	complemented
59	C₃×#416	C₂²	1	2	yes	complemented
60	C₂×C₃×#103	C₂²	1	2	yes	complemented
61	C₂×C₃×#102	C₂²	1	2	yes	complemented
62	C₃×#408	C₂²	1	4	yes	—
63	C₃×#408	C₂²	1	2	yes	complemented
64	C₃×#408	C₂²	1	2	yes	complemented
65	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
66	#3449	C₂×C₃	1	1	yes	characteristic
67	#3428	C₂×C₃	1	1	yes	characteristic, complemented
68	#3099	C₂×C₃	1	4	yes	complemented
69	#3098	C₂×C₃	1	4	yes	complemented
70	#3097	C₂×C₃	1	4	yes	complemented
71	#3096	C₂×C₃	1	4	yes	complemented
72	#3091	C₂×C₃	1	8	yes	complemented
73	#2911	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#427	C₂×C₃	1	1	yes	characteristic, complemented
75	#2896	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#416	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×#41	—	2	1	no	—
79	C₂×C₃×#41	—	2	1	no	—
80	C₂×C₃×#41	—	2	4	no	—
81	C₂×C₃×#41	—	2	4	no	—
82	C₂×C₃×#41	—	2	4	no	—
83	C₂×C₃×#41	—	2	4	no	—
84	C₂×C₃×#41	D₄	1	2	yes	—
85	C₂×C₃×#41	D₄	1	2	yes	—
86	C₂×C₃×#41	C₂³	1	2	yes	—
87	C₂×C₃×#41	C₂³	1	2	yes	—
88	C₂×C₃×#41	C₂³	1	2	yes	—
89	C₂×C₃×#41	C₂³	1	2	yes	—
90	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
91	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
92	C₂²×C₃×D₄	—	2	1	no	—
93	C₂²×C₃×D₄	D₄	1	2	yes	—
94	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
95	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
96	C₂³×C₃×C₄	—	2	1	no	—
97	C₂³×C₃×C₄	C₂³	1	2	yes	—
98	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
99	C₂×C₃×M₁₆	—	2	4	no	—
100	C₂×C₃×M₁₆	C₂³	1	2	yes	—
101	C₂×C₃×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₃×C₈	—	2	4	no	—
103	C₂²×C₃×C₈	C₂³	1	2	yes	—
104	C₂²×C₃×C₈	C₂³	1	2	yes	—
105	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂³	1	2	yes	—
108	C₃×C₄⋊Q₈	—	2	2	no	—
109	C₃×#127	—	2	2	no	—
110	C₃×#124	—	2	2	no	—
111	C₃×#124	—	2	2	no	—
112	C₃×#123	—	2	4	no	—
113	C₃×#123	—	2	4	no	—
114	C₃×C₂²⋊Q₈	—	2	4	no	—
115	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
116	C₃×#121	—	2	4	no	—
117	C₃×#121	—	2	8	no	—
118	C₃×#121	C₂³	1	8	yes	—
119	C₃×#120	—	2	4	no	—
120	C₃×#120	—	2	4	no	—
121	C₃×C₄×Q₈	—	2	4	no	—
122	C₃×C₄×Q₈	—	2	4	no	—
123	C₃×C₄×D₄	—	2	8	no	—
124	C₃×C₄×D₄	—	2	4	no	—
125	C₃×C₄×D₄	—	2	8	no	—
126	C₃×C₄×D₄	—	2	4	no	—
127	C₃×C₄×D₄	—	2	8	no	—
128	C₃×#117	—	2	1	no	—
129	C₃×#117	—	2	1	no	—
130	C₃×#117	—	2	1	no	—
131	C₃×#117	—	2	1	no	—
132	C₃×#117	—	2	1	no	—
133	C₃×#117	—	2	1	no	—
134	C₃×#117	—	2	4	no	—
135	C₃×#117	—	2	4	no	—
136	C₃×#117	C₂³	1	2	yes	—
137	C₃×#117	C₂³	1	2	yes	—
138	C₃×#117	C₂³	1	2	yes	—
139	C₃×#117	C₂³	1	2	yes	—
140	C₃×#117	C₂³	1	2	yes	—
141	C₃×#117	C₂³	1	2	yes	—
142	C₃×#117	C₂³	1	8	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
147	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
151	C₂×C₃×C₄²	—	2	1	no	—
152	C₂×C₃×C₄²	—	2	1	no	—
153	C₂×C₃×C₄²	—	2	1	no	—
154	C₂×C₃×C₄²	—	2	4	no	—
155	C₃×#107	C₂³	1	4	yes	—
156	C₃×#107	C₂³	1	4	yes	—
157	C₃×#107	C₂³	1	8	yes	—
158	C₃×#106	C₂³	1	4	yes	—
159	C₃×#106	C₂³	1	4	yes	—
160	C₃×#106	C₂³	1	8	yes	—
161	C₃×#103	C₂³	1	4	yes	—
162	C₃×#103	C₂³	1	4	yes	—
163	C₃×#103	C₂³	1	8	yes	—
164	C₃×#102	C₂³	1	4	yes	—
165	C₃×#102	C₂³	1	4	yes	—
166	C₃×#102	C₂³	1	8	yes	—
167	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
168	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
169	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
170	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
171	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
173	#537	C₂²×C₃	1	4	yes	—
174	#536	—	2	1	no	—
175	#536	C₂²×C₃	1	2	yes	—
176	#535	—	2	1	no	—
177	#535	C₂²×C₃	1	2	yes	—
178	#534	—	2	2	no	—
179	#532	—	2	2	no	—
180	#525	—	2	2	no	—
181	#525	C₂²×C₃	1	4	yes	—
182	#520	C₂²×C₃	1	4	yes	—
183	#520	C₂²×C₃	1	4	yes	complemented
184	#519	—	2	1	no	—
185	#518	—	2	2	no	—
186	#518	—	2	1	no	—
187	C₄×#41	—	2	2	no	—
188	C₄×#41	—	2	2	no	—
189	C₂×#117	C₂²×C₃	1	1	yes	characteristic
190	C₂×#117	C₂²×C₃	1	1	yes	characteristic
191	C₂×#117	C₂²×C₃	1	1	yes	characteristic
192	C₂×#117	C₂²×C₃	1	4	yes	complemented
193	#485	C₂²×C₃	1	8	yes	complemented
194	#485	C₂²×C₃	1	8	yes	complemented
195	#484	C₂²×C₃	1	8	yes	complemented
196	#483	C₂²×C₃	1	8	yes	complemented
197	#482	C₂²×C₃	1	8	yes	complemented
198	#482	C₂²×C₃	1	8	yes	complemented
199	#481	C₂²×C₃	1	8	yes	complemented
200	#480	C₂²×C₃	1	8	yes	complemented
201	#428	C₂²×C₃	1	4	yes	complemented
202	#428	C₂²×C₃	1	4	yes	complemented
203	#427	C₂²×C₃	1	4	yes	complemented
204	#427	C₂²×C₃	1	4	yes	complemented
205	#427	C₂²×C₃	1	4	yes	complemented
206	C₂×#107	C₂²×C₃	1	2	yes	complemented
207	C₂×#106	C₂²×C₃	1	2	yes	complemented
208	#419	C₂²×C₃	1	2	yes	complemented
209	#418	C₂²×C₃	1	2	yes	complemented
210	#417	C₂²×C₃	1	4	yes	complemented
211	#416	C₂²×C₃	1	4	yes	—
212	#416	C₂²×C₃	1	4	yes	—
213	#416	C₂²×C₃	1	2	yes	complemented
214	#416	C₂²×C₃	1	2	yes	complemented
215	C₂×#103	C₂²×C₃	1	2	yes	complemented
216	C₂×#102	C₂²×C₃	1	2	yes	complemented
217	#408	C₂²×C₃	1	4	yes	—
218	#408	C₂²×C₃	1	2	yes	complemented
219	#408	C₂²×C₃	1	2	yes	complemented
220	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
221	C₂⁴×C₃	—	2	1	no	—
222	C₂⁴×C₃	C₂×D₄	1	2	yes	—
223	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
224	C₃×#41	—	2	8	no	—
225	C₃×#41	—	2	8	no	—
226	C₃×#41	—	2	4	no	—
227	C₃×#41	—	2	4	no	—
228	C₃×#41	—	2	4	no	—
229	C₃×#41	—	2	4	no	—
230	C₃×#41	—	2	4	no	—
231	C₃×#41	—	2	4	no	—
232	C₃×#41	—	2	4	no	—
233	C₃×#41	—	2	4	no	—
234	C₃×#41	—	4	4	no	—
235	C₃×#41	—	4	4	no	—
236	C₂×C₃×Q₈	—	2	4	no	—
237	C₂×C₃×Q₈	—	2	1	no	—
238	C₂×C₃×Q₈	—	2	2	no	—
239	C₂×C₃×Q₈	—	2	2	no	—
240	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
241	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
242	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₃×D₄	—	2	8	no	—
244	C₂×C₃×D₄	—	2	2	no	—
245	C₂×C₃×D₄	—	2	2	no	—
246	C₂×C₃×D₄	—	2	8	no	—
247	C₂×C₃×D₄	—	2	4	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	2	no	—
250	C₂×C₃×D₄	—	2	2	no	—
251	C₂×C₃×D₄	—	4	4	no	—
252	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
253	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
254	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
255	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
256	C₂×C₃×D₄	C₂⁴	1	2	yes	—
257	C₂²×C₃×C₄	—	2	4	no	—
258	C₂²×C₃×C₄	—	2	4	no	—
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	2	8	no	—
261	C₂²×C₃×C₄	—	2	2	no	—
262	C₂²×C₃×C₄	—	2	2	no	—
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	—	4	4	no	—
267	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
268	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
269	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₃×C₄	#41	1	4	yes	—
273	C₂²×C₃×C₄	#41	1	4	yes	—
274	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
275	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₃×M₁₆	—	2	4	no	—
279	C₃×M₁₆	—	2	4	no	—
280	C₂×C₃×C₈	—	2	4	no	—
281	C₂×C₃×C₈	—	2	4	no	—
282	C₂×C₃×C₈	—	2	2	no	—
283	C₂×C₃×C₈	—	2	2	no	—
284	C₂×C₃×C₈	—	2	4	no	—
285	C₂×C₃×C₈	C₂⁴	1	2	yes	—
286	C₂×C₃×C₈	C₂⁴	1	4	yes	—
287	C₂×C₃×C₈	C₂⁴	1	2	yes	—
288	C₃×C₄⋊C₄	—	2	8	no	—
289	C₃×C₄⋊C₄	—	2	2	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	—	2	8	no	—
293	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
294	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
295	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	2	2	no	—
298	C₃×C₂²⋊C₄	—	2	8	no	—
299	C₃×C₂²⋊C₄	—	2	2	no	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	2	2	no	—
302	C₃×C₂²⋊C₄	—	2	2	no	—
303	C₃×C₂²⋊C₄	—	2	8	no	—
304	C₃×C₂²⋊C₄	—	2	8	no	—
305	C₃×C₄²	—	2	8	no	—
306	C₃×C₄²	—	2	2	no	—
307	C₃×C₄²	—	2	2	no	—
308	C₃×C₄²	—	2	2	no	—
309	C₃×C₄²	—	2	2	no	—
310	C₃×C₄²	—	2	2	no	—
311	C₃×C₄²	—	2	2	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	4	no	—
318	C₂×#41	C₃×D₄	1	2	yes	—
319	C₂×#41	C₃×D₄	1	2	yes	—
320	C₂×#41	C₂³×C₃	1	2	yes	—
321	C₂×#41	C₂³×C₃	1	2	yes	—
322	C₂×#41	C₂³×C₃	1	2	yes	—
323	C₂×#41	C₂³×C₃	1	2	yes	—
324	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₃×D₄	1	2	yes	—
328	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
329	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	C₂³×C₃	1	2	yes	—
332	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
333	C₂×M₁₆	—	2	4	no	—
334	C₂×M₁₆	C₂³×C₃	1	2	yes	—
335	C₂×M₁₆	C₂³×C₃	1	2	yes	—
336	C₂²×C₈	—	2	4	no	—
337	C₂²×C₈	C₂³×C₃	1	2	yes	—
338	C₂²×C₈	C₂³×C₃	1	2	yes	—
339	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₃	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	#127	—	2	2	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#123	—	2	4	no	—
347	#123	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
350	#121	—	2	4	no	—
351	#121	—	2	8	no	—
352	#121	C₂³×C₃	1	8	yes	—
353	#120	—	2	4	no	—
354	#120	—	2	4	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	4	no	—
357	C₄×D₄	—	2	8	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	4	no	—
361	C₄×D₄	—	2	8	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	4	no	—
369	#117	—	2	4	no	—
370	#117	C₂³×C₃	1	2	yes	—
371	#117	C₂³×C₃	1	2	yes	—
372	#117	C₂³×C₃	1	2	yes	—
373	#117	C₂³×C₃	1	2	yes	—
374	#117	C₂³×C₃	1	2	yes	—
375	#117	C₂³×C₃	1	2	yes	—
376	#117	C₂³×C₃	1	8	yes	—
377	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	4	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	4	no	—
389	#107	C₂³×C₃	1	4	yes	—
390	#107	C₂³×C₃	1	4	yes	—
391	#107	C₂³×C₃	1	8	yes	—
392	#106	C₂³×C₃	1	4	yes	—
393	#106	C₂³×C₃	1	4	yes	—
394	#106	C₂³×C₃	1	8	yes	—
395	#103	C₂³×C₃	1	4	yes	—
396	#103	C₂³×C₃	1	4	yes	—
397	#103	C₂³×C₃	1	8	yes	—
398	#102	C₂³×C₃	1	4	yes	—
399	#102	C₂³×C₃	1	4	yes	—
400	#102	C₂³×C₃	1	8	yes	—
401	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
402	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
403	C₂³×C₃	—	2	4	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	4	2	no	—
406	C₂³×C₃	—	4	4	no	—
407	C₂³×C₃	—	4	2	no	—
408	C₂³×C₃	—	8	2	no	—
409	C₂³×C₃	#123	1	4	yes	—
410	C₂³×C₃	C₂²×D₄	1	4	yes	—
411	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
414	C₃×Q₈	—	2	4	no	—
415	C₃×Q₈	—	2	4	no	—
416	C₃×Q₈	—	2	2	no	—
417	C₃×Q₈	—	2	2	no	—
418	C₃×Q₈	—	4	2	no	—
419	C₃×D₄	—	2	8	no	—
420	C₃×D₄	—	2	8	no	—
421	C₃×D₄	—	2	4	no	—
422	C₃×D₄	—	2	4	no	—
423	C₃×D₄	—	2	2	no	—
424	C₃×D₄	—	2	2	no	—
425	C₃×D₄	—	4	4	no	—
426	C₃×D₄	—	4	4	no	—
427	C₃×D₄	—	4	2	no	—
428	C₃×D₄	—	8	8	no	—
429	C₂×C₃×C₄	—	2	4	no	—
430	C₂×C₃×C₄	—	2	8	no	—
431	C₂×C₃×C₄	—	2	4	no	—
432	C₂×C₃×C₄	—	2	4	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	2	4	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	4	2	no	—
438	C₂×C₃×C₄	—	4	4	no	—
439	C₂×C₃×C₄	—	4	4	no	—
440	C₂×C₃×C₄	—	8	2	no	—
441	C₂×C₃×C₄	—	8	2	no	—
442	C₂×C₃×C₄	—	8	8	no	—
443	C₂×C₃×C₄	—	8	2	no	—
444	C₂×C₃×C₄	#123	1	4	yes	—
445	C₂×C₃×C₄	#123	1	4	yes	—
446	C₂×C₃×C₄	#123	1	4	yes	—
447	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
448	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₃×C₄	C₂×#41	1	2	yes	—
452	C₂×C₃×C₄	C₂×#41	1	2	yes	—
453	C₂×C₃×C₄	C₂×#41	1	2	yes	—
454	C₂×C₃×C₄	C₂×#41	1	2	yes	—
455	C₂×C₃×C₄	C₂×#41	1	2	yes	—
456	C₂×C₃×C₄	C₂×#41	1	2	yes	—
457	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
458	C₃×C₈	—	2	2	no	—
459	C₃×C₈	—	2	2	no	—
460	C₃×C₈	—	2	4	no	—
461	C₂⁴	—	2	1	no	—
462	C₂⁴	C₂×C₃×D₄	1	2	yes	—
463	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
464	#41	—	2	8	no	—
465	#41	—	2	8	no	—
466	#41	—	2	4	no	—
467	#41	—	2	4	no	—
468	#41	—	2	4	no	—
469	#41	—	2	4	no	—
470	#41	—	2	4	no	—
471	#41	—	2	4	no	—
472	#41	—	2	4	no	—
473	#41	—	2	4	no	—
474	#41	—	4	4	no	—
475	#41	—	4	4	no	—
476	C₂×Q₈	—	2	4	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
481	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
482	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	8	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
493	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
494	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
495	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
496	C₂×D₄	C₂⁴×C₃	1	2	yes	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
508	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
509	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
512	C₂²×C₄	C₃×#41	1	4	yes	—
513	C₂²×C₄	C₃×#41	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
518	M₁₆	—	2	4	no	—
519	M₁₆	—	2	4	no	—
520	C₂×C₈	—	2	4	no	—
521	C₂×C₈	—	2	4	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	4	no	—
525	C₂×C₈	C₂⁴×C₃	1	2	yes	—
526	C₂×C₈	C₂⁴×C₃	1	4	yes	—
527	C₂×C₈	C₂⁴×C₃	1	2	yes	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	8	no	—
533	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
534	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
535	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	8	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	8	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₂²×C₃	—	2	2	no	—
553	C₂²×C₃	—	2	2	no	—
554	C₂²×C₃	—	2	2	no	—
555	C₂²×C₃	—	2	8	no	—
556	C₂²×C₃	—	2	4	no	—
557	C₂²×C₃	—	4	4	no	—
558	C₂²×C₃	—	4	4	no	—
559	C₂²×C₃	—	4	2	no	—
560	C₂²×C₃	—	8	4	no	—
561	C₂²×C₃	—	8	4	no	—
562	C₂²×C₃	C₂×#123	1	2	yes	—
563	C₂²×C₃	C₂×#123	1	2	yes	—
564	C₂²×C₃	C₂×#123	1	2	yes	—
565	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
566	C₃×C₄	—	2	4	no	—
567	C₃×C₄	—	4	4	no	—
568	C₃×C₄	—	4	4	no	—
569	C₃×C₄	—	4	4	no	—
570	C₃×C₄	—	4	2	no	—
571	C₃×C₄	C₂×#123	1	2	yes	—
572	C₃×C₄	C₂×#123	1	2	yes	—
573	C₃×C₄	C₂×#123	1	2	yes	—
574	C₃×C₄	C₂²×#41	1	1	yes	characteristic
575	C₃×C₄	C₂²×#41	1	1	yes	characteristic
576	C₂³	—	2	4	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	4	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	8	2	no	—
582	C₂³	C₃×#123	1	4	yes	—
583	C₂³	C₂²×C₃×D₄	1	4	yes	—
584	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
585	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
586	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
587	Q₈	—	2	4	no	—
588	Q₈	—	2	4	no	—
589	Q₈	—	2	2	no	—
590	Q₈	—	2	2	no	—
591	Q₈	—	4	2	no	—
592	D₄	—	2	8	no	—
593	D₄	—	2	8	no	—
594	D₄	—	2	2	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	4	no	—
598	D₄	—	4	4	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	2	no	—
601	D₄	—	8	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	8	2	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	8	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	C₃×#123	1	4	yes	—
618	C₂×C₄	C₃×#123	1	4	yes	—
619	C₂×C₄	C₃×#123	1	4	yes	—
620	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
621	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
622	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
623	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
624	C₂×C₄	C₂×C₃×#41	1	2	yes	—
625	C₂×C₄	C₂×C₃×#41	1	2	yes	—
626	C₂×C₄	C₂×C₃×#41	1	2	yes	—
627	C₂×C₄	C₂×C₃×#41	1	2	yes	—
628	C₂×C₄	C₂×C₃×#41	1	2	yes	—
629	C₂×C₄	C₂×C₃×#41	1	2	yes	—
630	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
631	C₈	—	2	2	no	—
632	C₈	—	2	2	no	—
633	C₈	—	2	4	no	—
634	C₂×C₃	—	2	2	no	—
635	C₂×C₃	—	2	2	no	—
636	C₂×C₃	—	2	2	no	—
637	C₂×C₃	—	4	4	no	—
638	C₂×C₃	—	8	2	no	—
639	C₂×C₃	C₂²×#123	1	1	yes	characteristic
640	C₂×C₃	#3584	1	2	yes	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	8	4	no	—
650	C₂²	—	8	4	no	—
651	C₂²	C₂×C₃×#123	1	2	yes	—
652	C₂²	C₂×C₃×#123	1	2	yes	—
653	C₂²	C₂×C₃×#123	1	2	yes	—
654	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
655	C₄	—	2	4	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	4	no	—
660	C₄	C₂×C₃×#123	1	2	yes	—
661	C₄	C₂×C₃×#123	1	2	yes	—
662	C₄	C₂×C₃×#123	1	2	yes	—
663	C₄	C₂²×C₃×#41	1	1	yes	characteristic
664	C₄	C₂²×C₃×#41	1	1	yes	characteristic
665	C₃	#60516	1	1	yes	characteristic, direct product factor, Sylow
666	C₂	—	2	2	no	—
667	C₂	—	2	2	no	—
668	C₂	—	2	2	no	—
669	C₂	—	4	4	no	—
670	C₂	—	8	2	no	—
671	C₂	C₂²×C₃×#123	1	1	yes	characteristic
672	C₂	C₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
prime radical	C₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#3428	C₂	semidirect
3. C₃×#3099	C₂	semidirect
4. C₃×#3098	C₂	semidirect
5. C₃×#3097	C₂	semidirect
6. C₃×#3096	C₂	semidirect
7. C₃×#3091	C₂	semidirect
8. C₃×#2911	C₂	semidirect
9. C₂×C₃×#427	C₂	semidirect
10. C₃×#2896	C₂	semidirect
11. C₂×C₃×#416	C₂	semidirect
12. C₂×C₃×#408	C₂	semidirect
13. #60516	C₃	direct (N × H)
28. C₃×#520	C₂²	semidirect
37. C₂×C₃×#117	C₂²	semidirect
38. C₃×#485	C₂²	semidirect
39. C₃×#485	C₂²	semidirect
40. C₃×#484	C₂²	semidirect
41. C₃×#483	C₂²	semidirect
42. C₃×#482	C₂²	semidirect
43. C₃×#482	C₂²	semidirect
44. C₃×#481	C₂²	semidirect
45. C₃×#480	C₂²	semidirect
46. C₃×#428	C₂²	semidirect
47. C₃×#428	C₂²	semidirect
48. C₃×#427	C₂²	semidirect
49. C₃×#427	C₂²	semidirect
50. C₃×#427	C₂²	semidirect
51. C₂×C₃×#107	C₂²	semidirect
52. C₂×C₃×#106	C₂²	semidirect
53. C₃×#419	C₂²	semidirect
54. C₃×#418	C₂²	semidirect
55. C₃×#417	C₂²	semidirect
58. C₃×#416	C₂²	semidirect
59. C₃×#416	C₂²	semidirect
60. C₂×C₃×#103	C₂²	semidirect
61. C₂×C₃×#102	C₂²	semidirect
63. C₃×#408	C₂²	semidirect
64. C₃×#408	C₂²	semidirect
65. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
67. #3428	C₂×C₃	semidirect
68. #3099	C₂×C₃	semidirect
69. #3098	C₂×C₃	semidirect
70. #3097	C₂×C₃	semidirect
71. #3096	C₂×C₃	semidirect
72. #3091	C₂×C₃	semidirect
73. #2911	C₂×C₃	semidirect
74. C₂×#427	C₂×C₃	semidirect
75. #2896	C₂×C₃	semidirect
76. C₂×#416	C₂×C₃	semidirect
77. C₂×#408	C₂×C₃	semidirect
183. #520	C₂²×C₃	semidirect
192. C₂×#117	C₂²×C₃	semidirect
193. #485	C₂²×C₃	semidirect
194. #485	C₂²×C₃	semidirect
195. #484	C₂²×C₃	semidirect
196. #483	C₂²×C₃	semidirect
197. #482	C₂²×C₃	semidirect
198. #482	C₂²×C₃	semidirect
199. #481	C₂²×C₃	semidirect
200. #480	C₂²×C₃	semidirect
201. #428	C₂²×C₃	semidirect
202. #428	C₂²×C₃	semidirect
203. #427	C₂²×C₃	semidirect
204. #427	C₂²×C₃	semidirect
205. #427	C₂²×C₃	semidirect
206. C₂×#107	C₂²×C₃	semidirect
207. C₂×#106	C₂²×C₃	semidirect
208. #419	C₂²×C₃	semidirect
209. #418	C₂²×C₃	semidirect
210. #417	C₂²×C₃	semidirect
213. #416	C₂²×C₃	semidirect
214. #416	C₂²×C₃	semidirect
215. C₂×#103	C₂²×C₃	semidirect
216. C₂×#102	C₂²×C₃	semidirect
218. #408	C₂²×C₃	semidirect
219. #408	C₂²×C₃	semidirect
220. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
665. C₃	#60516	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3449	2
C₃×#3428	2
C₃×#3099	2
C₃×#3098	2
C₃×#3097	2
C₃×#3096	2
C₃×#3091	2
C₃×#2911	2
C₂×C₃×#427	2
C₃×#2896	2
C₂×C₃×#416	2
C₂×C₃×#408	2
#60516	3

Subgroups — C3×#60516 #10679123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60516 #10679123