Subgroups — C₃×#60612 #10679219

Order 768.

2050 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₃×#3137	C₂	1	8	yes	maximal, complemented
4	C₃×#3136	C₂	1	8	yes	maximal, complemented
5	C₃×#3135	C₂	1	4	yes	maximal, complemented
6	C₃×#3131	C₂	1	4	yes	maximal, complemented
7	C₃×#2896	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#416	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	#60612	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×#41	C₂²	1	2	yes	—
12	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₃×#544	—	2	2	no	—
15	C₃×#544	C₂²	1	8	yes	complemented
16	C₃×#543	—	2	2	no	—
17	C₃×#537	—	2	2	no	—
18	C₃×#536	C₂²	1	4	yes	—
19	C₃×#535	C₂²	1	4	yes	—
20	C₃×#534	—	2	2	no	—
21	C₃×#533	—	2	4	no	—
22	C₃×#533	C₂²	1	4	yes	complemented
23	C₃×#532	C₂²	1	4	yes	—
24	C₃×#525	—	2	4	no	—
25	C₂×C₃×#117	C₂²	1	2	yes	—
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₃×#491	C₂²	1	8	yes	complemented
28	C₃×#490	C₂²	1	8	yes	complemented
29	C₃×#489	C₂²	1	16	yes	complemented
30	C₃×#488	C₂²	1	16	yes	complemented
31	C₃×#487	C₂²	1	8	yes	complemented
32	C₃×#486	C₂²	1	8	yes	complemented
33	C₃×#419	C₂²	1	4	yes	complemented
34	C₃×#418	C₂²	1	4	yes	complemented
35	C₃×#417	C₂²	1	8	yes	—
36	C₃×#416	C₂²	1	8	yes	—
37	C₃×#416	C₂²	1	4	yes	complemented
38	C₃×#416	C₂²	1	8	yes	complemented
39	C₃×#416	C₂²	1	4	yes	complemented
40	C₂×C₃×#103	C₂²	1	4	yes	complemented
41	C₂×C₃×#102	C₂²	1	4	yes	complemented
42	C₃×#405	C₂²	1	8	yes	complemented
43	C₂×C₃×#97	C₂²	1	2	yes	complemented
44	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
45	#3458	C₂×C₃	1	1	yes	characteristic, complemented
46	#3449	C₂×C₃	1	1	yes	characteristic
47	#3137	C₂×C₃	1	8	yes	complemented
48	#3136	C₂×C₃	1	8	yes	complemented
49	#3135	C₂×C₃	1	4	yes	complemented
50	#3131	C₂×C₃	1	4	yes	complemented
51	#2896	C₂×C₃	1	2	yes	complemented
52	C₂×#416	C₂×C₃	1	2	yes	complemented
53	C₂×#405	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×#41	—	2	2	no	—
55	C₂×C₃×#41	—	2	2	no	—
56	C₂×C₃×#41	—	2	8	no	—
57	C₂×C₃×#41	—	2	8	no	—
58	C₂×C₃×#41	C₂³	1	4	yes	—
59	C₂×C₃×#41	C₂³	1	4	yes	—
60	C₂²×C₃×Q₈	C₂³	1	2	yes	—
61	C₂²×C₃×D₄	—	2	2	no	—
62	C₂²×C₃×D₄	C₂³	1	2	yes	—
63	C₂³×C₃×C₄	—	2	2	no	—
64	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃×M₁₆	—	2	4	no	—
66	C₂×C₃×M₁₆	C₂³	1	4	yes	—
67	C₂²×C₃×C₈	—	2	4	no	—
68	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂³	1	4	yes	—
71	C₂²×C₃×C₈	C₂³	1	2	yes	—
72	C₃×C₄⋊Q₈	—	2	8	no	—
73	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
75	C₃×#127	C₂³	1	4	yes	—
76	C₃×#125	—	2	8	no	—
77	C₃×#125	C₂³	1	8	yes	—
78	C₃×#124	C₂³	1	8	yes	—
79	C₃×#123	—	2	8	no	—
80	C₃×C₂²⋊Q₈	—	2	8	no	—
81	C₃×C₂²⋊Q₈	—	2	8	no	—
82	C₃×C₂²⋊Q₈	—	2	16	no	—
83	C₃×#121	—	2	8	no	—
84	C₃×#121	—	2	8	no	—
85	C₃×#120	—	2	8	no	—
86	C₃×C₄×Q₈	—	2	8	no	—
87	C₃×C₄×D₄	—	2	8	no	—
88	C₃×#117	—	2	2	no	—
89	C₃×#117	—	2	2	no	—
90	C₃×#117	D₄	1	4	yes	—
91	C₃×#117	C₂³	1	4	yes	—
92	C₃×#117	C₂³	1	4	yes	—
93	C₃×#117	C₂³	1	4	yes	—
94	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
98	C₂×C₃×C₄²	—	2	2	no	—
99	C₂×C₃×C₄²	C₂³	1	2	yes	—
100	C₃×#103	C₂³	1	8	yes	—
101	C₃×#103	C₂³	1	8	yes	—
102	C₃×#103	C₂³	1	16	yes	—
103	C₃×#102	C₂³	1	8	yes	—
104	C₃×#102	C₂³	1	8	yes	—
105	C₃×#102	C₂³	1	16	yes	—
106	C₃×#97	C₂³	1	8	yes	—
107	C₃×C₄×C₈	C₂³	1	8	yes	—
108	C₂²×#41	C₂²×C₃	1	2	yes	—
109	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
110	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
111	#544	—	2	2	no	—
112	#544	C₂²×C₃	1	8	yes	complemented
113	#543	—	2	2	no	—
114	#537	—	2	2	no	—
115	#536	C₂²×C₃	1	4	yes	—
116	#535	C₂²×C₃	1	4	yes	—
117	#534	—	2	2	no	—
118	#533	—	2	4	no	—
119	#533	C₂²×C₃	1	4	yes	complemented
120	#532	C₂²×C₃	1	4	yes	—
121	#525	—	2	4	no	—
122	C₂×#117	C₂²×C₃	1	2	yes	—
123	C₂×#117	C₂²×C₃	1	1	yes	characteristic
124	#491	C₂²×C₃	1	8	yes	complemented
125	#490	C₂²×C₃	1	8	yes	complemented
126	#489	C₂²×C₃	1	16	yes	complemented
127	#488	C₂²×C₃	1	16	yes	complemented
128	#487	C₂²×C₃	1	8	yes	complemented
129	#486	C₂²×C₃	1	8	yes	complemented
130	#419	C₂²×C₃	1	4	yes	complemented
131	#418	C₂²×C₃	1	4	yes	complemented
132	#417	C₂²×C₃	1	8	yes	—
133	#416	C₂²×C₃	1	8	yes	—
134	#416	C₂²×C₃	1	4	yes	complemented
135	#416	C₂²×C₃	1	8	yes	complemented
136	#416	C₂²×C₃	1	4	yes	complemented
137	C₂×#103	C₂²×C₃	1	4	yes	complemented
138	C₂×#102	C₂²×C₃	1	4	yes	complemented
139	#405	C₂²×C₃	1	8	yes	complemented
140	C₂×#97	C₂²×C₃	1	2	yes	complemented
141	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
142	C₂⁴×C₃	—	2	2	no	—
143	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
144	C₃×#41	—	2	8	no	—
145	C₃×#41	—	2	8	no	—
146	C₃×#41	—	2	8	no	—
147	C₃×#41	—	2	8	no	—
148	C₃×#41	—	4	8	no	—
149	C₃×#41	—	4	8	no	—
150	C₂×C₃×Q₈	—	2	2	no	—
151	C₂×C₃×Q₈	—	2	8	no	—
152	C₂×C₃×Q₈	—	2	4	no	—
153	C₂×C₃×Q₈	—	2	4	no	—
154	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
155	C₂×C₃×D₄	—	2	4	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	8	no	—
159	C₂×C₃×D₄	—	2	4	no	—
160	C₂×C₃×D₄	—	2	4	no	—
161	C₂×C₃×D₄	—	4	8	no	—
162	C₂×C₃×D₄	C₂⁴	1	4	yes	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	2	4	no	—
166	C₂²×C₃×C₄	—	2	4	no	—
167	C₂²×C₃×C₄	—	4	8	no	—
168	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
169	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
171	C₂²×C₃×C₄	#41	1	4	yes	—
172	C₂²×C₃×C₄	#41	1	4	yes	—
173	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
174	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
175	C₃×M₁₆	—	2	8	no	—
176	C₂×C₃×C₈	—	2	8	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	—	2	2	no	—
179	C₂×C₃×C₈	—	2	4	no	—
180	C₂×C₃×C₈	C₂⁴	1	2	yes	—
181	C₂×C₃×C₈	C₂⁴	1	4	yes	—
182	C₂×C₃×C₈	C₂⁴	1	2	yes	—
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	8	no	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₄⋊C₄	—	2	16	no	—
187	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
188	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
189	C₃×C₂²⋊C₄	—	2	4	no	—
190	C₃×C₂²⋊C₄	—	2	4	no	—
191	C₃×C₂²⋊C₄	—	2	16	no	—
192	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
193	C₃×C₄²	—	2	4	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	C₂×D₄	1	4	yes	—
196	C₃×C₄²	C₂⁴	1	4	yes	—
197	C₂×#41	—	2	2	no	—
198	C₂×#41	—	2	2	no	—
199	C₂×#41	—	2	8	no	—
200	C₂×#41	—	2	8	no	—
201	C₂×#41	C₂³×C₃	1	4	yes	—
202	C₂×#41	C₂³×C₃	1	4	yes	—
203	C₂²×Q₈	C₂³×C₃	1	2	yes	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	C₂³×C₃	1	2	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
208	C₂×M₁₆	—	2	4	no	—
209	C₂×M₁₆	C₂³×C₃	1	4	yes	—
210	C₂²×C₈	—	2	4	no	—
211	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₃	1	4	yes	—
214	C₂²×C₈	C₂³×C₃	1	2	yes	—
215	C₄⋊Q₈	—	2	8	no	—
216	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
217	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
218	#127	C₂³×C₃	1	4	yes	—
219	#125	—	2	8	no	—
220	#125	C₂³×C₃	1	8	yes	—
221	#124	C₂³×C₃	1	8	yes	—
222	#123	—	2	8	no	—
223	C₂²⋊Q₈	—	2	8	no	—
224	C₂²⋊Q₈	—	2	8	no	—
225	C₂²⋊Q₈	—	2	16	no	—
226	#121	—	2	8	no	—
227	#121	—	2	8	no	—
228	#120	—	2	8	no	—
229	C₄×Q₈	—	2	8	no	—
230	C₄×D₄	—	2	8	no	—
231	#117	—	2	2	no	—
232	#117	—	2	2	no	—
233	#117	C₃×D₄	1	4	yes	—
234	#117	C₂³×C₃	1	4	yes	—
235	#117	C₂³×C₃	1	4	yes	—
236	#117	C₂³×C₃	1	4	yes	—
237	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂³×C₃	1	2	yes	—
243	#103	C₂³×C₃	1	8	yes	—
244	#103	C₂³×C₃	1	8	yes	—
245	#103	C₂³×C₃	1	16	yes	—
246	#102	C₂³×C₃	1	8	yes	—
247	#102	C₂³×C₃	1	8	yes	—
248	#102	C₂³×C₃	1	16	yes	—
249	#97	C₂³×C₃	1	8	yes	—
250	C₄×C₈	C₂³×C₃	1	8	yes	—
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	4	2	no	—
253	C₂³×C₃	—	4	4	no	—
254	C₂³×C₃	—	8	4	no	—
255	C₂³×C₃	#124	1	4	yes	—
256	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
257	C₂³×C₃	C₂²×D₄	1	2	yes	—
258	C₃×Q₈	—	2	4	no	—
259	C₃×Q₈	—	2	4	no	—
260	C₃×Q₈	—	4	4	no	—
261	C₃×Q₈	—	8	8	no	—
262	C₃×D₄	—	2	4	no	—
263	C₃×D₄	—	2	4	no	—
264	C₃×D₄	—	4	8	no	—
265	C₃×D₄	—	4	8	no	—
266	C₃×D₄	—	4	4	no	—
267	C₃×D₄	—	8	8	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	4	4	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	4	8	no	—
273	C₂×C₃×C₄	—	4	8	no	—
274	C₂×C₃×C₄	—	8	4	no	—
275	C₂×C₃×C₄	#124	1	8	yes	—
276	C₂×C₃×C₄	#124	1	4	yes	—
277	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
278	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
279	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×#41	1	4	yes	—
281	C₂×C₃×C₄	C₂×#41	1	2	yes	—
282	C₂×C₃×C₄	C₂×#41	1	2	yes	—
283	C₂×C₃×C₄	C₂×#41	1	4	yes	—
284	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	2	2	no	—
287	C₃×C₈	—	2	4	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
290	#41	—	2	8	no	—
291	#41	—	2	8	no	—
292	#41	—	2	8	no	—
293	#41	—	2	8	no	—
294	#41	—	4	8	no	—
295	#41	—	4	8	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	C₂⁴×C₃	1	4	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	4	8	no	—
314	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
315	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₃×#41	1	4	yes	—
318	C₂²×C₄	C₃×#41	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
321	M₁₆	—	2	8	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	C₂⁴×C₃	1	2	yes	—
327	C₂×C₈	C₂⁴×C₃	1	4	yes	—
328	C₂×C₈	C₂⁴×C₃	1	2	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	16	no	—
333	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
334	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
339	C₄²	—	2	4	no	—
340	C₄²	—	2	4	no	—
341	C₄²	C₂×C₃×D₄	1	4	yes	—
342	C₄²	C₂⁴×C₃	1	4	yes	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	4	no	—
345	C₂²×C₃	—	4	4	no	—
346	C₂²×C₃	—	4	8	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	—	8	8	no	—
349	C₂²×C₃	C₂×#124	1	4	yes	—
350	C₂²×C₃	C₂×#124	1	2	yes	—
351	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
352	C₃×C₄	—	2	8	no	—
353	C₃×C₄	—	4	8	no	—
354	C₃×C₄	—	4	4	no	—
355	C₃×C₄	C₂×#124	1	2	yes	—
356	C₃×C₄	C₂×#124	1	4	yes	—
357	C₃×C₄	C₂²×#41	1	1	yes	characteristic
358	C₃×C₄	C₂²×#41	1	1	yes	characteristic
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	8	4	no	—
363	C₂³	C₃×#124	1	4	yes	—
364	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
365	C₂³	C₂²×C₃×D₄	1	2	yes	—
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	4	no	—
369	Q₈	—	8	8	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	8	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	8	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	8	4	no	—
383	C₂×C₄	C₃×#124	1	8	yes	—
384	C₂×C₄	C₃×#124	1	4	yes	—
385	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
386	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
388	C₂×C₄	C₂×C₃×#41	1	4	yes	—
389	C₂×C₄	C₂×C₃×#41	1	2	yes	—
390	C₂×C₄	C₂×C₃×#41	1	2	yes	—
391	C₂×C₄	C₂×C₃×#41	1	4	yes	—
392	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	2	4	no	—
396	C₂×C₃	—	2	4	no	—
397	C₂×C₃	—	2	2	no	—
398	C₂×C₃	—	8	4	no	—
399	C₂×C₃	C₂²×#124	1	1	yes	characteristic
400	C₂×C₃	#3584	1	2	yes	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	8	no	—
406	C₂²	—	8	8	no	—
407	C₂²	C₂×C₃×#124	1	4	yes	—
408	C₂²	C₂×C₃×#124	1	2	yes	—
409	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
410	C₄	—	2	8	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	8	no	—
413	C₄	C₂×C₃×#124	1	2	yes	—
414	C₄	C₂×C₃×#124	1	4	yes	—
415	C₄	C₂²×C₃×#41	1	1	yes	characteristic
416	C₄	C₂²×C₃×#41	1	1	yes	characteristic
417	C₃	#60612	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	2	4	no	—
419	C₂	—	2	2	no	—
420	C₂	—	8	4	no	—
421	C₂	C₂²×C₃×#124	1	1	yes	characteristic
422	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 ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3458	C₂	semidirect
3. C₃×#3137	C₂	semidirect
4. C₃×#3136	C₂	semidirect
5. C₃×#3135	C₂	semidirect
6. C₃×#3131	C₂	semidirect
7. C₃×#2896	C₂	semidirect
8. C₂×C₃×#416	C₂	semidirect
9. C₂×C₃×#405	C₂	semidirect
10. #60612	C₃	direct (N × H)
15. C₃×#544	C₂²	semidirect
22. C₃×#533	C₂²	semidirect
27. C₃×#491	C₂²	semidirect
28. C₃×#490	C₂²	semidirect
29. C₃×#489	C₂²	semidirect
30. C₃×#488	C₂²	semidirect
31. C₃×#487	C₂²	semidirect
32. C₃×#486	C₂²	semidirect
33. C₃×#419	C₂²	semidirect
34. C₃×#418	C₂²	semidirect
37. C₃×#416	C₂²	semidirect
38. C₃×#416	C₂²	semidirect
39. C₃×#416	C₂²	semidirect
40. C₂×C₃×#103	C₂²	semidirect
41. C₂×C₃×#102	C₂²	semidirect
42. C₃×#405	C₂²	semidirect
43. C₂×C₃×#97	C₂²	semidirect
44. C₂×C₃×C₄×C₈	C₂²	semidirect
45. #3458	C₂×C₃	semidirect
47. #3137	C₂×C₃	semidirect
48. #3136	C₂×C₃	semidirect
49. #3135	C₂×C₃	semidirect
50. #3131	C₂×C₃	semidirect
51. #2896	C₂×C₃	semidirect
52. C₂×#416	C₂×C₃	semidirect
53. C₂×#405	C₂×C₃	semidirect
112. #544	C₂²×C₃	semidirect
119. #533	C₂²×C₃	semidirect
124. #491	C₂²×C₃	semidirect
125. #490	C₂²×C₃	semidirect
126. #489	C₂²×C₃	semidirect
127. #488	C₂²×C₃	semidirect
128. #487	C₂²×C₃	semidirect
129. #486	C₂²×C₃	semidirect
130. #419	C₂²×C₃	semidirect
131. #418	C₂²×C₃	semidirect
134. #416	C₂²×C₃	semidirect
135. #416	C₂²×C₃	semidirect
136. #416	C₂²×C₃	semidirect
137. C₂×#103	C₂²×C₃	semidirect
138. C₂×#102	C₂²×C₃	semidirect
139. #405	C₂²×C₃	semidirect
140. C₂×#97	C₂²×C₃	semidirect
141. C₂×C₄×C₈	C₂²×C₃	semidirect
417. C₃	#60612	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×#3458	2
C₃×#3449	2
C₃×#3137	2
C₃×#3136	2
C₃×#3135	2
C₃×#3131	2
C₃×#2896	2
C₂×C₃×#416	2
C₂×C₃×#405	2
#60612	3

Subgroups — C3×#60612 #10679219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60612 #10679219