Subgroups — C₃×#60624 #10679231

Order 768.

2038 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3500	C₂	1	1	yes	maximal, characteristic
3	C₃×#3142	C₂	1	3	yes	maximal, complemented
4	C₃×#3140	C₂	1	3	yes	maximal, complemented
5	C₃×#3137	C₂	1	6	yes	maximal, complemented
6	C₃×#3136	C₂	1	6	yes	maximal, complemented
7	C₃×#3131	C₂	1	3	yes	maximal, complemented
8	C₂×C₃×#488	C₂	1	3	yes	maximal, complemented
9	C₃×#2898	C₂	1	2	yes	maximal, complemented
10	C₃×#2897	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	#60624	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
14	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂×C₃×#131	C₂²	1	2	yes	—
16	C₃×#557	—	2	2	no	—
17	C₃×#554	—	2	6	no	—
18	C₃×#548	—	2	2	no	—
19	C₃×#546	—	2	6	no	—
20	C₃×#544	C₂²	1	6	yes	complemented
21	C₃×#536	C₂²	1	3	yes	—
22	C₃×#535	C₂²	1	3	yes	—
23	C₃×#533	C₂²	1	3	yes	complemented
24	C₃×#532	C₂²	1	3	yes	—
25	C₂×C₃×#125	C₂²	1	3	yes	complemented
26	C₂×C₃×#124	C₂²	1	3	yes	—
27	C₃×#520	C₂²	1	2	yes	—
28	C₃×C₄×#41	C₂²	1	1	yes	characteristic
29	C₃×#491	C₂²	1	6	yes	complemented
30	C₃×#490	C₂²	1	6	yes	complemented
31	C₃×#489	C₂²	1	12	yes	complemented
32	C₃×#488	C₂²	1	3	yes	complemented
33	C₃×#488	C₂²	1	12	yes	complemented
34	C₃×#488	C₂²	1	6	yes	complemented
35	C₃×#488	C₂²	1	1	yes	characteristic, complemented
36	C₃×#488	C₂²	1	3	yes	complemented
37	C₃×#488	C₂²	1	3	yes	complemented
38	C₃×#487	C₂²	1	6	yes	complemented
39	C₃×#486	C₂²	1	6	yes	complemented
40	C₃×#419	C₂²	1	6	yes	complemented
41	C₃×#418	C₂²	1	6	yes	—
42	C₃×#417	C₂²	1	6	yes	—
43	C₃×#417	C₂²	1	6	yes	complemented
44	C₃×#416	C₂²	1	6	yes	—
45	C₃×#416	C₂²	1	6	yes	complemented
46	C₂×C₃×#103	C₂²	1	6	yes	complemented
47	C₂×C₃×#102	C₂²	1	6	yes	—
48	C₃×#405	C₂²	1	6	yes	complemented
49	C₃×C₄×M₁₆	C₂²	1	3	yes	complemented
50	C₂×C₃×C₄×C₈	C₂²	1	3	yes	complemented
51	#3504	C₂×C₃	1	1	yes	characteristic, complemented
52	#3500	C₂×C₃	1	1	yes	characteristic
53	#3142	C₂×C₃	1	3	yes	complemented
54	#3140	C₂×C₃	1	3	yes	complemented
55	#3137	C₂×C₃	1	6	yes	complemented
56	#3136	C₂×C₃	1	6	yes	complemented
57	#3131	C₂×C₃	1	3	yes	complemented
58	C₂×#488	C₂×C₃	1	3	yes	complemented
59	#2898	C₂×C₃	1	2	yes	complemented
60	#2897	C₂×C₃	1	2	yes	complemented
61	C₄×#131	C₂×C₃	1	1	yes	characteristic, complemented
62	C₃×2₋¹⁺⁴	—	2	8	no	—
63	C₃×H(5,𝔽₂)	—	2	8	no	—
64	C₂×C₃×#41	—	2	1	no	—
65	C₂×C₃×#41	—	2	3	no	—
66	C₂×C₃×#41	C₂³	1	3	yes	—
67	C₂×C₃×#41	C₂³	1	3	yes	—
68	C₂×C₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×C₃×Q₈	—	2	1	no	—
70	C₂²×C₃×Q₈	C₂³	1	3	yes	—
71	C₂²×C₃×D₄	—	2	3	no	—
72	C₂²×C₃×D₄	C₂³	1	3	yes	—
73	C₃×#131	—	2	8	no	—
74	C₂×C₃×M₁₆	C₂³	1	6	yes	—
75	C₂²×C₃×C₈	C₂³	1	6	yes	—
76	C₃×C₄⋊Q₈	—	2	6	no	—
77	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
78	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
79	C₃×#127	C₂³	1	3	yes	—
80	C₃×#125	—	2	6	no	—
81	C₃×#125	—	2	6	no	—
82	C₃×#125	C₂³	1	3	yes	—
83	C₃×#125	C₂³	1	6	yes	—
84	C₃×#125	C₂³	1	1	yes	characteristic
85	C₃×#124	—	2	6	no	—
86	C₃×#124	C₂³	1	3	yes	—
87	C₃×#124	C₂³	1	6	yes	—
88	C₃×#124	C₂³	1	1	yes	characteristic
89	C₃×#123	—	2	6	no	—
90	C₃×C₂²⋊Q₈	—	2	6	no	—
91	C₃×C₂²⋊Q₈	—	2	6	no	—
92	C₃×C₂²⋊Q₈	—	2	12	no	—
93	C₃×#121	—	2	6	no	—
94	C₃×#121	—	2	6	no	—
95	C₃×#120	—	2	6	no	—
96	C₃×C₄×Q₈	—	2	2	no	—
97	C₃×C₄×Q₈	—	2	6	no	—
98	C₃×C₄×Q₈	D₄	1	2	yes	—
99	C₃×C₄×D₄	—	2	6	no	—
100	C₃×C₄×D₄	—	2	6	no	—
101	C₃×C₄×D₄	D₄	1	6	yes	—
102	C₃×#117	C₂³	1	6	yes	—
103	C₃×#117	C₂³	1	3	yes	—
104	C₂×C₃×C₄⋊C₄	—	2	6	no	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
106	C₂×C₃×C₂²⋊C₄	—	2	6	no	—
107	C₂×C₃×C₄²	C₂³	1	3	yes	—
108	C₃×#103	C₂³	1	6	yes	—
109	C₃×#103	C₂³	1	12	yes	—
110	C₃×#103	C₂³	1	2	yes	—
111	C₃×#103	C₂³	1	6	yes	—
112	C₃×#103	C₂³	1	6	yes	—
113	C₃×#102	C₂³	1	6	yes	—
114	C₃×#102	C₂³	1	12	yes	—
115	C₃×#102	C₂³	1	6	yes	—
116	C₃×#102	C₂³	1	2	yes	—
117	C₃×#102	C₂³	1	6	yes	—
118	C₃×#97	C₂³	1	6	yes	—
119	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
120	C₃×C₄×C₈	C₂³	1	3	yes	—
121	C₃×C₄×C₈	C₂³	1	6	yes	—
122	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
123	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
124	C₂×#131	C₂²×C₃	1	2	yes	—
125	#557	—	2	2	no	—
126	#554	—	2	6	no	—
127	#548	—	2	2	no	—
128	#546	—	2	6	no	—
129	#544	C₂²×C₃	1	6	yes	complemented
130	#536	C₂²×C₃	1	3	yes	—
131	#535	C₂²×C₃	1	3	yes	—
132	#533	C₂²×C₃	1	3	yes	complemented
133	#532	C₂²×C₃	1	3	yes	—
134	C₂×#125	C₂²×C₃	1	3	yes	complemented
135	C₂×#124	C₂²×C₃	1	3	yes	—
136	#520	C₂²×C₃	1	2	yes	—
137	C₄×#41	C₂²×C₃	1	1	yes	characteristic
138	#491	C₂²×C₃	1	6	yes	complemented
139	#490	C₂²×C₃	1	6	yes	complemented
140	#489	C₂²×C₃	1	12	yes	complemented
141	#488	C₂²×C₃	1	3	yes	complemented
142	#488	C₂²×C₃	1	12	yes	complemented
143	#488	C₂²×C₃	1	6	yes	complemented
144	#488	C₂²×C₃	1	1	yes	characteristic, complemented
145	#488	C₂²×C₃	1	3	yes	complemented
146	#488	C₂²×C₃	1	3	yes	complemented
147	#487	C₂²×C₃	1	6	yes	complemented
148	#486	C₂²×C₃	1	6	yes	complemented
149	#419	C₂²×C₃	1	6	yes	complemented
150	#418	C₂²×C₃	1	6	yes	—
151	#417	C₂²×C₃	1	6	yes	—
152	#417	C₂²×C₃	1	6	yes	complemented
153	#416	C₂²×C₃	1	6	yes	—
154	#416	C₂²×C₃	1	6	yes	complemented
155	C₂×#103	C₂²×C₃	1	6	yes	complemented
156	C₂×#102	C₂²×C₃	1	6	yes	—
157	#405	C₂²×C₃	1	6	yes	complemented
158	C₄×M₁₆	C₂²×C₃	1	3	yes	complemented
159	C₂×C₄×C₈	C₂²×C₃	1	3	yes	complemented
160	C₂⁴×C₃	—	2	3	no	—
161	C₃×#41	—	2	12	no	—
162	C₃×#41	—	2	12	no	—
163	C₃×#41	—	4	4	no	—
164	C₃×#41	—	4	12	no	—
165	C₃×#41	#41	1	8	yes	—
166	C₂×C₃×Q₈	—	2	3	no	—
167	C₂×C₃×Q₈	—	2	6	no	—
168	C₂×C₃×Q₈	—	2	12	no	—
169	C₂×C₃×Q₈	—	4	4	no	—
170	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
172	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
173	C₂×C₃×D₄	—	2	3	no	—
174	C₂×C₃×D₄	—	2	3	no	—
175	C₂×C₃×D₄	—	2	3	no	—
176	C₂×C₃×D₄	—	2	6	no	—
177	C₂×C₃×D₄	—	2	12	no	—
178	C₂×C₃×D₄	—	4	12	no	—
179	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
180	C₂×C₃×D₄	C₂⁴	1	3	yes	—
181	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	3	no	—
183	C₂²×C₃×C₄	—	2	6	no	—
184	C₂²×C₃×C₄	—	2	3	no	—
185	C₂²×C₃×C₄	—	2	3	no	—
186	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
187	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
188	C₃×M₁₆	—	2	12	no	—
189	C₂×C₃×C₈	—	2	12	no	—
190	C₂×C₃×C₈	C₂⁴	1	2	yes	—
191	C₂×C₃×C₈	C₂⁴	1	6	yes	—
192	C₃×C₄⋊C₄	—	2	6	no	—
193	C₃×C₄⋊C₄	—	2	12	no	—
194	C₃×C₄⋊C₄	—	2	6	no	—
195	C₃×C₄⋊C₄	—	2	6	no	—
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	6	no	—
198	C₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
199	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
200	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₃×C₂²⋊C₄	—	2	6	no	—
202	C₃×C₂²⋊C₄	—	2	6	no	—
203	C₃×C₂²⋊C₄	—	2	12	no	—
204	C₃×C₂²⋊C₄	—	2	2	no	—
205	C₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
206	C₃×C₄²	—	2	6	no	—
207	C₃×C₄²	C₂×D₄	1	6	yes	—
208	C₃×C₄²	C₂⁴	1	1	yes	characteristic
209	C₃×C₄²	C₂⁴	1	3	yes	—
210	2₋¹⁺⁴	—	2	8	no	—
211	H(5,𝔽₂)	—	2	8	no	—
212	C₂×#41	—	2	1	no	—
213	C₂×#41	—	2	3	no	—
214	C₂×#41	C₂³×C₃	1	3	yes	—
215	C₂×#41	C₂³×C₃	1	3	yes	—
216	C₂×#41	C₂³×C₃	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	C₂³×C₃	1	3	yes	—
219	C₂²×D₄	—	2	3	no	—
220	C₂²×D₄	C₂³×C₃	1	3	yes	—
221	#131	—	2	8	no	—
222	C₂×M₁₆	C₂³×C₃	1	6	yes	—
223	C₂²×C₈	C₂³×C₃	1	6	yes	—
224	C₄⋊Q₈	—	2	6	no	—
225	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
226	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
227	#127	C₂³×C₃	1	3	yes	—
228	#125	—	2	6	no	—
229	#125	—	2	6	no	—
230	#125	C₂³×C₃	1	3	yes	—
231	#125	C₂³×C₃	1	6	yes	—
232	#125	C₂³×C₃	1	1	yes	characteristic
233	#124	—	2	6	no	—
234	#124	C₂³×C₃	1	3	yes	—
235	#124	C₂³×C₃	1	6	yes	—
236	#124	C₂³×C₃	1	1	yes	characteristic
237	#123	—	2	6	no	—
238	C₂²⋊Q₈	—	2	6	no	—
239	C₂²⋊Q₈	—	2	6	no	—
240	C₂²⋊Q₈	—	2	12	no	—
241	#121	—	2	6	no	—
242	#121	—	2	6	no	—
243	#120	—	2	6	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	6	no	—
246	C₄×Q₈	C₃×D₄	1	2	yes	—
247	C₄×D₄	—	2	6	no	—
248	C₄×D₄	—	2	6	no	—
249	C₄×D₄	C₃×D₄	1	6	yes	—
250	#117	C₂³×C₃	1	6	yes	—
251	#117	C₂³×C₃	1	3	yes	—
252	C₂×C₄⋊C₄	—	2	6	no	—
253	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
254	C₂×C₂²⋊C₄	—	2	6	no	—
255	C₂×C₄²	C₂³×C₃	1	3	yes	—
256	#103	C₂³×C₃	1	6	yes	—
257	#103	C₂³×C₃	1	12	yes	—
258	#103	C₂³×C₃	1	2	yes	—
259	#103	C₂³×C₃	1	6	yes	—
260	#103	C₂³×C₃	1	6	yes	—
261	#102	C₂³×C₃	1	6	yes	—
262	#102	C₂³×C₃	1	12	yes	—
263	#102	C₂³×C₃	1	6	yes	—
264	#102	C₂³×C₃	1	2	yes	—
265	#102	C₂³×C₃	1	6	yes	—
266	#97	C₂³×C₃	1	6	yes	—
267	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₃	1	3	yes	—
269	C₄×C₈	C₂³×C₃	1	6	yes	—
270	C₂³×C₃	—	2	3	no	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	—	4	6	no	—
273	C₂³×C₃	—	8	6	no	—
274	C₂³×C₃	C₂²×D₄	1	3	yes	—
275	C₃×Q₈	—	2	6	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	4	6	no	—
278	C₃×Q₈	—	8	6	no	—
279	C₃×Q₈	#124	1	4	yes	—
280	C₃×D₄	—	2	6	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	4	6	no	—
283	C₃×D₄	—	4	6	no	—
284	C₃×D₄	—	4	6	no	—
285	C₃×D₄	—	8	6	no	—
286	C₃×D₄	#124	1	12	yes	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	6	no	—
289	C₂×C₃×C₄	—	2	3	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	4	6	no	—
292	C₂×C₃×C₄	—	4	6	no	—
293	C₂×C₃×C₄	—	4	6	no	—
294	C₂×C₃×C₄	—	4	6	no	—
295	C₂×C₃×C₄	—	8	6	no	—
296	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
297	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
298	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
299	C₂×C₃×C₄	C₂×#41	1	12	yes	—
300	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
301	C₃×C₈	—	2	2	no	—
302	C₃×C₈	—	2	6	no	—
303	C₂⁴	—	2	3	no	—
304	#41	—	2	12	no	—
305	#41	—	2	12	no	—
306	#41	—	4	4	no	—
307	#41	—	4	12	no	—
308	#41	C₃×#41	1	8	yes	—
309	C₂×Q₈	—	2	3	no	—
310	C₂×Q₈	—	2	6	no	—
311	C₂×Q₈	—	2	12	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
315	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
316	C₂×D₄	—	2	3	no	—
317	C₂×D₄	—	2	3	no	—
318	C₂×D₄	—	2	3	no	—
319	C₂×D₄	—	2	6	no	—
320	C₂×D₄	—	2	12	no	—
321	C₂×D₄	—	4	12	no	—
322	C₂×D₄	C₂×C₃×D₄	1	3	yes	—
323	C₂×D₄	C₂⁴×C₃	1	3	yes	—
324	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
325	C₂²×C₄	—	2	3	no	—
326	C₂²×C₄	—	2	6	no	—
327	C₂²×C₄	—	2	3	no	—
328	C₂²×C₄	—	2	3	no	—
329	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
331	M₁₆	—	2	12	no	—
332	C₂×C₈	—	2	12	no	—
333	C₂×C₈	C₂⁴×C₃	1	2	yes	—
334	C₂×C₈	C₂⁴×C₃	1	6	yes	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	12	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	C₂×C₃×D₄	1	6	yes	—
342	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
343	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
344	C₂²⋊C₄	—	2	6	no	—
345	C₂²⋊C₄	—	2	6	no	—
346	C₂²⋊C₄	—	2	12	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	C₂×C₃×D₄	1	6	yes	—
349	C₄²	—	2	6	no	—
350	C₄²	C₂×C₃×D₄	1	6	yes	—
351	C₄²	C₂⁴×C₃	1	1	yes	characteristic
352	C₄²	C₂⁴×C₃	1	3	yes	—
353	C₂²×C₃	—	2	6	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	6	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	3	no	—
358	C₂²×C₃	—	16	6	no	—
359	C₂²×C₃	C₂×#124	1	6	yes	—
360	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	6	no	—
363	C₃×C₄	—	4	6	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	1	no	—
366	C₃×C₄	—	4	3	no	—
367	C₃×C₄	C₂×#124	1	6	yes	—
368	C₃×C₄	C₂²×#41	1	2	yes	—
369	C₂³	—	2	3	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	4	6	no	—
372	C₂³	—	8	6	no	—
373	C₂³	C₂²×C₃×D₄	1	3	yes	—
374	Q₈	—	2	6	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	6	no	—
377	Q₈	—	8	6	no	—
378	Q₈	C₃×#124	1	4	yes	—
379	D₄	—	2	6	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	6	no	—
382	D₄	—	4	6	no	—
383	D₄	—	4	6	no	—
384	D₄	—	8	6	no	—
385	D₄	C₃×#124	1	12	yes	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	2	3	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	6	no	—
391	C₂×C₄	—	4	6	no	—
392	C₂×C₄	—	4	6	no	—
393	C₂×C₄	—	4	6	no	—
394	C₂×C₄	—	8	6	no	—
395	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
396	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
397	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
398	C₂×C₄	C₂×C₃×#41	1	12	yes	—
399	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	6	no	—
402	C₂×C₃	—	2	6	no	—
403	C₂×C₃	—	8	1	no	—
404	C₂×C₃	—	8	3	no	—
405	C₂×C₃	C₂²×#124	1	1	yes	characteristic
406	C₂×C₃	#3584	1	2	yes	—
407	C₂²	—	2	6	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	3	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	6	no	—
412	C₂²	—	16	6	no	—
413	C₂²	C₂×C₃×#124	1	6	yes	—
414	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	6	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	3	no	—
419	C₄	—	4	6	no	—
420	C₄	—	4	2	no	—
421	C₄	C₂×C₃×#124	1	6	yes	—
422	C₄	C₂²×C₃×#41	1	2	yes	—
423	C₃	#60624	1	1	yes	characteristic, direct product factor, Sylow
424	C₂	—	2	6	no	—
425	C₂	—	8	3	no	—
426	C₂	—	8	1	no	—
427	C₂	C₂²×C₃×#124	1	1	yes	characteristic
428	C₂	C₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3504	C₂	semidirect
3. C₃×#3142	C₂	semidirect
4. C₃×#3140	C₂	semidirect
5. C₃×#3137	C₂	semidirect
6. C₃×#3136	C₂	semidirect
7. C₃×#3131	C₂	semidirect
8. C₂×C₃×#488	C₂	semidirect
9. C₃×#2898	C₂	semidirect
10. C₃×#2897	C₂	semidirect
11. C₃×C₄×#131	C₂	semidirect
12. #60624	C₃	direct (N × H)
20. C₃×#544	C₂²	semidirect
23. C₃×#533	C₂²	semidirect
25. C₂×C₃×#125	C₂²	semidirect
29. C₃×#491	C₂²	semidirect
30. C₃×#490	C₂²	semidirect
31. C₃×#489	C₂²	semidirect
32. C₃×#488	C₂²	semidirect
33. C₃×#488	C₂²	semidirect
34. C₃×#488	C₂²	semidirect
35. C₃×#488	C₂²	semidirect
36. C₃×#488	C₂²	semidirect
37. C₃×#488	C₂²	semidirect
38. C₃×#487	C₂²	semidirect
39. C₃×#486	C₂²	semidirect
40. C₃×#419	C₂²	semidirect
43. C₃×#417	C₂²	semidirect
45. C₃×#416	C₂²	semidirect
46. C₂×C₃×#103	C₂²	semidirect
48. C₃×#405	C₂²	semidirect
49. C₃×C₄×M₁₆	C₂²	semidirect
50. C₂×C₃×C₄×C₈	C₂²	semidirect
51. #3504	C₂×C₃	semidirect
53. #3142	C₂×C₃	semidirect
54. #3140	C₂×C₃	semidirect
55. #3137	C₂×C₃	semidirect
56. #3136	C₂×C₃	semidirect
57. #3131	C₂×C₃	semidirect
58. C₂×#488	C₂×C₃	semidirect
59. #2898	C₂×C₃	semidirect
60. #2897	C₂×C₃	semidirect
61. C₄×#131	C₂×C₃	semidirect
129. #544	C₂²×C₃	semidirect
132. #533	C₂²×C₃	semidirect
134. C₂×#125	C₂²×C₃	semidirect
138. #491	C₂²×C₃	semidirect
139. #490	C₂²×C₃	semidirect
140. #489	C₂²×C₃	semidirect
141. #488	C₂²×C₃	semidirect
142. #488	C₂²×C₃	semidirect
143. #488	C₂²×C₃	semidirect
144. #488	C₂²×C₃	semidirect
145. #488	C₂²×C₃	semidirect
146. #488	C₂²×C₃	semidirect
147. #487	C₂²×C₃	semidirect
148. #486	C₂²×C₃	semidirect
149. #419	C₂²×C₃	semidirect
152. #417	C₂²×C₃	semidirect
154. #416	C₂²×C₃	semidirect
155. C₂×#103	C₂²×C₃	semidirect
157. #405	C₂²×C₃	semidirect
158. C₄×M₁₆	C₂²×C₃	semidirect
159. C₂×C₄×C₈	C₂²×C₃	semidirect
423. C₃	#60624	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×#3504	2
C₃×#3500	2
C₃×#3142	2
C₃×#3140	2
C₃×#3137	2
C₃×#3136	2
C₃×#3131	2
C₂×C₃×#488	2
C₃×#2898	2
C₃×#2897	2
C₃×C₄×#131	2
#60624	3

Subgroups — C3×#60624 #10679231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60624 #10679231