Subgroups — C₃×#33056 #10651663

Order 768.

822 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic
3	C₃×#2629	C₂	1	1	yes	maximal, characteristic
4	C₃×#2621	C₂	1	1	yes	maximal, characteristic
5	C₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1935	C₂	1	2	yes	maximal, complemented
8	C₃×#1933	C₂	1	2	yes	maximal, complemented
9	C₃×#1894	C₂	1	2	yes	maximal
10	C₃×#1892	C₂	1	2	yes	maximal
11	C₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	#33056	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₃×#117	C₂²	1	1	yes	characteristic
19	C₃×#491	—	2	4	no	—
20	C₂×C₃×#103	C₂²	1	2	yes	—
21	C₂×C₃×#103	C₂²	1	2	yes	—
22	C₂×C₃×#103	C₂²	1	2	yes	—
23	C₂×C₃×#103	C₂²	1	2	yes	—
24	C₃×#405	—	2	4	no	—
25	C₂×C₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
29	C₃×#398	—	2	2	no	—
30	C₃×#398	—	2	2	no	—
31	C₃×#397	—	2	2	no	—
32	C₃×#396	—	2	2	no	—
33	C₃×#391	C₂²	1	2	yes	—
34	C₃×#389	C₂²	1	2	yes	—
35	C₃×#384	C₂²	1	1	yes	characteristic
36	C₃×#382	C₂²	1	1	yes	characteristic
37	C₃×#380	C₂²	1	2	yes	—
38	C₃×#340	C₂²	1	2	yes	—
39	C₃×#340	C₂²	1	2	yes	—
40	C₃×#340	C₂²	1	2	yes	—
41	C₃×#340	C₂²	1	2	yes	—
42	C₂×#491	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#405	C₂×C₃	1	1	yes	characteristic
44	#2629	C₂×C₃	1	1	yes	characteristic
45	#2621	C₂×C₃	1	1	yes	characteristic
46	#1991	C₂×C₃	1	1	yes	characteristic, complemented
47	#1956	C₂×C₃	1	1	yes	characteristic, complemented
48	#1935	C₂×C₃	1	2	yes	complemented
49	#1933	C₂×C₃	1	2	yes	complemented
50	#1894	C₂×C₃	1	2	yes	—
51	#1892	C₂×C₃	1	2	yes	—
52	#1836	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂²×C₃×Q₈	C₂³	1	2	yes	—
54	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
55	C₂×C₃×M₁₆	—	2	2	no	—
56	C₂×C₃×M₁₆	—	2	2	no	—
57	C₂×C₃×M₁₆	—	2	2	no	—
58	C₂²×C₃×C₈	—	2	2	no	—
59	C₂²×C₃×C₈	—	2	2	no	—
60	C₂²×C₃×C₈	—	2	2	no	—
61	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₄⋊Q₈	—	2	2	no	—
66	C₃×C₄⋊Q₈	—	2	2	no	—
67	C₃×#125	—	2	2	no	—
68	C₃×#125	—	2	2	no	—
69	C₃×C₂²⋊Q₈	—	2	4	no	—
70	C₃×C₂²⋊Q₈	—	2	4	no	—
71	C₃×#117	—	2	2	no	—
72	C₃×#117	—	2	2	no	—
73	C₂×C₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
79	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
85	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
87	C₃×#103	—	2	4	no	—
88	C₃×#103	—	2	4	no	—
89	C₃×#103	—	2	4	no	—
90	C₃×#103	—	2	4	no	—
91	C₃×#97	—	2	2	no	—
92	C₃×#97	D₄	1	4	yes	—
93	C₃×C₄×C₈	—	2	2	no	—
94	C₃×C₄×C₈	—	2	2	no	—
95	C₃×#95	—	2	2	no	—
96	C₃×#95	—	2	2	no	—
97	C₃×#95	—	2	2	no	—
98	C₃×#95	—	2	4	no	—
99	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₂×#125	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₂×#117	C₂²×C₃	1	1	yes	characteristic
105	#491	—	2	4	no	—
106	C₂×#103	C₂²×C₃	1	2	yes	—
107	C₂×#103	C₂²×C₃	1	2	yes	—
108	C₂×#103	C₂²×C₃	1	2	yes	—
109	C₂×#103	C₂²×C₃	1	2	yes	—
110	#405	—	2	4	no	—
111	C₂×#97	C₂²×C₃	1	1	yes	characteristic
112	C₂×#97	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
115	#398	—	2	2	no	—
116	#398	—	2	2	no	—
117	#397	—	2	2	no	—
118	#396	—	2	2	no	—
119	#391	C₂²×C₃	1	2	yes	—
120	#389	C₂²×C₃	1	2	yes	—
121	#384	C₂²×C₃	1	1	yes	characteristic
122	#382	C₂²×C₃	1	1	yes	characteristic
123	#380	C₂²×C₃	1	2	yes	—
124	#340	C₂²×C₃	1	2	yes	—
125	#340	C₂²×C₃	1	2	yes	—
126	#340	C₂²×C₃	1	2	yes	—
127	#340	C₂²×C₃	1	2	yes	—
128	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×Q₈	—	2	2	no	—
130	C₂×C₃×Q₈	—	2	2	no	—
131	C₂×C₃×Q₈	—	2	2	no	—
132	C₂×C₃×Q₈	—	2	2	no	—
133	C₂×C₃×Q₈	—	2	2	no	—
134	C₂×C₃×Q₈	—	2	2	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	—	2	2	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
144	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
145	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₄	#41	1	2	yes	—
147	C₂²×C₃×C₄	#41	1	2	yes	—
148	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
149	C₃×M₁₆	—	2	8	no	—
150	C₂×C₃×C₈	—	2	8	no	—
151	C₂×C₃×C₈	—	2	1	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
159	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₈	#41	1	2	yes	—
162	C₂×C₃×C₈	#41	1	2	yes	—
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	4	4	no	—
171	C₃×C₄⋊C₄	—	4	4	no	—
172	C₃×C₄⋊C₄	—	4	4	no	—
173	C₃×C₄⋊C₄	—	8	2	no	—
174	C₃×C₄⋊C₄	—	8	2	no	—
175	C₃×C₂²⋊C₄	—	2	4	no	—
176	C₃×C₂²⋊C₄	—	4	4	no	—
177	C₃×C₂²⋊C₄	—	8	2	no	—
178	C₃×C₄²	—	2	1	no	—
179	C₃×C₄²	—	2	1	no	—
180	C₃×C₄²	C₂×D₄	1	2	yes	—
181	C₃×C₄²	#41	1	2	yes	—
182	C₂²×Q₈	C₂³×C₃	1	2	yes	—
183	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂×M₁₆	—	2	2	no	—
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	2	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₄⋊Q₈	—	2	2	no	—
195	C₄⋊Q₈	—	2	2	no	—
196	#125	—	2	2	no	—
197	#125	—	2	2	no	—
198	C₂²⋊Q₈	—	2	4	no	—
199	C₂²⋊Q₈	—	2	4	no	—
200	#117	—	2	2	no	—
201	#117	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
209	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
214	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
216	#103	—	2	4	no	—
217	#103	—	2	4	no	—
218	#103	—	2	4	no	—
219	#103	—	2	4	no	—
220	#97	—	2	2	no	—
221	#97	C₃×D₄	1	4	yes	—
222	C₄×C₈	—	2	2	no	—
223	C₄×C₈	—	2	2	no	—
224	#95	—	2	2	no	—
225	#95	—	2	2	no	—
226	#95	—	2	2	no	—
227	#95	—	2	4	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	#124	1	2	yes	—
233	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
234	C₃×Q₈	—	4	2	no	—
235	C₃×Q₈	—	4	2	no	—
236	C₃×Q₈	—	4	2	no	—
237	C₃×Q₈	—	4	2	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	4	2	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	—	4	2	no	—
252	C₂×C₃×C₄	—	4	2	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	4	2	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	4	2	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	4	2	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	#121	1	4	yes	—
262	C₂×C₃×C₄	#124	1	2	yes	—
263	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
269	C₃×C₈	—	2	2	no	—
270	C₃×C₈	—	2	2	no	—
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	2	2	no	—
273	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
289	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
290	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂²×C₄	C₃×#41	1	2	yes	—
292	C₂²×C₄	C₃×#41	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
305	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
306	C₂×C₈	C₃×#41	1	2	yes	—
307	C₂×C₈	C₃×#41	1	2	yes	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	8	2	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	C₂×C₃×D₄	1	2	yes	—
326	C₄²	C₃×#41	1	2	yes	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	4	1	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	C₂×#121	1	1	yes	characteristic
333	C₂²×C₃	C₂×#124	1	1	yes	characteristic
334	C₂²×C₃	#532	1	1	yes	characteristic
335	C₂²×C₃	#577	1	2	yes	—
336	C₂²×C₃	#578	1	2	yes	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	4	2	no	—
340	C₃×C₄	—	8	2	no	—
341	C₃×C₄	—	8	2	no	—
342	C₃×C₄	—	8	2	no	—
343	C₃×C₄	—	8	2	no	—
344	C₃×C₄	#525	1	1	yes	characteristic
345	C₃×C₄	#525	1	1	yes	characteristic
346	C₃×C₄	#529	1	1	yes	characteristic
347	C₃×C₄	#529	1	1	yes	characteristic
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	C₃×#124	1	2	yes	—
353	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₃×#121	1	4	yes	—
382	C₂×C₄	C₃×#124	1	2	yes	—
383	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
384	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	#2850	1	1	yes	characteristic
395	C₂×C₃	#3063	1	2	yes	—
396	C₂×C₃	#3137	1	2	yes	—
397	C₂×C₃	#3174	1	1	yes	characteristic
398	C₂×C₃	#3177	1	1	yes	characteristic
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	C₂×C₃×#121	1	1	yes	characteristic
405	C₂²	C₂×C₃×#124	1	1	yes	characteristic
406	C₂²	C₃×#532	1	1	yes	characteristic
407	C₂²	C₃×#577	1	2	yes	—
408	C₂²	C₃×#578	1	2	yes	—
409	C₄	—	2	4	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	—	8	2	no	—
416	C₄	C₃×#525	1	1	yes	characteristic
417	C₄	C₃×#525	1	1	yes	characteristic
418	C₄	C₃×#529	1	1	yes	characteristic
419	C₄	C₃×#529	1	1	yes	characteristic
420	C₃	#33056	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	4	2	no	—
422	C₂	C₃×#2850	1	1	yes	characteristic
423	C₂	C₃×#3063	1	2	yes	—
424	C₂	C₃×#3137	1	2	yes	—
425	C₂	C₃×#3174	1	1	yes	characteristic
426	C₂	C₃×#3177	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#491	C₂	semidirect
5. C₃×#1991	C₂	semidirect
6. C₃×#1956	C₂	semidirect
7. C₃×#1935	C₂	semidirect
8. C₃×#1933	C₂	semidirect
11. C₃×#1836	C₂	semidirect
12. #33056	C₃	direct (N × H)
42. C₂×#491	C₂×C₃	semidirect
46. #1991	C₂×C₃	semidirect
47. #1956	C₂×C₃	semidirect
48. #1935	C₂×C₃	semidirect
49. #1933	C₂×C₃	semidirect
52. #1836	C₂×C₃	semidirect
420. C₃	#33056	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#491	2
C₂×C₃×#405	2
C₃×#2629	2
C₃×#2621	2
C₃×#1991	2
C₃×#1956	2
C₃×#1935	2
C₃×#1933	2
C₃×#1894	2
C₃×#1892	2
C₃×#1836	2
#33056	3

Subgroups — C3×#33056 #10651663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33056 #10651663