Subgroups — C₃×#18022 #10636629

Order 768.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3106	C₂	1	1	yes	maximal, characteristic
2	C₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1592	C₂	1	2	yes	maximal, complemented
5	C₃×#1582	C₂	1	2	yes	maximal, complemented
6	C₃×#1581	C₂	1	2	yes	maximal, complemented
7	C₃×#1580	C₂	1	2	yes	maximal, complemented
8	C₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	#18022	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#532	C₂²	1	1	yes	characteristic
14	C₃×C₄×#41	C₂²	1	1	yes	characteristic
15	C₃×#482	C₄	1	2	yes	—
16	C₃×#477	C₄	1	1	yes	characteristic
17	C₃×#476	C₄	1	1	yes	characteristic
18	C₃×#460	C₄	1	1	yes	characteristic
19	C₃×#459	C₄	1	1	yes	characteristic
20	C₃×#449	C₄	1	2	yes	—
21	C₃×#446	C₂²	1	2	yes	—
22	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
23	C₃×C₄×D₈	C₂²	1	2	yes	—
24	C₃×#436	—	2	1	no	—
25	C₃×#436	C₂²	1	2	yes	—
26	C₃×#435	—	2	2	no	—
27	C₃×C₈×D₄	—	2	1	no	—
28	C₃×C₈×D₄	C₂²	1	2	yes	—
29	C₃×C₈×D₄	C₂²	1	2	yes	—
30	C₃×#432	—	2	1	no	—
31	C₃×#431	C₂²	1	1	yes	characteristic
32	C₃×#431	C₂²	1	1	yes	characteristic
33	C₃×#431	C₂²	1	1	yes	characteristic
34	C₃×#423	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄⋊C₈	—	2	1	no	—
36	C₃×#408	—	2	2	no	—
37	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
38	C₃×#335	C₂²	1	2	yes	—
39	C₃×#334	C₂²	1	2	yes	—
40	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×D₄⋊C₈	C₂²	1	2	yes	—
43	C₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₃×#322	C₂²	1	2	yes	—
47	C₃×#322	C₂²	1	2	yes	—
48	#3106	C₂×C₃	1	1	yes	characteristic
49	#2990	C₂×C₃	1	1	yes	characteristic, complemented
50	#2979	C₂×C₃	1	1	yes	characteristic, complemented
51	#1592	C₂×C₃	1	2	yes	complemented
52	#1582	C₂×C₃	1	2	yes	complemented
53	#1581	C₂×C₃	1	2	yes	complemented
54	#1580	C₂×C₃	1	2	yes	complemented
55	#1574	C₂×C₃	1	1	yes	characteristic, complemented
56	#1492	C₂×C₃	1	1	yes	characteristic, complemented
57	#1476	C₂×C₃	1	1	yes	characteristic, complemented
58	#1452	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#41	—	2	1	no	—
60	C₂×C₃×#41	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×SD₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₃×D₈	C₂×C₄	1	2	yes	—
63	C₂×C₃×M₁₆	—	2	1	no	—
64	C₂×C₃×M₁₆	—	2	2	no	—
65	C₂²×C₃×C₈	—	2	1	no	—
66	C₂²×C₃×C₈	—	2	2	no	—
67	C₂²×C₃×C₈	—	2	2	no	—
68	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
69	C₃×#127	C₂×C₄	1	1	yes	characteristic
70	C₃×#124	—	2	1	no	—
71	C₃×#121	—	2	1	no	—
72	C₃×#121	C₂×C₄	1	2	yes	—
73	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
75	C₃×C₄×D₄	—	2	1	no	—
76	C₃×C₄×D₄	—	2	1	no	—
77	C₃×C₄×D₄	—	2	1	no	—
78	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
80	C₃×C₄×D₄	C₂³	1	2	yes	—
81	C₃×#117	—	2	1	no	—
82	C₃×#117	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
85	C₃×#107	C₂×C₄	1	2	yes	—
86	C₃×#106	C₂×C₄	1	2	yes	—
87	C₃×C₄⋊C₈	—	2	2	no	—
88	C₃×C₄⋊C₈	—	2	1	no	—
89	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₃×C₄⋊C₈	C₂³	1	2	yes	—
94	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×#103	C₂×C₄	1	2	yes	—
97	C₃×#102	C₂×C₄	1	2	yes	—
98	C₃×#102	C₂×C₄	1	2	yes	—
99	C₃×#102	C₂×C₄	1	2	yes	—
100	C₃×C₂²⋊C₈	—	2	1	no	—
101	C₃×C₂²⋊C₈	—	2	2	no	—
102	C₃×C₂²⋊C₈	—	2	2	no	—
103	C₃×C₂²⋊C₈	—	2	2	no	—
104	C₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
105	C₃×C₂²⋊C₈	D₄	1	2	yes	—
106	C₃×#97	—	2	2	no	—
107	C₃×C₄×C₈	—	2	1	no	—
108	C₃×C₄×C₈	—	2	1	no	—
109	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
111	C₃×C₄×C₈	C₂³	1	2	yes	—
112	C₃×C₄×C₈	C₂³	1	2	yes	—
113	#532	C₂²×C₃	1	1	yes	characteristic
114	C₄×#41	C₂²×C₃	1	1	yes	characteristic
115	#482	C₃×C₄	1	2	yes	—
116	#477	C₃×C₄	1	1	yes	characteristic
117	#476	C₃×C₄	1	1	yes	characteristic
118	#460	C₃×C₄	1	1	yes	characteristic
119	#459	C₃×C₄	1	1	yes	characteristic
120	#449	C₃×C₄	1	2	yes	—
121	#446	C₂²×C₃	1	2	yes	—
122	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
123	C₄×D₈	C₂²×C₃	1	2	yes	—
124	#436	—	2	1	no	—
125	#436	C₂²×C₃	1	2	yes	—
126	#435	—	2	2	no	—
127	C₈×D₄	—	2	1	no	—
128	C₈×D₄	C₂²×C₃	1	2	yes	—
129	C₈×D₄	C₂²×C₃	1	2	yes	—
130	#432	—	2	1	no	—
131	#431	C₂²×C₃	1	1	yes	characteristic
132	#431	C₂²×C₃	1	1	yes	characteristic
133	#431	C₂²×C₃	1	1	yes	characteristic
134	#423	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	2	1	no	—
136	#408	—	2	2	no	—
137	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
138	#335	C₂²×C₃	1	2	yes	—
139	#334	C₂²×C₃	1	2	yes	—
140	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
141	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
142	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
143	D₄⋊C₈	C₂²×C₃	1	2	yes	—
144	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
145	D₄⋊C₈	C₂²×C₃	1	2	yes	—
146	#322	C₂²×C₃	1	2	yes	—
147	#322	C₂²×C₃	1	2	yes	—
148	C₃×#41	—	2	2	no	—
149	C₃×#41	—	4	1	no	—
150	C₃×#41	—	8	1	no	—
151	C₃×#41	—	8	1	no	—
152	C₂×C₃×Q₈	—	2	1	no	—
153	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×D₄	—	2	1	no	—
155	C₂×C₃×D₄	—	2	2	no	—
156	C₂×C₃×D₄	—	2	1	no	—
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
159	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	#41	1	1	yes	characteristic
167	C₃×SD₁₆	—	4	2	no	—
168	C₃×D₈	—	2	4	no	—
169	C₃×M₁₆	—	8	2	no	—
170	C₃×M₁₆	—	8	1	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	4	2	no	—
177	C₂×C₃×C₈	—	8	2	no	—
178	C₂×C₃×C₈	—	8	2	no	—
179	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
182	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₂²⋊C₄	—	2	1	no	—
191	C₃×C₂²⋊C₄	—	2	2	no	—
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	2	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
199	C₃×C₄²	#41	1	1	yes	characteristic
200	C₃×C₄²	C₂⁴	1	1	yes	characteristic
201	C₂×#41	—	2	1	no	—
202	C₂×#41	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×SD₁₆	C₂×C₃×C₄	1	2	yes	—
204	C₂×D₈	C₂×C₃×C₄	1	2	yes	—
205	C₂×M₁₆	—	2	1	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	—	2	2	no	—
210	C₄⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
211	#127	C₂×C₃×C₄	1	1	yes	characteristic
212	#124	—	2	1	no	—
213	#121	—	2	1	no	—
214	#121	C₂×C₃×C₄	1	2	yes	—
215	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
216	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
221	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
222	C₄×D₄	C₂³×C₃	1	2	yes	—
223	#117	—	2	1	no	—
224	#117	C₂×C₃×C₄	1	1	yes	characteristic
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
227	#107	C₂×C₃×C₄	1	2	yes	—
228	#106	C₂×C₃×C₄	1	2	yes	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
232	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
233	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
234	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
235	C₄⋊C₈	C₂³×C₃	1	2	yes	—
236	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
237	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
238	#103	C₂×C₃×C₄	1	2	yes	—
239	#102	C₂×C₃×C₄	1	2	yes	—
240	#102	C₂×C₃×C₄	1	2	yes	—
241	#102	C₂×C₃×C₄	1	2	yes	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	C₂×C₃×C₄	1	2	yes	—
247	C₂²⋊C₈	C₃×D₄	1	2	yes	—
248	#97	—	2	2	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₃	1	2	yes	—
254	C₄×C₈	C₂³×C₃	1	2	yes	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
258	C₃×Q₈	—	2	1	no	—
259	C₃×Q₈	—	2	1	no	—
260	C₃×Q₈	—	8	1	no	—
261	C₃×D₄	—	2	2	no	—
262	C₃×D₄	—	2	1	no	—
263	C₃×D₄	—	2	2	no	—
264	C₃×D₄	—	4	2	no	—
265	C₃×D₄	—	4	2	no	—
266	C₃×D₄	—	8	1	no	—
267	C₃×D₄	—	8	2	no	—
268	C₃×D₄	#131	1	2	yes	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	4	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	2	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	—	2	2	no	—
294	C₃×C₈	—	4	1	no	—
295	C₃×C₈	—	4	1	no	—
296	C₃×C₈	—	4	2	no	—
297	C₃×C₈	—	4	1	no	—
298	C₃×C₈	—	4	1	no	—
299	#41	—	2	2	no	—
300	#41	—	4	1	no	—
301	#41	—	8	1	no	—
302	#41	—	8	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
310	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₃×#41	1	1	yes	characteristic
318	SD₁₆	—	4	2	no	—
319	D₈	—	2	4	no	—
320	M₁₆	—	8	2	no	—
321	M₁₆	—	8	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	8	2	no	—
329	C₂×C₈	—	8	2	no	—
330	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
331	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
332	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
333	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
349	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
350	C₄²	C₃×#41	1	1	yes	characteristic
351	C₄²	C₂⁴×C₃	1	1	yes	characteristic
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	4	1	no	—
366	C₃×C₄	—	4	1	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	#444	1	2	yes	—
370	C₃×C₄	C₂×#131	1	1	yes	characteristic
371	C₃×C₄	#568	1	1	yes	characteristic
372	C₃×C₄	#576	1	1	yes	characteristic
373	C₃×C₄	#577	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	—	2	1	no	—
379	Q₈	—	8	1	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	2	no	—
387	D₄	C₃×#131	1	2	yes	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
404	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
405	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂×C₃	—	4	1	no	—
419	C₂×C₃	—	4	2	no	—
420	C₂×C₃	—	8	2	no	—
421	C₂×C₃	#2933	1	1	yes	characteristic
422	C₂×C₃	#2946	1	1	yes	characteristic
423	C₂×C₃	C₂×#444	1	1	yes	characteristic
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	C₃×#444	1	2	yes	—
442	C₄	C₂×C₃×#131	1	1	yes	characteristic
443	C₄	C₃×#568	1	1	yes	characteristic
444	C₄	C₃×#576	1	1	yes	characteristic
445	C₄	C₃×#577	1	1	yes	characteristic
446	C₃	#18022	1	1	yes	characteristic, direct product factor, Sylow
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	2	no	—
450	C₂	C₃×#2933	1	1	yes	characteristic
451	C₂	C₃×#2946	1	1	yes	characteristic
452	C₂	C₂×C₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₄²	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2990	C₂	semidirect
3. C₃×#2979	C₂	semidirect
4. C₃×#1592	C₂	semidirect
5. C₃×#1582	C₂	semidirect
6. C₃×#1581	C₂	semidirect
7. C₃×#1580	C₂	semidirect
8. C₃×#1574	C₂	semidirect
9. C₃×#1492	C₂	semidirect
10. C₃×#1476	C₂	semidirect
11. C₃×#1452	C₂	semidirect
12. #18022	C₃	direct (N × H)
49. #2990	C₂×C₃	semidirect
50. #2979	C₂×C₃	semidirect
51. #1592	C₂×C₃	semidirect
52. #1582	C₂×C₃	semidirect
53. #1581	C₂×C₃	semidirect
54. #1580	C₂×C₃	semidirect
55. #1574	C₂×C₃	semidirect
56. #1492	C₂×C₃	semidirect
57. #1476	C₂×C₃	semidirect
58. #1452	C₂×C₃	semidirect
446. C₃	#18022	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×#3106	2
C₃×#2990	2
C₃×#2979	2
C₃×#1592	2
C₃×#1582	2
C₃×#1581	2
C₃×#1580	2
C₃×#1574	2
C₃×#1492	2
C₃×#1476	2
C₃×#1452	2
#18022	3

Subgroups — C3×#18022 #10636629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18022 #10636629