Subgroups — C₂×C₃×#5143 #11867965

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#951	C₂	1	2	yes	maximal
3	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5143	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#824	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#473	—	3	1	no	maximal
8	C₂×#5143	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₃²×#131	—	2	2	no	—
12	C₃²×#131	C₂²	1	4	yes	—
13	C₂×C₃²×M₁₆	—	2	1	no	—
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	—	2	1	no	—
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃×#951	—	2	4	no	—
18	C₃×#951	C₂²	1	8	yes	—
19	C₂×C₃×#216	—	2	2	no	—
20	C₂×C₃×#214	—	2	2	no	—
21	C₂×C₃×#208	C₂²	1	2	yes	—
22	C₂×C₃×Dic₁₂	—	2	1	no	—
23	C₂×C₃×Dic₁₂	—	2	1	no	—
24	C₂×C₃×Dic₁₂	—	2	2	no	—
25	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
26	C₃×#824	C₂²	1	8	yes	complemented
27	C₃×#819	C₂²	1	4	yes	complemented
28	C₂×C₃×#137	—	3	2	no	—
29	C₂²×C₃×Q₁₆	—	3	1	no	—
30	C₂×C₃×#131	—	2	1	no	—
31	C₂×C₃×#131	D₃	1	1	yes	characteristic
32	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic
33	C₂×#951	C₂×C₃	1	2	yes	—
34	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#473	—	3	8	no	—
36	C₂×C₃×#108	—	3	1	no	—
37	C₂×C₃×#101	—	3	2	no	—
38	#5143	C₂×C₃	1	8	yes	direct product factor
39	C₂×#824	C₂×C₃	1	2	yes	complemented
40	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃²×#41	—	2	1	no	—
42	C₃²×#41	—	2	1	no	—
43	C₃²×#41	D₄	1	2	yes	—
44	C₃²×#41	C₂³	1	2	yes	—
45	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
46	C₂×C₃²×D₄	—	2	1	no	—
47	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	—	2	1	no	—
49	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₃	—	2	2	no	—
51	C₂×C₃×Dic₆	—	2	2	no	—
52	C₂×C₃×Dic₆	—	2	2	no	—
53	C₂×C₃×Dic₆	—	2	2	no	—
54	C₂×C₃×Dic₆	—	2	2	no	—
55	C₂×C₃×Dic₆	—	2	2	no	—
56	C₂×C₃×Dic₆	C₂³	1	4	yes	—
57	C₃²×M₁₆	—	2	1	no	—
58	C₃²×M₁₆	—	2	4	no	—
59	C₃²×M₁₆	C₂³	1	2	yes	—
60	C₂×C₃²×C₈	—	2	1	no	—
61	C₂×C₃²×C₈	—	2	4	no	—
62	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
63	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
64	C₂×C₃²×C₈	D₄	1	2	yes	—
65	C₂×C₃²×C₈	C₂³	1	2	yes	—
66	C₃×#216	—	2	8	no	—
67	C₃×#214	—	2	8	no	—
68	C₃×#208	—	2	2	no	—
69	C₃×#208	C₂³	1	4	yes	—
70	C₂×C₃×C₃⋊C₈	—	2	2	no	—
71	C₃×Dic₁₂	—	2	4	no	—
72	C₃×Dic₁₂	—	2	4	no	—
73	C₂×#473	—	3	1	no	Sylow
74	C₂×C₃×#41	—	2	1	no	—
75	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃×Q₈	—	3	2	no	—
78	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
79	C₃×#137	—	3	8	no	—
80	C₃×#137	—	6	4	no	—
81	C₂×C₃×Q₁₆	—	3	4	no	—
82	C₂×C₃×Q₁₆	—	6	2	no	—
83	C₂×C₃×Q₁₆	—	6	1	no	—
84	C₂×C₃×Q₁₆	—	6	1	no	—
85	C₂×C₃×Q₁₆	—	6	2	no	—
86	C₂×C₃×SD₁₆	—	6	2	no	—
87	C₃×#131	—	2	4	no	—
88	C₃×#131	—	2	2	no	—
89	C₃×#131	—	2	2	no	—
90	C₃×#131	—	2	4	no	—
91	C₃×#131	C₂×D₃	1	4	yes	—
92	C₃×#131	C₂²×C₃	1	4	yes	—
93	C₂×C₃×M₁₆	—	2	2	no	—
94	C₂×C₃×M₁₆	—	2	1	no	—
95	C₂×C₃×M₁₆	—	2	1	no	—
96	C₂×C₃×M₁₆	—	2	1	no	—
97	C₂×C₃×M₁₆	—	3	2	no	—
98	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
99	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₃×C₈	—	2	2	no	—
101	C₂²×C₃×C₈	—	2	1	no	—
102	C₂²×C₃×C₈	—	2	1	no	—
103	C₂²×C₃×C₈	—	2	1	no	—
104	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
106	#951	—	2	4	no	—
107	#951	C₂²×C₃	1	8	yes	—
108	C₂×#216	—	2	2	no	—
109	C₂×#214	—	2	2	no	—
110	C₂×#208	C₂²×C₃	1	2	yes	—
111	C₂×Dic₁₂	—	2	1	no	—
112	C₂×Dic₁₂	—	2	1	no	—
113	C₂×Dic₁₂	—	2	2	no	—
114	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
115	C₃×#108	—	3	4	no	—
116	C₃×#101	—	3	8	no	—
117	#824	C₂²×C₃	1	8	yes	complemented
118	#819	C₂²×C₃	1	4	yes	complemented
119	C₂³×C₃²	—	2	1	no	—
120	C₂³×C₃²	#41	1	1	yes	characteristic
121	C₃²×Q₈	—	2	1	no	—
122	C₃²×Q₈	C₂×D₄	1	2	yes	—
123	C₃²×D₄	—	2	2	no	—
124	C₃²×D₄	—	2	2	no	—
125	C₃²×D₄	—	2	1	no	—
126	C₃²×D₄	C₂×D₄	1	2	yes	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	2	no	—
129	C₂×C₃²×C₄	—	2	2	no	—
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃²×C₄	#41	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×Dic₃	—	2	4	no	—
137	C₂×C₃×Dic₃	—	4	2	no	—
138	C₂×C₃×Dic₃	—	4	2	no	—
139	C₃×Dic₆	—	2	4	no	—
140	C₃×Dic₆	—	2	4	no	—
141	C₃×Dic₆	—	4	2	no	—
142	C₃×Dic₆	—	4	2	no	—
143	C₃²×C₈	—	2	2	no	—
144	C₃²×C₈	C₂×D₄	1	2	yes	—
145	C₃²×C₈	C₂×D₄	1	2	yes	—
146	C₃×C₃⋊C₈	—	2	4	no	—
147	C₂×#137	—	3	2	no	—
148	C₂²×Q₁₆	—	3	1	no	—
149	C₂×#131	C₃×D₃	1	1	yes	characteristic
150	#473	—	3	8	no	—
151	C₂×#108	—	3	1	no	—
152	C₂×#101	—	3	2	no	—
153	C₃×#41	—	2	2	no	—
154	C₃×#41	—	2	2	no	—
155	C₃×#41	—	2	1	no	—
156	C₃×#41	—	2	1	no	—
157	C₃×#41	—	2	1	no	—
158	C₃×#41	—	2	1	no	—
159	C₃×#41	—	2	2	no	—
160	C₃×#41	—	2	2	no	—
161	C₃×#41	D₁₂	1	2	yes	—
162	C₃×#41	C₃×D₄	1	2	yes	—
163	C₃×#41	C₂²×D₃	1	2	yes	—
164	C₃×#41	C₂³×C₃	1	2	yes	—
165	C₂×C₃×Q₈	—	2	1	no	—
166	C₂×C₃×Q₈	—	3	4	no	—
167	C₂×C₃×Q₈	—	6	2	no	—
168	C₂×C₃×Q₈	—	6	2	no	—
169	C₂×C₃×Q₈	—	6	2	no	—
170	C₂×C₃×Q₈	—	6	2	no	—
171	C₂×C₃×Q₈	—	6	2	no	—
172	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
173	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
174	C₂×C₃×D₄	—	2	2	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	—	2	1	no	—
178	C₂×C₃×D₄	D₁₂	1	1	yes	characteristic
179	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	6	2	no	—
185	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₂²×Dic₃	—	2	2	no	—
188	C₂×Dic₆	—	2	2	no	—
189	C₂×Dic₆	—	2	2	no	—
190	C₂×Dic₆	—	2	2	no	—
191	C₂×Dic₆	—	2	2	no	—
192	C₂×Dic₆	—	2	2	no	—
193	C₂×Dic₆	C₂³×C₃	1	4	yes	—
194	C₃×Q₁₆	—	6	8	no	—
195	C₃×Q₁₆	—	6	4	no	—
196	C₃×Q₁₆	—	6	4	no	—
197	C₃×SD₁₆	—	6	8	no	—
198	C₃×M₁₆	—	2	2	no	—
199	C₃×M₁₆	—	2	8	no	—
200	C₃×M₁₆	—	2	1	no	—
201	C₃×M₁₆	—	2	1	no	—
202	C₃×M₁₆	—	2	4	no	—
203	C₃×M₁₆	—	2	4	no	—
204	C₃×M₁₆	—	2	2	no	—
205	C₃×M₁₆	—	3	4	no	—
206	C₃×M₁₆	—	6	2	no	—
207	C₃×M₁₆	C₂²×D₃	1	2	yes	—
208	C₃×M₁₆	C₂³×C₃	1	2	yes	—
209	C₂×C₃×C₈	—	2	2	no	—
210	C₂×C₃×C₈	—	2	8	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	4	no	—
214	C₂×C₃×C₈	—	2	4	no	—
215	C₂×C₃×C₈	—	2	1	no	—
216	C₂×C₃×C₈	—	2	1	no	—
217	C₂×C₃×C₈	—	2	2	no	—
218	C₂×C₃×C₈	—	2	2	no	—
219	C₂×C₃×C₈	—	6	2	no	—
220	C₂×C₃×C₈	#67	1	1	yes	characteristic
221	C₂×C₃×C₈	#67	1	1	yes	characteristic
222	C₂×C₃×C₈	#67	1	2	yes	—
223	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
224	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
225	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
226	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
227	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
228	#216	—	2	8	no	—
229	#214	—	2	8	no	—
230	#208	—	2	2	no	—
231	#208	C₂³×C₃	1	4	yes	—
232	C₂×C₃⋊C₈	—	2	2	no	—
233	Dic₁₂	—	2	4	no	—
234	Dic₁₂	—	2	4	no	—
235	C₂²×C₃²	—	2	2	no	—
236	C₂²×C₃²	—	2	2	no	—
237	C₂²×C₃²	—	4	2	no	—
238	C₂²×C₃²	#121	1	1	yes	characteristic
239	C₂²×C₃²	#121	1	1	yes	characteristic
240	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
241	C₃²×C₄	—	2	2	no	—
242	C₃²×C₄	#121	1	1	yes	characteristic
243	C₃²×C₄	#121	1	1	yes	characteristic
244	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₃×Dic₃	—	4	4	no	—
247	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
248	C₂²×Q₈	—	3	2	no	—
249	#137	—	3	8	no	—
250	#137	—	6	4	no	—
251	C₂×Q₁₆	—	3	4	no	—
252	C₂×Q₁₆	—	6	2	no	—
253	C₂×Q₁₆	—	6	1	no	—
254	C₂×Q₁₆	—	6	1	no	—
255	C₂×Q₁₆	—	6	2	no	—
256	C₂×SD₁₆	—	6	2	no	—
257	#131	—	2	2	no	—
258	#131	C₂×C₃×D₃	1	4	yes	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	3	2	no	—
261	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
264	#108	—	3	4	no	—
265	#101	—	3	8	no	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	2	1	no	—
269	C₂³×C₃	—	2	1	no	—
270	C₂³×C₃	#235	1	1	yes	characteristic
271	C₂³×C₃	C₃×#41	1	1	yes	characteristic
272	C₃×Q₈	—	2	2	no	—
273	C₃×Q₈	—	2	1	no	—
274	C₃×Q₈	—	2	1	no	—
275	C₃×Q₈	—	2	2	no	—
276	C₃×Q₈	—	6	4	no	—
277	C₃×Q₈	—	6	4	no	—
278	C₃×Q₈	—	12	2	no	—
279	C₃×Q₈	—	12	2	no	—
280	C₃×Q₈	C₂×D₁₂	1	2	yes	—
281	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
282	C₃×D₄	—	2	4	no	—
283	C₃×D₄	—	2	4	no	—
284	C₃×D₄	—	2	2	no	—
285	C₃×D₄	—	2	2	no	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	2	1	no	—
290	C₃×D₄	—	2	1	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	C₂×D₁₂	1	2	yes	—
293	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	6	4	no	—
310	C₂×C₃×C₄	—	12	2	no	—
311	C₂×C₃×C₄	—	12	2	no	—
312	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
314	C₂×C₃×C₄	#235	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
324	C₂×Dic₃	—	2	4	no	—
325	C₂×Dic₃	—	4	2	no	—
326	C₂×Dic₃	—	4	2	no	—
327	Dic₆	—	2	4	no	—
328	Dic₆	—	2	4	no	—
329	Dic₆	—	4	2	no	—
330	Dic₆	—	4	2	no	—
331	C₃×C₈	—	2	4	no	—
332	C₃×C₈	—	2	2	no	—
333	C₃×C₈	—	2	2	no	—
334	C₃×C₈	—	2	2	no	—
335	C₃×C₈	—	2	2	no	—
336	C₃×C₈	—	6	4	no	—
337	C₃×C₈	C₂×#67	1	2	yes	—
338	C₃×C₈	C₂×#67	1	2	yes	—
339	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
340	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
341	C₃⋊C₈	—	2	4	no	—
342	C₂×C₃²	—	2	1	no	—
343	C₂×C₃²	—	2	1	no	—
344	C₂×C₃²	—	4	2	no	—
345	C₂×C₃²	#473	1	2	yes	complemented
346	C₂×C₃²	C₂×#121	1	1	yes	characteristic
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	C₃×D₁₂	1	2	yes	—
350	#41	C₂²×C₃×D₃	1	2	yes	—
351	C₂×Q₈	—	3	4	no	—
352	C₂×Q₈	—	6	2	no	—
353	C₂×Q₈	—	6	2	no	—
354	C₂×Q₈	—	6	2	no	—
355	C₂×Q₈	—	6	2	no	—
356	C₂×Q₈	—	6	2	no	—
357	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₃×D₁₂	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	6	2	no	—
362	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
363	Q₁₆	—	6	8	no	—
364	Q₁₆	—	6	4	no	—
365	Q₁₆	—	6	4	no	—
366	SD₁₆	—	6	8	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	3	4	no	—
370	M₁₆	—	6	2	no	—
371	M₁₆	C₂²×C₃×D₃	1	2	yes	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	6	2	no	—
375	C₂×C₈	C₃×#67	1	1	yes	characteristic
376	C₂×C₈	C₃×#67	1	1	yes	characteristic
377	C₂×C₈	C₃×#67	1	2	yes	—
378	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	4	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	#930	1	1	yes	characteristic
392	C₂²×C₃	#930	1	1	yes	characteristic
393	C₂²×C₃	C₃×#121	1	1	yes	characteristic
394	C₂²×C₃	C₃×#121	1	1	yes	characteristic
395	C₂²×C₃	C₂×#235	1	1	yes	characteristic
396	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
397	C₃×C₄	—	2	4	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	12	4	no	—
405	C₃×C₄	#930	1	1	yes	characteristic
406	C₃×C₄	#930	1	1	yes	characteristic
407	C₃×C₄	C₃×#121	1	1	yes	characteristic
408	C₃×C₄	C₃×#121	1	1	yes	characteristic
409	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
410	C₃×C₄	C₂²×#67	1	1	yes	characteristic
411	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
412	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
413	Dic₃	—	4	4	no	—
414	C₃²	C₂×#473	1	1	yes	characteristic, complemented, Sylow
415	C₂³	—	2	1	no	—
416	C₂³	C₃×#235	1	1	yes	characteristic
417	Q₈	—	2	1	no	—
418	Q₈	—	6	4	no	—
419	Q₈	—	6	4	no	—
420	Q₈	—	12	2	no	—
421	Q₈	—	12	2	no	—
422	Q₈	C₂×C₃×D₁₂	1	2	yes	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	—	2	1	no	—
426	D₄	C₂×C₃×D₁₂	1	2	yes	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	6	4	no	—
431	C₂×C₄	—	12	2	no	—
432	C₂×C₄	—	12	2	no	—
433	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
434	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
435	C₂×C₄	C₃×#235	1	1	yes	characteristic
436	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
437	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
438	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	6	4	no	—
441	C₈	C₂×C₃×#67	1	2	yes	—
442	C₈	C₂×C₃×#67	1	2	yes	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	2	no	—
449	C₂×C₃	—	4	1	no	—
450	C₂×C₃	—	4	1	no	—
451	C₂×C₃	—	4	4	no	—
452	C₂×C₃	—	4	2	no	—
453	C₂×C₃	—	4	2	no	—
454	C₂×C₃	#5143	1	2	yes	direct product factor
455	C₂×C₃	C₃×#473	1	2	yes	complemented
456	C₂×C₃	C₂×#930	1	1	yes	characteristic
457	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₃×#930	1	1	yes	characteristic
462	C₂²	C₃×#930	1	1	yes	characteristic
463	C₂²	C₂×C₃×#235	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	12	4	no	—
466	C₄	C₃×#930	1	1	yes	characteristic
467	C₄	C₃×#930	1	1	yes	characteristic
468	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
469	C₄	C₂²×C₃×#67	1	1	yes	characteristic
470	C₃	—	2	1	no	—
471	C₃	C₂×#5143	1	1	yes	characteristic, direct product factor
472	C₃	C₂×C₃×#473	1	1	yes	characteristic, complemented
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	2	no	—
476	C₂	C₃×#5143	1	2	yes	direct product factor
477	C₂	C₂×C₃×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#930
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂²×C₃²	#121
prime radical	C₂×C₃²×#41	C₂²
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₂×C₃×#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₃×#5143	C₂	direct (N × H)
5. C₂×C₃×#824	C₂	semidirect
6. C₂×C₃×#819	C₂	semidirect
8. C₂×#5143	C₃	direct (N × H)
25. C₂×C₃×Dic₁₂	C₂²	semidirect
26. C₃×#824	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
34. C₂²×Dic₁₂	C₂×C₃	semidirect
38. #5143	C₂×C₃	direct (N × H)
39. C₂×#824	C₂×C₃	semidirect
40. C₂×#819	C₂×C₃	semidirect
114. C₂×Dic₁₂	C₂²×C₃	semidirect
117. #824	C₂²×C₃	semidirect
118. #819	C₂²×C₃	semidirect
345. C₂×C₃²	#473	semidirect
414. C₃²	C₂×#473	semidirect
454. C₂×C₃	#5143	direct (N × H)
455. C₂×C₃	C₃×#473	semidirect
471. C₃	C₂×#5143	direct (N × H)
472. C₃	C₂×C₃×#473	semidirect
476. C₂	C₃×#5143	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×C₃²×#131	2
C₂×C₃×#951	2
C₂²×C₃×Dic₁₂	2
C₃×#5143	2
C₂×C₃×#824	2
C₂×C₃×#819	2
C₂×C₃×#473	3
C₂×#5143	3

Subgroups — C2×C3×#5143 #11867965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5143 #11867965