Subgroups — C₂×C₃×#5142 #11867918

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 499 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, complemented
2	C₂×C₃×#949	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5142	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#823	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#472	—	3	1	no	maximal
8	C₂×#5142	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
11	C₃²×#131	—	2	2	no	—
12	C₃²×#131	C₂²	1	4	yes	complemented
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×#949	—	2	4	no	—
18	C₃×#949	C₂²	1	8	yes	complemented
19	C₂×C₃×#215	—	2	2	no	—
20	C₂×C₃×#213	—	2	2	no	—
21	C₂×C₃×#208	C₂²	1	2	yes	—
22	C₂×C₃×D₂₄	—	2	1	no	—
23	C₂×C₃×D₂₄	—	2	1	no	—
24	C₂×C₃×D₂₄	—	2	2	no	—
25	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
26	C₃×#823	C₂²	1	8	yes	complemented
27	C₃×#819	C₂²	1	4	yes	complemented
28	C₂×C₃×AGL(1,ℤ/8)	—	3	2	no	—
29	C₂²×C₃×D₈	—	3	1	no	—
30	C₂×C₃×#131	—	2	1	no	—
31	C₂×C₃×#131	D₃	1	1	yes	characteristic, complemented
32	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#949	C₂×C₃	1	2	yes	complemented
34	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#472	—	3	8	no	—
36	C₂×C₃×#108	—	3	1	no	—
37	C₂×C₃×#100	—	3	2	no	—
38	#5142	C₂×C₃	1	8	yes	direct product factor
39	C₂×#823	C₂×C₃	1	2	yes	complemented
40	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂³×C₃×D₃	—	2	2	no	—
42	C₃²×#41	—	2	1	no	—
43	C₃²×#41	—	2	1	no	—
44	C₃²×#41	D₄	1	2	yes	—
45	C₃²×#41	C₂³	1	2	yes	—
46	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
47	C₂×C₃²×D₄	—	2	1	no	—
48	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
49	C₂²×C₃²×C₄	—	2	1	no	—
50	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×D₁₂	—	2	2	no	—
52	C₂×C₃×D₁₂	—	2	2	no	—
53	C₂×C₃×D₁₂	—	2	2	no	—
54	C₂×C₃×D₁₂	—	2	2	no	—
55	C₂×C₃×D₁₂	—	2	2	no	—
56	C₂×C₃×D₁₂	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×#215	—	2	8	no	—
67	C₃×#213	—	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×D₂₄	—	2	4	no	—
72	C₃×D₂₄	—	2	4	no	—
73	C₂×#472	—	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×D₄	—	3	2	no	—
78	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
79	C₃×AGL(1,ℤ/8)	—	3	8	no	—
80	C₃×AGL(1,ℤ/8)	—	6	4	no	—
81	C₂×C₃×SD₁₆	—	6	2	no	—
82	C₂×C₃×D₈	—	3	4	no	—
83	C₂×C₃×D₈	—	6	2	no	—
84	C₂×C₃×D₈	—	6	1	no	—
85	C₂×C₃×D₈	—	6	1	no	—
86	C₂×C₃×D₈	—	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	complemented
92	C₃×#131	C₂²×C₃	1	4	yes	complemented
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	#949	—	2	4	no	—
107	#949	C₂²×C₃	1	8	yes	complemented
108	C₂×#215	—	2	2	no	—
109	C₂×#213	—	2	2	no	—
110	C₂×#208	C₂²×C₃	1	2	yes	—
111	C₂×D₂₄	—	2	1	no	—
112	C₂×D₂₄	—	2	1	no	—
113	C₂×D₂₄	—	2	2	no	—
114	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
115	C₃×#108	—	3	4	no	—
116	C₃×#100	—	3	8	no	—
117	#823	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	C₂²×C₃×D₃	—	2	4	no	—
122	C₂²×C₃×D₃	—	4	2	no	—
123	C₂²×C₃×D₃	—	4	2	no	—
124	C₂²×C₃×D₃	—	8	4	no	—
125	C₃²×Q₈	—	2	1	no	—
126	C₃²×Q₈	C₂×D₄	1	2	yes	—
127	C₃²×D₄	—	2	2	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	1	no	—
130	C₃²×D₄	C₂×D₄	1	2	yes	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	2	2	no	—
134	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	#41	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
140	C₃×D₁₂	—	2	4	no	—
141	C₃×D₁₂	—	2	4	no	—
142	C₃×D₁₂	—	4	2	no	—
143	C₃×D₁₂	—	4	2	no	—
144	C₃²×C₈	—	2	2	no	—
145	C₃²×C₈	C₂×D₄	1	2	yes	—
146	C₃²×C₈	C₂×D₄	1	2	yes	—
147	C₃×C₃⋊C₈	—	2	4	no	—
148	C₂×AGL(1,ℤ/8)	—	3	2	no	—
149	C₂²×D₈	—	3	1	no	—
150	C₂×#131	C₃×D₃	1	1	yes	characteristic, complemented
151	#472	—	3	8	no	—
152	C₂×#108	—	3	1	no	—
153	C₂×#100	—	3	2	no	—
154	C₂⁴×C₃	—	6	2	no	—
155	C₂³×D₃	—	2	2	no	—
156	C₃×#41	—	2	2	no	—
157	C₃×#41	—	2	2	no	—
158	C₃×#41	—	2	1	no	—
159	C₃×#41	—	2	1	no	—
160	C₃×#41	—	2	1	no	—
161	C₃×#41	—	2	1	no	—
162	C₃×#41	—	2	2	no	—
163	C₃×#41	—	2	2	no	—
164	C₃×#41	D₁₂	1	2	yes	—
165	C₃×#41	C₃×D₄	1	2	yes	—
166	C₃×#41	C₂²×D₃	1	2	yes	—
167	C₃×#41	C₂³×C₃	1	2	yes	—
168	C₂×C₃×Q₈	—	2	1	no	—
169	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
170	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	—	3	4	no	—
176	C₂×C₃×D₄	—	6	2	no	—
177	C₂×C₃×D₄	—	6	2	no	—
178	C₂×C₃×D₄	—	6	2	no	—
179	C₂×C₃×D₄	—	6	2	no	—
180	C₂×C₃×D₄	—	6	2	no	—
181	C₂×C₃×D₄	D₁₂	1	1	yes	characteristic
182	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×D₁₂	—	2	2	no	—
190	C₂×D₁₂	—	2	2	no	—
191	C₂×D₁₂	—	2	2	no	—
192	C₂×D₁₂	—	2	2	no	—
193	C₂×D₁₂	—	2	2	no	—
194	C₂×D₁₂	C₂³×C₃	1	4	yes	—
195	C₃×SD₁₆	—	6	8	no	—
196	C₃×D₈	—	6	8	no	—
197	C₃×D₈	—	6	4	no	—
198	C₃×D₈	—	6	4	no	—
199	C₃×M₁₆	—	2	2	no	—
200	C₃×M₁₆	—	2	8	no	—
201	C₃×M₁₆	—	2	1	no	—
202	C₃×M₁₆	—	2	1	no	—
203	C₃×M₁₆	—	2	4	no	—
204	C₃×M₁₆	—	2	4	no	—
205	C₃×M₁₆	—	2	2	no	—
206	C₃×M₁₆	—	3	4	no	—
207	C₃×M₁₆	—	6	2	no	—
208	C₃×M₁₆	C₂²×D₃	1	2	yes	—
209	C₃×M₁₆	C₂³×C₃	1	2	yes	—
210	C₂×C₃×C₈	—	2	2	no	—
211	C₂×C₃×C₈	—	2	8	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	2	4	no	—
215	C₂×C₃×C₈	—	2	4	no	—
216	C₂×C₃×C₈	—	2	1	no	—
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	2	no	—
219	C₂×C₃×C₈	—	2	2	no	—
220	C₂×C₃×C₈	—	6	2	no	—
221	C₂×C₃×C₈	#67	1	1	yes	characteristic
222	C₂×C₃×C₈	#67	1	1	yes	characteristic
223	C₂×C₃×C₈	#67	1	2	yes	—
224	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
225	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
226	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
227	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
228	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
229	#215	—	2	8	no	—
230	#213	—	2	8	no	—
231	#208	—	2	2	no	—
232	#208	C₂³×C₃	1	4	yes	—
233	C₂×C₃⋊C₈	—	2	2	no	—
234	D₂₄	—	2	4	no	—
235	D₂₄	—	2	4	no	—
236	C₂²×C₃²	—	2	2	no	—
237	C₂²×C₃²	—	2	2	no	—
238	C₂²×C₃²	—	4	2	no	—
239	C₂²×C₃²	#121	1	1	yes	characteristic
240	C₂²×C₃²	#121	1	1	yes	characteristic
241	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
242	C₂×C₃×D₃	—	4	4	no	—
243	C₂×C₃×D₃	—	8	4	no	—
244	C₂×C₃×D₃	—	8	4	no	—
245	C₂×C₃×D₃	—	8	4	no	—
246	C₃²×C₄	—	2	2	no	—
247	C₃²×C₄	#121	1	1	yes	characteristic
248	C₃²×C₄	#121	1	1	yes	characteristic
249	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
250	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
251	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂²×D₄	—	3	2	no	—
253	AGL(1,ℤ/8)	—	3	8	no	—
254	AGL(1,ℤ/8)	—	6	4	no	—
255	C₂×SD₁₆	—	6	2	no	—
256	C₂×D₈	—	3	4	no	—
257	C₂×D₈	—	6	2	no	—
258	C₂×D₈	—	6	1	no	—
259	C₂×D₈	—	6	1	no	—
260	C₂×D₈	—	6	2	no	—
261	#131	—	2	2	no	—
262	#131	C₂×C₃×D₃	1	4	yes	complemented
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	3	2	no	—
265	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
268	#108	—	3	4	no	—
269	#100	—	3	8	no	—
270	C₂³×C₃	—	2	2	no	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	—	6	4	no	—
275	C₂³×C₃	—	12	2	no	—
276	C₂³×C₃	—	12	2	no	—
277	C₂³×C₃	—	24	4	no	—
278	C₂³×C₃	#235	1	1	yes	characteristic
279	C₂³×C₃	C₃×#41	1	1	yes	characteristic
280	C₂²×D₃	—	2	4	no	—
281	C₂²×D₃	—	4	2	no	—
282	C₂²×D₃	—	4	2	no	—
283	C₂²×D₃	—	8	4	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	—	2	1	no	—
286	C₃×Q₈	—	2	1	no	—
287	C₃×Q₈	—	2	2	no	—
288	C₃×Q₈	C₂×D₁₂	1	2	yes	—
289	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	4	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	2	2	no	—
294	C₃×D₄	—	2	2	no	—
295	C₃×D₄	—	2	2	no	—
296	C₃×D₄	—	2	2	no	—
297	C₃×D₄	—	2	1	no	—
298	C₃×D₄	—	2	1	no	—
299	C₃×D₄	—	2	2	no	—
300	C₃×D₄	—	6	4	no	—
301	C₃×D₄	—	6	4	no	—
302	C₃×D₄	—	12	2	no	—
303	C₃×D₄	—	12	2	no	—
304	C₃×D₄	C₂×D₁₂	1	2	yes	—
305	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
323	C₂×C₃×C₄	#235	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
333	D₁₂	—	2	4	no	—
334	D₁₂	—	2	4	no	—
335	D₁₂	—	4	2	no	—
336	D₁₂	—	4	2	no	—
337	C₃×C₈	—	2	4	no	—
338	C₃×C₈	—	2	2	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃×C₈	—	2	2	no	—
341	C₃×C₈	—	2	2	no	—
342	C₃×C₈	—	6	4	no	—
343	C₃×C₈	C₂×#67	1	2	yes	—
344	C₃×C₈	C₂×#67	1	2	yes	—
345	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
346	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
347	C₃⋊C₈	—	2	4	no	—
348	C₂×C₃²	—	2	1	no	—
349	C₂×C₃²	—	2	1	no	—
350	C₂×C₃²	—	4	2	no	—
351	C₂×C₃²	#472	1	2	yes	complemented
352	C₂×C₃²	C₂×#121	1	1	yes	characteristic
353	C₃×D₃	—	8	4	no	—
354	C₂⁴	—	6	2	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	C₃×D₁₂	1	2	yes	—
358	#41	C₂²×C₃×D₃	1	2	yes	—
359	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	3	4	no	—
362	C₂×D₄	—	6	2	no	—
363	C₂×D₄	—	6	2	no	—
364	C₂×D₄	—	6	2	no	—
365	C₂×D₄	—	6	2	no	—
366	C₂×D₄	—	6	2	no	—
367	C₂×D₄	C₃×D₁₂	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
370	SD₁₆	—	6	8	no	—
371	D₈	—	6	8	no	—
372	D₈	—	6	4	no	—
373	D₈	—	6	4	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	3	4	no	—
377	M₁₆	—	6	2	no	—
378	M₁₆	C₂²×C₃×D₃	1	2	yes	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	6	2	no	—
382	C₂×C₈	C₃×#67	1	1	yes	characteristic
383	C₂×C₈	C₃×#67	1	1	yes	characteristic
384	C₂×C₈	C₃×#67	1	2	yes	—
385	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	2	2	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	4	no	—
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	12	4	no	—
399	C₂²×C₃	—	24	4	no	—
400	C₂²×C₃	—	24	4	no	—
401	C₂²×C₃	—	24	4	no	—
402	C₂²×C₃	#930	1	1	yes	characteristic
403	C₂²×C₃	#930	1	1	yes	characteristic
404	C₂²×C₃	C₃×#121	1	1	yes	characteristic
405	C₂²×C₃	C₃×#121	1	1	yes	characteristic
406	C₂²×C₃	C₂×#235	1	1	yes	characteristic
407	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
408	C₂×D₃	—	4	4	no	—
409	C₂×D₃	—	8	4	no	—
410	C₂×D₃	—	8	4	no	—
411	C₂×D₃	—	8	4	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	#930	1	1	yes	characteristic
420	C₃×C₄	#930	1	1	yes	characteristic
421	C₃×C₄	C₃×#121	1	1	yes	characteristic
422	C₃×C₄	C₃×#121	1	1	yes	characteristic
423	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
424	C₃×C₄	C₂²×#67	1	1	yes	characteristic
425	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
426	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
427	C₃²	C₂×#472	1	1	yes	characteristic, complemented, Sylow
428	C₂³	—	2	1	no	—
429	C₂³	—	6	4	no	—
430	C₂³	—	12	2	no	—
431	C₂³	—	12	2	no	—
432	C₂³	—	24	4	no	—
433	C₂³	C₃×#235	1	1	yes	characteristic
434	Q₈	—	2	1	no	—
435	Q₈	C₂×C₃×D₁₂	1	2	yes	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	1	no	—
439	D₄	—	6	4	no	—
440	D₄	—	6	4	no	—
441	D₄	—	12	2	no	—
442	D₄	—	12	2	no	—
443	D₄	C₂×C₃×D₁₂	1	2	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
448	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
449	C₂×C₄	C₃×#235	1	1	yes	characteristic
450	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
452	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	6	4	no	—
455	C₈	C₂×C₃×#67	1	2	yes	—
456	C₈	C₂×C₃×#67	1	2	yes	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	2	1	no	—
461	C₂×C₃	—	2	1	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	4	1	no	—
464	C₂×C₃	—	4	1	no	—
465	C₂×C₃	—	4	4	no	—
466	C₂×C₃	—	4	2	no	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	—	24	4	no	—
469	C₂×C₃	#5142	1	2	yes	direct product factor
470	C₂×C₃	C₃×#472	1	2	yes	complemented
471	C₂×C₃	C₂×#930	1	1	yes	characteristic
472	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
473	D₃	—	8	4	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	12	4	no	—
478	C₂²	—	24	4	no	—
479	C₂²	—	24	4	no	—
480	C₂²	—	24	4	no	—
481	C₂²	C₃×#930	1	1	yes	characteristic
482	C₂²	C₃×#930	1	1	yes	characteristic
483	C₂²	C₂×C₃×#235	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	C₃×#930	1	1	yes	characteristic
486	C₄	C₃×#930	1	1	yes	characteristic
487	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
488	C₄	C₂²×C₃×#67	1	1	yes	characteristic
489	C₃	—	2	1	no	—
490	C₃	C₂×#5142	1	1	yes	characteristic, direct product factor
491	C₃	C₂×C₃×#472	1	1	yes	characteristic, complemented
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	4	2	no	—
495	C₂	—	24	4	no	—
496	C₂	C₃×#5142	1	2	yes	direct product factor
497	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
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₂×C₃×#472
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
1. C₂×C₃²×#131	C₂	semidirect
2. C₂×C₃×#949	C₂	semidirect
3. C₂²×C₃×D₂₄	C₂	semidirect
4. C₃×#5142	C₂	direct (N × H)
5. C₂×C₃×#823	C₂	semidirect
6. C₂×C₃×#819	C₂	semidirect
8. C₂×#5142	C₃	direct (N × H)
12. C₃²×#131	C₂²	semidirect
18. C₃×#949	C₂²	semidirect
25. C₂×C₃×D₂₄	C₂²	semidirect
26. C₃×#823	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
31. C₂×C₃×#131	D₃	semidirect
32. C₂×C₃×#131	C₂×C₃	semidirect
33. C₂×#949	C₂×C₃	semidirect
34. C₂²×D₂₄	C₂×C₃	semidirect
38. #5142	C₂×C₃	direct (N × H)
39. C₂×#823	C₂×C₃	semidirect
40. C₂×#819	C₂×C₃	semidirect
91. C₃×#131	C₂×D₃	semidirect
92. C₃×#131	C₂²×C₃	semidirect
107. #949	C₂²×C₃	semidirect
114. C₂×D₂₄	C₂²×C₃	semidirect
117. #823	C₂²×C₃	semidirect
118. #819	C₂²×C₃	semidirect
150. C₂×#131	C₃×D₃	semidirect
262. #131	C₂×C₃×D₃	semidirect
351. C₂×C₃²	#472	semidirect
427. C₃²	C₂×#472	semidirect
469. C₂×C₃	#5142	direct (N × H)
470. C₂×C₃	C₃×#472	semidirect
490. C₃	C₂×#5142	direct (N × H)
491. C₃	C₂×C₃×#472	semidirect
496. C₂	C₃×#5142	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×#949	2
C₂²×C₃×D₂₄	2
C₃×#5142	2
C₂×C₃×#823	2
C₂×C₃×#819	2
C₂×C₃×#472	3
C₂×#5142	3

Subgroups — C2×C3×#5142 #11867918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5142 #11867918