Subgroups — C₂×C₃×#4898 #11867856

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#909	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#908	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#204	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#824	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#823	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4898	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#471	—	3	1	no	maximal
10	C₂×#4898	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	1	yes	characteristic
18	C₃×#909	—	2	2	no	—
19	C₃×#909	C₂²	1	4	yes	complemented
20	C₃×#908	—	2	2	no	—
21	C₃×#908	C₂²	1	4	yes	—
22	C₂×C₃×Dic₁₂	—	2	1	no	—
23	C₂×C₃×D₂₄	—	2	1	no	—
24	C₂×C₃×#204	—	2	1	no	—
25	C₂×C₃×#204	—	2	1	no	—
26	C₂×C₃×#204	—	2	1	no	—
27	C₂×C₃×#204	—	2	1	no	—
28	C₂×C₃×#204	—	2	2	no	—
29	C₂×C₃×#204	C₂²	1	4	yes	complemented
30	C₃×#901	—	2	2	no	—
31	C₃×#901	C₂²	1	4	yes	complemented
32	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
33	C₂×C₃×D₃×C₈	—	2	1	no	—
34	C₃²×#108	C₂²	1	4	yes	complemented
35	C₃×#824	C₂²	1	4	yes	complemented
36	C₃×#823	C₂²	1	4	yes	complemented
37	C₂×C₃×#137	—	3	1	no	—
38	C₂×C₃×AGL(1,ℤ/8)	—	3	1	no	—
39	C₂²×C₃×SD₁₆	—	3	1	no	—
40	C₂×C₃×#131	—	3	1	no	—
41	C₂×#909	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#908	C₂×C₃	1	1	yes	characteristic
43	C₂²×#204	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#471	—	3	8	no	—
46	C₂×C₃×#108	—	2	1	no	—
47	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
48	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₃×#101	—	3	1	no	—
50	C₂×C₃×#100	—	3	1	no	—
51	C₂×#824	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#823	C₂×C₃	1	1	yes	characteristic, complemented
53	#4898	C₂×C₃	1	8	yes	direct product factor
54	C₂³×C₃×D₃	—	2	1	no	—
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×#67	—	2	1	no	—
57	C₂²×C₃×Dic₃	—	2	1	no	—
58	C₃×#235	—	2	1	no	—
59	C₃×#235	—	2	1	no	—
60	C₃×#235	D₄	1	2	yes	—
61	C₃×#235	C₂³	1	2	yes	—
62	C₂×C₃×D₁₂	—	2	1	no	—
63	C₂×C₃×D₁₂	—	2	1	no	—
64	C₂×C₃×D₁₂	—	2	1	no	—
65	C₂×C₃×D₁₂	—	2	1	no	—
66	C₂×C₃×D₁₂	—	2	1	no	—
67	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
68	C₂×C₃×D₁₂	C₂³	1	2	yes	—
69	C₂×C₃×C₄×D₃	—	2	1	no	—
70	C₂×C₃×Dic₆	—	2	1	no	—
71	C₂×C₃×Dic₆	—	2	1	no	—
72	C₂×C₃×Dic₆	—	2	1	no	—
73	C₂×C₃×Dic₆	—	2	1	no	—
74	C₂×C₃×Dic₆	—	2	1	no	—
75	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
76	C₂×C₃×Dic₆	C₂³	1	2	yes	—
77	C₃²×M₁₆	—	2	1	no	—
78	C₃²×M₁₆	—	2	1	no	—
79	C₃²×M₁₆	C₂³	1	2	yes	—
80	C₃²×M₁₆	C₂³	1	2	yes	—
81	C₂×C₃²×C₈	—	2	1	no	—
82	C₂×C₃²×C₈	—	2	1	no	—
83	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
84	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
85	C₂×C₃²×C₈	D₄	1	2	yes	—
86	C₂×C₃²×C₈	C₂³	1	2	yes	—
87	C₃×#208	—	2	1	no	—
88	C₃×#208	C₂³	1	2	yes	—
89	C₂×C₃×C₃⋊C₈	—	2	1	no	—
90	C₃×Dic₁₂	—	2	4	no	—
91	C₃×D₂₄	—	2	4	no	—
92	C₃×#204	—	2	4	no	—
93	C₃×#204	—	2	4	no	—
94	C₃×#204	—	2	4	no	—
95	C₃×#204	—	2	4	no	—
96	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
97	C₃×D₃×C₈	—	2	4	no	—
98	C₂×#471	—	3	1	no	Sylow
99	C₂×C₃×#41	—	3	1	no	—
100	C₂²×C₃×Q₈	—	3	1	no	—
101	C₂²×C₃×D₄	—	3	1	no	—
102	C₂×#235	C₂²×C₃	1	1	yes	characteristic
103	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
104	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
105	C₃×#137	—	3	4	no	—
106	C₃×#137	—	6	2	no	—
107	C₃×AGL(1,ℤ/8)	—	3	4	no	—
108	C₃×AGL(1,ℤ/8)	—	6	2	no	—
109	C₂×C₃×Q₁₆	—	6	1	no	—
110	C₂×C₃×SD₁₆	—	3	4	no	—
111	C₂×C₃×SD₁₆	—	6	1	no	—
112	C₂×C₃×SD₁₆	—	6	1	no	—
113	C₂×C₃×SD₁₆	—	6	1	no	—
114	C₂×C₃×SD₁₆	—	6	1	no	—
115	C₂×C₃×SD₁₆	—	6	2	no	—
116	C₂×C₃×D₈	—	6	1	no	—
117	C₃×#131	—	3	4	no	—
118	C₃×#131	—	6	2	no	—
119	C₂×C₃×M₁₆	—	2	1	no	—
120	C₂×C₃×M₁₆	—	2	1	no	—
121	C₂×C₃×M₁₆	—	3	1	no	—
122	C₂×C₃×M₁₆	—	6	1	no	—
123	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
124	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
125	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₃×C₈	—	2	1	no	—
128	C₂²×C₃×C₈	—	6	1	no	—
129	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
131	C₂×#208	C₂²×C₃	1	1	yes	characteristic
132	#909	—	2	2	no	—
133	#909	C₂²×C₃	1	4	yes	complemented
134	#908	—	2	2	no	—
135	#908	C₂²×C₃	1	4	yes	—
136	C₂×Dic₁₂	—	2	1	no	—
137	C₂×D₂₄	—	2	1	no	—
138	C₂×#204	—	2	1	no	—
139	C₂×#204	—	2	1	no	—
140	C₂×#204	—	2	1	no	—
141	C₂×#204	—	2	1	no	—
142	C₂×#204	—	2	2	no	—
143	C₂×#204	C₂²×C₃	1	4	yes	complemented
144	#901	—	2	2	no	—
145	#901	C₂²×C₃	1	4	yes	complemented
146	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
147	C₂×D₃×C₈	—	2	1	no	—
148	C₃×#108	—	2	4	no	—
149	C₃×#108	C₂×D₃	1	4	yes	complemented
150	C₃×#108	C₂²×C₃	1	4	yes	complemented
151	C₃×#101	—	3	4	no	—
152	C₃×#100	—	3	4	no	—
153	#824	C₂²×C₃	1	4	yes	complemented
154	#823	C₂²×C₃	1	4	yes	complemented
155	C₂³×C₃²	#41	1	1	yes	characteristic
156	C₂²×C₃×D₃	—	2	1	no	—
157	C₂²×C₃×D₃	—	2	2	no	—
158	C₂²×C₃×D₃	—	4	1	no	—
159	C₂²×C₃×D₃	—	4	1	no	—
160	C₂²×C₃×D₃	—	8	2	no	—
161	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃²×C₄	#41	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
167	C₃×#67	—	2	2	no	—
168	C₃×#67	—	2	2	no	—
169	C₂×C₃×Dic₃	—	2	1	no	—
170	C₂×C₃×Dic₃	—	2	2	no	—
171	C₂×C₃×Dic₃	—	4	1	no	—
172	C₂×C₃×Dic₃	—	4	1	no	—
173	C₃×D₁₂	—	2	1	no	—
174	C₃×D₁₂	—	2	2	no	—
175	C₃×D₁₂	—	2	2	no	—
176	C₃×D₁₂	—	4	1	no	—
177	C₃×D₁₂	—	4	1	no	—
178	C₃×D₁₂	C₂×D₄	1	2	yes	—
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×C₄×D₃	—	2	2	no	—
181	C₃×Dic₆	—	2	1	no	—
182	C₃×Dic₆	—	2	2	no	—
183	C₃×Dic₆	—	2	2	no	—
184	C₃×Dic₆	—	4	1	no	—
185	C₃×Dic₆	—	4	1	no	—
186	C₃×Dic₆	C₂×D₄	1	2	yes	—
187	C₃²×C₈	—	2	2	no	—
188	C₃²×C₈	—	2	2	no	—
189	C₃²×C₈	C₂×D₄	1	2	yes	—
190	C₃²×C₈	C₂×D₄	1	2	yes	—
191	C₃×C₃⋊C₈	—	2	2	no	—
192	C₂×#137	—	3	1	no	—
193	C₂×AGL(1,ℤ/8)	—	3	1	no	—
194	C₂²×SD₁₆	—	3	1	no	—
195	C₂×#131	—	3	1	no	—
196	#471	—	3	8	no	—
197	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
198	C₂×#101	—	3	1	no	—
199	C₂×#100	—	3	1	no	—
200	C₂⁴×C₃	—	6	1	no	—
201	C₂³×D₃	—	2	1	no	—
202	C₃×#41	—	3	2	no	—
203	C₃×#41	—	3	2	no	—
204	C₃×#41	—	6	1	no	—
205	C₃×#41	—	6	1	no	—
206	C₂×C₃×Q₈	—	3	1	no	—
207	C₂×C₃×Q₈	—	3	2	no	—
208	C₂×C₃×Q₈	—	6	1	no	—
209	C₂×C₃×Q₈	—	6	1	no	—
210	C₂×C₃×Q₈	—	6	1	no	—
211	C₂×C₃×Q₈	—	6	1	no	—
212	C₂×C₃×Q₈	—	6	1	no	—
213	C₂×C₃×D₄	—	3	1	no	—
214	C₂×C₃×D₄	—	3	2	no	—
215	C₂×C₃×D₄	—	6	1	no	—
216	C₂×C₃×D₄	—	6	1	no	—
217	C₂×C₃×D₄	—	6	1	no	—
218	C₂×C₃×D₄	—	6	1	no	—
219	C₂×C₃×D₄	—	6	1	no	—
220	C₂×C₃×D₄	—	6	1	no	—
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	—	6	1	no	—
223	C₂²×C₃×C₄	—	6	1	no	—
224	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂×#67	—	2	1	no	—
227	C₂²×Dic₃	—	2	1	no	—
228	#235	—	2	1	no	—
229	#235	—	2	1	no	—
230	#235	C₃×D₄	1	2	yes	—
231	#235	C₂³×C₃	1	2	yes	—
232	C₂×D₁₂	—	2	1	no	—
233	C₂×D₁₂	—	2	1	no	—
234	C₂×D₁₂	—	2	1	no	—
235	C₂×D₁₂	—	2	1	no	—
236	C₂×D₁₂	—	2	1	no	—
237	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
238	C₂×D₁₂	C₂³×C₃	1	2	yes	—
239	C₂×C₄×D₃	—	2	1	no	—
240	C₂×Dic₆	—	2	1	no	—
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	—	2	1	no	—
243	C₂×Dic₆	—	2	1	no	—
244	C₂×Dic₆	—	2	1	no	—
245	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
246	C₂×Dic₆	C₂³×C₃	1	2	yes	—
247	C₃×Q₁₆	—	6	4	no	—
248	C₃×SD₁₆	—	6	4	no	—
249	C₃×SD₁₆	—	6	4	no	—
250	C₃×SD₁₆	—	6	4	no	—
251	C₃×SD₁₆	—	6	4	no	—
252	C₃×D₈	—	6	4	no	—
253	C₃×M₁₆	—	2	1	no	—
254	C₃×M₁₆	—	2	1	no	—
255	C₃×M₁₆	—	2	1	no	—
256	C₃×M₁₆	—	2	1	no	—
257	C₃×M₁₆	—	2	2	no	—
258	C₃×M₁₆	—	2	2	no	—
259	C₃×M₁₆	—	3	2	no	—
260	C₃×M₁₆	—	4	1	no	—
261	C₃×M₁₆	—	4	1	no	—
262	C₃×M₁₆	—	6	1	no	—
263	C₃×M₁₆	—	6	4	no	—
264	C₃×M₁₆	C₂²×D₃	1	2	yes	—
265	C₃×M₁₆	C₂²×D₃	1	2	yes	—
266	C₃×M₁₆	C₂³×C₃	1	2	yes	—
267	C₃×M₁₆	C₂³×C₃	1	2	yes	—
268	C₂×C₃×C₈	—	2	1	no	—
269	C₂×C₃×C₈	—	2	1	no	—
270	C₂×C₃×C₈	—	2	1	no	—
271	C₂×C₃×C₈	—	2	1	no	—
272	C₂×C₃×C₈	—	2	1	no	—
273	C₂×C₃×C₈	—	2	1	no	—
274	C₂×C₃×C₈	—	2	2	no	—
275	C₂×C₃×C₈	—	2	2	no	—
276	C₂×C₃×C₈	—	4	1	no	—
277	C₂×C₃×C₈	—	4	1	no	—
278	C₂×C₃×C₈	—	6	1	no	—
279	C₂×C₃×C₈	—	6	4	no	—
280	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
281	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
282	C₂×C₃×C₈	D₁₂	1	2	yes	—
283	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
284	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
286	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
287	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
288	#208	—	2	1	no	—
289	#208	C₂³×C₃	1	2	yes	—
290	C₂×C₃⋊C₈	—	2	1	no	—
291	Dic₁₂	—	2	4	no	—
292	D₂₄	—	2	4	no	—
293	#204	—	2	4	no	—
294	#204	—	2	4	no	—
295	#204	—	2	4	no	—
296	#204	—	2	4	no	—
297	ΓL(1,𝔽₂₅)	—	2	4	no	—
298	D₃×C₈	—	2	4	no	—
299	C₂²×C₃²	—	2	2	no	—
300	C₂²×C₃²	#121	1	1	yes	characteristic
301	C₂²×C₃²	#121	1	1	yes	characteristic
302	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
303	C₂×C₃×D₃	—	2	2	no	—
304	C₂×C₃×D₃	—	4	2	no	—
305	C₂×C₃×D₃	—	4	2	no	—
306	C₂×C₃×D₃	—	8	2	no	—
307	C₂×C₃×D₃	—	8	2	no	—
308	C₂×C₃×D₃	—	8	2	no	—
309	C₃²×C₄	#121	1	1	yes	characteristic
310	C₃²×C₄	#121	1	1	yes	characteristic
311	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
312	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₃×Dic₃	—	2	2	no	—
314	C₃×Dic₃	—	4	2	no	—
315	C₂×#41	—	3	1	no	—
316	C₂²×Q₈	—	3	1	no	—
317	C₂²×D₄	—	3	1	no	—
318	#137	—	3	4	no	—
319	#137	—	6	2	no	—
320	AGL(1,ℤ/8)	—	3	4	no	—
321	AGL(1,ℤ/8)	—	6	2	no	—
322	C₂×Q₁₆	—	6	1	no	—
323	C₂×SD₁₆	—	3	4	no	—
324	C₂×SD₁₆	—	6	1	no	—
325	C₂×SD₁₆	—	6	1	no	—
326	C₂×SD₁₆	—	6	1	no	—
327	C₂×SD₁₆	—	6	1	no	—
328	C₂×SD₁₆	—	6	2	no	—
329	C₂×D₈	—	6	1	no	—
330	#131	—	3	4	no	—
331	#131	—	6	2	no	—
332	C₂×M₁₆	—	3	1	no	—
333	C₂×M₁₆	—	6	1	no	—
334	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
335	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
336	C₂²×C₈	—	6	1	no	—
337	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
338	#108	C₂×C₃×D₃	1	4	yes	complemented
339	#101	—	3	4	no	—
340	#100	—	3	4	no	—
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	6	1	no	—
343	C₂³×C₃	—	6	2	no	—
344	C₂³×C₃	—	12	1	no	—
345	C₂³×C₃	—	12	1	no	—
346	C₂³×C₃	—	24	2	no	—
347	C₂³×C₃	#239	1	1	yes	characteristic
348	C₂³×C₃	C₃×#41	1	1	yes	characteristic
349	C₂²×D₃	—	2	1	no	—
350	C₂²×D₃	—	2	2	no	—
351	C₂²×D₃	—	4	1	no	—
352	C₂²×D₃	—	4	1	no	—
353	C₂²×D₃	—	8	2	no	—
354	C₃×Q₈	—	3	2	no	—
355	C₃×Q₈	—	6	1	no	—
356	C₃×Q₈	—	6	2	no	—
357	C₃×Q₈	—	6	2	no	—
358	C₃×Q₈	—	12	1	no	—
359	C₃×Q₈	—	12	1	no	—
360	C₃×D₄	—	3	2	no	—
361	C₃×D₄	—	6	2	no	—
362	C₃×D₄	—	6	2	no	—
363	C₃×D₄	—	6	1	no	—
364	C₃×D₄	—	6	2	no	—
365	C₃×D₄	—	6	2	no	—
366	C₃×D₄	—	12	1	no	—
367	C₃×D₄	—	12	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	6	1	no	—
375	C₂×C₃×C₄	—	6	2	no	—
376	C₂×C₃×C₄	—	6	2	no	—
377	C₂×C₃×C₄	—	6	2	no	—
378	C₂×C₃×C₄	—	12	1	no	—
379	C₂×C₃×C₄	—	12	1	no	—
380	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
382	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	#239	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
392	#67	—	2	2	no	—
393	#67	—	2	2	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	—	2	2	no	—
396	C₂×Dic₃	—	4	1	no	—
397	C₂×Dic₃	—	4	1	no	—
398	D₁₂	—	2	1	no	—
399	D₁₂	—	2	2	no	—
400	D₁₂	—	2	2	no	—
401	D₁₂	—	4	1	no	—
402	D₁₂	—	4	1	no	—
403	D₁₂	C₂×C₃×D₄	1	2	yes	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	Dic₆	—	2	1	no	—
407	Dic₆	—	2	2	no	—
408	Dic₆	—	2	2	no	—
409	Dic₆	—	4	1	no	—
410	Dic₆	—	4	1	no	—
411	Dic₆	C₂×C₃×D₄	1	2	yes	—
412	C₃×C₈	—	2	2	no	—
413	C₃×C₈	—	2	2	no	—
414	C₃×C₈	—	2	2	no	—
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	2	2	no	—
418	C₃×C₈	—	4	2	no	—
419	C₃×C₈	—	4	2	no	—
420	C₃×C₈	—	6	2	no	—
421	C₃×C₈	C₂×D₁₂	1	2	yes	—
422	C₃×C₈	C₂×D₁₂	1	2	yes	—
423	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
424	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
425	C₃⋊C₈	—	2	2	no	—
426	C₂×C₃²	—	2	1	no	—
427	C₂×C₃²	—	2	1	no	—
428	C₂×C₃²	#471	1	2	yes	complemented
429	C₂×C₃²	C₂×#121	1	1	yes	characteristic
430	C₃×D₃	—	4	2	no	—
431	C₃×D₃	—	8	2	no	—
432	C₂⁴	—	6	1	no	—
433	#41	—	3	2	no	—
434	#41	—	3	2	no	—
435	#41	—	6	1	no	—
436	#41	—	6	1	no	—
437	C₂×Q₈	—	3	2	no	—
438	C₂×Q₈	—	3	1	no	—
439	C₂×Q₈	—	6	1	no	—
440	C₂×Q₈	—	6	1	no	—
441	C₂×Q₈	—	6	1	no	—
442	C₂×Q₈	—	6	1	no	—
443	C₂×Q₈	—	6	1	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	1	no	—
446	C₂×D₄	—	6	1	no	—
447	C₂×D₄	—	6	1	no	—
448	C₂×D₄	—	6	1	no	—
449	C₂×D₄	—	6	1	no	—
450	C₂×D₄	—	6	1	no	—
451	C₂×D₄	—	6	1	no	—
452	C₂²×C₄	—	6	1	no	—
453	C₂²×C₄	—	6	1	no	—
454	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
455	Q₁₆	—	6	4	no	—
456	SD₁₆	—	6	4	no	—
457	SD₁₆	—	6	4	no	—
458	SD₁₆	—	6	4	no	—
459	SD₁₆	—	6	4	no	—
460	D₈	—	6	4	no	—
461	M₁₆	—	2	1	no	—
462	M₁₆	—	2	1	no	—
463	M₁₆	—	3	2	no	—
464	M₁₆	—	6	1	no	—
465	M₁₆	—	6	4	no	—
466	M₁₆	C₂²×C₃×D₃	1	2	yes	—
467	M₁₆	C₂²×C₃×D₃	1	2	yes	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	6	1	no	—
471	C₂×C₈	—	6	4	no	—
472	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
473	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
474	C₂×C₈	C₃×D₁₂	1	2	yes	—
475	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	6	2	no	—
483	C₂²×C₃	—	12	2	no	—
484	C₂²×C₃	—	12	2	no	—
485	C₂²×C₃	—	24	2	no	—
486	C₂²×C₃	—	24	2	no	—
487	C₂²×C₃	—	24	2	no	—
488	C₂²×C₃	#895	1	1	yes	characteristic
489	C₂²×C₃	#895	1	1	yes	characteristic
490	C₂²×C₃	C₃×#121	1	1	yes	characteristic
491	C₂²×C₃	C₃×#121	1	1	yes	characteristic
492	C₂²×C₃	C₂×#239	1	1	yes	characteristic
493	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	4	2	no	—
496	C₂×D₃	—	4	2	no	—
497	C₂×D₃	—	8	2	no	—
498	C₂×D₃	—	8	2	no	—
499	C₂×D₃	—	8	2	no	—
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	6	2	no	—
505	C₃×C₄	—	12	2	no	—
506	C₃×C₄	#895	1	1	yes	characteristic
507	C₃×C₄	#895	1	1	yes	characteristic
508	C₃×C₄	C₃×#121	1	1	yes	characteristic
509	C₃×C₄	C₃×#121	1	1	yes	characteristic
510	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
511	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
512	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
513	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
514	Dic₃	—	2	2	no	—
515	Dic₃	—	4	2	no	—
516	C₃²	C₂×#471	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	6	1	no	—
518	C₂³	—	6	2	no	—
519	C₂³	—	12	1	no	—
520	C₂³	—	12	1	no	—
521	C₂³	—	24	2	no	—
522	C₂³	C₃×#239	1	1	yes	characteristic
523	Q₈	—	3	2	no	—
524	Q₈	—	6	1	no	—
525	Q₈	—	6	2	no	—
526	Q₈	—	6	2	no	—
527	Q₈	—	12	1	no	—
528	Q₈	—	12	1	no	—
529	D₄	—	3	2	no	—
530	D₄	—	6	2	no	—
531	D₄	—	6	2	no	—
532	D₄	—	6	1	no	—
533	D₄	—	6	2	no	—
534	D₄	—	6	2	no	—
535	D₄	—	12	1	no	—
536	D₄	—	12	1	no	—
537	C₂×C₄	—	6	1	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	—	12	1	no	—
542	C₂×C₄	—	12	1	no	—
543	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
544	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
545	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
546	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
547	C₂×C₄	C₃×#239	1	1	yes	characteristic
548	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
549	C₈	—	2	2	no	—
550	C₈	—	2	2	no	—
551	C₈	—	6	2	no	—
552	C₈	C₂×C₃×D₁₂	1	2	yes	—
553	C₈	C₂×C₃×D₁₂	1	2	yes	—
554	C₂×C₃	—	2	1	no	—
555	C₂×C₃	—	2	1	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	2	2	no	—
560	C₂×C₃	—	4	1	no	—
561	C₂×C₃	—	4	1	no	—
562	C₂×C₃	—	12	2	no	—
563	C₂×C₃	—	24	2	no	—
564	C₂×C₃	#4898	1	2	yes	direct product factor
565	C₂×C₃	C₃×#471	1	2	yes	complemented
566	C₂×C₃	C₂×#895	1	1	yes	characteristic
567	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
568	D₃	—	4	2	no	—
569	D₃	—	8	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	6	2	no	—
572	C₂²	—	12	2	no	—
573	C₂²	—	12	2	no	—
574	C₂²	—	24	2	no	—
575	C₂²	—	24	2	no	—
576	C₂²	—	24	2	no	—
577	C₂²	C₃×#895	1	1	yes	characteristic
578	C₂²	C₃×#895	1	1	yes	characteristic
579	C₂²	C₂×C₃×#239	1	1	yes	characteristic
580	C₄	—	6	2	no	—
581	C₄	—	12	2	no	—
582	C₄	C₃×#895	1	1	yes	characteristic
583	C₄	C₃×#895	1	1	yes	characteristic
584	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
585	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
586	C₃	—	2	1	no	—
587	C₃	C₂×#4898	1	1	yes	characteristic, direct product factor
588	C₃	C₂×C₃×#471	1	1	yes	characteristic, complemented
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	12	2	no	—
592	C₂	—	24	2	no	—
593	C₂	C₃×#4898	1	2	yes	direct product factor
594	C₂	C₂×C₃×#895	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#895
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	#121
prime radical	C₂×C₃×#908	C₂
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂×C₃×#471
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#909	C₂	semidirect
3. C₂²×C₃×#204	C₂	semidirect
4. C₂×C₃×#901	C₂	semidirect
5. C₂×C₃²×#108	C₂	semidirect
6. C₂×C₃×#824	C₂	semidirect
7. C₂×C₃×#823	C₂	semidirect
8. C₃×#4898	C₂	direct (N × H)
10. C₂×#4898	C₃	direct (N × H)
19. C₃×#909	C₂²	semidirect
29. C₂×C₃×#204	C₂²	semidirect
31. C₃×#901	C₂²	semidirect
34. C₃²×#108	C₂²	semidirect
35. C₃×#824	C₂²	semidirect
36. C₃×#823	C₂²	semidirect
41. C₂×#909	C₂×C₃	semidirect
43. C₂²×#204	C₂×C₃	semidirect
44. C₂×#901	C₂×C₃	semidirect
47. C₂×C₃×#108	D₃	semidirect
48. C₂×C₃×#108	C₂×C₃	semidirect
51. C₂×#824	C₂×C₃	semidirect
52. C₂×#823	C₂×C₃	semidirect
53. #4898	C₂×C₃	direct (N × H)
133. #909	C₂²×C₃	semidirect
143. C₂×#204	C₂²×C₃	semidirect
145. #901	C₂²×C₃	semidirect
149. C₃×#108	C₂×D₃	semidirect
150. C₃×#108	C₂²×C₃	semidirect
153. #824	C₂²×C₃	semidirect
154. #823	C₂²×C₃	semidirect
197. C₂×#108	C₃×D₃	semidirect
338. #108	C₂×C₃×D₃	semidirect
428. C₂×C₃²	#471	semidirect
516. C₃²	C₂×#471	semidirect
564. C₂×C₃	#4898	direct (N × H)
565. C₂×C₃	C₃×#471	semidirect
587. C₃	C₂×#4898	direct (N × H)
588. C₃	C₂×C₃×#471	semidirect
593. C₂	C₃×#4898	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×#909	2
C₂×C₃×#908	2
C₂²×C₃×#204	2
C₂×C₃×#901	2
C₂×C₃²×#108	2
C₂×C₃×#824	2
C₂×C₃×#823	2
C₃×#4898	2
C₂×C₃×#471	3
C₂×#4898	3

Subgroups — C2×C3×#4898 #11867856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4898 #11867856