Subgroups — C₂×C₃×#4897 #11867921

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#908	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#823	C₂	1	2	yes	maximal, complemented
6	C₃×#4897	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#472	—	3	1	no	maximal
8	C₂×#4897	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	1	yes	characteristic
14	C₃×#908	—	2	4	no	—
15	C₃×#908	C₂²	1	8	yes	complemented
16	C₂×C₃×D₂₄	—	2	2	no	—
17	C₂×C₃×D₂₄	—	2	1	no	—
18	C₂×C₃×D₂₄	—	2	1	no	—
19	C₂×C₃×D₂₄	—	2	2	no	—
20	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
21	C₂×C₃×#204	—	2	2	no	—
22	C₃×#901	—	2	2	no	—
23	C₃×#901	C₂²	1	4	yes	complemented
24	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
25	C₂×C₃×D₃×C₈	—	2	1	no	—
26	C₃²×#108	C₂²	1	4	yes	complemented
27	C₃×#823	C₂²	1	8	yes	complemented
28	C₂×C₃×AGL(1,ℤ/8)	—	3	2	no	—
29	C₂²×C₃×D₈	—	3	1	no	—
30	C₂×C₃×#131	—	3	1	no	—
31	C₂×#908	C₂×C₃	1	2	yes	complemented
32	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×#472	—	3	8	no	—
35	C₂×C₃×#108	—	2	1	no	—
36	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
37	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃×#100	—	3	2	no	—
39	C₂×#823	C₂×C₃	1	2	yes	complemented
40	#4897	C₂×C₃	1	8	yes	direct product factor
41	C₂³×C₃×D₃	—	2	2	no	—
42	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
43	C₂×C₃×#67	—	2	1	no	—
44	C₃×#235	—	2	1	no	—
45	C₃×#235	—	2	1	no	—
46	C₃×#235	D₄	1	2	yes	—
47	C₃×#235	C₂³	1	2	yes	—
48	C₂×C₃×D₁₂	—	2	2	no	—
49	C₂×C₃×D₁₂	—	2	2	no	—
50	C₂×C₃×D₁₂	—	2	2	no	—
51	C₂×C₃×D₁₂	—	2	2	no	—
52	C₂×C₃×D₁₂	—	2	2	no	—
53	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
54	C₂×C₃×D₁₂	C₂³	1	4	yes	—
55	C₂×C₃×C₄×D₃	—	2	1	no	—
56	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
57	C₃²×M₁₆	—	2	2	no	—
58	C₃²×M₁₆	C₂³	1	4	yes	—
59	C₂×C₃²×C₈	—	2	2	no	—
60	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
62	C₂×C₃²×C₈	D₄	1	2	yes	—
63	C₂×C₃²×C₈	C₂³	1	2	yes	—
64	C₃×#208	—	2	1	no	—
65	C₃×#208	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊C₈	—	2	1	no	—
67	C₃×D₂₄	—	2	8	no	—
68	C₃×D₂₄	—	2	4	no	—
69	C₃×D₂₄	—	2	4	no	—
70	C₃×#204	—	2	8	no	—
71	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
72	C₃×D₃×C₈	—	2	4	no	—
73	C₂×#472	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	1	no	—
75	C₂²×C₃×D₄	—	3	2	no	—
76	C₂×#235	C₂²×C₃	1	1	yes	characteristic
77	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
78	C₃×AGL(1,ℤ/8)	—	3	8	no	—
79	C₃×AGL(1,ℤ/8)	—	6	4	no	—
80	C₂×C₃×SD₁₆	—	6	2	no	—
81	C₂×C₃×D₈	—	3	4	no	—
82	C₂×C₃×D₈	—	6	2	no	—
83	C₂×C₃×D₈	—	6	1	no	—
84	C₂×C₃×D₈	—	6	1	no	—
85	C₂×C₃×D₈	—	6	2	no	—
86	C₃×#131	—	3	4	no	—
87	C₃×#131	—	6	2	no	—
88	C₂×C₃×M₁₆	—	2	2	no	—
89	C₂×C₃×M₁₆	—	3	1	no	—
90	C₂×C₃×M₁₆	—	6	1	no	—
91	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
92	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
93	C₂²×C₃×C₈	—	2	1	no	—
94	C₂²×C₃×C₈	—	6	1	no	—
95	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₂×#208	C₂²×C₃	1	1	yes	characteristic
98	#908	—	2	4	no	—
99	#908	C₂²×C₃	1	8	yes	complemented
100	C₂×D₂₄	—	2	2	no	—
101	C₂×D₂₄	—	2	1	no	—
102	C₂×D₂₄	—	2	1	no	—
103	C₂×D₂₄	—	2	2	no	—
104	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
105	C₂×#204	—	2	2	no	—
106	#901	—	2	2	no	—
107	#901	C₂²×C₃	1	4	yes	complemented
108	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
109	C₂×D₃×C₈	—	2	1	no	—
110	C₃×#108	—	2	4	no	—
111	C₃×#108	C₂×D₃	1	4	yes	complemented
112	C₃×#108	C₂²×C₃	1	4	yes	complemented
113	C₃×#100	—	3	8	no	—
114	#823	C₂²×C₃	1	8	yes	complemented
115	C₂³×C₃²	#41	1	1	yes	characteristic
116	C₂²×C₃×D₃	—	2	1	no	—
117	C₂²×C₃×D₃	—	2	4	no	—
118	C₂²×C₃×D₃	—	4	2	no	—
119	C₂²×C₃×D₃	—	4	2	no	—
120	C₂²×C₃×D₃	—	8	4	no	—
121	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	#41	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
127	C₃×#67	—	2	2	no	—
128	C₃×#67	—	2	2	no	—
129	C₂×C₃×Dic₃	—	2	1	no	—
130	C₃×D₁₂	—	2	1	no	—
131	C₃×D₁₂	—	2	4	no	—
132	C₃×D₁₂	—	2	4	no	—
133	C₃×D₁₂	—	4	2	no	—
134	C₃×D₁₂	—	4	2	no	—
135	C₃×D₁₂	C₂×D₄	1	2	yes	—
136	C₃×C₄×D₃	—	2	2	no	—
137	C₃×C₄×D₃	—	2	2	no	—
138	C₃×Dic₆	—	2	1	no	—
139	C₃×Dic₆	C₂×D₄	1	2	yes	—
140	C₃²×C₈	—	2	4	no	—
141	C₃²×C₈	C₂×D₄	1	2	yes	—
142	C₃²×C₈	C₂×D₄	1	2	yes	—
143	C₃×C₃⋊C₈	—	2	2	no	—
144	C₂×AGL(1,ℤ/8)	—	3	2	no	—
145	C₂²×D₈	—	3	1	no	—
146	C₂×#131	—	3	1	no	—
147	#472	—	3	8	no	—
148	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
149	C₂×#100	—	3	2	no	—
150	C₂⁴×C₃	—	6	2	no	—
151	C₂³×D₃	—	2	2	no	—
152	C₃×#41	—	3	2	no	—
153	C₃×#41	—	3	2	no	—
154	C₃×#41	—	6	1	no	—
155	C₃×#41	—	6	1	no	—
156	C₂×C₃×Q₈	—	3	1	no	—
157	C₂×C₃×D₄	—	3	1	no	—
158	C₂×C₃×D₄	—	3	4	no	—
159	C₂×C₃×D₄	—	6	1	no	—
160	C₂×C₃×D₄	—	6	2	no	—
161	C₂×C₃×D₄	—	6	2	no	—
162	C₂×C₃×D₄	—	6	2	no	—
163	C₂×C₃×D₄	—	6	2	no	—
164	C₂×C₃×D₄	—	6	2	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	6	1	no	—
167	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₂×#67	—	2	1	no	—
170	#235	—	2	1	no	—
171	#235	—	2	1	no	—
172	#235	C₃×D₄	1	2	yes	—
173	#235	C₂³×C₃	1	2	yes	—
174	C₂×D₁₂	—	2	2	no	—
175	C₂×D₁₂	—	2	2	no	—
176	C₂×D₁₂	—	2	2	no	—
177	C₂×D₁₂	—	2	2	no	—
178	C₂×D₁₂	—	2	2	no	—
179	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
180	C₂×D₁₂	C₂³×C₃	1	4	yes	—
181	C₂×C₄×D₃	—	2	1	no	—
182	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
183	C₃×SD₁₆	—	6	8	no	—
184	C₃×D₈	—	6	8	no	—
185	C₃×D₈	—	6	4	no	—
186	C₃×D₈	—	6	4	no	—
187	C₃×M₁₆	—	2	2	no	—
188	C₃×M₁₆	—	2	2	no	—
189	C₃×M₁₆	—	2	4	no	—
190	C₃×M₁₆	—	3	2	no	—
191	C₃×M₁₆	—	4	2	no	—
192	C₃×M₁₆	—	6	1	no	—
193	C₃×M₁₆	—	6	4	no	—
194	C₃×M₁₆	C₂²×D₃	1	4	yes	—
195	C₃×M₁₆	C₂³×C₃	1	4	yes	—
196	C₂×C₃×C₈	—	2	2	no	—
197	C₂×C₃×C₈	—	2	2	no	—
198	C₂×C₃×C₈	—	2	1	no	—
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	2	2	no	—
202	C₂×C₃×C₈	—	4	2	no	—
203	C₂×C₃×C₈	—	6	1	no	—
204	C₂×C₃×C₈	—	6	4	no	—
205	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
206	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
207	C₂×C₃×C₈	D₁₂	1	2	yes	—
208	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
209	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
210	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
211	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
212	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
213	#208	—	2	1	no	—
214	#208	C₂³×C₃	1	2	yes	—
215	C₂×C₃⋊C₈	—	2	1	no	—
216	D₂₄	—	2	8	no	—
217	D₂₄	—	2	4	no	—
218	D₂₄	—	2	4	no	—
219	#204	—	2	8	no	—
220	ΓL(1,𝔽₂₅)	—	2	4	no	—
221	D₃×C₈	—	2	4	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	#121	1	1	yes	characteristic
224	C₂²×C₃²	#121	1	1	yes	characteristic
225	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
226	C₂×C₃×D₃	—	2	2	no	—
227	C₂×C₃×D₃	—	4	2	no	—
228	C₂×C₃×D₃	—	4	4	no	—
229	C₂×C₃×D₃	—	8	4	no	—
230	C₂×C₃×D₃	—	8	4	no	—
231	C₂×C₃×D₃	—	8	4	no	—
232	C₃²×C₄	#121	1	1	yes	characteristic
233	C₃²×C₄	#121	1	1	yes	characteristic
234	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
235	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
236	C₃×Dic₃	—	2	2	no	—
237	C₂×#41	—	3	1	no	—
238	C₂²×D₄	—	3	2	no	—
239	AGL(1,ℤ/8)	—	3	8	no	—
240	AGL(1,ℤ/8)	—	6	4	no	—
241	C₂×SD₁₆	—	6	2	no	—
242	C₂×D₈	—	3	4	no	—
243	C₂×D₈	—	6	2	no	—
244	C₂×D₈	—	6	1	no	—
245	C₂×D₈	—	6	1	no	—
246	C₂×D₈	—	6	2	no	—
247	#131	—	3	4	no	—
248	#131	—	6	2	no	—
249	C₂×M₁₆	—	3	1	no	—
250	C₂×M₁₆	—	6	1	no	—
251	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
252	C₂²×C₈	—	6	1	no	—
253	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
254	#108	C₂×C₃×D₃	1	4	yes	complemented
255	#100	—	3	8	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	6	1	no	—
258	C₂³×C₃	—	6	4	no	—
259	C₂³×C₃	—	12	2	no	—
260	C₂³×C₃	—	12	2	no	—
261	C₂³×C₃	—	24	4	no	—
262	C₂³×C₃	#239	1	1	yes	characteristic
263	C₂³×C₃	C₃×#41	1	1	yes	characteristic
264	C₂²×D₃	—	2	1	no	—
265	C₂²×D₃	—	2	4	no	—
266	C₂²×D₃	—	4	2	no	—
267	C₂²×D₃	—	4	2	no	—
268	C₂²×D₃	—	8	4	no	—
269	C₃×Q₈	—	3	2	no	—
270	C₃×Q₈	—	6	1	no	—
271	C₃×D₄	—	3	2	no	—
272	C₃×D₄	—	6	2	no	—
273	C₃×D₄	—	6	2	no	—
274	C₃×D₄	—	6	1	no	—
275	C₃×D₄	—	6	4	no	—
276	C₃×D₄	—	6	4	no	—
277	C₃×D₄	—	12	2	no	—
278	C₃×D₄	—	12	2	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	6	1	no	—
286	C₂×C₃×C₄	—	6	2	no	—
287	C₂×C₃×C₄	—	6	2	no	—
288	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
290	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	#239	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
300	#67	—	2	2	no	—
301	#67	—	2	2	no	—
302	C₂×Dic₃	—	2	1	no	—
303	D₁₂	—	2	1	no	—
304	D₁₂	—	2	4	no	—
305	D₁₂	—	2	4	no	—
306	D₁₂	—	4	2	no	—
307	D₁₂	—	4	2	no	—
308	D₁₂	C₂×C₃×D₄	1	2	yes	—
309	C₄×D₃	—	2	2	no	—
310	C₄×D₃	—	2	2	no	—
311	Dic₆	—	2	1	no	—
312	Dic₆	C₂×C₃×D₄	1	2	yes	—
313	C₃×C₈	—	2	4	no	—
314	C₃×C₈	—	2	4	no	—
315	C₃×C₈	—	2	2	no	—
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	—	4	4	no	—
318	C₃×C₈	—	6	2	no	—
319	C₃×C₈	C₂×D₁₂	1	2	yes	—
320	C₃×C₈	C₂×D₁₂	1	2	yes	—
321	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
322	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
323	C₃⋊C₈	—	2	2	no	—
324	C₂×C₃²	—	2	1	no	—
325	C₂×C₃²	—	2	1	no	—
326	C₂×C₃²	#472	1	2	yes	complemented
327	C₂×C₃²	C₂×#121	1	1	yes	characteristic
328	C₃×D₃	—	4	2	no	—
329	C₃×D₃	—	8	4	no	—
330	C₂⁴	—	6	2	no	—
331	#41	—	3	2	no	—
332	#41	—	3	2	no	—
333	#41	—	6	1	no	—
334	#41	—	6	1	no	—
335	C₂×Q₈	—	3	1	no	—
336	C₂×D₄	—	3	4	no	—
337	C₂×D₄	—	3	1	no	—
338	C₂×D₄	—	6	1	no	—
339	C₂×D₄	—	6	2	no	—
340	C₂×D₄	—	6	2	no	—
341	C₂×D₄	—	6	2	no	—
342	C₂×D₄	—	6	2	no	—
343	C₂×D₄	—	6	2	no	—
344	C₂²×C₄	—	6	1	no	—
345	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
346	SD₁₆	—	6	8	no	—
347	D₈	—	6	8	no	—
348	D₈	—	6	4	no	—
349	D₈	—	6	4	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	3	2	no	—
352	M₁₆	—	6	1	no	—
353	M₁₆	—	6	4	no	—
354	M₁₆	C₂²×C₃×D₃	1	4	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	6	1	no	—
357	C₂×C₈	—	6	4	no	—
358	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
359	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
360	C₂×C₈	C₃×D₁₂	1	2	yes	—
361	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	—	4	2	no	—
368	C₂²×C₃	—	6	2	no	—
369	C₂²×C₃	—	12	2	no	—
370	C₂²×C₃	—	12	4	no	—
371	C₂²×C₃	—	24	4	no	—
372	C₂²×C₃	—	24	4	no	—
373	C₂²×C₃	—	24	4	no	—
374	C₂²×C₃	#895	1	1	yes	characteristic
375	C₂²×C₃	#895	1	1	yes	characteristic
376	C₂²×C₃	C₃×#121	1	1	yes	characteristic
377	C₂²×C₃	C₃×#121	1	1	yes	characteristic
378	C₂²×C₃	C₂×#239	1	1	yes	characteristic
379	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	4	2	no	—
382	C₂×D₃	—	4	4	no	—
383	C₂×D₃	—	8	4	no	—
384	C₂×D₃	—	8	4	no	—
385	C₂×D₃	—	8	4	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	6	2	no	—
391	C₃×C₄	#895	1	1	yes	characteristic
392	C₃×C₄	#895	1	1	yes	characteristic
393	C₃×C₄	C₃×#121	1	1	yes	characteristic
394	C₃×C₄	C₃×#121	1	1	yes	characteristic
395	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
396	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
397	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
398	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
399	Dic₃	—	2	2	no	—
400	C₃²	C₂×#472	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	6	1	no	—
402	C₂³	—	6	4	no	—
403	C₂³	—	12	2	no	—
404	C₂³	—	12	2	no	—
405	C₂³	—	24	4	no	—
406	C₂³	C₃×#239	1	1	yes	characteristic
407	Q₈	—	3	2	no	—
408	Q₈	—	6	1	no	—
409	D₄	—	3	2	no	—
410	D₄	—	6	2	no	—
411	D₄	—	6	2	no	—
412	D₄	—	6	1	no	—
413	D₄	—	6	4	no	—
414	D₄	—	6	4	no	—
415	D₄	—	12	2	no	—
416	D₄	—	12	2	no	—
417	C₂×C₄	—	6	1	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	2	no	—
420	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
421	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
422	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
423	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
424	C₂×C₄	C₃×#239	1	1	yes	characteristic
425	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	6	2	no	—
428	C₈	C₂×C₃×D₁₂	1	2	yes	—
429	C₈	C₂×C₃×D₁₂	1	2	yes	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	2	no	—
436	C₂×C₃	—	4	1	no	—
437	C₂×C₃	—	4	1	no	—
438	C₂×C₃	—	12	2	no	—
439	C₂×C₃	—	24	4	no	—
440	C₂×C₃	#4897	1	2	yes	direct product factor
441	C₂×C₃	C₃×#472	1	2	yes	complemented
442	C₂×C₃	C₂×#895	1	1	yes	characteristic
443	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
444	D₃	—	4	2	no	—
445	D₃	—	8	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	12	2	no	—
449	C₂²	—	12	4	no	—
450	C₂²	—	24	4	no	—
451	C₂²	—	24	4	no	—
452	C₂²	—	24	4	no	—
453	C₂²	C₃×#895	1	1	yes	characteristic
454	C₂²	C₃×#895	1	1	yes	characteristic
455	C₂²	C₂×C₃×#239	1	1	yes	characteristic
456	C₄	—	6	2	no	—
457	C₄	C₃×#895	1	1	yes	characteristic
458	C₄	C₃×#895	1	1	yes	characteristic
459	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
460	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
461	C₃	—	2	1	no	—
462	C₃	C₂×#4897	1	1	yes	characteristic, direct product factor
463	C₃	C₂×C₃×#472	1	1	yes	characteristic, complemented
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	12	2	no	—
467	C₂	—	24	4	no	—
468	C₂	C₃×#4897	1	2	yes	direct product factor
469	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
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂×C₃×#472
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×#908	C₂	semidirect
2. C₂²×C₃×D₂₄	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₂×C₃²×#108	C₂	semidirect
5. C₂×C₃×#823	C₂	semidirect
6. C₃×#4897	C₂	direct (N × H)
8. C₂×#4897	C₃	direct (N × H)
15. C₃×#908	C₂²	semidirect
20. C₂×C₃×D₂₄	C₂²	semidirect
23. C₃×#901	C₂²	semidirect
26. C₃²×#108	C₂²	semidirect
27. C₃×#823	C₂²	semidirect
31. C₂×#908	C₂×C₃	semidirect
32. C₂²×D₂₄	C₂×C₃	semidirect
33. C₂×#901	C₂×C₃	semidirect
36. C₂×C₃×#108	D₃	semidirect
37. C₂×C₃×#108	C₂×C₃	semidirect
39. C₂×#823	C₂×C₃	semidirect
40. #4897	C₂×C₃	direct (N × H)
99. #908	C₂²×C₃	semidirect
104. C₂×D₂₄	C₂²×C₃	semidirect
107. #901	C₂²×C₃	semidirect
111. C₃×#108	C₂×D₃	semidirect
112. C₃×#108	C₂²×C₃	semidirect
114. #823	C₂²×C₃	semidirect
148. C₂×#108	C₃×D₃	semidirect
254. #108	C₂×C₃×D₃	semidirect
326. C₂×C₃²	#472	semidirect
400. C₃²	C₂×#472	semidirect
440. C₂×C₃	#4897	direct (N × H)
441. C₂×C₃	C₃×#472	semidirect
462. C₃	C₂×#4897	direct (N × H)
463. C₃	C₂×C₃×#472	semidirect
468. C₂	C₃×#4897	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×#908	2
C₂²×C₃×D₂₄	2
C₂×C₃×#901	2
C₂×C₃²×#108	2
C₂×C₃×#823	2
C₃×#4897	2
C₂×C₃×#472	3
C₂×#4897	3

Subgroups — C2×C3×#4897 #11867921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4897 #11867921