Subgroups — C₃×#70479 #11785174

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#821	C₂	1	2	yes	maximal
4	C₃×#4935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4551	C₂	1	2	yes	maximal, complemented
6	C₃×#1802	—	3	1	no	maximal
7	#70479	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₃	—	2	1	no	—
10	C₂²×C₃²×C₈	C₂²	1	2	yes	—
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
13	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
14	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
15	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₃×C₄×D₁₂	—	2	2	no	—
18	C₃×C₄×D₁₂	C₄	1	4	yes	complemented
19	C₃²×C₄⋊C₈	—	2	2	no	—
20	C₃×#821	—	2	4	no	—
21	C₂×C₃×C₄×D₄	—	3	1	no	—
22	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×C₄⋊C₈	—	2	1	no	—
24	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#102	—	3	2	no	—
27	C₃×#384	—	3	1	no	—
28	C₂×#821	C₂×C₃	1	2	yes	—
29	#4935	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×#340	—	3	2	no	—
31	#4551	C₂×C₃	1	2	yes	complemented
32	C₂³×C₃×D₃	—	2	1	no	—
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
36	C₂²×C₃×Dic₃	—	2	1	no	—
37	C₂²×C₃×Dic₃	—	2	2	no	—
38	C₂×C₃×D₁₂	—	2	1	no	—
39	C₂×C₃×D₁₂	—	2	1	no	—
40	C₂×C₃×D₁₂	—	2	1	no	—
41	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
42	C₂×C₃×D₁₂	D₄	1	2	yes	—
43	C₂×C₃×D₁₂	Q₈	1	2	yes	—
44	C₂×C₃×C₄×D₃	—	2	4	no	—
45	C₂×C₃×C₄×D₃	—	4	2	no	—
46	C₂×C₃×C₄×D₃	—	4	2	no	—
47	C₂×C₃²×C₈	—	2	2	no	—
48	C₂×C₃²×C₈	—	2	2	no	—
49	C₂×C₃²×C₈	—	2	2	no	—
50	C₃²×C₄²	C₂×C₄	1	2	yes	—
51	C₃²×C₄²	D₄	1	2	yes	—
52	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
53	C₃×C₄⋊Dic₃	—	2	1	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄⋊Dic₃	—	2	2	no	—
56	C₃×C₄⋊Dic₃	—	4	2	no	—
57	C₃×C₄⋊Dic₃	—	4	2	no	—
58	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
59	#1802	—	3	1	no	Sylow
60	C₂²×C₃×D₄	—	3	1	no	—
61	C₂³×C₃×C₄	—	6	1	no	—
62	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₄×D₃	—	2	1	no	—
64	C₂²×C₃×C₈	—	2	2	no	—
65	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
66	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
67	C₃×C₄×D₄	—	3	4	no	—
68	C₃×C₄×D₄	—	6	2	no	—
69	C₂×C₃×C₄⋊C₄	—	3	1	no	—
70	C₂×C₃×C₄⋊C₄	—	3	2	no	—
71	C₂×C₃×C₄⋊C₄	—	6	1	no	—
72	C₂×C₃×C₄⋊C₄	—	6	1	no	—
73	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
74	C₂×C₃×C₄²	—	2	1	no	—
75	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
78	C₂×C₄⋊Dic₃	—	2	1	no	—
79	C₂×C₄⋊Dic₃	—	2	1	no	—
80	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
81	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
82	C₄×D₁₂	—	2	2	no	—
83	C₄×D₁₂	C₃×C₄	1	4	yes	complemented
84	C₃×C₄⋊C₈	—	2	4	no	—
85	C₃×C₄⋊C₈	—	2	2	no	—
86	C₃×C₄⋊C₈	—	2	2	no	—
87	C₃×#102	—	6	4	no	—
88	#821	—	2	4	no	—
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	2	no	—
91	C₂²×C₃×D₃	—	2	2	no	—
92	C₂²×C₃×D₃	—	2	2	no	—
93	C₂²×C₃×D₃	—	4	1	no	—
94	C₂²×C₃×D₃	—	4	1	no	—
95	C₂²×C₃×D₃	—	4	1	no	—
96	C₂²×C₃×D₃	—	4	1	no	—
97	C₂×C₃²×C₄	—	2	1	no	—
98	C₂×C₃²×C₄	—	2	1	no	—
99	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
100	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
101	C₂×C₃²×C₄	D₈	1	2	yes	—
102	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
103	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃²×C₄	#41	1	1	yes	characteristic
108	C₂×C₃²×C₄	#41	1	1	yes	characteristic
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	4	1	no	—
111	C₂×C₃×Dic₃	—	4	1	no	—
112	C₂×C₃×Dic₃	—	4	2	no	—
113	C₂×C₃×Dic₃	—	4	2	no	—
114	C₂×C₃×Dic₃	—	4	2	no	—
115	C₃×D₁₂	—	2	2	no	—
116	C₃×D₁₂	—	2	2	no	—
117	C₃×D₁₂	—	2	2	no	—
118	C₃×D₁₂	C₄⋊C₄	1	4	yes	complemented
119	C₃×C₄×D₃	—	4	8	no	—
120	C₃²×C₈	—	4	2	no	—
121	C₂×C₄×D₄	—	3	1	no	—
122	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
123	C₂×#102	—	3	2	no	—
124	#384	—	3	1	no	—
125	#340	—	3	2	no	—
126	C₂⁴×C₃	—	6	1	no	—
127	C₂³×D₃	—	2	1	no	—
128	C₂×C₃×D₄	—	3	2	no	—
129	C₂×C₃×D₄	—	3	2	no	—
130	C₂×C₃×D₄	—	3	2	no	—
131	C₂×C₃×D₄	—	6	1	no	—
132	C₂×C₃×D₄	—	6	1	no	—
133	C₂×C₃×D₄	—	6	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	6	1	no	—
138	C₂²×C₃×C₄	—	6	4	no	—
139	C₂²×C₃×C₄	—	6	2	no	—
140	C₂²×C₃×C₄	—	12	2	no	—
141	C₂²×C₃×C₄	—	12	2	no	—
142	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
143	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂²×Dic₃	—	2	1	no	—
149	C₂²×Dic₃	—	2	2	no	—
150	C₂×D₁₂	—	2	1	no	—
151	C₂×D₁₂	—	2	1	no	—
152	C₂×D₁₂	—	2	1	no	—
153	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
154	C₂×D₁₂	C₃×D₄	1	2	yes	—
155	C₂×D₁₂	C₃×Q₈	1	2	yes	—
156	C₂×C₄×D₃	—	2	4	no	—
157	C₂×C₄×D₃	—	4	2	no	—
158	C₂×C₄×D₃	—	4	2	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	4	2	no	—
167	C₂×C₃×C₈	—	4	2	no	—
168	C₃×C₄⋊C₄	—	3	2	no	—
169	C₃×C₄⋊C₄	—	6	1	no	—
170	C₃×C₄⋊C₄	—	6	2	no	—
171	C₃×C₄⋊C₄	—	6	2	no	—
172	C₃×C₄⋊C₄	—	12	2	no	—
173	C₃×C₄⋊C₄	—	12	2	no	—
174	C₃×C₂²⋊C₄	—	6	4	no	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	C₄×D₃	1	2	yes	—
178	C₃×C₄²	#67	1	2	yes	—
179	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
180	C₃×C₄²	C₃×D₄	1	2	yes	—
181	(C₂×D₃)⋊C₄	—	2	4	no	—
182	C₄⋊Dic₃	—	2	1	no	—
183	C₄⋊Dic₃	—	2	2	no	—
184	C₄⋊Dic₃	—	2	2	no	—
185	C₄⋊Dic₃	—	4	2	no	—
186	C₄⋊Dic₃	—	4	2	no	—
187	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
188	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₃²	#121	1	1	yes	characteristic
190	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
192	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
193	C₂²×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂²×C₃²	#137	1	1	yes	characteristic
195	C₂×C₃×D₃	—	2	4	no	—
196	C₂×C₃×D₃	—	4	2	no	—
197	C₂×C₃×D₃	—	4	2	no	—
198	C₂×C₃×D₃	—	4	2	no	—
199	C₂×C₃×D₃	—	4	2	no	—
200	C₂×C₃×D₃	—	4	2	no	—
201	C₂×C₃×D₃	—	4	2	no	—
202	C₃²×C₄	—	2	2	no	—
203	C₃²×C₄	#102	1	4	yes	complemented
204	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₃²×C₄	#117	1	1	yes	characteristic
206	C₃²×C₄	#121	1	1	yes	characteristic
207	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
208	C₃×Dic₃	—	4	2	no	—
209	C₃×Dic₃	—	8	2	no	—
210	C₂²×D₄	—	3	1	no	—
211	C₂³×C₄	—	6	1	no	—
212	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
213	C₄×D₄	—	3	4	no	—
214	C₄×D₄	—	6	2	no	—
215	C₂×C₄⋊C₄	—	3	1	no	—
216	C₂×C₄⋊C₄	—	3	2	no	—
217	C₂×C₄⋊C₄	—	6	1	no	—
218	C₂×C₄⋊C₄	—	6	1	no	—
219	C₂×C₂²⋊C₄	—	6	1	no	—
220	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	#102	—	6	4	no	—
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	—	6	2	no	—
225	C₂³×C₃	—	6	2	no	—
226	C₂³×C₃	—	6	2	no	—
227	C₂³×C₃	—	12	1	no	—
228	C₂³×C₃	—	12	1	no	—
229	C₂³×C₃	—	12	1	no	—
230	C₂³×C₃	—	12	1	no	—
231	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
232	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂²×D₃	—	2	2	no	—
234	C₂²×D₃	—	2	2	no	—
235	C₂²×D₃	—	2	2	no	—
236	C₂²×D₃	—	4	1	no	—
237	C₂²×D₃	—	4	1	no	—
238	C₂²×D₃	—	4	1	no	—
239	C₂²×D₃	—	4	1	no	—
240	C₃×D₄	—	3	4	no	—
241	C₃×D₄	—	6	2	no	—
242	C₃×D₄	—	6	2	no	—
243	C₃×D₄	—	6	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	6	2	no	—
261	C₂×C₃×C₄	—	12	1	no	—
262	C₂×C₃×C₄	—	12	1	no	—
263	C₂×C₃×C₄	—	12	8	no	—
264	C₂×C₃×C₄	—	12	2	no	—
265	C₂×C₃×C₄	—	12	2	no	—
266	C₂×C₃×C₄	—	12	2	no	—
267	C₂×C₃×C₄	#204	1	2	yes	—
268	C₂×C₃×C₄	D₂₄	1	2	yes	—
269	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
270	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
271	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
272	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
273	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
274	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	#237	1	1	yes	characteristic
278	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
279	C₂×C₃×C₄	#239	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
285	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
286	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	—	4	1	no	—
289	C₂×Dic₃	—	4	1	no	—
290	C₂×Dic₃	—	4	2	no	—
291	C₂×Dic₃	—	4	2	no	—
292	C₂×Dic₃	—	4	2	no	—
293	D₁₂	—	2	2	no	—
294	D₁₂	—	2	2	no	—
295	D₁₂	—	2	2	no	—
296	D₁₂	C₃×C₄⋊C₄	1	4	yes	complemented
297	C₄×D₃	—	4	8	no	—
298	C₃×C₈	—	4	4	no	—
299	C₃×C₈	—	4	2	no	—
300	C₃×C₈	—	4	2	no	—
301	C₂×C₃²	#380	1	1	yes	characteristic
302	C₂×C₃²	C₂×#102	1	1	yes	characteristic
303	C₂×C₃²	#417	1	1	yes	characteristic
304	C₂×C₃²	#459	1	1	yes	characteristic
305	C₂×C₃²	#461	1	1	yes	characteristic
306	C₂×C₃²	#474	1	1	yes	characteristic
307	C₂×C₃²	#476	1	1	yes	characteristic
308	C₃×D₃	—	4	4	no	—
309	C₂⁴	—	6	1	no	—
310	C₂×D₄	—	3	2	no	—
311	C₂×D₄	—	3	2	no	—
312	C₂×D₄	—	3	2	no	—
313	C₂×D₄	—	6	1	no	—
314	C₂×D₄	—	6	1	no	—
315	C₂×D₄	—	6	1	no	—
316	C₂²×C₄	—	6	1	no	—
317	C₂²×C₄	—	6	4	no	—
318	C₂²×C₄	—	6	2	no	—
319	C₂²×C₄	—	12	2	no	—
320	C₂²×C₄	—	12	2	no	—
321	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
322	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₄⋊C₄	—	3	2	no	—
328	C₄⋊C₄	—	6	1	no	—
329	C₄⋊C₄	—	6	2	no	—
330	C₄⋊C₄	—	6	2	no	—
331	C₄⋊C₄	—	12	2	no	—
332	C₄⋊C₄	—	12	2	no	—
333	C₂²⋊C₄	—	6	4	no	—
334	C₄²	C₃×C₄×D₃	1	2	yes	—
335	C₄²	C₃×#67	1	2	yes	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	2	1	no	—
341	C₂²×C₃	—	2	1	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	6	4	no	—
344	C₂²×C₃	—	12	2	no	—
345	C₂²×C₃	—	12	2	no	—
346	C₂²×C₃	—	12	2	no	—
347	C₂²×C₃	—	12	2	no	—
348	C₂²×C₃	—	12	2	no	—
349	C₂²×C₃	—	12	2	no	—
350	C₂²×C₃	#895	1	1	yes	characteristic
351	C₂²×C₃	#897	1	1	yes	characteristic
352	C₂²×C₃	C₂×#204	1	1	yes	characteristic
353	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
354	C₂²×C₃	#908	1	1	yes	characteristic
355	C₂²×C₃	#909	1	1	yes	characteristic
356	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	C₃×#121	1	1	yes	characteristic
359	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
360	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
361	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
362	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₂²×C₃	C₃×#137	1	1	yes	characteristic
364	C₂×D₃	—	2	4	no	—
365	C₂×D₃	—	4	2	no	—
366	C₂×D₃	—	4	2	no	—
367	C₂×D₃	—	4	2	no	—
368	C₂×D₃	—	4	2	no	—
369	C₂×D₃	—	4	2	no	—
370	C₂×D₃	—	4	2	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	4	2	no	—
379	C₃×C₄	—	12	2	no	—
380	C₃×C₄	—	24	2	no	—
381	C₃×C₄	#821	1	4	yes	complemented
382	C₃×C₄	C₃×#102	1	4	yes	complemented
383	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
384	C₃×C₄	#892	1	1	yes	characteristic
385	C₃×C₄	#938	1	1	yes	characteristic
386	C₃×C₄	#946	1	1	yes	characteristic
387	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
388	C₃×C₄	C₃×#117	1	1	yes	characteristic
389	C₃×C₄	C₃×#121	1	1	yes	characteristic
390	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
391	Dic₃	—	4	2	no	—
392	Dic₃	—	8	2	no	—
393	C₃²	#1802	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	6	2	no	—
395	C₂³	—	6	2	no	—
396	C₂³	—	6	2	no	—
397	C₂³	—	12	1	no	—
398	C₂³	—	12	1	no	—
399	C₂³	—	12	1	no	—
400	C₂³	—	12	1	no	—
401	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
402	D₄	—	3	4	no	—
403	D₄	—	6	2	no	—
404	D₄	—	6	2	no	—
405	D₄	—	6	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	12	1	no	—
410	C₂×C₄	—	12	1	no	—
411	C₂×C₄	—	12	8	no	—
412	C₂×C₄	—	12	2	no	—
413	C₂×C₄	—	12	2	no	—
414	C₂×C₄	—	12	2	no	—
415	C₂×C₄	C₃×#204	1	2	yes	—
416	C₂×C₄	C₃×D₂₄	1	2	yes	—
417	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
418	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
419	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
420	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
421	C₂×C₄	C₃×#237	1	1	yes	characteristic
422	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
423	C₂×C₄	C₃×#239	1	1	yes	characteristic
424	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
425	C₈	—	4	2	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	12	4	no	—
434	C₂×C₃	#4841	1	1	yes	characteristic
435	C₂×C₃	#4842	1	1	yes	characteristic
436	C₂×C₃	#4843	1	1	yes	characteristic
437	C₂×C₃	#4846	1	1	yes	characteristic
438	C₂×C₃	#4987	1	1	yes	characteristic
439	C₂×C₃	C₂×#821	1	1	yes	characteristic
440	C₂×C₃	#5133	1	1	yes	characteristic
441	C₂×C₃	C₃×#380	1	1	yes	characteristic
442	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
443	C₂×C₃	C₃×#417	1	1	yes	characteristic
444	C₂×C₃	C₃×#459	1	1	yes	characteristic
445	C₂×C₃	C₃×#461	1	1	yes	characteristic
446	C₂×C₃	C₃×#474	1	1	yes	characteristic
447	C₂×C₃	C₃×#476	1	1	yes	characteristic
448	D₃	—	4	4	no	—
449	C₂²	—	6	4	no	—
450	C₂²	—	12	2	no	—
451	C₂²	—	12	2	no	—
452	C₂²	—	12	2	no	—
453	C₂²	—	12	2	no	—
454	C₂²	—	12	2	no	—
455	C₂²	—	12	2	no	—
456	C₂²	C₃×#895	1	1	yes	characteristic
457	C₂²	C₃×#897	1	1	yes	characteristic
458	C₂²	C₂×C₃×#204	1	1	yes	characteristic
459	C₂²	C₂×C₃×D₂₄	1	1	yes	characteristic
460	C₂²	C₃×#908	1	1	yes	characteristic
461	C₂²	C₃×#909	1	1	yes	characteristic
462	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	12	2	no	—
465	C₄	—	24	2	no	—
466	C₄	C₃×#821	1	4	yes	complemented
467	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
468	C₄	C₃×#892	1	1	yes	characteristic
469	C₄	C₃×#938	1	1	yes	characteristic
470	C₄	C₃×#946	1	1	yes	characteristic
471	C₃	—	2	1	no	—
472	C₃	#70479	1	1	yes	characteristic, direct product factor
473	C₃	C₃×#1802	1	1	yes	characteristic, complemented
474	C₂	—	12	4	no	—
475	C₂	C₃×#4841	1	1	yes	characteristic
476	C₂	C₃×#4842	1	1	yes	characteristic
477	C₂	C₃×#4843	1	1	yes	characteristic
478	C₂	C₃×#4846	1	1	yes	characteristic
479	C₂	C₃×#4987	1	1	yes	characteristic
480	C₂	C₂×C₃×#821	1	1	yes	characteristic
481	C₂	C₃×#5133	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄⋊C₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₃×#1802
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄⋊C₈	C₂	semidirect
4. C₃×#4935	C₂	semidirect
5. C₃×#4551	C₂	semidirect
7. #70479	C₃	direct (N × H)
18. C₃×C₄×D₁₂	C₄	semidirect
24. C₂×C₃×C₄⋊C₈	D₃	semidirect
25. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
29. #4935	C₂×C₃	semidirect
31. #4551	C₂×C₃	semidirect
83. C₄×D₁₂	C₃×C₄	semidirect
118. C₃×D₁₂	C₄⋊C₄	semidirect
122. C₂×C₄⋊C₈	C₃×D₃	semidirect
203. C₃²×C₄	#102	semidirect
296. D₁₂	C₃×C₄⋊C₄	semidirect
381. C₃×C₄	#821	semidirect
382. C₃×C₄	C₃×#102	semidirect
393. C₃²	#1802	semidirect
466. C₄	C₃×#821	semidirect
472. C₃	#70479	direct (N × H)
473. C₃	C₃×#1802	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄×D₁₂	2
C₂×C₃²×C₄⋊C₈	2
C₂×C₃×#821	2
C₃×#4935	2
C₃×#4551	2
C₃×#1802	3
#70479	3

Subgroups — C3×#70479 #11785174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70479 #11785174