Subgroups — C₃×#78572 #11860736

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#204	C₂	1	1	yes	maximal, characteristic
2	C₃×#5521	C₂	1	1	yes	maximal, characteristic
3	C₃×#5516	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5131	C₂	1	1	yes	maximal, characteristic
6	C₃×#5120	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4710	C₂	1	4	yes	maximal, complemented
9	C₃×C₄×#204	C₂	1	4	yes	maximal, complemented
10	C₃×#2949	—	3	1	no	maximal
11	#78572	C₃	1	1	yes	maximal, characteristic, direct product factor
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	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃²×#117	C₂²	1	1	yes	characteristic
17	C₃×#926	C₂²	1	1	yes	characteristic
18	C₃×#926	C₂²	1	1	yes	characteristic
19	C₂×C₃×#204	C₄	1	8	yes	complemented
20	C₂×C₃×#204	C₂²	1	2	yes	—
21	C₂×C₃×#204	C₂²	1	2	yes	—
22	C₃×#893	—	2	2	no	—
23	C₃×#887	—	2	2	no	—
24	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
25	C₃×#877	—	2	2	no	—
26	C₃×C₄×D₁₂	C₂²	1	4	yes	—
27	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
28	C₃²×#97	C₂²	1	2	yes	complemented
29	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
30	C₃×#821	C₂²	1	4	yes	—
31	C₃×#818	C₂²	1	2	yes	complemented
32	C₃×#817	C₂²	1	2	yes	complemented
33	C₃×#816	C₂²	1	4	yes	complemented
34	C₂²×C₃×SD₁₆	—	3	1	no	—
35	C₃×#519	—	3	1	no	—
36	C₃×#518	—	3	1	no	—
37	C₂²×#204	C₂×C₃	1	1	yes	characteristic
38	#5521	C₂×C₃	1	1	yes	characteristic
39	#5516	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×#440	—	3	4	no	—
41	C₃×C₄×SD₁₆	—	3	4	no	—
42	C₃×#427	—	3	1	no	—
43	C₃×#419	—	3	1	no	—
44	C₃×#418	—	3	1	no	—
45	C₃×#405	—	2	1	no	—
46	C₃×#405	D₃	1	1	yes	characteristic, complemented
47	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
48	#5131	C₂×C₃	1	1	yes	characteristic
49	#5120	C₂×C₃	1	1	yes	characteristic, complemented
50	#5106	C₂×C₃	1	1	yes	characteristic, complemented
51	#4710	C₂×C₃	1	4	yes	complemented
52	C₄×#204	C₂×C₃	1	4	yes	complemented
53	C₂³×C₃×D₃	—	2	1	no	—
54	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
55	C₂²×C₃×Dic₃	—	2	1	no	—
56	C₂×C₃×D₁₂	—	2	1	no	—
57	C₂×C₃×D₁₂	—	2	2	no	—
58	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
59	C₂×C₃×D₁₂	C₂³	1	2	yes	—
60	C₂×C₃×C₄×D₃	—	2	4	no	—
61	C₂×C₃×Dic₆	—	2	1	no	—
62	C₂×C₃×Dic₆	—	2	2	no	—
63	C₂×C₃×Dic₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×Dic₆	C₂³	1	2	yes	—
65	C₃²×M₁₆	—	2	2	no	—
66	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
67	C₂×C₃²×C₈	C₂³	1	2	yes	—
68	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
70	C₃²×C₄⋊C₄	D₄	1	2	yes	—
71	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
72	C₃²×C₄²	C₂³	1	2	yes	—
73	C₃×#217	—	2	1	no	—
74	C₃×#217	—	2	1	no	—
75	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
76	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
77	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
78	C₃×Dic₃⋊C₄	—	2	4	no	—
79	C₃×C₄×Dic₃	—	2	4	no	—
80	C₃×C₄×Dic₃	—	2	1	no	—
81	C₃×C₄×Dic₃	—	2	1	no	—
82	C₃×#204	C₂×C₄	1	8	yes	complemented
83	C₃×#204	C₂×C₄	1	8	yes	complemented
84	#2949	—	3	1	no	Sylow
85	C₂²×C₃×Q₈	—	3	1	no	—
86	C₂²×C₃×D₄	—	3	1	no	—
87	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
88	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×SD₁₆	—	3	8	no	—
90	C₂×C₃×SD₁₆	—	3	2	no	—
91	C₂×C₃×SD₁₆	—	3	2	no	—
92	C₂×C₃×M₁₆	—	2	1	no	—
93	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
94	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃×C₈	—	2	1	no	—
96	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
97	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄×Q₈	—	3	4	no	—
99	C₃×C₄×Q₈	—	6	2	no	—
100	C₃×C₄×D₄	—	3	4	no	—
101	C₃×C₄×D₄	—	6	2	no	—
102	C₃×#117	—	2	1	no	—
103	C₃×#117	—	3	1	no	—
104	C₃×#117	—	3	1	no	—
105	C₃×#117	—	6	2	no	—
106	C₃×#117	C₂×D₃	1	1	yes	characteristic
107	C₃×#117	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
109	#926	C₂²×C₃	1	1	yes	characteristic
110	#926	C₂²×C₃	1	1	yes	characteristic
111	C₂×#204	C₃×C₄	1	8	yes	complemented
112	C₂×#204	C₂²×C₃	1	2	yes	—
113	C₂×#204	C₂²×C₃	1	2	yes	—
114	#893	—	2	2	no	—
115	#887	—	2	2	no	—
116	D₃×C₂²⋊C₄	—	2	2	no	—
117	#877	—	2	2	no	—
118	C₄×D₁₂	C₂²×C₃	1	4	yes	—
119	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
120	C₃×#107	—	3	2	no	—
121	C₃×#106	—	3	2	no	—
122	C₃×#103	—	3	4	no	—
123	C₃×#102	—	3	4	no	—
124	C₃×#97	—	2	2	no	—
125	C₃×#97	C₂×D₃	1	2	yes	complemented
126	C₃×#97	C₂²×C₃	1	2	yes	complemented
127	C₃×C₄×C₈	—	2	2	no	—
128	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
129	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
130	#821	C₂²×C₃	1	4	yes	—
131	#818	C₂²×C₃	1	2	yes	complemented
132	#817	C₂²×C₃	1	2	yes	complemented
133	#816	C₂²×C₃	1	4	yes	complemented
134	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₃×D₃	—	2	2	no	—
136	C₂²×C₃×D₃	—	2	4	no	—
137	C₂²×C₃×D₃	—	8	2	no	—
138	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
139	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
140	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	#41	1	2	yes	—
142	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
143	C₂×C₃×Dic₃	—	2	4	no	—
144	C₂×C₃×Dic₃	—	2	2	no	—
145	C₂×C₃×Dic₃	—	2	2	no	—
146	C₂×C₃×Dic₃	—	2	2	no	—
147	C₃×D₁₂	—	2	4	no	—
148	C₃×D₁₂	—	2	2	no	—
149	C₃×D₁₂	C₂²×C₄	1	4	yes	—
150	C₃×C₄×D₃	—	8	4	no	—
151	C₃×Dic₆	—	2	4	no	—
152	C₃×Dic₆	—	2	2	no	—
153	C₃×Dic₆	C₂²×C₄	1	4	yes	—
154	C₃²×C₈	—	2	2	no	—
155	C₃²×C₈	C₂²×C₄	1	2	yes	—
156	C₃²×C₈	C₂²×C₄	1	2	yes	—
157	C₂²×SD₁₆	—	3	1	no	—
158	#519	—	3	1	no	—
159	#518	—	3	1	no	—
160	#440	—	3	4	no	—
161	C₄×SD₁₆	—	3	4	no	—
162	#427	—	3	1	no	—
163	#419	—	3	1	no	—
164	#418	—	3	1	no	—
165	#405	C₃×D₃	1	1	yes	characteristic, complemented
166	C₂⁴×C₃	—	6	1	no	—
167	C₂³×D₃	—	2	1	no	—
168	C₂×C₃×Q₈	—	3	4	no	—
169	C₂×C₃×Q₈	—	3	2	no	—
170	C₂×C₃×Q₈	—	6	1	no	—
171	C₂×C₃×Q₈	—	6	2	no	—
172	C₂×C₃×D₄	—	3	4	no	—
173	C₂×C₃×D₄	—	3	2	no	—
174	C₂×C₃×D₄	—	6	1	no	—
175	C₂×C₃×D₄	—	6	2	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	6	1	no	—
178	C₂²×C₃×C₄	—	6	4	no	—
179	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×Dic₃	—	2	1	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	2	no	—
184	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
185	C₂×D₁₂	C₂³×C₃	1	2	yes	—
186	C₂×C₄×D₃	—	2	4	no	—
187	C₂×Dic₆	—	2	1	no	—
188	C₂×Dic₆	—	2	2	no	—
189	C₂×Dic₆	C₂×C₃×C₄	1	4	yes	complemented
190	C₂×Dic₆	C₂³×C₃	1	2	yes	—
191	C₃×SD₁₆	—	3	8	no	—
192	C₃×SD₁₆	—	3	8	no	—
193	C₃×M₁₆	—	2	4	no	—
194	C₃×M₁₆	—	2	2	no	—
195	C₃×M₁₆	—	2	2	no	—
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	—	2	1	no	—
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
201	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
202	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
203	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
206	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	3	2	no	—
210	C₃×C₄⋊C₄	—	3	2	no	—
211	C₃×C₄⋊C₄	—	6	4	no	—
212	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
213	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
214	C₃×C₂²⋊C₄	—	2	2	no	—
215	C₃×C₂²⋊C₄	—	6	1	no	—
216	C₃×C₂²⋊C₄	—	6	1	no	—
217	C₃×C₂²⋊C₄	—	6	4	no	—
218	C₃×C₂²⋊C₄	D₁₂	1	2	yes	—
219	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
220	C₃×C₄²	—	2	2	no	—
221	C₃×C₄²	—	6	1	no	—
222	C₃×C₄²	—	6	1	no	—
223	C₃×C₄²	—	6	4	no	—
224	C₃×C₄²	C₂²×D₃	1	2	yes	—
225	C₃×C₄²	C₂³×C₃	1	2	yes	—
226	#217	—	2	1	no	—
227	#217	—	2	1	no	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
230	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
231	Dic₃⋊C₄	—	2	4	no	—
232	C₄×Dic₃	—	2	4	no	—
233	C₄×Dic₃	—	2	1	no	—
234	C₄×Dic₃	—	2	1	no	—
235	#204	C₂×C₃×C₄	1	8	yes	complemented
236	#204	C₂×C₃×C₄	1	8	yes	complemented
237	C₂²×C₃²	—	2	2	no	—
238	C₂²×C₃²	C₄×D₄	1	2	yes	—
239	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₃×D₃	—	2	4	no	—
241	C₂×C₃×D₃	—	4	4	no	—
242	C₂×C₃×D₃	—	8	4	no	—
243	C₃²×C₄	—	2	4	no	—
244	C₃²×C₄	C₄×D₄	1	2	yes	—
245	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
246	C₃²×C₄	C₂×#41	1	1	yes	characteristic
247	C₃×Dic₃	—	2	4	no	—
248	C₃×Dic₃	—	4	2	no	—
249	C₃×Dic₃	—	4	2	no	—
250	C₂²×Q₈	—	3	1	no	—
251	C₂²×D₄	—	3	1	no	—
252	C₂×SD₁₆	—	3	8	no	—
253	C₂×SD₁₆	—	3	2	no	—
254	C₂×SD₁₆	—	3	2	no	—
255	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
256	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
257	C₄×Q₈	—	3	4	no	—
258	C₄×Q₈	—	6	2	no	—
259	C₄×D₄	—	3	4	no	—
260	C₄×D₄	—	6	2	no	—
261	#117	—	3	1	no	—
262	#117	—	3	1	no	—
263	#117	—	6	2	no	—
264	#117	C₂×C₃×D₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	6	2	no	—
266	#107	—	3	2	no	—
267	#106	—	3	2	no	—
268	#103	—	3	4	no	—
269	#102	—	3	4	no	—
270	#97	C₂×C₃×D₃	1	2	yes	complemented
271	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	6	2	no	—
274	C₂³×C₃	—	6	4	no	—
275	C₂³×C₃	—	24	2	no	—
276	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
277	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂²×D₃	—	2	2	no	—
279	C₂²×D₃	—	2	4	no	—
280	C₂²×D₃	—	8	2	no	—
281	C₃×Q₈	—	3	4	no	—
282	C₃×Q₈	—	6	4	no	—
283	C₃×Q₈	—	6	2	no	—
284	C₃×D₄	—	3	4	no	—
285	C₃×D₄	—	6	4	no	—
286	C₃×D₄	—	6	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	6	4	no	—
293	C₂×C₃×C₄	—	6	2	no	—
294	C₂×C₃×C₄	—	6	2	no	—
295	C₂×C₃×C₄	—	6	2	no	—
296	C₂×C₃×C₄	—	24	4	no	—
297	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
298	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
299	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
300	C₂×C₃×C₄	#235	1	2	yes	—
301	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
303	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₃×#41	1	2	yes	—
305	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
307	C₂×Dic₃	—	2	4	no	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	2	no	—
311	D₁₂	—	2	4	no	—
312	D₁₂	—	2	2	no	—
313	D₁₂	C₂²×C₃×C₄	1	4	yes	—
314	C₄×D₃	—	8	4	no	—
315	Dic₆	—	2	4	no	—
316	Dic₆	—	2	2	no	—
317	Dic₆	C₂²×C₃×C₄	1	4	yes	—
318	C₃×C₈	—	2	4	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	2	2	no	—
322	C₃×C₈	—	2	2	no	—
323	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
324	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
325	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
326	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
327	C₂×C₃²	—	2	2	no	—
328	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂×C₃²	#577	1	2	yes	—
330	C₃×D₃	—	4	4	no	—
331	C₂⁴	—	6	1	no	—
332	C₂×Q₈	—	3	2	no	—
333	C₂×Q₈	—	3	4	no	—
334	C₂×Q₈	—	6	1	no	—
335	C₂×Q₈	—	6	2	no	—
336	C₂×D₄	—	3	2	no	—
337	C₂×D₄	—	3	4	no	—
338	C₂×D₄	—	6	1	no	—
339	C₂×D₄	—	6	2	no	—
340	C₂²×C₄	—	6	1	no	—
341	C₂²×C₄	—	6	4	no	—
342	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
343	SD₁₆	—	3	8	no	—
344	SD₁₆	—	3	8	no	—
345	M₁₆	—	2	2	no	—
346	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
347	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
348	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
349	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₄⋊C₄	—	3	2	no	—
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	6	4	no	—
353	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
354	C₂²⋊C₄	—	6	1	no	—
355	C₂²⋊C₄	—	6	1	no	—
356	C₂²⋊C₄	—	6	4	no	—
357	C₂²⋊C₄	C₃×D₁₂	1	2	yes	—
358	C₄²	—	6	1	no	—
359	C₄²	—	6	1	no	—
360	C₄²	—	6	4	no	—
361	C₄²	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	2	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	6	4	no	—
368	C₂²×C₃	—	12	4	no	—
369	C₂²×C₃	—	24	4	no	—
370	C₂²×C₃	C₄×D₁₂	1	2	yes	—
371	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
372	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
373	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
374	C₂×D₃	—	2	4	no	—
375	C₂×D₃	—	4	4	no	—
376	C₂×D₃	—	8	4	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	4	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	4	4	no	—
383	C₃×C₄	—	6	4	no	—
384	C₃×C₄	—	12	2	no	—
385	C₃×C₄	—	12	2	no	—
386	C₃×C₄	C₄×D₁₂	1	2	yes	—
387	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
388	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
389	C₃×C₄	C₂×#235	1	1	yes	characteristic
390	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
391	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
392	Dic₃	—	2	4	no	—
393	Dic₃	—	4	2	no	—
394	Dic₃	—	4	2	no	—
395	C₃²	#2949	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	6	2	no	—
397	C₂³	—	6	4	no	—
398	C₂³	—	24	2	no	—
399	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
400	Q₈	—	3	4	no	—
401	Q₈	—	6	2	no	—
402	Q₈	—	6	4	no	—
403	D₄	—	3	4	no	—
404	D₄	—	6	2	no	—
405	D₄	—	6	4	no	—
406	C₂×C₄	—	6	2	no	—
407	C₂×C₄	—	6	4	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	24	4	no	—
411	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
412	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
413	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
414	C₂×C₄	C₃×#235	1	2	yes	—
415	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
418	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	2	2	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	4	2	no	—
424	C₂×C₃	—	12	4	no	—
425	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
426	C₂×C₃	#5751	1	2	yes	—
427	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
428	C₂×C₃	C₃×#577	1	2	yes	—
429	D₃	—	4	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	6	4	no	—
432	C₂²	—	12	4	no	—
433	C₂²	—	24	4	no	—
434	C₂²	C₃×C₄×D₁₂	1	2	yes	—
435	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	6	4	no	—
438	C₄	—	12	2	no	—
439	C₄	—	12	2	no	—
440	C₄	C₃×C₄×D₁₂	1	2	yes	—
441	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
442	C₄	C₂×C₃×#235	1	1	yes	characteristic
443	C₃	—	2	1	no	—
444	C₃	#78572	1	1	yes	characteristic, direct product factor
445	C₃	C₃×#2949	1	1	yes	characteristic, complemented
446	C₂	—	2	2	no	—
447	C₂	—	12	4	no	—
448	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
449	C₂	C₃×#5751	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2949
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
3. C₃×#5516	C₂	semidirect
4. C₃²×#405	C₂	semidirect
6. C₃×#5120	C₂	semidirect
7. C₃×#5106	C₂	semidirect
8. C₃×#4710	C₂	semidirect
9. C₃×C₄×#204	C₂	semidirect
11. #78572	C₃	direct (N × H)
19. C₂×C₃×#204	C₄	semidirect
27. C₃×C₄×Dic₆	C₂²	semidirect
28. C₃²×#97	C₂²	semidirect
29. C₃²×C₄×C₈	C₂²	semidirect
31. C₃×#818	C₂²	semidirect
32. C₃×#817	C₂²	semidirect
33. C₃×#816	C₂²	semidirect
39. #5516	C₂×C₃	semidirect
46. C₃×#405	D₃	semidirect
47. C₃×#405	C₂×C₃	semidirect
49. #5120	C₂×C₃	semidirect
50. #5106	C₂×C₃	semidirect
51. #4710	C₂×C₃	semidirect
52. C₄×#204	C₂×C₃	semidirect
63. C₂×C₃×Dic₆	C₂×C₄	semidirect
66. C₂×C₃²×C₈	C₂×C₄	semidirect
82. C₃×#204	C₂×C₄	semidirect
83. C₃×#204	C₂×C₄	semidirect
111. C₂×#204	C₃×C₄	semidirect
119. C₄×Dic₆	C₂²×C₃	semidirect
125. C₃×#97	C₂×D₃	semidirect
126. C₃×#97	C₂²×C₃	semidirect
128. C₃×C₄×C₈	C₂×D₃	semidirect
129. C₃×C₄×C₈	C₂²×C₃	semidirect
131. #818	C₂²×C₃	semidirect
132. #817	C₂²×C₃	semidirect
133. #816	C₂²×C₃	semidirect
165. #405	C₃×D₃	semidirect
189. C₂×Dic₆	C₂×C₃×C₄	semidirect
200. C₂×C₃×C₈	C₄×D₃	semidirect
201. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
235. #204	C₂×C₃×C₄	semidirect
236. #204	C₂×C₃×C₄	semidirect
270. #97	C₂×C₃×D₃	semidirect
271. C₄×C₈	C₂×C₃×D₃	semidirect
346. C₂×C₈	C₃×C₄×D₃	semidirect
395. C₃²	#2949	semidirect
444. C₃	#78572	direct (N × H)
445. C₃	C₃×#2949	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×#204	2
C₃×#5521	2
C₃×#5516	2
C₃²×#405	2
C₃×#5131	2
C₃×#5120	2
C₃×#5106	2
C₃×#4710	2
C₃×C₄×#204	2
C₃×#2949	3
#78572	3

Subgroups — C3×#78572 #11860736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78572 #11860736