Subgroups — C₃×#78562 #11860866

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₃×#5523	C₂	1	2	yes	maximal, complemented
3	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5133	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4710	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×Dic₁₂	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₂₄	C₂	1	2	yes	maximal, complemented
9	C₃×#2951	—	3	1	no	maximal
10	#78562	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	2	yes	—
12	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃²×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
17	C₃×#904	C₄	1	8	yes	complemented
18	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×#204	C₂²	1	2	yes	—
20	C₃×#892	—	2	2	no	—
21	C₃×D₃×C₄⋊C₄	—	2	2	no	—
22	C₃×#67⋊C₄	—	2	4	no	—
23	C₃×C₄×D₁₂	C₂²	1	4	yes	—
24	C₃×C₄×Dic₆	C₂²	1	4	yes	—
25	C₃²×#97	C₂²	1	2	yes	—
26	C₃²×C₄×C₈	C₂²	1	2	yes	—
27	C₃×#821	C₂²	1	4	yes	—
28	C₃×#818	C₂²	1	2	yes	—
29	C₃×#818	C₂²	1	2	yes	—
30	C₃×#816	C₂²	1	4	yes	—
31	C₂×C₃×#135	—	3	1	no	—
32	C₃×#520	—	3	2	no	—
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	#5523	C₂×C₃	1	2	yes	complemented
35	C₃×#440	—	3	4	no	—
36	C₃×C₄×Q₁₆	—	3	2	no	—
37	C₃×C₄×D₈	—	3	2	no	—
38	C₂×C₃×#107	—	3	1	no	—
39	C₃×#417	—	3	2	no	—
40	C₃×#405	—	2	1	no	—
41	C₃×#405	D₃	1	1	yes	characteristic, complemented
42	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
43	#5133	C₂×C₃	1	2	yes	complemented
44	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
45	#4710	C₂×C₃	1	4	yes	complemented
46	C₄×Dic₁₂	C₂×C₃	1	2	yes	complemented
47	C₄×D₂₄	C₂×C₃	1	2	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	2	no	—
50	C₂²×C₃×Dic₃	—	2	2	no	—
51	C₃×#235	—	2	4	no	—
52	C₃×#235	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×D₁₂	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₃	—	2	2	no	—
55	C₂×C₃×C₄×D₃	—	2	4	no	—
56	C₂×C₃×Dic₆	C₂³	1	2	yes	—
57	C₃²×M₁₆	—	2	2	no	—
58	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
59	C₂×C₃²×C₈	C₂³	1	2	yes	—
60	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
62	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
65	C₃²×C₄²	C₂³	1	2	yes	—
66	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
67	C₃×C₄⋊Dic₃	—	2	2	no	—
68	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
69	C₃×Dic₃⋊C₄	—	2	4	no	—
70	C₃×C₄×Dic₃	—	2	4	no	—
71	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
72	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
73	C₃×#204	C₂×C₄	1	8	yes	complemented
74	#2951	—	3	1	no	Sylow
75	C₂×C₃×#41	—	3	2	no	—
76	C₂×#235	C₂²×C₃	1	2	yes	—
77	C₃×#135	—	3	8	no	—
78	C₂×C₃×Q₁₆	—	3	1	no	—
79	C₂×C₃×SD₁₆	—	3	2	no	—
80	C₂×C₃×D₈	—	3	1	no	—
81	C₂×C₃×M₁₆	—	2	1	no	—
82	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	—	2	1	no	—
85	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
87	C₃×C₄×Q₈	—	3	4	no	—
88	C₃×C₄×D₄	—	3	4	no	—
89	C₃×C₄×D₄	—	6	4	no	—
90	C₃×#117	—	2	1	no	—
91	C₃×#117	—	6	2	no	—
92	C₃×#117	C₂×D₃	1	1	yes	characteristic
93	C₃×#117	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	—	3	2	no	—
95	C₂×C₃×C₄⋊C₄	—	6	2	no	—
96	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
97	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
98	#904	C₃×C₄	1	8	yes	complemented
99	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×#204	C₂²×C₃	1	2	yes	—
101	#892	—	2	2	no	—
102	D₃×C₄⋊C₄	—	2	2	no	—
103	#67⋊C₄	—	2	4	no	—
104	C₄×D₁₂	C₂²×C₃	1	4	yes	—
105	C₄×Dic₆	C₂²×C₃	1	4	yes	—
106	C₃×#107	—	3	2	no	—
107	C₃×#107	—	3	2	no	—
108	C₃×#103	—	3	4	no	—
109	C₃×#102	—	3	4	no	—
110	C₃×#97	—	2	2	no	—
111	C₃×#97	C₂×D₃	1	2	yes	—
112	C₃×#97	C₂²×C₃	1	2	yes	—
113	C₃×C₄×C₈	—	2	2	no	—
114	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
115	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
116	#821	C₂²×C₃	1	4	yes	—
117	#818	C₂²×C₃	1	2	yes	—
118	#818	C₂²×C₃	1	2	yes	—
119	#816	C₂²×C₃	1	4	yes	—
120	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	2	2	no	—
122	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
123	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
124	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
125	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	#41	1	2	yes	—
127	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
128	C₃×#67	—	2	8	no	—
129	C₂×C₃×Dic₃	—	2	2	no	—
130	C₂×C₃×Dic₃	—	2	4	no	—
131	C₂×C₃×Dic₃	—	8	2	no	—
132	C₃×D₁₂	—	2	2	no	—
133	C₃×D₁₂	C₂²×C₄	1	4	yes	—
134	C₃×C₄×D₃	—	2	8	no	—
135	C₃×C₄×D₃	—	8	4	no	—
136	C₃×Dic₆	—	2	2	no	—
137	C₃×Dic₆	C₂²×C₄	1	4	yes	—
138	C₃²×C₈	—	2	2	no	—
139	C₃²×C₈	C₂²×C₄	1	2	yes	—
140	C₃²×C₈	C₂²×C₄	1	2	yes	—
141	C₂×#135	—	3	1	no	—
142	#520	—	3	2	no	—
143	#440	—	3	4	no	—
144	C₄×Q₁₆	—	3	2	no	—
145	C₄×D₈	—	3	2	no	—
146	C₂×#107	—	3	1	no	—
147	#417	—	3	2	no	—
148	#405	C₃×D₃	1	1	yes	characteristic, complemented
149	C₃×#41	—	3	8	no	—
150	C₃×#41	—	6	4	no	—
151	C₂×C₃×Q₈	—	3	2	no	—
152	C₂×C₃×D₄	—	3	2	no	—
153	C₂×C₃×D₄	—	6	2	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	6	2	no	—
156	C₂²×C₃×C₄	—	6	2	no	—
157	C₂²×C₃×C₄	—	6	4	no	—
158	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂×#67	—	2	2	no	—
161	C₂²×Dic₃	—	2	2	no	—
162	#235	—	2	4	no	—
163	#235	C₂×C₃×C₄	1	8	yes	complemented
164	C₂×D₁₂	C₂³×C₃	1	2	yes	—
165	C₂×C₄×D₃	—	2	2	no	—
166	C₂×C₄×D₃	—	2	4	no	—
167	C₂×Dic₆	C₂³×C₃	1	2	yes	—
168	C₃×Q₁₆	—	3	4	no	—
169	C₃×SD₁₆	—	3	8	no	—
170	C₃×D₈	—	3	4	no	—
171	C₃×M₁₆	—	2	4	no	—
172	C₃×M₁₆	—	2	2	no	—
173	C₃×M₁₆	—	2	2	no	—
174	C₂×C₃×C₈	—	2	4	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
179	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
180	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
181	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
183	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
184	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	3	4	no	—
189	C₃×C₄⋊C₄	—	6	4	no	—
190	C₃×C₄⋊C₄	—	6	2	no	—
191	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
192	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
195	C₃×C₂²⋊C₄	—	2	2	no	—
196	C₃×C₂²⋊C₄	—	6	4	no	—
197	C₃×C₂²⋊C₄	D₁₂	1	2	yes	—
198	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
199	C₃×C₄²	—	2	2	no	—
200	C₃×C₄²	—	6	4	no	—
201	C₃×C₄²	C₂²×D₃	1	2	yes	—
202	C₃×C₄²	C₂³×C₃	1	2	yes	—
203	(C₂×D₃)⋊C₄	—	2	4	no	—
204	C₄⋊Dic₃	—	2	2	no	—
205	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
206	Dic₃⋊C₄	—	2	4	no	—
207	C₄×Dic₃	—	2	4	no	—
208	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
209	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
210	#204	C₂×C₃×C₄	1	8	yes	complemented
211	C₂²×C₃²	—	2	1	no	—
212	C₂²×C₃²	—	2	1	no	—
213	C₂²×C₃²	C₄×D₄	1	2	yes	—
214	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₃×D₃	—	2	4	no	—
216	C₂×C₃×D₃	—	4	2	no	—
217	C₂×C₃×D₃	—	4	2	no	—
218	C₃²×C₄	—	2	2	no	—
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	C₄×D₄	1	2	yes	—
221	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
222	C₃²×C₄	C₂×#41	1	1	yes	characteristic
223	C₃×Dic₃	—	2	4	no	—
224	C₃×Dic₃	—	4	4	no	—
225	C₂×#41	—	3	2	no	—
226	#135	—	3	8	no	—
227	C₂×Q₁₆	—	3	1	no	—
228	C₂×SD₁₆	—	3	2	no	—
229	C₂×D₈	—	3	1	no	—
230	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
231	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
232	C₄×Q₈	—	3	4	no	—
233	C₄×D₄	—	3	4	no	—
234	C₄×D₄	—	6	4	no	—
235	#117	—	6	2	no	—
236	#117	C₂×C₃×D₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	—	3	2	no	—
238	C₂×C₄⋊C₄	—	6	2	no	—
239	#107	—	3	2	no	—
240	#107	—	3	2	no	—
241	#103	—	3	4	no	—
242	#102	—	3	4	no	—
243	#97	C₂×C₃×D₃	1	2	yes	—
244	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	6	2	no	—
247	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
248	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂²×D₃	—	2	2	no	—
250	C₃×Q₈	—	3	4	no	—
251	C₃×Q₈	—	6	2	no	—
252	C₃×D₄	—	3	4	no	—
253	C₃×D₄	—	6	8	no	—
254	C₃×D₄	—	6	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	6	2	no	—
262	C₂×C₃×C₄	—	6	8	no	—
263	C₂×C₃×C₄	—	6	4	no	—
264	C₂×C₃×C₄	—	24	4	no	—
265	C₂×C₃×C₄	—	24	2	no	—
266	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
267	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
268	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
269	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
270	C₂×C₃×C₄	#235	1	2	yes	—
271	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₃×#41	1	2	yes	—
276	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
278	#67	—	2	8	no	—
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	2	4	no	—
281	C₂×Dic₃	—	8	2	no	—
282	D₁₂	—	2	2	no	—
283	D₁₂	C₂²×C₃×C₄	1	4	yes	—
284	C₄×D₃	—	2	8	no	—
285	C₄×D₃	—	8	4	no	—
286	Dic₆	—	2	2	no	—
287	Dic₆	C₂²×C₃×C₄	1	4	yes	—
288	C₃×C₈	—	2	4	no	—
289	C₃×C₈	—	2	2	no	—
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
294	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
295	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
296	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
297	C₂×C₃²	—	2	2	no	—
298	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂×C₃²	#576	1	1	yes	characteristic
300	C₂×C₃²	#578	1	1	yes	characteristic
301	C₃×D₃	—	4	4	no	—
302	#41	—	3	8	no	—
303	#41	—	6	4	no	—
304	C₂×Q₈	—	3	2	no	—
305	C₂×D₄	—	3	2	no	—
306	C₂×D₄	—	6	2	no	—
307	C₂²×C₄	—	6	2	no	—
308	C₂²×C₄	—	6	2	no	—
309	C₂²×C₄	—	6	4	no	—
310	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
311	Q₁₆	—	3	4	no	—
312	SD₁₆	—	3	8	no	—
313	D₈	—	3	4	no	—
314	M₁₆	—	2	2	no	—
315	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
316	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
317	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
318	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
319	C₄⋊C₄	—	3	4	no	—
320	C₄⋊C₄	—	6	2	no	—
321	C₄⋊C₄	—	6	4	no	—
322	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
323	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
324	C₂²⋊C₄	—	6	4	no	—
325	C₂²⋊C₄	C₃×D₁₂	1	2	yes	—
326	C₄²	—	6	4	no	—
327	C₄²	C₂²×C₃×D₃	1	2	yes	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	4	1	no	—
335	C₂²×C₃	—	4	1	no	—
336	C₂²×C₃	—	6	4	no	—
337	C₂²×C₃	—	12	2	no	—
338	C₂²×C₃	—	12	2	no	—
339	C₂²×C₃	C₄×D₁₂	1	2	yes	—
340	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
341	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
342	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₂×D₃	—	2	4	no	—
344	C₂×D₃	—	4	2	no	—
345	C₂×D₃	—	4	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	2	no	—
354	C₃×C₄	—	4	2	no	—
355	C₃×C₄	—	6	4	no	—
356	C₃×C₄	—	12	4	no	—
357	C₃×C₄	C₄×D₁₂	1	2	yes	—
358	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
359	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₃×C₄	C₂×#235	1	1	yes	characteristic
361	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
362	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
363	Dic₃	—	2	4	no	—
364	Dic₃	—	4	4	no	—
365	C₃²	#2951	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	6	2	no	—
367	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
368	Q₈	—	3	4	no	—
369	Q₈	—	6	2	no	—
370	D₄	—	3	4	no	—
371	D₄	—	6	8	no	—
372	D₄	—	6	2	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	8	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	—	24	4	no	—
377	C₂×C₄	—	24	2	no	—
378	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
379	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
380	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
381	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
382	C₂×C₄	C₃×#235	1	2	yes	—
383	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
386	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
387	C₂×C₃	—	2	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	4	2	no	—
393	C₂×C₃	—	12	4	no	—
394	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
395	C₂×C₃	#5752	1	1	yes	characteristic
396	C₂×C₃	#5753	1	1	yes	characteristic
397	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
398	C₂×C₃	C₃×#576	1	1	yes	characteristic
399	C₂×C₃	C₃×#578	1	1	yes	characteristic
400	D₃	—	4	4	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	6	4	no	—
404	C₂²	—	12	2	no	—
405	C₂²	—	12	2	no	—
406	C₂²	C₃×C₄×D₁₂	1	2	yes	—
407	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	6	4	no	—
411	C₄	—	12	4	no	—
412	C₄	C₃×C₄×D₁₂	1	2	yes	—
413	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
414	C₄	C₂×C₃×#235	1	1	yes	characteristic
415	C₃	—	2	1	no	—
416	C₃	#78562	1	1	yes	characteristic, direct product factor
417	C₃	C₃×#2951	1	1	yes	characteristic, complemented
418	C₂	—	2	2	no	—
419	C₂	—	12	4	no	—
420	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
421	C₂	C₃×#5752	1	1	yes	characteristic
422	C₂	C₃×#5753	1	1	yes	characteristic

	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	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2951
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
2. C₃×#5523	C₂	semidirect
3. C₃²×#405	C₂	semidirect
4. C₃×#5133	C₂	semidirect
5. C₂×C₃×#818	C₂	semidirect
6. C₃×#4710	C₂	semidirect
7. C₃×C₄×Dic₁₂	C₂	semidirect
8. C₃×C₄×D₂₄	C₂	semidirect
10. #78562	C₃	direct (N × H)
17. C₃×#904	C₄	semidirect
34. #5523	C₂×C₃	semidirect
41. C₃×#405	D₃	semidirect
42. C₃×#405	C₂×C₃	semidirect
43. #5133	C₂×C₃	semidirect
44. C₂×#818	C₂×C₃	semidirect
45. #4710	C₂×C₃	semidirect
46. C₄×Dic₁₂	C₂×C₃	semidirect
47. C₄×D₂₄	C₂×C₃	semidirect
52. C₃×#235	C₂×C₄	semidirect
58. C₂×C₃²×C₈	C₂×C₄	semidirect
71. C₃×Dic₁₂	C₂×C₄	semidirect
72. C₃×D₂₄	C₂×C₄	semidirect
73. C₃×#204	C₂×C₄	semidirect
98. #904	C₃×C₄	semidirect
148. #405	C₃×D₃	semidirect
163. #235	C₂×C₃×C₄	semidirect
178. C₂×C₃×C₈	C₄×D₃	semidirect
179. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
208. Dic₁₂	C₂×C₃×C₄	semidirect
209. D₂₄	C₂×C₃×C₄	semidirect
210. #204	C₂×C₃×C₄	semidirect
315. C₂×C₈	C₃×C₄×D₃	semidirect
365. C₃²	#2951	semidirect
416. C₃	#78562	direct (N × H)
417. C₃	C₃×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#904	2
C₃×#5523	2
C₃²×#405	2
C₃×#5133	2
C₂×C₃×#818	2
C₃×#4710	2
C₃×C₄×Dic₁₂	2
C₃×C₄×D₂₄	2
C₃×#2951	3
#78562	3

Subgroups — C3×#78562 #11860866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78562 #11860866