Subgroups — C₃×#68680 #11795381

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#821	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#821	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4939	C₂	1	1	yes	maximal, characteristic
6	C₃×#4936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2092	—	3	1	no	maximal
9	#68680	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
15	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₃×C₃⋊#95	—	2	2	no	—
19	C₃×#821	—	2	2	no	—
20	C₃×#821	—	2	2	no	—
21	C₃×#818	—	2	2	no	—
22	C₃×#817	—	2	2	no	—
23	C₂×C₃×#107	—	3	1	no	—
24	C₂×C₃×#106	—	3	1	no	—
25	C₂×C₃×#102	—	3	1	no	—
26	C₂×C₃×#102	—	3	1	no	—
27	C₃×#390	—	3	1	no	—
28	C₃×#382	—	3	1	no	—
29	C₂×#821	C₂×C₃	1	1	yes	characteristic
30	C₂×#821	C₂×C₃	1	1	yes	characteristic
31	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
33	#4939	C₂×C₃	1	1	yes	characteristic
34	#4936	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#336	—	2	1	no	—
36	C₃×#336	D₃	1	1	yes	characteristic, complemented
37	C₃×#336	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₃	—	2	1	no	—
39	C₂²×C₃²×C₄	D₄	1	2	yes	—
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	—	2	1	no	—
42	C₂²×C₃×Dic₃	—	2	1	no	—
43	C₂²×C₃×Dic₃	—	2	1	no	—
44	C₂×C₃×D₁₂	—	2	1	no	—
45	C₂×C₃×D₁₂	—	2	1	no	—
46	C₂×C₃×D₁₂	—	2	1	no	—
47	C₂×C₃×D₁₂	—	2	1	no	—
48	C₂×C₃×D₁₂	—	2	1	no	—
49	C₂×C₃×D₁₂	Q₈	1	2	yes	—
50	C₂×C₃²×C₈	—	2	1	no	—
51	C₂×C₃²×C₈	—	2	1	no	—
52	C₂×C₃²×C₈	—	2	1	no	—
53	C₂×C₃²×C₈	—	2	1	no	—
54	C₂×C₃²×C₈	D₄	1	2	yes	—
55	C₂×C₃²×C₈	D₄	1	2	yes	—
56	C₃²×C₄²	—	2	1	no	—
57	C₃²×C₄²	—	2	1	no	—
58	C₃×(C₂×D₃)⋊C₄	—	4	4	no	—
59	C₃×C₄⋊Dic₃	—	2	1	no	—
60	C₃×C₄⋊Dic₃	—	2	1	no	—
61	C₃×C₄⋊Dic₃	—	2	1	no	—
62	C₃×C₄⋊Dic₃	—	2	1	no	—
63	C₃×C₄⋊Dic₃	—	2	1	no	—
64	C₃×C₄⋊Dic₃	—	2	1	no	—
65	#2092	—	3	1	no	Sylow
66	C₂²×C₃×D₄	—	3	1	no	—
67	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×C₈	—	2	1	no	—
69	C₂²×C₃×C₈	—	2	1	no	—
70	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₄⋊C₄	—	3	1	no	—
75	C₂×C₃×C₄⋊C₄	—	3	1	no	—
76	C₂×C₃×C₄⋊C₄	—	3	1	no	—
77	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
78	C₂×C₃×C₄²	—	2	1	no	—
79	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
85	C₃×#107	—	6	2	no	—
86	C₃×#106	—	6	2	no	—
87	C₃×#102	—	6	2	no	—
88	C₃×#102	—	6	2	no	—
89	C₃×#95	—	6	2	no	—
90	C₃⋊#95	—	2	2	no	—
91	#821	—	2	2	no	—
92	#821	—	2	2	no	—
93	#818	—	2	2	no	—
94	#817	—	2	2	no	—
95	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	—	4	1	no	—
98	C₂²×C₃×D₃	—	4	1	no	—
99	C₂²×C₃×D₃	—	4	2	no	—
100	C₂²×C₃×D₃	—	4	2	no	—
101	C₂×C₃²×C₄	—	2	2	no	—
102	C₂×C₃²×C₄	—	2	2	no	—
103	C₂×C₃²×C₄	—	2	2	no	—
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×C₃²×C₄	#41	1	1	yes	characteristic
110	C₂×C₃×Dic₃	—	4	1	no	—
111	C₂×C₃×Dic₃	—	4	1	no	—
112	C₂×C₃×Dic₃	—	4	1	no	—
113	C₂×C₃×Dic₃	—	4	2	no	—
114	C₂×C₃×Dic₃	—	4	2	no	—
115	C₂×C₃×Dic₃	—	4	2	no	—
116	C₃×D₁₂	—	2	2	no	—
117	C₃×D₁₂	—	2	2	no	—
118	C₃×D₁₂	—	4	1	no	—
119	C₃×D₁₂	—	4	1	no	—
120	C₃²×C₈	—	2	2	no	—
121	C₃²×C₈	—	2	2	no	—
122	C₂×#107	—	3	1	no	—
123	C₂×#106	—	3	1	no	—
124	C₂×#102	—	3	1	no	—
125	C₂×#102	—	3	1	no	—
126	#390	—	3	1	no	—
127	#382	—	3	1	no	—
128	#336	C₃×D₃	1	1	yes	characteristic, complemented
129	C₂⁴×C₃	—	6	1	no	—
130	C₂³×D₃	—	2	1	no	—
131	C₂×C₃×D₄	—	3	2	no	—
132	C₂×C₃×D₄	—	6	1	no	—
133	C₂×C₃×D₄	—	6	1	no	—
134	C₂×C₃×D₄	—	6	1	no	—
135	C₂×C₃×D₄	—	6	1	no	—
136	C₂×C₃×D₄	—	6	1	no	—
137	C₂²×C₃×C₄	—	2	2	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	6	1	no	—
140	C₂²×C₃×C₄	—	6	1	no	—
141	C₂²×C₃×C₄	—	6	1	no	—
142	C₂²×C₃×C₄	D₁₂	1	2	yes	—
143	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
144	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₃	—	2	1	no	—
147	C₂²×Dic₃	—	2	1	no	—
148	C₂²×Dic₃	—	2	1	no	—
149	C₂×D₁₂	—	2	1	no	—
150	C₂×D₁₂	—	2	1	no	—
151	C₂×D₁₂	—	2	1	no	—
152	C₂×D₁₂	—	2	1	no	—
153	C₂×D₁₂	—	2	1	no	—
154	C₂×D₁₂	C₃×Q₈	1	2	yes	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	4	1	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	4	1	no	—
168	C₂×C₃×C₈	—	4	1	no	—
169	C₂×C₃×C₈	D₁₂	1	2	yes	—
170	C₂×C₃×C₈	D₁₂	1	2	yes	—
171	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
172	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
173	C₃×C₄⋊C₄	—	6	1	no	—
174	C₃×C₄⋊C₄	—	6	1	no	—
175	C₃×C₄⋊C₄	—	6	1	no	—
176	C₃×C₄⋊C₄	—	6	1	no	—
177	C₃×C₄⋊C₄	—	6	1	no	—
178	C₃×C₄⋊C₄	—	6	1	no	—
179	C₃×C₂²⋊C₄	—	12	4	no	—
180	C₃×C₄²	—	2	1	no	—
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	—	2	1	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	—	4	1	no	—
185	C₃×C₄²	—	4	1	no	—
186	(C₂×D₃)⋊C₄	—	4	4	no	—
187	C₄⋊Dic₃	—	2	1	no	—
188	C₄⋊Dic₃	—	2	1	no	—
189	C₄⋊Dic₃	—	2	1	no	—
190	C₄⋊Dic₃	—	2	1	no	—
191	C₄⋊Dic₃	—	2	1	no	—
192	C₄⋊Dic₃	—	2	1	no	—
193	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂²×C₃²	#123	1	1	yes	characteristic
195	C₂²×C₃²	#127	1	1	yes	characteristic
196	C₂²×C₃²	#135	1	2	yes	—
197	C₂²×C₃²	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₃×D₃	—	4	2	no	—
199	C₂×C₃×D₃	—	4	4	no	—
200	C₂×C₃×D₃	—	8	2	no	—
201	C₂×C₃×D₃	—	8	1	no	—
202	C₂×C₃×D₃	—	8	1	no	—
203	C₃²×C₄	—	4	2	no	—
204	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
205	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
206	C₃²×C₄	#123	1	1	yes	characteristic
207	C₃²×C₄	#123	1	1	yes	characteristic
208	C₃×Dic₃	—	8	1	no	—
209	C₃×Dic₃	—	8	1	no	—
210	C₃×Dic₃	—	8	1	no	—
211	C₂²×D₄	—	3	1	no	—
212	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
214	C₂×C₄⋊C₄	—	3	1	no	—
215	C₂×C₄⋊C₄	—	3	1	no	—
216	C₂×C₄⋊C₄	—	3	1	no	—
217	C₂×C₂²⋊C₄	—	6	2	no	—
218	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
219	#107	—	6	2	no	—
220	#106	—	6	2	no	—
221	#102	—	6	2	no	—
222	#102	—	6	2	no	—
223	#95	—	6	2	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	6	2	no	—
226	C₂³×C₃	—	12	1	no	—
227	C₂³×C₃	—	12	1	no	—
228	C₂³×C₃	—	12	2	no	—
229	C₂³×C₃	—	12	2	no	—
230	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
231	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂²×D₃	—	2	2	no	—
233	C₂²×D₃	—	4	1	no	—
234	C₂²×D₃	—	4	1	no	—
235	C₂²×D₃	—	4	2	no	—
236	C₂²×D₃	—	4	2	no	—
237	C₃×D₄	—	6	2	no	—
238	C₃×D₄	—	6	2	no	—
239	C₃×D₄	—	12	1	no	—
240	C₃×D₄	—	12	1	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	4	2	no	—
256	C₂×C₃×C₄	—	12	1	no	—
257	C₂×C₃×C₄	—	12	1	no	—
258	C₂×C₃×C₄	—	12	1	no	—
259	C₂×C₃×C₄	—	12	2	no	—
260	C₂×C₃×C₄	—	12	2	no	—
261	C₂×C₃×C₄	—	12	2	no	—
262	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
264	C₂×C₃×C₄	#237	1	1	yes	characteristic
265	C₂×C₃×C₄	#237	1	1	yes	characteristic
266	C₂×C₃×C₄	#237	1	1	yes	characteristic
267	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
271	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
272	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
273	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
274	C₂×Dic₃	—	4	1	no	—
275	C₂×Dic₃	—	4	1	no	—
276	C₂×Dic₃	—	4	1	no	—
277	C₂×Dic₃	—	4	2	no	—
278	C₂×Dic₃	—	4	2	no	—
279	C₂×Dic₃	—	4	2	no	—
280	D₁₂	—	2	2	no	—
281	D₁₂	—	2	2	no	—
282	D₁₂	—	4	1	no	—
283	D₁₂	—	4	1	no	—
284	C₃×C₈	—	2	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	2	2	no	—
287	C₃×C₈	—	2	2	no	—
288	C₃×C₈	—	4	2	no	—
289	C₃×C₈	—	4	2	no	—
290	C₂×C₃²	#399	1	1	yes	characteristic
291	C₂×C₃²	#478	1	2	yes	—
292	C₂×C₃²	#482	1	2	yes	—
293	C₂×C₃²	#495	1	1	yes	characteristic
294	C₂×C₃²	#496	1	1	yes	characteristic
295	C₃×D₃	—	8	2	no	—
296	C₂⁴	—	6	1	no	—
297	C₂×D₄	—	3	2	no	—
298	C₂×D₄	—	6	1	no	—
299	C₂×D₄	—	6	1	no	—
300	C₂×D₄	—	6	1	no	—
301	C₂×D₄	—	6	1	no	—
302	C₂×D₄	—	6	1	no	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	—	6	1	no	—
305	C₂²×C₄	—	6	1	no	—
306	C₂²×C₄	C₃×D₁₂	1	2	yes	—
307	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	C₃×D₁₂	1	2	yes	—
313	C₂×C₈	C₃×D₁₂	1	2	yes	—
314	C₄⋊C₄	—	6	1	no	—
315	C₄⋊C₄	—	6	1	no	—
316	C₄⋊C₄	—	6	1	no	—
317	C₄⋊C₄	—	6	1	no	—
318	C₄⋊C₄	—	6	1	no	—
319	C₄⋊C₄	—	6	1	no	—
320	C₂²⋊C₄	—	12	4	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	12	2	no	—
329	C₂²×C₃	—	12	4	no	—
330	C₂²×C₃	—	24	1	no	—
331	C₂²×C₃	—	24	1	no	—
332	C₂²×C₃	—	24	2	no	—
333	C₂²×C₃	#874	1	1	yes	characteristic
334	C₂²×C₃	#886	1	1	yes	characteristic
335	C₂²×C₃	#897	1	1	yes	characteristic
336	C₂²×C₃	#904	1	2	yes	—
337	C₂²×C₃	#908	1	2	yes	—
338	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂²×C₃	C₃×#123	1	1	yes	characteristic
340	C₂²×C₃	C₃×#127	1	1	yes	characteristic
341	C₂²×C₃	C₃×#135	1	2	yes	—
342	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
343	C₂×D₃	—	4	2	no	—
344	C₂×D₃	—	4	4	no	—
345	C₂×D₃	—	8	2	no	—
346	C₂×D₃	—	8	1	no	—
347	C₂×D₃	—	8	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	4	4	no	—
353	C₃×C₄	—	4	2	no	—
354	C₃×C₄	—	4	2	no	—
355	C₃×C₄	—	24	1	no	—
356	C₃×C₄	—	24	1	no	—
357	C₃×C₄	—	24	1	no	—
358	C₃×C₄	#886	1	1	yes	characteristic
359	C₃×C₄	#886	1	1	yes	characteristic
360	C₃×C₄	#897	1	1	yes	characteristic
361	C₃×C₄	#897	1	1	yes	characteristic
362	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
363	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
364	C₃×C₄	C₃×#123	1	1	yes	characteristic
365	C₃×C₄	C₃×#123	1	1	yes	characteristic
366	Dic₃	—	8	1	no	—
367	Dic₃	—	8	1	no	—
368	Dic₃	—	8	1	no	—
369	C₃²	#2092	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	6	2	no	—
371	C₂³	—	12	1	no	—
372	C₂³	—	12	2	no	—
373	C₂³	—	12	2	no	—
374	C₂³	—	12	1	no	—
375	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
376	D₄	—	6	2	no	—
377	D₄	—	6	2	no	—
378	D₄	—	12	1	no	—
379	D₄	—	12	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	12	2	no	—
384	C₂×C₄	—	12	2	no	—
385	C₂×C₄	—	12	2	no	—
386	C₂×C₄	—	12	1	no	—
387	C₂×C₄	—	12	1	no	—
388	C₂×C₄	—	12	1	no	—
389	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
390	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
391	C₂×C₄	C₃×#237	1	1	yes	characteristic
392	C₂×C₄	C₃×#237	1	1	yes	characteristic
393	C₂×C₄	C₃×#237	1	1	yes	characteristic
394	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	24	2	no	—
403	C₂×C₃	#4677	1	1	yes	characteristic
404	C₂×C₃	#4696	1	1	yes	characteristic
405	C₂×C₃	#4712	1	1	yes	characteristic
406	C₂×C₃	#4737	1	2	yes	—
407	C₂×C₃	#4847	1	2	yes	—
408	C₂×C₃	C₃×#399	1	1	yes	characteristic
409	C₂×C₃	C₃×#478	1	2	yes	—
410	C₂×C₃	C₃×#482	1	2	yes	—
411	C₂×C₃	C₃×#495	1	1	yes	characteristic
412	C₂×C₃	C₃×#496	1	1	yes	characteristic
413	D₃	—	8	2	no	—
414	C₂²	—	12	2	no	—
415	C₂²	—	12	4	no	—
416	C₂²	—	24	1	no	—
417	C₂²	—	24	1	no	—
418	C₂²	—	24	2	no	—
419	C₂²	C₃×#874	1	1	yes	characteristic
420	C₂²	C₃×#886	1	1	yes	characteristic
421	C₂²	C₃×#897	1	1	yes	characteristic
422	C₂²	C₃×#904	1	2	yes	—
423	C₂²	C₃×#908	1	2	yes	—
424	C₄	—	4	2	no	—
425	C₄	—	24	1	no	—
426	C₄	—	24	1	no	—
427	C₄	—	24	1	no	—
428	C₄	C₃×#886	1	1	yes	characteristic
429	C₄	C₃×#886	1	1	yes	characteristic
430	C₄	C₃×#897	1	1	yes	characteristic
431	C₄	C₃×#897	1	1	yes	characteristic
432	C₃	—	2	1	no	—
433	C₃	#68680	1	1	yes	characteristic, direct product factor
434	C₃	C₃×#2092	1	1	yes	characteristic, complemented
435	C₂	—	24	2	no	—
436	C₂	C₃×#4677	1	1	yes	characteristic
437	C₂	C₃×#4696	1	1	yes	characteristic
438	C₂	C₃×#4712	1	1	yes	characteristic
439	C₂	C₃×#4737	1	2	yes	—
440	C₂	C₃×#4847	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator, cosocle	C₂²×C₃×C₄	C₂³×C₃
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#336	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₃×#336	D₃
hypocenter	C₃	C₃×#2092
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#336

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#818	C₂	semidirect
4. C₂×C₃×#817	C₂	semidirect
6. C₃×#4936	C₂	semidirect
7. C₃²×#336	C₂	semidirect
9. #68680	C₃	direct (N × H)
31. C₂×#818	C₂×C₃	semidirect
32. C₂×#817	C₂×C₃	semidirect
34. #4936	C₂×C₃	semidirect
36. C₃×#336	D₃	semidirect
37. C₃×#336	C₂×C₃	semidirect
128. #336	C₃×D₃	semidirect
369. C₃²	#2092	semidirect
433. C₃	#68680	direct (N × H)
434. C₃	C₃×#2092	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#821	2
C₂×C₃×#818	2
C₂×C₃×#817	2
C₃×#4939	2
C₃×#4936	2
C₃²×#336	2
C₃×#2092	3
#68680	3

Subgroups — C3×#68680 #11795381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68680 #11795381