Subgroups — C₃×#68417 #11776125

Order 1152.

544 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5725	C₂	1	1	yes	maximal, characteristic
2	C₃×#4833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1540	—	3	1	no	maximal
9	#68417	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#239	—	2	1	no	—
11	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×#947	—	2	1	no	—
13	C₂×C₃×D₃×C₈	—	2	1	no	—
14	C₃×#895	—	2	1	no	—
15	C₃×#895	C₄	1	2	yes	—
16	C₃×#893	—	2	1	no	—
17	C₃×#893	C₄	1	2	yes	—
18	C₃×#874	C₂²	1	1	yes	characteristic
19	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
20	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×(C₂×D₃)⋊C₈	—	2	1	no	—
23	C₃×Dic₃⋊C₈	—	2	1	no	—
24	C₃×C₈×Dic₃	—	2	1	no	—
25	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₃×#532	—	3	1	no	—
28	#5725	C₂×C₃	1	1	yes	characteristic
29	C₃×#431	—	3	1	no	—
30	C₂×C₃×C₄⋊C₈	—	3	1	no	—
31	#4833	C₂×C₃	1	1	yes	characteristic, complemented
32	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#332	—	2	1	no	—
34	C₃×#332	—	3	1	no	—
35	C₃×#332	D₃	1	1	yes	characteristic, complemented
36	C₃×#332	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#331	—	3	1	no	—
38	C₃×#331	—	3	1	no	—
39	#4547	C₂×C₃	1	1	yes	characteristic, complemented
40	#4485	C₂×C₃	1	1	yes	characteristic, complemented
41	#4485	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃²×Q₈	—	2	1	no	—
43	C₃×#239	—	4	2	no	—
44	C₃×#239	—	4	2	no	—
45	C₂×C₃×D₁₂	—	2	2	no	—
46	C₂×C₃×D₁₂	—	2	1	no	—
47	C₂×C₃×D₁₂	—	2	1	no	—
48	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	—	2	2	no	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
53	C₂×C₃²×C₈	—	2	1	no	—
54	C₂×C₃²×C₈	—	2	1	no	—
55	C₃²×C₄⋊C₄	—	2	1	no	—
56	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₃²×C₄²	C₂³	1	1	yes	characteristic
58	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
59	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
60	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
62	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₃×C₃⋊C₈	—	2	1	no	—
64	C₂×C₃×C₃⋊C₈	—	2	1	no	—
65	C₃×D₃×C₈	—	4	2	no	—
66	#1540	—	3	1	no	Sylow
67	C₂×C₃×#41	—	6	1	no	—
68	C₂×#239	—	2	1	no	—
69	C₂²×C₃×C₈	—	6	1	no	—
70	C₃×C₄⋊Q₈	—	2	1	no	—
71	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
72	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₃×#127	—	3	1	no	—
74	C₃×#124	—	6	1	no	—
75	C₃×#121	—	3	2	no	—
76	C₃×#121	—	6	1	no	—
77	C₃×C₄×D₄	—	3	2	no	—
78	C₃×C₄×D₄	—	6	1	no	—
79	C₂×C₃×C₄²	—	3	1	no	—
80	#947	—	2	1	no	—
81	C₂×D₃×C₈	—	2	1	no	—
82	#895	—	2	1	no	—
83	#895	C₃×C₄	1	2	yes	—
84	#893	—	2	1	no	—
85	#893	C₃×C₄	1	2	yes	—
86	#874	C₂²×C₃	1	1	yes	characteristic
87	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄⋊C₈	—	2	1	no	—
89	C₃×C₄⋊C₈	—	2	1	no	—
90	C₃×C₄⋊C₈	—	3	1	no	—
91	C₃×C₄⋊C₈	—	3	1	no	—
92	C₃×C₄⋊C₈	—	6	1	no	—
93	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
94	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
95	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
96	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₂²⋊C₈	—	6	1	no	—
98	C₃×C₄×C₈	—	6	1	no	—
99	(C₂×D₃)⋊C₈	—	2	1	no	—
100	Dic₃⋊C₈	—	2	1	no	—
101	C₈×Dic₃	—	2	1	no	—
102	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
103	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₃×D₃	—	2	2	no	—
105	C₂²×C₃×D₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₃²×Q₈	—	4	1	no	—
107	C₃²×Q₈	—	4	1	no	—
108	C₂×C₃²×C₄	—	2	2	no	—
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₃×D₁₂	—	4	2	no	—
116	C₃×D₁₂	—	4	4	no	—
117	C₃×D₁₂	—	4	1	no	—
118	C₃×D₁₂	—	4	1	no	—
119	C₃×D₁₂	—	4	1	no	—
120	C₃×D₁₂	—	4	1	no	—
121	C₃×C₄×D₃	—	2	1	no	—
122	C₃×C₄×D₃	—	2	1	no	—
123	C₃×C₄×D₃	—	4	1	no	—
124	C₃×C₄×D₃	—	4	4	no	—
125	C₃×C₄×D₃	D₈	1	2	yes	—
126	C₃×C₄×D₃	SD₁₆	1	2	yes	—
127	C₃²×C₈	—	4	1	no	—
128	C₃²×C₈	—	4	1	no	—
129	C₃×C₃⋊C₈	—	4	1	no	—
130	C₃×C₃⋊C₈	—	4	1	no	—
131	#532	—	3	1	no	—
132	#431	—	3	1	no	—
133	C₂×C₄⋊C₈	—	3	1	no	—
134	#332	—	3	1	no	—
135	#332	C₃×D₃	1	1	yes	characteristic, complemented
136	#331	—	3	1	no	—
137	#331	—	3	1	no	—
138	C₃×#41	—	12	2	no	—
139	C₃×#41	—	12	2	no	—
140	C₂×C₃×Q₈	—	2	1	no	—
141	C₂×C₃×Q₈	—	2	1	no	—
142	C₂×C₃×Q₈	—	4	1	no	—
143	C₂×C₃×D₄	—	3	2	no	—
144	C₂×C₃×D₄	—	6	2	no	—
145	C₂×C₃×D₄	—	6	1	no	—
146	C₂×C₃×D₄	—	6	1	no	—
147	C₂²×C₃×C₄	—	3	1	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	1	no	—
150	C₂²×C₃×C₄	—	6	2	no	—
151	#239	—	4	2	no	—
152	#239	—	4	2	no	—
153	C₂×D₁₂	—	2	2	no	—
154	C₂×D₁₂	—	2	1	no	—
155	C₂×D₁₂	—	2	1	no	—
156	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
157	C₂×C₄×D₃	—	2	2	no	—
158	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
160	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	4	1	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	6	1	no	—
168	C₂×C₃×C₈	—	6	1	no	—
169	C₂×C₃×C₈	—	12	2	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	4	1	no	—
174	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
175	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
176	C₃×C₂²⋊C₄	—	6	2	no	—
177	C₃×C₂²⋊C₄	—	6	2	no	—
178	C₃×C₄²	—	2	1	no	—
179	C₃×C₄²	—	3	1	no	—
180	C₃×C₄²	—	3	1	no	—
181	C₃×C₄²	—	3	1	no	—
182	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
183	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
184	(C₂×D₃)⋊C₄	—	2	2	no	—
185	(C₂×D₃)⋊C₄	—	2	2	no	—
186	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
187	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
188	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
189	C₂×C₃⋊C₈	—	2	1	no	—
190	C₂×C₃⋊C₈	—	2	1	no	—
191	D₃×C₈	—	4	2	no	—
192	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	1	no	—
194	C₂×C₃×D₃	—	2	1	no	—
195	C₂×C₃×D₃	—	4	2	no	—
196	C₂×C₃×D₃	—	4	2	no	—
197	C₂×C₃×D₃	—	4	2	no	—
198	C₂×C₃×D₃	#102	1	2	yes	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	4	2	no	—
201	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
202	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
203	C₃²×C₄	#135	1	1	yes	characteristic
204	C₃²×C₄	#135	1	1	yes	characteristic
205	C₃×Dic₃	—	2	1	no	—
206	C₃×Dic₃	—	2	1	no	—
207	C₃×Dic₃	#102	1	2	yes	—
208	C₂×#41	—	6	1	no	—
209	C₂²×C₈	—	6	1	no	—
210	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
211	#127	—	3	1	no	—
212	#124	—	6	1	no	—
213	#121	—	3	2	no	—
214	#121	—	6	1	no	—
215	C₄×D₄	—	3	2	no	—
216	C₄×D₄	—	6	1	no	—
217	C₂×C₄²	—	3	1	no	—
218	C₄⋊C₈	—	3	1	no	—
219	C₄⋊C₈	—	3	1	no	—
220	C₄⋊C₈	—	6	1	no	—
221	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
222	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²⋊C₈	—	6	1	no	—
224	C₄×C₈	—	6	1	no	—
225	C₂³×C₃	—	3	1	no	—
226	C₂³×C₃	—	6	2	no	—
227	C₂²×D₃	—	2	2	no	—
228	C₂²×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₃×Q₈	—	4	1	no	—
230	C₃×Q₈	—	4	1	no	—
231	C₃×Q₈	—	4	1	no	—
232	C₃×Q₈	—	4	1	no	—
233	C₃×Q₈	—	8	1	no	—
234	C₃×Q₈	—	8	1	no	—
235	C₃×D₄	—	12	2	no	—
236	C₃×D₄	—	12	4	no	—
237	C₃×D₄	—	12	1	no	—
238	C₃×D₄	—	12	1	no	—
239	C₃×D₄	—	12	1	no	—
240	C₃×D₄	—	12	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	3	1	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	2	no	—
249	C₂×C₃×C₄	—	3	1	no	—
250	C₂×C₃×C₄	—	3	1	no	—
251	C₂×C₃×C₄	—	4	2	no	—
252	C₂×C₃×C₄	—	6	1	no	—
253	C₂×C₃×C₄	—	6	1	no	—
254	C₂×C₃×C₄	—	12	1	no	—
255	C₂×C₃×C₄	—	12	4	no	—
256	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
265	D₁₂	—	4	2	no	—
266	D₁₂	—	4	4	no	—
267	D₁₂	—	4	1	no	—
268	D₁₂	—	4	1	no	—
269	D₁₂	—	4	1	no	—
270	D₁₂	—	4	1	no	—
271	C₄×D₃	—	2	1	no	—
272	C₄×D₃	—	2	1	no	—
273	C₄×D₃	—	4	1	no	—
274	C₄×D₃	—	4	4	no	—
275	C₄×D₃	C₃×D₈	1	2	yes	—
276	C₄×D₃	C₃×SD₁₆	1	2	yes	—
277	C₃×C₈	—	4	1	no	—
278	C₃×C₈	—	4	1	no	—
279	C₃×C₈	—	4	1	no	—
280	C₃×C₈	—	4	1	no	—
281	C₃×C₈	—	8	1	no	—
282	C₃×C₈	—	8	1	no	—
283	C₃×C₈	—	12	1	no	—
284	C₃×C₈	—	12	1	no	—
285	C₃⋊C₈	—	4	1	no	—
286	C₃⋊C₈	—	4	1	no	—
287	C₂×C₃²	#413	1	1	yes	characteristic
288	C₂×C₃²	C₂×#102	1	1	yes	characteristic
289	C₂×C₃²	#416	1	1	yes	characteristic
290	C₃×D₃	—	2	2	no	—
291	C₃×D₃	—	8	2	no	—
292	#41	—	12	2	no	—
293	#41	—	12	2	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	3	2	no	—
296	C₂×D₄	—	6	2	no	—
297	C₂×D₄	—	6	1	no	—
298	C₂×D₄	—	6	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	3	1	no	—
302	C₂²×C₄	—	6	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	6	1	no	—
306	C₂×C₈	—	6	1	no	—
307	C₂×C₈	—	12	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
310	C₂²⋊C₄	—	6	2	no	—
311	C₂²⋊C₄	—	6	2	no	—
312	C₄²	—	3	1	no	—
313	C₄²	—	3	1	no	—
314	C₄²	—	3	1	no	—
315	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	3	2	no	—
318	C₂²×C₃	—	6	1	no	—
319	C₂²×C₃	—	6	1	no	—
320	C₂²×C₃	—	12	2	no	—
321	C₂²×C₃	—	12	2	no	—
322	C₂²×C₃	—	12	2	no	—
323	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×D₃	—	2	1	no	—
326	C₂×D₃	—	2	1	no	—
327	C₂×D₃	—	4	2	no	—
328	C₂×D₃	—	4	2	no	—
329	C₂×D₃	—	4	2	no	—
330	C₂×D₃	C₃×#102	1	2	yes	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	3	2	no	—
338	C₃×C₄	—	4	1	no	—
339	C₃×C₄	—	4	2	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	6	1	no	—
342	C₃×C₄	—	6	1	no	—
343	C₃×C₄	—	8	2	no	—
344	C₃×C₄	D₃×D₈	1	1	yes	characteristic
345	C₃×C₄	D₃×SD₁₆	1	1	yes	characteristic
346	C₃×C₄	#916	1	1	yes	characteristic
347	C₃×C₄	#919	1	1	yes	characteristic
348	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
349	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
350	C₃×C₄	C₃×#135	1	1	yes	characteristic
351	C₃×C₄	C₃×#135	1	1	yes	characteristic
352	Dic₃	—	2	1	no	—
353	Dic₃	—	2	1	no	—
354	Dic₃	C₃×#102	1	2	yes	—
355	C₃²	#1540	1	1	yes	characteristic, complemented, Sylow
356	C₂³	—	3	1	no	—
357	C₂³	—	6	2	no	—
358	Q₈	—	4	1	no	—
359	Q₈	—	4	1	no	—
360	D₄	—	12	2	no	—
361	D₄	—	12	4	no	—
362	D₄	—	12	1	no	—
363	D₄	—	12	1	no	—
364	D₄	—	12	1	no	—
365	D₄	—	12	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	3	1	no	—
368	C₂×C₄	—	3	2	no	—
369	C₂×C₄	—	3	2	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	6	1	no	—
373	C₂×C₄	—	6	1	no	—
374	C₂×C₄	—	12	1	no	—
375	C₂×C₄	—	12	4	no	—
376	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
377	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
378	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	12	1	no	—
382	C₈	—	12	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	6	2	no	—
387	C₂×C₃	—	24	2	no	—
388	C₂×C₃	#4751	1	1	yes	characteristic
389	C₂×C₃	D₃×#102	1	1	yes	characteristic
390	C₂×C₃	#4804	1	1	yes	characteristic
391	C₂×C₃	C₃×#413	1	1	yes	characteristic
392	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
393	C₂×C₃	C₃×#416	1	1	yes	characteristic
394	D₃	—	2	2	no	—
395	D₃	—	8	2	no	—
396	C₂²	—	3	2	no	—
397	C₂²	—	6	1	no	—
398	C₂²	—	6	1	no	—
399	C₂²	—	12	2	no	—
400	C₂²	—	12	2	no	—
401	C₂²	—	12	2	no	—
402	C₂²	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	3	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	6	1	no	—
407	C₄	—	6	1	no	—
408	C₄	C₃×D₃×D₈	1	1	yes	characteristic
409	C₄	C₃×D₃×SD₁₆	1	1	yes	characteristic
410	C₄	C₃×#916	1	1	yes	characteristic
411	C₄	C₃×#919	1	1	yes	characteristic
412	C₃	—	2	1	no	—
413	C₃	#68417	1	1	yes	characteristic, direct product factor
414	C₃	C₃×#1540	1	1	yes	characteristic, complemented
415	C₂	—	6	2	no	—
416	C₂	—	24	2	no	—
417	C₂	C₃×#4751	1	1	yes	characteristic
418	C₂	C₃×D₃×#102	1	1	yes	characteristic
419	C₂	C₃×#4804	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×#332	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#5725	C₂
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×#332	D₃
hypocenter	C₃	C₃×#1540
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#332

Complements

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

N	H ≅ G/N	type
2. C₃×#4833	C₂	semidirect
3. C₃×D₃×C₄⋊C₈	C₂	semidirect
4. C₃²×#332	C₂	semidirect
5. C₃×#4547	C₂	semidirect
6. C₃×#4485	C₂	semidirect
7. C₃×#4485	C₂	semidirect
9. #68417	C₃	direct (N × H)
31. #4833	C₂×C₃	semidirect
32. D₃×C₄⋊C₈	C₂×C₃	semidirect
35. C₃×#332	D₃	semidirect
36. C₃×#332	C₂×C₃	semidirect
39. #4547	C₂×C₃	semidirect
40. #4485	C₂×C₃	semidirect
41. #4485	C₂×C₃	semidirect
135. #332	C₃×D₃	semidirect
355. C₃²	#1540	semidirect
413. C₃	#68417	direct (N × H)
414. C₃	C₃×#1540	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5725	2
C₃×#4833	2
C₃×D₃×C₄⋊C₈	2
C₃²×#332	2
C₃×#4547	2
C₃×#4485	2
C₃×#1540	3
#68417	3

Subgroups — C3×#68417 #11776125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68417 #11776125