Subgroups — C₃×#68635 #11794646

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 413 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	2	yes	maximal
2	C₃×#4939	C₂	1	1	yes	maximal, characteristic
3	C₃×#4935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#336	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4551	C₂	1	2	yes	maximal, complemented
6	C₃×#2071	—	3	1	no	maximal
7	#68635	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
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×#821	—	2	4	no	—
18	C₂×C₃×#102	—	3	2	no	—
19	C₃×#390	—	3	1	no	—
20	C₃×#384	—	3	1	no	—
21	C₂×#821	C₂×C₃	1	2	yes	—
22	#4939	C₂×C₃	1	1	yes	characteristic
23	#4935	C₂×C₃	1	1	yes	characteristic, complemented
24	C₃×#340	—	3	2	no	—
25	C₃×#336	—	2	1	no	—
26	C₃×#336	D₃	1	1	yes	characteristic, complemented
27	C₃×#336	C₂×C₃	1	1	yes	characteristic, complemented
28	#4551	C₂×C₃	1	2	yes	complemented
29	C₂³×C₃×D₃	—	2	1	no	—
30	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃×Dic₃	—	2	2	no	—
34	C₂²×C₃×Dic₃	—	2	1	no	—
35	C₂×C₃×D₁₂	—	2	2	no	—
36	C₂×C₃×D₁₂	—	2	2	no	—
37	C₂×C₃×D₁₂	—	2	1	no	—
38	C₂×C₃×D₁₂	D₄	1	2	yes	—
39	C₂×C₃²×C₈	—	2	2	no	—
40	C₂×C₃²×C₈	—	2	2	no	—
41	C₂×C₃²×C₈	—	2	2	no	—
42	C₃²×C₄²	—	2	2	no	—
43	C₃×(C₂×D₃)⋊C₄	—	4	2	no	—
44	C₃×(C₂×D₃)⋊C₄	—	4	2	no	—
45	C₃×C₄⋊Dic₃	—	2	2	no	—
46	C₃×C₄⋊Dic₃	—	2	2	no	—
47	C₃×C₄⋊Dic₃	—	2	2	no	—
48	C₃×C₄⋊Dic₃	—	4	2	no	—
49	C₃×C₄⋊Dic₃	—	4	2	no	—
50	#2071	—	3	1	no	Sylow
51	C₂²×C₃×D₄	—	3	1	no	—
52	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃×C₈	—	2	2	no	—
54	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
55	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
56	C₂×C₃×C₄⋊C₄	—	3	2	no	—
57	C₂×C₃×C₄⋊C₄	—	3	1	no	—
58	C₂×C₃×C₄⋊C₄	—	6	1	no	—
59	C₂×C₃×C₄⋊C₄	—	6	1	no	—
60	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
61	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
62	C₂×C₃×C₄²	—	2	1	no	—
63	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
65	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
66	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
67	C₂×C₄⋊Dic₃	—	2	1	no	—
68	C₂×C₄⋊Dic₃	—	2	1	no	—
69	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
70	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₃×#102	—	6	4	no	—
72	#821	—	2	4	no	—
73	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₃×D₃	—	2	2	no	—
75	C₂²×C₃×D₃	—	4	1	no	—
76	C₂²×C₃×D₃	—	4	1	no	—
77	C₂²×C₃×D₃	—	4	1	no	—
78	C₂²×C₃×D₃	—	4	1	no	—
79	C₂²×C₃×D₃	—	4	1	no	—
80	C₂²×C₃×D₃	—	4	1	no	—
81	C₂×C₃²×C₄	—	2	1	no	—
82	C₂×C₃²×C₄	—	2	1	no	—
83	C₂×C₃²×C₄	—	2	1	no	—
84	C₂×C₃²×C₄	—	2	1	no	—
85	C₂×C₃²×C₄	D₈	1	2	yes	—
86	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
87	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃²×C₄	#41	1	2	yes	—
89	C₂×C₃²×C₄	#41	1	2	yes	—
90	C₂×C₃²×C₄	#41	1	1	yes	characteristic
91	C₂×C₃×Dic₃	—	4	2	no	—
92	C₂×C₃×Dic₃	—	4	1	no	—
93	C₂×C₃×Dic₃	—	4	2	no	—
94	C₂×C₃×Dic₃	—	4	1	no	—
95	C₂×C₃×Dic₃	—	4	1	no	—
96	C₂×C₃×Dic₃	—	4	2	no	—
97	C₃×D₁₂	—	2	4	no	—
98	C₃×D₁₂	—	4	2	no	—
99	C₃²×C₈	—	4	2	no	—
100	C₂×#102	—	3	2	no	—
101	#390	—	3	1	no	—
102	#384	—	3	1	no	—
103	#340	—	3	2	no	—
104	#336	C₃×D₃	1	1	yes	characteristic, complemented
105	C₂⁴×C₃	—	6	1	no	—
106	C₂³×D₃	—	2	1	no	—
107	C₂×C₃×D₄	—	3	2	no	—
108	C₂×C₃×D₄	—	6	2	no	—
109	C₂×C₃×D₄	—	6	2	no	—
110	C₂×C₃×D₄	—	6	1	no	—
111	C₂²×C₃×C₄	—	2	1	no	—
112	C₂²×C₃×C₄	—	2	1	no	—
113	C₂²×C₃×C₄	—	2	1	no	—
114	C₂²×C₃×C₄	—	6	1	no	—
115	C₂²×C₃×C₄	—	6	2	no	—
116	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
117	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
122	C₂²×Dic₃	—	2	2	no	—
123	C₂²×Dic₃	—	2	1	no	—
124	C₂×D₁₂	—	2	2	no	—
125	C₂×D₁₂	—	2	2	no	—
126	C₂×D₁₂	—	2	1	no	—
127	C₂×D₁₂	C₃×D₄	1	2	yes	—
128	C₂×C₃×C₈	—	2	4	no	—
129	C₂×C₃×C₈	—	2	2	no	—
130	C₂×C₃×C₈	—	2	2	no	—
131	C₂×C₃×C₈	—	2	2	no	—
132	C₂×C₃×C₈	—	2	2	no	—
133	C₂×C₃×C₈	—	2	2	no	—
134	C₂×C₃×C₈	—	2	2	no	—
135	C₂×C₃×C₈	—	4	2	no	—
136	C₂×C₃×C₈	—	4	2	no	—
137	C₃×C₄⋊C₄	—	6	2	no	—
138	C₃×C₄⋊C₄	—	6	2	no	—
139	C₃×C₄⋊C₄	—	6	2	no	—
140	C₃×C₄⋊C₄	—	12	2	no	—
141	C₃×C₄⋊C₄	—	12	2	no	—
142	C₃×C₂²⋊C₄	—	12	2	no	—
143	C₃×C₂²⋊C₄	—	12	2	no	—
144	C₃×C₄²	—	2	2	no	—
145	C₃×C₄²	—	2	2	no	—
146	C₃×C₄²	—	4	2	no	—
147	(C₂×D₃)⋊C₄	—	4	2	no	—
148	(C₂×D₃)⋊C₄	—	4	2	no	—
149	C₄⋊Dic₃	—	2	2	no	—
150	C₄⋊Dic₃	—	2	2	no	—
151	C₄⋊Dic₃	—	2	2	no	—
152	C₄⋊Dic₃	—	4	2	no	—
153	C₄⋊Dic₃	—	4	2	no	—
154	C₂²×C₃²	#121	1	1	yes	characteristic
155	C₂²×C₃²	#123	1	1	yes	characteristic
156	C₂²×C₃²	#124	1	1	yes	characteristic
157	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
158	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
159	C₂²×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂²×C₃²	#137	1	1	yes	characteristic
161	C₂×C₃×D₃	—	4	2	no	—
162	C₂×C₃×D₃	—	4	2	no	—
163	C₂×C₃×D₃	—	4	2	no	—
164	C₂×C₃×D₃	—	8	1	no	—
165	C₂×C₃×D₃	—	8	1	no	—
166	C₂×C₃×D₃	—	8	1	no	—
167	C₂×C₃×D₃	—	8	1	no	—
168	C₃²×C₄	—	2	2	no	—
169	C₃²×C₄	—	2	2	no	—
170	C₃²×C₄	#123	1	2	yes	—
171	C₃²×C₄	#126	1	2	yes	—
172	C₃×Dic₃	—	8	2	no	—
173	C₃×Dic₃	—	8	1	no	—
174	C₂²×D₄	—	3	1	no	—
175	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
176	C₂×C₄⋊C₄	—	3	1	no	—
177	C₂×C₄⋊C₄	—	3	2	no	—
178	C₂×C₄⋊C₄	—	6	1	no	—
179	C₂×C₄⋊C₄	—	6	1	no	—
180	C₂×C₂²⋊C₄	—	6	1	no	—
181	C₂×C₂²⋊C₄	—	6	1	no	—
182	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
183	#102	—	6	4	no	—
184	C₂³×C₃	—	2	1	no	—
185	C₂³×C₃	—	6	2	no	—
186	C₂³×C₃	—	12	1	no	—
187	C₂³×C₃	—	12	1	no	—
188	C₂³×C₃	—	12	1	no	—
189	C₂³×C₃	—	12	1	no	—
190	C₂³×C₃	—	12	1	no	—
191	C₂³×C₃	—	12	1	no	—
192	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
193	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂²×D₃	—	2	2	no	—
195	C₂²×D₃	—	4	1	no	—
196	C₂²×D₃	—	4	1	no	—
197	C₂²×D₃	—	4	1	no	—
198	C₂²×D₃	—	4	1	no	—
199	C₂²×D₃	—	4	1	no	—
200	C₂²×D₃	—	4	1	no	—
201	C₃×D₄	—	6	4	no	—
202	C₃×D₄	—	12	2	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	1	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	1	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	4	1	no	—
218	C₂×C₃×C₄	—	4	1	no	—
219	C₂×C₃×C₄	—	4	1	no	—
220	C₂×C₃×C₄	—	4	1	no	—
221	C₂×C₃×C₄	—	12	1	no	—
222	C₂×C₃×C₄	—	12	2	no	—
223	C₂×C₃×C₄	—	12	1	no	—
224	C₂×C₃×C₄	—	12	1	no	—
225	C₂×C₃×C₄	—	12	2	no	—
226	C₂×C₃×C₄	—	12	2	no	—
227	C₂×C₃×C₄	#204	1	2	yes	—
228	C₂×C₃×C₄	D₂₄	1	2	yes	—
229	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
230	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
231	C₂×C₃×C₄	#235	1	2	yes	—
232	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	#237	1	2	yes	—
234	C₂×C₃×C₄	#239	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₃×#41	1	2	yes	—
237	C₂×C₃×C₄	C₃×#41	1	2	yes	—
238	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
239	C₂×Dic₃	—	4	2	no	—
240	C₂×Dic₃	—	4	1	no	—
241	C₂×Dic₃	—	4	2	no	—
242	C₂×Dic₃	—	4	1	no	—
243	C₂×Dic₃	—	4	1	no	—
244	C₂×Dic₃	—	4	2	no	—
245	D₁₂	—	2	4	no	—
246	D₁₂	—	4	2	no	—
247	C₃×C₈	—	4	4	no	—
248	C₃×C₈	—	4	2	no	—
249	C₃×C₈	—	4	2	no	—
250	C₂×C₃²	#397	1	1	yes	characteristic
251	C₂×C₃²	#459	1	1	yes	characteristic
252	C₂×C₃²	#461	1	1	yes	characteristic
253	C₂×C₃²	#480	1	1	yes	characteristic
254	C₂×C₃²	#481	1	1	yes	characteristic
255	C₂×C₃²	#486	1	1	yes	characteristic
256	C₂×C₃²	#489	1	1	yes	characteristic
257	C₃×D₃	—	8	2	no	—
258	C₂⁴	—	6	1	no	—
259	C₂×D₄	—	3	2	no	—
260	C₂×D₄	—	6	2	no	—
261	C₂×D₄	—	6	2	no	—
262	C₂×D₄	—	6	1	no	—
263	C₂²×C₄	—	6	1	no	—
264	C₂²×C₄	—	6	2	no	—
265	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
266	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₄⋊C₄	—	6	2	no	—
272	C₄⋊C₄	—	6	2	no	—
273	C₄⋊C₄	—	6	2	no	—
274	C₄⋊C₄	—	12	2	no	—
275	C₄⋊C₄	—	12	2	no	—
276	C₂²⋊C₄	—	12	2	no	—
277	C₂²⋊C₄	—	12	2	no	—
278	C₄²	—	2	2	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	12	2	no	—
287	C₂²×C₃	—	12	2	no	—
288	C₂²×C₃	—	12	2	no	—
289	C₂²×C₃	—	24	1	no	—
290	C₂²×C₃	—	24	1	no	—
291	C₂²×C₃	—	24	1	no	—
292	C₂²×C₃	—	24	1	no	—
293	C₂²×C₃	#875	1	1	yes	characteristic
294	C₂²×C₃	#886	1	1	yes	characteristic
295	C₂²×C₃	#895	1	1	yes	characteristic
296	C₂²×C₃	C₂×#204	1	1	yes	characteristic
297	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
298	C₂²×C₃	#908	1	1	yes	characteristic
299	C₂²×C₃	#909	1	1	yes	characteristic
300	C₂²×C₃	C₃×#121	1	1	yes	characteristic
301	C₂²×C₃	C₃×#123	1	1	yes	characteristic
302	C₂²×C₃	C₃×#124	1	1	yes	characteristic
303	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
305	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂²×C₃	C₃×#137	1	1	yes	characteristic
307	C₂×D₃	—	4	2	no	—
308	C₂×D₃	—	4	2	no	—
309	C₂×D₃	—	4	2	no	—
310	C₂×D₃	—	8	1	no	—
311	C₂×D₃	—	8	1	no	—
312	C₂×D₃	—	8	1	no	—
313	C₂×D₃	—	8	1	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	4	2	no	—
322	C₃×C₄	—	24	1	no	—
323	C₃×C₄	—	24	2	no	—
324	C₃×C₄	#883	1	2	yes	—
325	C₃×C₄	#898	1	2	yes	—
326	C₃×C₄	C₃×#123	1	2	yes	—
327	C₃×C₄	C₃×#126	1	2	yes	—
328	Dic₃	—	8	2	no	—
329	Dic₃	—	8	1	no	—
330	C₃²	#2071	1	1	yes	characteristic, complemented, Sylow
331	C₂³	—	6	2	no	—
332	C₂³	—	12	1	no	—
333	C₂³	—	12	1	no	—
334	C₂³	—	12	1	no	—
335	C₂³	—	12	1	no	—
336	C₂³	—	12	1	no	—
337	C₂³	—	12	1	no	—
338	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
339	D₄	—	6	4	no	—
340	D₄	—	12	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	12	2	no	—
346	C₂×C₄	—	12	1	no	—
347	C₂×C₄	—	12	1	no	—
348	C₂×C₄	—	12	2	no	—
349	C₂×C₄	—	12	2	no	—
350	C₂×C₄	—	12	1	no	—
351	C₂×C₄	C₃×#204	1	2	yes	—
352	C₂×C₄	C₃×D₂₄	1	2	yes	—
353	C₂×C₄	C₃×#235	1	2	yes	—
354	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
355	C₂×C₄	C₃×#237	1	2	yes	—
356	C₂×C₄	C₃×#239	1	1	yes	characteristic
357	C₈	—	4	2	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	24	2	no	—
366	C₂×C₃	#4674	1	1	yes	characteristic
367	C₂×C₃	#4694	1	1	yes	characteristic
368	C₂×C₃	#4714	1	1	yes	characteristic
369	C₂×C₃	#4735	1	1	yes	characteristic
370	C₂×C₃	#4736	1	1	yes	characteristic
371	C₂×C₃	#4841	1	1	yes	characteristic
372	C₂×C₃	#4843	1	1	yes	characteristic
373	C₂×C₃	C₃×#397	1	1	yes	characteristic
374	C₂×C₃	C₃×#459	1	1	yes	characteristic
375	C₂×C₃	C₃×#461	1	1	yes	characteristic
376	C₂×C₃	C₃×#480	1	1	yes	characteristic
377	C₂×C₃	C₃×#481	1	1	yes	characteristic
378	C₂×C₃	C₃×#486	1	1	yes	characteristic
379	C₂×C₃	C₃×#489	1	1	yes	characteristic
380	D₃	—	8	2	no	—
381	C₂²	—	12	2	no	—
382	C₂²	—	12	2	no	—
383	C₂²	—	12	2	no	—
384	C₂²	—	24	1	no	—
385	C₂²	—	24	1	no	—
386	C₂²	—	24	1	no	—
387	C₂²	—	24	1	no	—
388	C₂²	C₃×#875	1	1	yes	characteristic
389	C₂²	C₃×#886	1	1	yes	characteristic
390	C₂²	C₃×#895	1	1	yes	characteristic
391	C₂²	C₂×C₃×#204	1	1	yes	characteristic
392	C₂²	C₂×C₃×D₂₄	1	1	yes	characteristic
393	C₂²	C₃×#908	1	1	yes	characteristic
394	C₂²	C₃×#909	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	24	1	no	—
398	C₄	—	24	2	no	—
399	C₄	C₃×#883	1	2	yes	—
400	C₄	C₃×#898	1	2	yes	—
401	C₃	—	2	1	no	—
402	C₃	#68635	1	1	yes	characteristic, direct product factor
403	C₃	C₃×#2071	1	1	yes	characteristic, complemented
404	C₂	—	24	2	no	—
405	C₂	C₃×#4674	1	1	yes	characteristic
406	C₂	C₃×#4694	1	1	yes	characteristic
407	C₂	C₃×#4714	1	1	yes	characteristic
408	C₂	C₃×#4735	1	1	yes	characteristic
409	C₂	C₃×#4736	1	1	yes	characteristic
410	C₂	C₃×#4841	1	1	yes	characteristic
411	C₂	C₃×#4843	1	1	yes	characteristic

	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×#2071
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. C₃×#4935	C₂	semidirect
4. C₃²×#336	C₂	semidirect
5. C₃×#4551	C₂	semidirect
7. #68635	C₃	direct (N × H)
23. #4935	C₂×C₃	semidirect
26. C₃×#336	D₃	semidirect
27. C₃×#336	C₂×C₃	semidirect
28. #4551	C₂×C₃	semidirect
104. #336	C₃×D₃	semidirect
330. C₃²	#2071	semidirect
402. C₃	#68635	direct (N × H)
403. C₃	C₃×#2071	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
C₃×#4939	2
C₃×#4935	2
C₃²×#336	2
C₃×#4551	2
C₃×#2071	3
#68635	3

Subgroups — C3×#68635 #11794646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68635 #11794646