Subgroups — C₃×#10596250 #13179530

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64367	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64159	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3756	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64127	C₂	1	2	yes	maximal, complemented
7	C₃×Q₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
8	C₃×#64125	C₂	1	2	yes	maximal, complemented
9	C₃×#64124	C₂	1	2	yes	maximal, complemented
10	C₃×#64118	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64116	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596250	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5779	—	3	4	no	maximal
14	C₃³×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
16	C₃×#3832	—	2	1	no	—
17	C₃×#3832	C₂²	1	2	yes	—
18	C₃×Q₈×C₃⋊D₃	—	2	1	no	—
19	C₃×Q₈×C₃⋊D₃	C₂²	1	2	yes	—
20	C₃×Q₈×C₃⋊D₃	C₂²	1	2	yes	—
21	C₃×#3830	—	2	2	no	—
22	C₃×#3830	C₂²	1	2	yes	—
23	C₃×#3828	—	2	2	no	—
24	C₃×#3828	—	2	1	no	—
25	C₃×#3828	C₂²	1	1	yes	characteristic
26	C₃×#3828	C₂²	1	1	yes	characteristic
27	C₂×C₃×#634	—	2	1	no	—
28	C₂×C₃×#634	C₂²	1	1	yes	characteristic
29	C₃³×Q₁₆	C₂²	1	2	yes	—
30	C₃³×SD₁₆	C₂²	1	2	yes	—
31	C₃³×M₁₆	C₂²	1	1	yes	characteristic
32	C₃×#3756	C₂²	1	2	yes	—
33	C₃×#3756	C₂²	1	2	yes	—
34	C₃×#3756	C₂²	1	1	yes	characteristic
35	C₃×#3755	C₂²	1	1	yes	characteristic
36	C₃×#3754	C₂²	1	1	yes	characteristic
37	C₃×#3753	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₃×#3746	C₂²	1	2	yes	—
40	C₃×#3744	C₂²	1	2	yes	—
41	C₃×#3743	C₂²	1	2	yes	—
42	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	—
43	#64367	C₂×C₃	1	1	yes	characteristic, complemented
44	#64364	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#1010	—	3	4	no	—
46	C₃×#1007	—	3	4	no	—
47	C₃²×#137	—	2	4	no	—
48	C₃²×#137	D₃	1	4	yes	complemented
49	C₃²×#137	C₂×C₃	1	1	yes	characteristic, complemented
50	#64159	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×#3756	C₂×C₃	1	1	yes	characteristic, complemented
52	#64127	C₂×C₃	1	2	yes	complemented
53	Q₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
54	#64125	C₂×C₃	1	2	yes	complemented
55	#64124	C₂×C₃	1	2	yes	complemented
56	#64118	C₂×C₃	1	1	yes	characteristic, complemented
57	#64116	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×#950	—	3	4	no	—
59	C₂×C₃×#216	—	3	4	no	—
60	C₃×#918	—	3	8	no	—
61	C₃×D₃×Q₁₆	—	3	8	no	—
62	C₃×#916	—	3	8	no	—
63	C₃×#915	—	3	8	no	—
64	C₃×#909	—	3	4	no	—
65	C₃×#907	—	3	4	no	—
66	C₃³×Q₈	—	2	1	no	—
67	C₃³×Q₈	C₂³	1	1	yes	characteristic
68	C₃³×Q₈	C₂³	1	2	yes	—
69	C₃³×D₄	—	2	1	no	—
70	C₃³×D₄	C₂³	1	1	yes	characteristic
71	C₂×C₃³×C₄	—	2	1	no	—
72	C₂×C₃³×C₄	—	2	1	no	—
73	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
74	C₃×#638	—	2	1	no	—
75	C₃×#638	—	2	2	no	—
76	C₃×#638	D₄	1	2	yes	—
77	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
78	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
79	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
80	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
81	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
82	C₃×C₄×C₃⋊D₃	—	2	2	no	—
83	C₃×C₄×C₃⋊D₃	—	2	2	no	—
84	C₃×C₄×C₃⋊D₃	—	2	1	no	—
85	C₃×C₄×C₃⋊D₃	—	2	2	no	—
86	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
87	C₃×#634	—	2	1	no	—
88	C₃×#634	—	2	2	no	—
89	C₃×#634	—	2	2	no	—
90	C₃×#634	D₄	1	1	yes	characteristic
91	C₃×#634	C₂³	1	2	yes	—
92	C₃×#634	C₂³	1	1	yes	characteristic
93	C₃³×C₈	C₂³	1	2	yes	—
94	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
95	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
96	C₃×#578	—	9	1	no	—
97	#5779	—	3	4	no	—
98	C₃²×#41	—	2	4	no	—
99	C₃²×#41	C₂×D₃	1	4	yes	—
100	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃²×Q₈	—	2	4	no	—
102	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
103	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
104	#3832	—	2	1	no	—
105	#3832	C₂²×C₃	1	2	yes	—
106	Q₈×C₃⋊D₃	—	2	1	no	—
107	Q₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
108	Q₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
109	#3830	—	2	2	no	—
110	#3830	C₂²×C₃	1	2	yes	—
111	#3828	—	2	2	no	—
112	#3828	—	2	1	no	—
113	#3828	C₂²×C₃	1	1	yes	characteristic
114	#3828	C₂²×C₃	1	1	yes	characteristic
115	C₂×#634	—	2	1	no	—
116	C₂×#634	C₂²×C₃	1	1	yes	characteristic
117	C₃×#239	—	3	8	no	—
118	C₃×#239	—	6	4	no	—
119	C₃×D₃×Q₈	—	3	8	no	—
120	C₃×D₃×Q₈	—	3	8	no	—
121	C₃×D₃×Q₈	—	6	4	no	—
122	C₃×#237	—	3	8	no	—
123	C₃×#237	—	6	8	no	—
124	C₃×#235	—	3	4	no	—
125	C₃×#235	—	3	4	no	—
126	C₃×#235	—	6	4	no	—
127	C₃×#235	—	6	8	no	—
128	C₂×C₃×Dic₆	—	3	4	no	—
129	C₂×C₃×Dic₆	—	6	4	no	—
130	C₃²×Q₁₆	—	2	8	no	—
131	C₃²×Q₁₆	C₂×D₃	1	8	yes	—
132	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
133	C₃²×SD₁₆	—	2	8	no	—
134	C₃²×SD₁₆	C₂×D₃	1	8	yes	—
135	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
136	C₃²×M₁₆	—	2	4	no	—
137	C₃²×M₁₆	C₂×D₃	1	4	yes	—
138	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
139	#3756	C₂²×C₃	1	2	yes	—
140	#3756	C₂²×C₃	1	2	yes	—
141	#3756	C₂²×C₃	1	1	yes	characteristic
142	#3755	C₂²×C₃	1	1	yes	characteristic
143	#3754	C₂²×C₃	1	1	yes	characteristic
144	#3753	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
146	#3746	C₂²×C₃	1	2	yes	—
147	#3744	C₂²×C₃	1	2	yes	—
148	#3743	C₂²×C₃	1	2	yes	—
149	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
150	C₃×#216	—	3	8	no	—
151	C₃×#216	—	3	8	no	—
152	C₃×#216	—	3	4	no	—
153	C₃×#215	—	3	4	no	—
154	C₃×#214	—	3	4	no	—
155	C₃×#213	—	3	4	no	—
156	C₂×C₃×C₃⋊C₈	—	3	4	no	—
157	C₃×Dic₁₂	—	3	8	no	—
158	C₃×#204	—	3	8	no	—
159	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
160	C₃×D₃×C₈	—	3	8	no	—
161	C₂²×C₃³	—	2	1	no	—
162	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₃⋊D₃	—	2	1	no	—
164	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
165	C₃³×C₄	—	2	1	no	—
166	C₃³×C₄	—	2	2	no	—
167	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
168	C₃³×C₄	C₂⁴	1	1	yes	characteristic
169	C₃×C₃⋊Dic₃	—	2	1	no	—
170	C₃×C₃⋊Dic₃	—	2	2	no	—
171	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
172	C₃×2₋¹⁺⁴	—	9	1	no	—
173	C₃×2₋¹⁺⁴	—	9	1	no	—
174	#1010	—	3	4	no	—
175	#1007	—	3	4	no	—
176	C₃×#137	—	2	4	no	—
177	C₃×#137	—	9	2	no	—
178	C₃×#137	—	9	2	no	—
179	C₃×#137	—	9	1	no	—
180	C₃×#137	C₃×D₃	1	4	yes	complemented
181	C₃×#137	C₃⋊D₃	1	1	yes	characteristic, complemented
182	C₃×#135	—	9	1	no	—
183	C₃×#135	—	9	2	no	—
184	C₂×C₃×Q₁₆	—	9	1	no	—
185	C₂×C₃×Q₁₆	—	9	2	no	—
186	C₃×#131	—	9	1	no	—
187	#950	—	3	4	no	—
188	C₂×#216	—	3	4	no	—
189	#918	—	3	8	no	—
190	D₃×Q₁₆	—	3	8	no	—
191	#916	—	3	8	no	—
192	#915	—	3	8	no	—
193	#909	—	3	4	no	—
194	#907	—	3	4	no	—
195	C₃²×Q₈	—	2	1	no	—
196	C₃²×Q₈	—	2	8	no	—
197	C₃²×Q₈	—	2	4	no	—
198	C₃²×Q₈	—	2	4	no	—
199	C₃²×Q₈	—	4	4	no	—
200	C₃²×Q₈	C₂²×D₃	1	4	yes	—
201	C₃²×Q₈	C₂²×D₃	1	8	yes	—
202	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
203	C₃²×Q₈	C₂³×C₃	1	2	yes	—
204	C₃²×D₄	—	2	1	no	—
205	C₃²×D₄	—	2	4	no	—
206	C₃²×D₄	—	2	4	no	—
207	C₃²×D₄	—	4	4	no	—
208	C₃²×D₄	C₂²×D₃	1	4	yes	—
209	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₃²×C₄	—	2	1	no	—
211	C₂×C₃²×C₄	—	2	1	no	—
212	C₂×C₃²×C₄	—	2	4	no	—
213	C₂×C₃²×C₄	—	2	4	no	—
214	C₂×C₃²×C₄	—	2	4	no	—
215	C₂×C₃²×C₄	—	4	4	no	—
216	C₂×C₃²×C₄	—	4	4	no	—
217	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
218	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
219	#638	—	2	1	no	—
220	#638	—	2	2	no	—
221	#638	C₃×D₄	1	2	yes	—
222	C₂×C₃⋊Dic₃	—	2	1	no	—
223	C₂×C₃⋊Dic₃	—	2	2	no	—
224	C₄⋊(C₃⋊D₃)	—	2	2	no	—
225	C₄⋊(C₃⋊D₃)	C₃×D₄	1	1	yes	characteristic
226	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	1	yes	characteristic
227	C₄×C₃⋊D₃	—	2	2	no	—
228	C₄×C₃⋊D₃	—	2	2	no	—
229	C₄×C₃⋊D₃	—	2	1	no	—
230	C₄×C₃⋊D₃	—	2	2	no	—
231	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
232	#634	—	2	1	no	—
233	#634	—	2	2	no	—
234	#634	—	2	2	no	—
235	#634	C₃×D₄	1	1	yes	characteristic
236	#634	C₂³×C₃	1	2	yes	—
237	#634	C₂³×C₃	1	1	yes	characteristic
238	C₃×#67	—	3	8	no	—
239	C₃×#67	—	6	8	no	—
240	C₃×#67	—	6	4	no	—
241	C₂×C₃×Dic₃	—	6	8	no	—
242	C₂×C₃×Dic₃	—	6	4	no	—
243	C₃×D₁₂	—	3	4	no	—
244	C₃×D₁₂	—	3	4	no	—
245	C₃×D₁₂	—	6	8	no	—
246	C₃×C₄×D₃	—	3	8	no	—
247	C₃×C₄×D₃	—	6	8	no	—
248	C₃×C₄×D₃	—	6	8	no	—
249	C₃×C₄×D₃	—	6	8	no	—
250	C₃×C₄×D₃	—	6	4	no	—
251	C₃×Dic₆	—	3	4	no	—
252	C₃×Dic₆	—	3	8	no	—
253	C₃×Dic₆	—	3	4	no	—
254	C₃×Dic₆	—	6	8	no	—
255	C₃×Dic₆	—	6	8	no	—
256	C₃×Dic₆	—	6	4	no	—
257	C₃²×C₈	—	2	8	no	—
258	C₃²×C₈	C₂²×D₃	1	8	yes	—
259	C₃²×C₈	C₂³×C₃	1	2	yes	—
260	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
261	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
262	C₃×C₃⋊C₈	—	3	4	no	—
263	C₃×C₃⋊C₈	—	3	4	no	—
264	#578	—	9	1	no	Sylow
265	C₂×C₃³	—	2	1	no	—
266	C₂×C₃³	—	4	1	no	—
267	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
268	C₃×C₃⋊D₃	—	2	2	no	—
269	C₃×C₃⋊D₃	—	4	1	no	—
270	C₃×#41	—	2	4	no	—
271	C₃×#41	—	9	1	no	—
272	C₃×#41	—	9	2	no	—
273	C₃×#41	—	9	2	no	—
274	C₃×#41	—	9	1	no	—
275	C₃×#41	—	18	2	no	—
276	C₃×#41	—	18	1	no	—
277	C₃×#41	—	18	2	no	—
278	C₃×#41	—	18	1	no	—
279	C₃×#41	C₂×C₃×D₃	1	4	yes	—
280	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic
281	C₂×C₃×Q₈	—	2	4	no	—
282	C₂×C₃×Q₈	—	9	2	no	—
283	C₂×C₃×Q₈	—	9	2	no	—
284	C₂×C₃×Q₈	—	9	1	no	—
285	C₂×C₃×Q₈	—	18	1	no	—
286	C₂×C₃×Q₈	—	18	1	no	—
287	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
288	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
289	#239	—	3	8	no	—
290	#239	—	6	4	no	—
291	D₃×Q₈	—	3	8	no	—
292	D₃×Q₈	—	3	8	no	—
293	D₃×Q₈	—	6	4	no	—
294	#237	—	3	8	no	—
295	#237	—	6	8	no	—
296	#235	—	3	4	no	—
297	#235	—	3	4	no	—
298	#235	—	6	4	no	—
299	#235	—	6	8	no	—
300	C₂×Dic₆	—	3	4	no	—
301	C₂×Dic₆	—	6	4	no	—
302	C₃×Q₁₆	—	2	8	no	—
303	C₃×Q₁₆	—	9	1	no	—
304	C₃×Q₁₆	—	9	2	no	—
305	C₃×Q₁₆	—	9	2	no	—
306	C₃×Q₁₆	—	9	2	no	—
307	C₃×Q₁₆	C₂×C₃×D₃	1	8	yes	—
308	C₃×Q₁₆	C₂×C₃⋊D₃	1	2	yes	—
309	C₃×SD₁₆	—	2	8	no	—
310	C₃×SD₁₆	—	9	1	no	—
311	C₃×SD₁₆	—	9	1	no	—
312	C₃×SD₁₆	—	9	2	no	—
313	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	—
314	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	—
315	C₃×D₈	—	9	1	no	—
316	C₃×M₁₆	—	2	4	no	—
317	C₃×M₁₆	—	9	2	no	—
318	C₃×M₁₆	C₂×C₃×D₃	1	4	yes	—
319	C₃×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
320	C₂×C₃×C₈	—	9	1	no	—
321	C₂×C₃×C₈	—	9	2	no	—
322	#216	—	3	8	no	—
323	#216	—	3	8	no	—
324	#216	—	3	4	no	—
325	#215	—	3	4	no	—
326	#214	—	3	4	no	—
327	#213	—	3	4	no	—
328	C₂×C₃⋊C₈	—	3	4	no	—
329	Dic₁₂	—	3	8	no	—
330	#204	—	3	8	no	—
331	ΓL(1,𝔽₂₅)	—	3	8	no	—
332	D₃×C₈	—	3	8	no	—
333	C₂²×C₃²	—	2	1	no	—
334	C₂²×C₃²	—	2	4	no	—
335	C₂²×C₃²	—	2	4	no	—
336	C₂²×C₃²	—	4	4	no	—
337	C₂²×C₃²	D₃×D₄	1	4	yes	—
338	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₃⋊D₃	—	2	1	no	—
340	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
341	C₂×C₃×D₃	—	3	8	no	—
342	C₂×C₃×D₃	—	6	4	no	—
343	C₃²×C₄	—	2	1	no	—
344	C₃²×C₄	—	2	2	no	—
345	C₃²×C₄	—	2	4	no	—
346	C₃²×C₄	—	2	4	no	—
347	C₃²×C₄	—	2	4	no	—
348	C₃²×C₄	—	2	8	no	—
349	C₃²×C₄	—	4	4	no	—
350	C₃²×C₄	—	4	8	no	—
351	C₃²×C₄	D₃×D₄	1	4	yes	—
352	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
353	C₃²×C₄	C₂³×D₃	1	4	yes	—
354	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
355	C₃⋊Dic₃	—	2	1	no	—
356	C₃⋊Dic₃	—	2	2	no	—
357	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
358	C₃×Dic₃	—	3	8	no	—
359	C₃×Dic₃	—	6	4	no	—
360	C₃×Dic₃	—	6	8	no	—
361	2₋¹⁺⁴	—	9	1	no	—
362	2₋¹⁺⁴	—	9	1	no	—
363	#137	—	9	2	no	—
364	#137	—	9	2	no	—
365	#137	—	9	1	no	—
366	#137	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
367	#135	—	9	1	no	—
368	#135	—	9	2	no	—
369	C₂×Q₁₆	—	9	1	no	—
370	C₂×Q₁₆	—	9	2	no	—
371	#131	—	9	1	no	—
372	C₃³	#578	1	1	yes	characteristic, complemented, Sylow
373	C₃×Q₈	—	2	4	no	—
374	C₃×Q₈	—	2	1	no	—
375	C₃×Q₈	—	2	8	no	—
376	C₃×Q₈	—	2	4	no	—
377	C₃×Q₈	—	4	4	no	—
378	C₃×Q₈	—	9	1	no	—
379	C₃×Q₈	—	9	2	no	—
380	C₃×Q₈	—	9	1	no	—
381	C₃×Q₈	—	18	2	no	—
382	C₃×Q₈	—	18	2	no	—
383	C₃×Q₈	—	18	1	no	—
384	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
385	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
386	C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
387	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
388	C₃×D₄	—	2	4	no	—
389	C₃×D₄	—	2	1	no	—
390	C₃×D₄	—	2	4	no	—
391	C₃×D₄	—	4	4	no	—
392	C₃×D₄	—	9	2	no	—
393	C₃×D₄	—	9	1	no	—
394	C₃×D₄	—	9	1	no	—
395	C₃×D₄	—	18	2	no	—
396	C₃×D₄	—	18	2	no	—
397	C₃×D₄	—	18	1	no	—
398	C₃×D₄	C₂²×C₃×D₃	1	4	yes	—
399	C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	4	no	—
405	C₂×C₃×C₄	—	4	4	no	—
406	C₂×C₃×C₄	—	4	4	no	—
407	C₂×C₃×C₄	—	9	2	no	—
408	C₂×C₃×C₄	—	18	2	no	—
409	C₂×C₃×C₄	—	18	2	no	—
410	C₂×C₃×C₄	—	18	2	no	—
411	C₂×C₃×C₄	—	18	2	no	—
412	C₂×C₃×C₄	—	18	1	no	—
413	C₂×C₃×C₄	—	18	1	no	—
414	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
415	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
416	#67	—	3	8	no	—
417	#67	—	6	8	no	—
418	#67	—	6	4	no	—
419	C₂×Dic₃	—	6	8	no	—
420	C₂×Dic₃	—	6	4	no	—
421	D₁₂	—	3	4	no	—
422	D₁₂	—	3	4	no	—
423	D₁₂	—	6	8	no	—
424	C₄×D₃	—	3	8	no	—
425	C₄×D₃	—	6	8	no	—
426	C₄×D₃	—	6	8	no	—
427	C₄×D₃	—	6	8	no	—
428	C₄×D₃	—	6	4	no	—
429	Dic₆	—	3	4	no	—
430	Dic₆	—	3	8	no	—
431	Dic₆	—	3	4	no	—
432	Dic₆	—	6	8	no	—
433	Dic₆	—	6	8	no	—
434	Dic₆	—	6	4	no	—
435	C₃×C₈	—	2	8	no	—
436	C₃×C₈	—	9	1	no	—
437	C₃×C₈	—	9	1	no	—
438	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
439	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
440	C₃⋊C₈	—	3	4	no	—
441	C₃⋊C₈	—	3	4	no	—
442	C₂×C₃²	—	2	1	no	—
443	C₂×C₃²	—	2	4	no	—
444	C₂×C₃²	—	2	4	no	—
445	C₂×C₃²	—	4	4	no	—
446	C₂×C₃²	—	4	1	no	—
447	C₂×C₃²	—	4	4	no	—
448	C₂×C₃²	—	8	4	no	—
449	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
450	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
451	C₃⋊D₃	—	2	2	no	—
452	C₃⋊D₃	—	4	1	no	—
453	C₃×D₃	—	6	8	no	—
454	C₃×D₃	—	12	4	no	—
455	#41	—	9	1	no	—
456	#41	—	9	2	no	—
457	#41	—	9	2	no	—
458	#41	—	9	1	no	—
459	#41	—	18	2	no	—
460	#41	—	18	1	no	—
461	#41	—	18	2	no	—
462	#41	—	18	1	no	—
463	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
464	C₂×Q₈	—	9	2	no	—
465	C₂×Q₈	—	9	2	no	—
466	C₂×Q₈	—	9	1	no	—
467	C₂×Q₈	—	18	1	no	—
468	C₂×Q₈	—	18	1	no	—
469	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
470	Q₁₆	—	9	1	no	—
471	Q₁₆	—	9	2	no	—
472	Q₁₆	—	9	2	no	—
473	Q₁₆	—	9	2	no	—
474	Q₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
475	SD₁₆	—	9	1	no	—
476	SD₁₆	—	9	1	no	—
477	SD₁₆	—	9	2	no	—
478	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
479	D₈	—	9	1	no	—
480	M₁₆	—	9	2	no	—
481	M₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
482	C₂×C₈	—	9	1	no	—
483	C₂×C₈	—	9	2	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	4	no	—
487	C₂²×C₃	—	4	4	no	—
488	C₂²×C₃	—	9	2	no	—
489	C₂²×C₃	—	18	1	no	—
490	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
491	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
492	C₂×D₃	—	3	8	no	—
493	C₂×D₃	—	6	4	no	—
494	C₃×C₄	—	2	4	no	—
495	C₃×C₄	—	2	8	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	2	4	no	—
499	C₃×C₄	—	2	4	no	—
500	C₃×C₄	—	4	4	no	—
501	C₃×C₄	—	4	8	no	—
502	C₃×C₄	—	9	2	no	—
503	C₃×C₄	—	18	1	no	—
504	C₃×C₄	—	18	2	no	—
505	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
506	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
507	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
508	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
509	Dic₃	—	3	8	no	—
510	Dic₃	—	6	4	no	—
511	Dic₃	—	6	8	no	—
512	C₃²	—	2	4	no	—
513	C₃²	#5779	1	4	yes	complemented
514	C₃²	C₃×#578	1	1	yes	characteristic, complemented
515	Q₈	—	2	1	no	—
516	Q₈	—	9	1	no	—
517	Q₈	—	9	1	no	—
518	Q₈	—	9	2	no	—
519	Q₈	—	18	2	no	—
520	Q₈	—	18	2	no	—
521	Q₈	—	18	1	no	—
522	Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
523	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
524	D₄	—	2	1	no	—
525	D₄	—	9	2	no	—
526	D₄	—	9	1	no	—
527	D₄	—	9	1	no	—
528	D₄	—	18	2	no	—
529	D₄	—	18	2	no	—
530	D₄	—	18	1	no	—
531	D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	9	2	no	—
535	C₂×C₄	—	18	2	no	—
536	C₂×C₄	—	18	2	no	—
537	C₂×C₄	—	18	2	no	—
538	C₂×C₄	—	18	2	no	—
539	C₂×C₄	—	18	1	no	—
540	C₂×C₄	—	18	1	no	—
541	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
542	C₈	—	9	1	no	—
543	C₈	—	9	1	no	—
544	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
545	C₂×C₃	—	2	4	no	—
546	C₂×C₃	—	2	1	no	—
547	C₂×C₃	—	2	4	no	—
548	C₂×C₃	—	4	4	no	—
549	C₂×C₃	—	4	4	no	—
550	C₂×C₃	—	4	1	no	—
551	C₂×C₃	—	8	4	no	—
552	C₂×C₃	—	18	2	no	—
553	C₂×C₃	—	36	1	no	—
554	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
555	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
556	D₃	—	6	8	no	—
557	D₃	—	12	4	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	9	2	no	—
560	C₂²	—	18	1	no	—
561	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	9	2	no	—
565	C₄	—	18	1	no	—
566	C₄	—	18	2	no	—
567	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
568	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
569	C₃	—	2	4	no	—
570	C₃	C₃×#5779	1	4	yes	complemented
571	C₃	#10596250	1	1	yes	characteristic, direct product factor
572	C₂	—	2	1	no	—
573	C₂	—	4	1	no	—
574	C₂	—	18	2	no	—
575	C₂	—	36	1	no	—
576	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#137	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×#137	C₃⋊D₃
hypocenter	C₃²	C₃×#578
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₃×#64367	C₂	semidirect
2. C₃×#64364	C₂	semidirect
3. C₃³×#137	C₂	semidirect
4. C₃×#64159	C₂	semidirect
5. C₂×C₃×#3756	C₂	semidirect
6. C₃×#64127	C₂	semidirect
7. C₃×Q₁₆×C₃⋊D₃	C₂	semidirect
8. C₃×#64125	C₂	semidirect
9. C₃×#64124	C₂	semidirect
10. C₃×#64118	C₂	semidirect
11. C₃×#64116	C₂	semidirect
12. #10596250	C₃	direct (N × H)
43. #64367	C₂×C₃	semidirect
44. #64364	C₂×C₃	semidirect
48. C₃²×#137	D₃	semidirect
49. C₃²×#137	C₂×C₃	semidirect
50. #64159	C₂×C₃	semidirect
51. C₂×#3756	C₂×C₃	semidirect
52. #64127	C₂×C₃	semidirect
53. Q₁₆×C₃⋊D₃	C₂×C₃	semidirect
54. #64125	C₂×C₃	semidirect
55. #64124	C₂×C₃	semidirect
56. #64118	C₂×C₃	semidirect
57. #64116	C₂×C₃	semidirect
180. C₃×#137	C₃×D₃	semidirect
181. C₃×#137	C₃⋊D₃	semidirect
366. #137	C₃×C₃⋊D₃	semidirect
372. C₃³	#578	semidirect
513. C₃²	#5779	semidirect
514. C₃²	C₃×#578	semidirect
570. C₃	C₃×#5779	semidirect
571. C₃	#10596250	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#64367	2
C₃×#64364	2
C₃³×#137	2
C₃×#64159	2
C₂×C₃×#3756	2
C₃×#64127	2
C₃×Q₁₆×C₃⋊D₃	2
C₃×#64125	2
C₃×#64124	2
C₃×#64118	2
C₃×#64116	2
#10596250	3
C₃×#5779	3

Subgroups — C3×#10596250 #13179530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596250 #13179530