Subgroups — C₃×#10596239 #13179519

Order 1728.

1820 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₃³×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64159	C₂	1	2	yes	maximal, complemented
4	C₃×#64127	C₂	1	2	yes	maximal, complemented
5	C₃×#64124	C₂	1	2	yes	maximal, complemented
6	C₃×#64123	C₂	1	2	yes	maximal, complemented
7	C₃×#64120	C₂	1	2	yes	maximal, complemented
8	C₃×#64113	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#3743	C₂	1	1	yes	maximal, characteristic, complemented
10	#10596239	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#5768	—	3	4	no	maximal
12	C₃³×#41	C₂²	1	2	yes	complemented
13	C₃×#3832	C₂²	1	2	yes	—
14	C₃×Q₈×C₃⋊D₃	C₂²	1	2	yes	complemented
15	C₃×#3830	—	2	2	no	—
16	C₃×#3830	C₂²	1	2	yes	—
17	C₃×D₄×C₃⋊D₃	—	2	2	no	—
18	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	complemented
19	C₃×#3828	—	2	2	no	—
20	C₃×#3828	C₂²	1	2	yes	complemented
21	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
22	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
23	C₃³×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃³×SD₁₆	C₂²	1	2	yes	complemented
25	C₃³×D₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×#3756	C₂²	1	2	yes	complemented
28	C₃×#3755	C₂²	1	2	yes	complemented
29	C₃×#3754	C₂²	1	2	yes	complemented
30	C₃×#3753	C₂²	1	2	yes	complemented
31	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3746	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3745	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3744	C₂²	1	2	yes	complemented
35	C₃×#3743	C₂²	1	2	yes	complemented
36	C₃×#3743	C₂²	1	2	yes	complemented
37	#41×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
38	C₃×D₃×#41	—	3	8	no	—
39	C₃²×#135	—	2	4	no	—
40	C₃²×#135	D₃	1	4	yes	complemented
41	C₃²×#135	C₂×C₃	1	1	yes	characteristic, complemented
42	#64159	C₂×C₃	1	2	yes	complemented
43	#64127	C₂×C₃	1	2	yes	complemented
44	#64124	C₂×C₃	1	2	yes	complemented
45	#64123	C₂×C₃	1	2	yes	complemented
46	#64120	C₂×C₃	1	2	yes	complemented
47	#64113	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#3743	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#950	—	3	8	no	—
50	C₃×#918	—	3	8	no	—
51	C₃×#915	—	3	8	no	—
52	C₃×#914	—	3	8	no	—
53	C₃×#911	—	3	8	no	—
54	C₃×#904	—	3	4	no	—
55	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
56	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
57	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
58	C₃³×Q₈	C₂³	1	2	yes	—
59	C₃³×D₄	—	2	2	no	—
60	C₃³×D₄	C₂³	1	2	yes	—
61	C₂×C₃³×C₄	—	2	2	no	—
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
63	C₃×#638	—	2	2	no	—
64	C₃×#638	—	2	2	no	—
65	C₃×#638	—	2	2	no	—
66	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
67	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
68	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
69	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
70	C₃×C₄×C₃⋊D₃	—	2	2	no	—
71	C₃×C₄×C₃⋊D₃	—	2	2	no	—
72	C₃×C₄×C₃⋊D₃	—	2	2	no	—
73	C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
74	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
75	C₃×#634	—	2	2	no	—
76	C₃×#634	C₂³	1	2	yes	—
77	C₃³×C₈	C₂³	1	1	yes	characteristic
78	C₃³×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
80	C₃×#575	—	9	1	no	—
81	#5768	—	3	4	no	—
82	C₃²×#41	—	2	8	no	—
83	C₃²×#41	C₂×D₃	1	8	yes	complemented
84	C₃²×#41	C₂²×C₃	1	2	yes	complemented
85	#3832	C₂²×C₃	1	2	yes	—
86	Q₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
87	#3830	—	2	2	no	—
88	#3830	C₂²×C₃	1	2	yes	—
89	D₄×C₃⋊D₃	—	2	2	no	—
90	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
91	#3828	—	2	2	no	—
92	#3828	C₂²×C₃	1	2	yes	complemented
93	C₂×C₄×C₃⋊D₃	—	2	2	no	—
94	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×#239	—	3	8	no	—
96	C₃×D₃×Q₈	—	3	8	no	—
97	C₃×#237	—	3	8	no	—
98	C₃×#237	—	6	8	no	—
99	C₃×D₃×D₄	—	3	8	no	—
100	C₃×D₃×D₄	—	6	8	no	—
101	C₃×#235	—	3	8	no	—
102	C₃×#235	—	6	8	no	—
103	C₂×C₃×C₄×D₃	—	3	4	no	—
104	C₂×C₃×C₄×D₃	—	6	8	no	—
105	C₃²×Q₁₆	—	2	4	no	—
106	C₃²×Q₁₆	C₂×D₃	1	4	yes	complemented
107	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₃²×SD₁₆	—	2	8	no	—
109	C₃²×SD₁₆	C₂×D₃	1	8	yes	complemented
110	C₃²×SD₁₆	C₂²×C₃	1	2	yes	complemented
111	C₃²×D₈	—	2	4	no	—
112	C₃²×D₈	C₂×D₃	1	4	yes	complemented
113	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×C₃²×C₈	—	2	4	no	—
115	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
116	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
117	#3756	C₂²×C₃	1	2	yes	complemented
118	#3755	C₂²×C₃	1	2	yes	complemented
119	#3754	C₂²×C₃	1	2	yes	complemented
120	#3753	C₂²×C₃	1	2	yes	complemented
121	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
122	#3746	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3745	C₂²×C₃	1	1	yes	characteristic, complemented
124	#3744	C₂²×C₃	1	2	yes	complemented
125	#3743	C₂²×C₃	1	2	yes	complemented
126	#3743	C₂²×C₃	1	2	yes	complemented
127	C₃×#216	—	3	8	no	—
128	C₃×#215	—	3	8	no	—
129	C₃×#214	—	3	8	no	—
130	C₃×#213	—	3	8	no	—
131	C₂×C₃×C₃⋊C₈	—	3	4	no	—
132	C₃×Dic₁₂	—	3	4	no	—
133	C₃×D₂₄	—	3	4	no	—
134	C₃×#204	—	3	8	no	—
135	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
136	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
137	C₂²×C₃³	—	2	2	no	—
138	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₃⋊D₃	—	2	2	no	—
140	C₂×C₃×C₃⋊D₃	—	4	1	no	—
141	C₂×C₃×C₃⋊D₃	—	4	4	no	—
142	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
143	C₃³×C₄	—	2	2	no	—
144	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
145	C₃³×C₄	C₂⁴	1	1	yes	characteristic
146	C₃×C₃⋊Dic₃	—	2	2	no	—
147	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
148	C₂×C₃×#41	—	9	2	no	—
149	D₃×#41	—	3	8	no	—
150	C₃×#137	—	9	2	no	—
151	C₃×#137	—	9	2	no	—
152	C₃×AGL(1,ℤ/8)	—	9	2	no	—
153	C₃×AGL(1,ℤ/8)	—	9	2	no	—
154	C₃×#135	—	2	4	no	—
155	C₃×#135	—	9	2	no	—
156	C₃×#135	—	9	1	no	—
157	C₃×#135	C₃×D₃	1	4	yes	complemented
158	C₃×#135	C₃⋊D₃	1	1	yes	characteristic, complemented
159	C₂×C₃×M₁₆	—	9	1	no	—
160	#950	—	3	8	no	—
161	#918	—	3	8	no	—
162	#915	—	3	8	no	—
163	#914	—	3	8	no	—
164	#911	—	3	8	no	—
165	#904	—	3	4	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
167	C₂²×C₃⋊D₃	—	2	2	no	—
168	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
169	C₂²×C₃×D₃	—	3	4	no	—
170	C₂²×C₃×D₃	—	6	8	no	—
171	C₃²×Q₈	—	2	8	no	—
172	C₃²×Q₈	C₂²×D₃	1	8	yes	—
173	C₃²×Q₈	C₂³×C₃	1	2	yes	—
174	C₃²×D₄	—	2	2	no	—
175	C₃²×D₄	—	2	8	no	—
176	C₃²×D₄	—	2	8	no	—
177	C₃²×D₄	—	4	8	no	—
178	C₃²×D₄	C₂²×D₃	1	8	yes	—
179	C₃²×D₄	C₂³×C₃	1	2	yes	—
180	C₂×C₃²×C₄	—	2	2	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	8	no	—
183	C₂×C₃²×C₄	—	4	8	no	—
184	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	#638	—	2	2	no	—
187	#638	—	2	2	no	—
188	#638	—	2	2	no	—
189	C₂×C₃⋊Dic₃	—	2	2	no	—
190	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
191	C₄⋊(C₃⋊D₃)	—	2	2	no	—
192	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
193	C₄×C₃⋊D₃	—	2	2	no	—
194	C₄×C₃⋊D₃	—	2	2	no	—
195	C₄×C₃⋊D₃	—	2	2	no	—
196	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
197	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
198	#634	—	2	2	no	—
199	#634	C₂³×C₃	1	2	yes	—
200	C₃×#67	—	6	8	no	—
201	C₃×#67	—	6	8	no	—
202	C₃×#67	—	6	8	no	—
203	C₂×C₃×Dic₃	—	3	4	no	—
204	C₂×C₃×Dic₃	—	6	8	no	—
205	C₃×D₁₂	—	3	8	no	—
206	C₃×D₁₂	—	6	8	no	—
207	C₃×C₄×D₃	—	3	8	no	—
208	C₃×C₄×D₃	—	3	8	no	—
209	C₃×C₄×D₃	—	6	8	no	—
210	C₃×C₄×D₃	—	6	8	no	—
211	C₃×C₄×D₃	—	6	8	no	—
212	C₃×Dic₆	—	3	8	no	—
213	C₃×Dic₆	—	6	8	no	—
214	C₃²×C₈	—	2	4	no	—
215	C₃²×C₈	—	2	4	no	—
216	C₃²×C₈	C₂²×D₃	1	4	yes	—
217	C₃²×C₈	C₂²×D₃	1	4	yes	—
218	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
221	C₃×C₃⋊C₈	—	3	8	no	—
222	#575	—	9	1	no	Sylow
223	C₂×C₃³	—	2	1	no	—
224	C₂×C₃³	—	4	2	no	—
225	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
226	C₃×C₃⋊D₃	—	2	2	no	—
227	C₃×C₃⋊D₃	—	4	2	no	—
228	C₃×#41	—	2	8	no	—
229	C₃×#41	—	9	2	no	—
230	C₃×#41	—	9	2	no	—
231	C₃×#41	—	9	2	no	—
232	C₃×#41	—	18	2	no	—
233	C₃×#41	—	18	2	no	—
234	C₃×#41	C₂×C₃×D₃	1	8	yes	complemented
235	C₃×#41	C₂×C₃⋊D₃	1	2	yes	complemented
236	C₂×C₃×Q₈	—	9	2	no	—
237	C₂×C₃×D₄	—	9	2	no	—
238	C₂×C₃×D₄	—	18	2	no	—
239	C₂²×C₃×C₄	—	9	1	no	—
240	C₂²×C₃×C₄	—	18	2	no	—
241	#239	—	3	8	no	—
242	D₃×Q₈	—	3	8	no	—
243	#237	—	3	8	no	—
244	#237	—	6	8	no	—
245	D₃×D₄	—	3	8	no	—
246	D₃×D₄	—	6	8	no	—
247	#235	—	3	8	no	—
248	#235	—	6	8	no	—
249	C₂×C₄×D₃	—	3	4	no	—
250	C₂×C₄×D₃	—	6	8	no	—
251	C₃×Q₁₆	—	2	4	no	—
252	C₃×Q₁₆	—	9	2	no	—
253	C₃×Q₁₆	—	9	1	no	—
254	C₃×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
255	C₃×Q₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
256	C₃×SD₁₆	—	2	8	no	—
257	C₃×SD₁₆	—	9	2	no	—
258	C₃×SD₁₆	—	9	2	no	—
259	C₃×SD₁₆	—	9	2	no	—
260	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
261	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
262	C₃×D₈	—	2	4	no	—
263	C₃×D₈	—	9	2	no	—
264	C₃×D₈	—	9	1	no	—
265	C₃×D₈	C₂×C₃×D₃	1	4	yes	complemented
266	C₃×D₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
267	C₃×M₁₆	—	9	2	no	—
268	C₃×M₁₆	—	9	2	no	—
269	C₂×C₃×C₈	—	2	4	no	—
270	C₂×C₃×C₈	—	9	1	no	—
271	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
272	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
273	#216	—	3	8	no	—
274	#215	—	3	8	no	—
275	#214	—	3	8	no	—
276	#213	—	3	8	no	—
277	C₂×C₃⋊C₈	—	3	4	no	—
278	Dic₁₂	—	3	4	no	—
279	D₂₄	—	3	4	no	—
280	#204	—	3	8	no	—
281	ΓL(1,𝔽₂₅)	—	3	8	no	—
282	ΓL(1,𝔽₂₅)	—	3	8	no	—
283	C₂²×C₃²	—	2	2	no	—
284	C₂²×C₃²	—	2	4	no	—
285	C₂²×C₃²	—	2	8	no	—
286	C₂²×C₃²	—	4	8	no	—
287	C₂²×C₃²	D₃×D₄	1	4	yes	—
288	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃⋊D₃	—	2	2	no	—
290	C₂×C₃⋊D₃	—	4	1	no	—
291	C₂×C₃⋊D₃	—	4	4	no	—
292	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
293	C₂×C₃×D₃	—	3	8	no	—
294	C₂×C₃×D₃	—	6	8	no	—
295	C₂×C₃×D₃	—	12	4	no	—
296	C₂×C₃×D₃	—	12	16	no	—
297	C₃²×C₄	—	2	2	no	—
298	C₃²×C₄	—	2	4	no	—
299	C₃²×C₄	—	2	4	no	—
300	C₃²×C₄	—	2	8	no	—
301	C₃²×C₄	—	4	8	no	—
302	C₃²×C₄	D₃×D₄	1	4	yes	—
303	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
304	C₃²×C₄	C₂³×D₃	1	4	yes	—
305	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₃⋊Dic₃	—	2	2	no	—
307	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
308	C₃×Dic₃	—	3	8	no	—
309	C₃×Dic₃	—	6	8	no	—
310	C₂×#41	—	9	2	no	—
311	#137	—	9	2	no	—
312	#137	—	9	2	no	—
313	AGL(1,ℤ/8)	—	9	2	no	—
314	AGL(1,ℤ/8)	—	9	2	no	—
315	#135	—	9	2	no	—
316	#135	—	9	1	no	—
317	#135	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
318	C₂×M₁₆	—	9	1	no	—
319	C₃³	#575	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₃	—	9	1	no	—
321	C₂³×C₃	—	18	2	no	—
322	C₂²×D₃	—	3	4	no	—
323	C₂²×D₃	—	6	8	no	—
324	C₃×Q₈	—	2	8	no	—
325	C₃×Q₈	—	9	2	no	—
326	C₃×Q₈	—	18	2	no	—
327	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
328	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
329	C₃×D₄	—	2	8	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	8	no	—
332	C₃×D₄	—	4	8	no	—
333	C₃×D₄	—	9	2	no	—
334	C₃×D₄	—	18	2	no	—
335	C₃×D₄	—	18	2	no	—
336	C₃×D₄	—	18	2	no	—
337	C₃×D₄	—	18	2	no	—
338	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
339	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
340	C₂×C₃×C₄	—	2	8	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	4	8	no	—
344	C₂×C₃×C₄	—	9	1	no	—
345	C₂×C₃×C₄	—	9	2	no	—
346	C₂×C₃×C₄	—	9	2	no	—
347	C₂×C₃×C₄	—	18	2	no	—
348	C₂×C₃×C₄	—	18	2	no	—
349	C₂×C₃×C₄	—	18	2	no	—
350	C₂×C₃×C₄	—	18	2	no	—
351	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
352	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
353	#67	—	6	8	no	—
354	#67	—	6	8	no	—
355	#67	—	6	8	no	—
356	C₂×Dic₃	—	3	4	no	—
357	C₂×Dic₃	—	6	8	no	—
358	D₁₂	—	3	8	no	—
359	D₁₂	—	6	8	no	—
360	C₄×D₃	—	3	8	no	—
361	C₄×D₃	—	3	8	no	—
362	C₄×D₃	—	6	8	no	—
363	C₄×D₃	—	6	8	no	—
364	C₄×D₃	—	6	8	no	—
365	Dic₆	—	3	8	no	—
366	Dic₆	—	6	8	no	—
367	C₃×C₈	—	2	4	no	—
368	C₃×C₈	—	2	4	no	—
369	C₃×C₈	—	9	2	no	—
370	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
371	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
372	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
373	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
374	C₃⋊C₈	—	3	8	no	—
375	C₂×C₃²	—	2	1	no	—
376	C₂×C₃²	—	2	4	no	—
377	C₂×C₃²	—	2	4	no	—
378	C₂×C₃²	—	4	4	no	—
379	C₂×C₃²	—	4	2	no	—
380	C₂×C₃²	—	4	8	no	—
381	C₂×C₃²	—	8	8	no	—
382	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
383	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
384	C₃⋊D₃	—	2	2	no	—
385	C₃⋊D₃	—	4	2	no	—
386	C₃×D₃	—	6	8	no	—
387	C₃×D₃	—	12	8	no	—
388	#41	—	9	2	no	—
389	#41	—	9	2	no	—
390	#41	—	9	2	no	—
391	#41	—	18	2	no	—
392	#41	—	18	2	no	—
393	#41	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
394	C₂×Q₈	—	9	2	no	—
395	C₂×D₄	—	9	2	no	—
396	C₂×D₄	—	18	2	no	—
397	C₂²×C₄	—	9	1	no	—
398	C₂²×C₄	—	18	2	no	—
399	Q₁₆	—	9	2	no	—
400	Q₁₆	—	9	1	no	—
401	Q₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
402	SD₁₆	—	9	2	no	—
403	SD₁₆	—	9	2	no	—
404	SD₁₆	—	9	2	no	—
405	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
406	D₈	—	9	2	no	—
407	D₈	—	9	1	no	—
408	D₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
409	M₁₆	—	9	2	no	—
410	M₁₆	—	9	2	no	—
411	C₂×C₈	—	9	1	no	—
412	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
413	C₂²×C₃	—	2	8	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	—	4	8	no	—
417	C₂²×C₃	—	9	2	no	—
418	C₂²×C₃	—	18	2	no	—
419	C₂²×C₃	—	36	1	no	—
420	C₂²×C₃	—	36	4	no	—
421	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
422	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
423	C₂×D₃	—	3	8	no	—
424	C₂×D₃	—	6	8	no	—
425	C₂×D₃	—	12	4	no	—
426	C₂×D₃	—	12	16	no	—
427	C₃×C₄	—	2	8	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	4	no	—
430	C₃×C₄	—	2	4	no	—
431	C₃×C₄	—	4	8	no	—
432	C₃×C₄	—	9	2	no	—
433	C₃×C₄	—	18	2	no	—
434	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
435	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
436	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
437	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
438	Dic₃	—	3	8	no	—
439	Dic₃	—	6	8	no	—
440	C₃²	—	2	4	no	—
441	C₃²	#5768	1	4	yes	complemented
442	C₃²	C₃×#575	1	1	yes	characteristic, complemented
443	C₂³	—	9	1	no	—
444	C₂³	—	18	2	no	—
445	Q₈	—	9	2	no	—
446	Q₈	—	18	2	no	—
447	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	9	2	no	—
450	D₄	—	18	2	no	—
451	D₄	—	18	2	no	—
452	D₄	—	18	2	no	—
453	D₄	—	18	2	no	—
454	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	9	1	no	—
457	C₂×C₄	—	9	2	no	—
458	C₂×C₄	—	9	2	no	—
459	C₂×C₄	—	18	2	no	—
460	C₂×C₄	—	18	2	no	—
461	C₂×C₄	—	18	2	no	—
462	C₂×C₄	—	18	2	no	—
463	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
464	C₈	—	9	2	no	—
465	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
466	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
467	C₂×C₃	—	2	4	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	4	no	—
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	—	4	8	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	—	8	8	no	—
474	C₂×C₃	—	18	2	no	—
475	C₂×C₃	—	36	2	no	—
476	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
477	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
478	D₃	—	6	8	no	—
479	D₃	—	12	8	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	9	2	no	—
482	C₂²	—	18	2	no	—
483	C₂²	—	36	1	no	—
484	C₂²	—	36	4	no	—
485	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	9	2	no	—
488	C₄	—	18	2	no	—
489	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
490	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
491	C₃	—	2	4	no	—
492	C₃	C₃×#5768	1	4	yes	complemented
493	C₃	#10596239	1	1	yes	characteristic, direct product factor
494	C₂	—	2	1	no	—
495	C₂	—	4	2	no	—
496	C₂	—	18	2	no	—
497	C₂	—	36	2	no	—
498	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#135	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×#135	C₃⋊D₃
hypocenter	C₃²	C₃×#575
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#41×C₃⋊D₃	C₂	semidirect
2. C₃³×#135	C₂	semidirect
3. C₃×#64159	C₂	semidirect
4. C₃×#64127	C₂	semidirect
5. C₃×#64124	C₂	semidirect
6. C₃×#64123	C₂	semidirect
7. C₃×#64120	C₂	semidirect
8. C₃×#64113	C₂	semidirect
9. C₂×C₃×#3743	C₂	semidirect
10. #10596239	C₃	direct (N × H)
12. C₃³×#41	C₂²	semidirect
14. C₃×Q₈×C₃⋊D₃	C₂²	semidirect
18. C₃×D₄×C₃⋊D₃	C₂²	semidirect
20. C₃×#3828	C₂²	semidirect
23. C₃³×Q₁₆	C₂²	semidirect
24. C₃³×SD₁₆	C₂²	semidirect
25. C₃³×D₈	C₂²	semidirect
26. C₂×C₃³×C₈	C₂²	semidirect
27. C₃×#3756	C₂²	semidirect
28. C₃×#3755	C₂²	semidirect
29. C₃×#3754	C₂²	semidirect
30. C₃×#3753	C₂²	semidirect
31. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
32. C₃×#3746	C₂²	semidirect
33. C₃×#3745	C₂²	semidirect
34. C₃×#3744	C₂²	semidirect
35. C₃×#3743	C₂²	semidirect
36. C₃×#3743	C₂²	semidirect
37. #41×C₃⋊D₃	C₂×C₃	semidirect
40. C₃²×#135	D₃	semidirect
41. C₃²×#135	C₂×C₃	semidirect
42. #64159	C₂×C₃	semidirect
43. #64127	C₂×C₃	semidirect
44. #64124	C₂×C₃	semidirect
45. #64123	C₂×C₃	semidirect
46. #64120	C₂×C₃	semidirect
47. #64113	C₂×C₃	semidirect
48. C₂×#3743	C₂×C₃	semidirect
83. C₃²×#41	C₂×D₃	semidirect
84. C₃²×#41	C₂²×C₃	semidirect
86. Q₈×C₃⋊D₃	C₂²×C₃	semidirect
90. D₄×C₃⋊D₃	C₂²×C₃	semidirect
92. #3828	C₂²×C₃	semidirect
106. C₃²×Q₁₆	C₂×D₃	semidirect
107. C₃²×Q₁₆	C₂²×C₃	semidirect
109. C₃²×SD₁₆	C₂×D₃	semidirect
110. C₃²×SD₁₆	C₂²×C₃	semidirect
112. C₃²×D₈	C₂×D₃	semidirect
113. C₃²×D₈	C₂²×C₃	semidirect
115. C₂×C₃²×C₈	C₂×D₃	semidirect
116. C₂×C₃²×C₈	C₂²×C₃	semidirect
117. #3756	C₂²×C₃	semidirect
118. #3755	C₂²×C₃	semidirect
119. #3754	C₂²×C₃	semidirect
120. #3753	C₂²×C₃	semidirect
121. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
122. #3746	C₂²×C₃	semidirect
123. #3745	C₂²×C₃	semidirect
124. #3744	C₂²×C₃	semidirect
125. #3743	C₂²×C₃	semidirect
126. #3743	C₂²×C₃	semidirect
157. C₃×#135	C₃×D₃	semidirect
158. C₃×#135	C₃⋊D₃	semidirect
234. C₃×#41	C₂×C₃×D₃	semidirect
235. C₃×#41	C₂×C₃⋊D₃	semidirect
254. C₃×Q₁₆	C₂×C₃×D₃	semidirect
255. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
260. C₃×SD₁₆	C₂×C₃×D₃	semidirect
261. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
265. C₃×D₈	C₂×C₃×D₃	semidirect
266. C₃×D₈	C₂×C₃⋊D₃	semidirect
271. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
272. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
317. #135	C₃×C₃⋊D₃	semidirect
319. C₃³	#575	semidirect
393. #41	C₂×C₃×C₃⋊D₃	semidirect
401. Q₁₆	C₂×C₃×C₃⋊D₃	semidirect
405. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
408. D₈	C₂×C₃×C₃⋊D₃	semidirect
412. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
441. C₃²	#5768	semidirect
442. C₃²	C₃×#575	semidirect
492. C₃	C₃×#5768	semidirect
493. C₃	#10596239	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×#41×C₃⋊D₃	2
C₃³×#135	2
C₃×#64159	2
C₃×#64127	2
C₃×#64124	2
C₃×#64123	2
C₃×#64120	2
C₃×#64113	2
C₂×C₃×#3743	2
#10596239	3
C₃×#5768	3

Subgroups — C3×#10596239 #13179519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596239 #13179519