Subgroups — C₃×#10596186 #13179467

Order 1728.

2436 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3830	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64149	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64148	C₂	1	4	yes	maximal, complemented
6	C₃×#64146	C₂	1	4	yes	maximal, complemented
7	C₃×#64145	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64084	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64081	C₂	1	1	yes	maximal, characteristic, complemented
10	#10596186	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#5715	—	3	4	no	maximal
12	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
13	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
16	C₂×C₃×#638	C₂²	1	2	yes	—
17	C₂×C₃×#638	C₂²	1	2	yes	—
18	C₂×C₃×#638	C₂²	1	4	yes	complemented
19	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
20	C₃×#3830	—	2	4	no	—
21	C₃×D₄×C₃⋊D₃	—	2	4	no	—
22	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
25	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3757	C₂²	1	4	yes	complemented
27	C₃×#3752	C₂²	1	2	yes	—
28	C₃×#3752	C₂²	1	4	yes	complemented
29	C₃×#3750	C₂²	1	2	yes	complemented
30	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#3830	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#237	—	3	4	no	—
34	C₂×C₃×D₃×D₄	—	3	4	no	—
35	C₃²×#127	—	2	4	no	—
36	C₃²×#127	D₃	1	4	yes	complemented
37	C₃²×#127	C₂×C₃	1	1	yes	characteristic, complemented
38	#64149	C₂×C₃	1	1	yes	characteristic, complemented
39	#64148	C₂×C₃	1	4	yes	complemented
40	#64146	C₂×C₃	1	4	yes	complemented
41	#64145	C₂×C₃	1	1	yes	characteristic, complemented
42	#64084	C₂×C₃	1	1	yes	characteristic, complemented
43	#64081	C₂×C₃	1	1	yes	characteristic, complemented
44	C₃×#940	—	3	4	no	—
45	C₃×#939	—	3	16	no	—
46	C₃×#937	—	3	16	no	—
47	C₃×#936	—	3	4	no	—
48	C₃×#875	—	3	4	no	—
49	C₃×#872	—	3	4	no	—
50	C₂³×C₃³	C₂³	1	2	yes	—
51	C₂³×C₃³	C₂³	1	2	yes	—
52	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
53	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
54	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
55	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
56	C₃³×D₄	—	2	2	no	—
57	C₃³×D₄	—	2	2	no	—
58	C₃³×D₄	—	4	4	no	—
59	C₂×C₃³×C₄	C₂³	1	2	yes	—
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₃×#638	—	2	4	no	—
62	C₃×#638	—	2	4	no	—
63	C₃×#638	—	4	4	no	—
64	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
65	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
67	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
68	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
69	C₃×C₄×C₃⋊D₃	D₄	1	4	yes	complemented
70	C₃×#634	—	2	2	no	—
71	C₃×#535	—	9	1	no	—
72	#5715	—	3	4	no	—
73	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
74	C₂³×C₃×D₃	—	3	8	no	—
75	C₂×C₃²×D₄	—	2	4	no	—
76	C₂×C₃²×D₄	—	2	4	no	—
77	C₂×C₃²×D₄	—	2	16	no	—
78	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
79	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
80	C₂×C₃²×D₄	C₂×D₃	1	16	yes	complemented
81	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
84	C₂×#638	C₂²×C₃	1	2	yes	—
85	C₂×#638	C₂²×C₃	1	2	yes	—
86	C₂×#638	C₂²×C₃	1	4	yes	complemented
87	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
88	#3830	—	2	4	no	—
89	D₄×C₃⋊D₃	—	2	4	no	—
90	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
92	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂×C₃×#67	—	3	8	no	—
94	C₂×C₃×#67	—	3	8	no	—
95	C₂×C₃×#67	—	3	16	no	—
96	C₂²×C₃×Dic₃	—	3	8	no	—
97	C₃×#237	—	6	16	no	—
98	C₃×D₃×D₄	—	6	16	no	—
99	C₂×C₃×D₁₂	—	3	4	no	—
100	C₂×C₃×C₄×D₃	—	3	4	no	—
101	C₂×C₃×Dic₆	—	3	4	no	—
102	C₃²×C₄²	—	2	4	no	—
103	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
104	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
105	#3757	C₂²×C₃	1	4	yes	complemented
106	#3752	C₂²×C₃	1	2	yes	—
107	#3752	C₂²×C₃	1	4	yes	complemented
108	#3750	C₂²×C₃	1	2	yes	complemented
109	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₃×#217	—	3	16	no	—
111	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
112	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
113	C₃×Dic₃⋊C₄	—	3	8	no	—
114	C₃×C₄×Dic₃	—	3	4	no	—
115	C₂²×C₃³	—	2	2	no	—
116	C₂²×C₃³	—	2	2	no	—
117	C₂²×C₃³	—	2	4	no	—
118	C₂²×C₃³	—	2	4	no	—
119	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
120	C₂×C₃×C₃⋊D₃	—	2	2	no	—
121	C₂×C₃×C₃⋊D₃	—	2	2	no	—
122	C₂×C₃×C₃⋊D₃	—	2	4	no	—
123	C₂×C₃×C₃⋊D₃	—	4	8	no	—
124	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
125	C₃³×C₄	—	2	2	no	—
126	C₃³×C₄	C₂×D₄	1	2	yes	—
127	C₃×C₃⋊Dic₃	—	2	2	no	—
128	C₃×C₃⋊Dic₃	—	2	2	no	—
129	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
130	C₂×C₃×#41	—	9	1	no	—
131	C₂²×C₃×D₄	—	9	1	no	—
132	C₂×#237	—	3	4	no	—
133	C₂×D₃×D₄	—	3	4	no	—
134	C₃×#127	—	2	4	no	—
135	C₃×#127	—	9	1	no	—
136	C₃×#127	C₃×D₃	1	4	yes	complemented
137	C₃×#127	C₃⋊D₃	1	1	yes	characteristic, complemented
138	C₃×#124	—	9	1	no	—
139	C₃×#124	—	9	1	no	—
140	C₃×#121	—	9	4	no	—
141	C₃×#120	—	9	4	no	—
142	C₃×#117	—	9	1	no	—
143	#940	—	3	4	no	—
144	#939	—	3	16	no	—
145	#937	—	3	16	no	—
146	#936	—	3	4	no	—
147	#875	—	3	4	no	—
148	#872	—	3	4	no	—
149	C₂³×C₃²	—	2	8	no	—
150	C₂³×C₃²	—	2	8	no	—
151	C₂³×C₃²	C₂²×D₃	1	8	yes	—
152	C₂³×C₃²	C₂²×D₃	1	8	yes	—
153	C₂³×C₃²	C₂³×C₃	1	2	yes	—
154	C₂³×C₃²	C₂³×C₃	1	2	yes	—
155	C₂²×C₃⋊D₃	—	2	4	no	—
156	C₂²×C₃⋊D₃	—	4	4	no	—
157	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
158	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×D₃	—	3	4	no	—
160	C₂²×C₃×D₃	—	3	8	no	—
161	C₂²×C₃×D₃	—	6	16	no	—
162	C₂²×C₃×D₃	—	12	16	no	—
163	C₃²×D₄	—	2	2	no	—
164	C₃²×D₄	—	2	2	no	—
165	C₃²×D₄	—	2	8	no	—
166	C₃²×D₄	—	2	8	no	—
167	C₃²×D₄	—	4	8	no	—
168	C₃²×D₄	—	4	8	no	—
169	C₃²×D₄	—	4	16	no	—
170	C₃²×D₄	—	4	4	no	—
171	C₃²×D₄	—	4	32	no	—
172	C₂×C₃²×C₄	—	2	8	no	—
173	C₂×C₃²×C₄	—	2	4	no	—
174	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
175	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
176	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
177	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
178	#638	—	2	4	no	—
179	#638	—	2	4	no	—
180	#638	—	4	4	no	—
181	C₂×C₃⋊Dic₃	—	2	4	no	—
182	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
183	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
184	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
185	C₄⋊(C₃⋊D₃)	—	2	2	no	—
186	C₄×C₃⋊D₃	C₃×D₄	1	4	yes	complemented
187	#634	—	2	2	no	—
188	C₃×#67	—	6	16	no	—
189	C₃×#67	—	6	16	no	—
190	C₃×#67	—	12	16	no	—
191	C₂×C₃×Dic₃	—	3	4	no	—
192	C₂×C₃×Dic₃	—	3	8	no	—
193	C₂×C₃×Dic₃	—	3	8	no	—
194	C₂×C₃×Dic₃	—	6	16	no	—
195	C₃×D₁₂	—	6	8	no	—
196	C₃×C₄×D₃	—	3	16	no	—
197	C₃×Dic₆	—	6	8	no	—
198	#535	—	9	1	no	Sylow
199	C₂×C₃³	—	4	2	no	—
200	C₂×C₃³	—	4	2	no	—
201	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
203	C₃×C₃⋊D₃	—	2	2	no	—
204	C₃×C₃⋊D₃	—	4	2	no	—
205	C₂⁴×C₃	—	9	2	no	—
206	C₂³×D₃	—	3	8	no	—
207	C₃×#41	—	18	4	no	—
208	C₂×C₃×Q₈	—	9	1	no	—
209	C₂×C₃×D₄	—	2	4	no	—
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	—	2	16	no	—
212	C₂×C₃×D₄	—	9	2	no	—
213	C₂×C₃×D₄	—	9	2	no	—
214	C₂×C₃×D₄	—	9	4	no	—
215	C₂×C₃×D₄	—	9	1	no	—
216	C₂×C₃×D₄	—	18	4	no	—
217	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
218	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
219	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
220	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
222	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
223	C₂²×C₃×C₄	—	9	1	no	—
224	C₂²×C₃×C₄	—	9	2	no	—
225	C₂×#67	—	3	8	no	—
226	C₂×#67	—	3	8	no	—
227	C₂×#67	—	3	16	no	—
228	C₂²×Dic₃	—	3	8	no	—
229	#237	—	6	16	no	—
230	D₃×D₄	—	6	16	no	—
231	C₂×D₁₂	—	3	4	no	—
232	C₂×C₄×D₃	—	3	4	no	—
233	C₂×Dic₆	—	3	4	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	4	no	—
236	C₃×C₂²⋊C₄	—	9	2	no	—
237	C₃×C₂²⋊C₄	—	9	4	no	—
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	—	9	1	no	—
240	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
241	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
242	#217	—	3	16	no	—
243	(C₂×D₃)⋊C₄	—	3	8	no	—
244	(C₂×D₃)⋊C₄	—	3	16	no	—
245	Dic₃⋊C₄	—	3	8	no	—
246	C₄×Dic₃	—	3	4	no	—
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	4	no	—
251	C₂²×C₃²	—	2	4	no	—
252	C₂²×C₃²	—	2	8	no	—
253	C₂²×C₃²	—	2	8	no	—
254	C₂²×C₃²	—	2	16	no	—
255	C₂²×C₃²	—	2	16	no	—
256	C₂²×C₃²	—	4	8	no	—
257	C₂²×C₃²	—	4	8	no	—
258	C₂²×C₃²	—	4	16	no	—
259	C₂²×C₃²	—	4	16	no	—
260	C₂²×C₃²	C₂³×D₃	1	4	yes	—
261	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
262	C₂×C₃⋊D₃	—	2	2	no	—
263	C₂×C₃⋊D₃	—	2	2	no	—
264	C₂×C₃⋊D₃	—	2	4	no	—
265	C₂×C₃⋊D₃	—	4	8	no	—
266	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₃×D₃	—	3	8	no	—
268	C₂×C₃×D₃	—	6	8	no	—
269	C₂×C₃×D₃	—	6	8	no	—
270	C₂×C₃×D₃	—	6	16	no	—
271	C₂×C₃×D₃	—	12	32	no	—
272	C₃²×C₄	—	2	16	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃²×C₄	—	2	8	no	—
276	C₃²×C₄	D₃×D₄	1	8	yes	—
277	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
278	C₃⋊Dic₃	—	2	2	no	—
279	C₃⋊Dic₃	—	2	2	no	—
280	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
281	C₃×Dic₃	—	3	8	no	—
282	C₃×Dic₃	—	6	8	no	—
283	C₃×Dic₃	—	6	8	no	—
284	C₂×#41	—	9	1	no	—
285	C₂²×D₄	—	9	1	no	—
286	#127	—	9	1	no	—
287	#127	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
288	#124	—	9	1	no	—
289	#124	—	9	1	no	—
290	#121	—	9	4	no	—
291	#120	—	9	4	no	—
292	#117	—	9	1	no	—
293	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₃	—	2	8	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	9	1	no	—
297	C₂³×C₃	—	9	2	no	—
298	C₂³×C₃	—	18	4	no	—
299	C₂³×C₃	—	36	4	no	—
300	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
301	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
302	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
303	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
304	C₂²×D₃	—	3	4	no	—
305	C₂²×D₃	—	3	8	no	—
306	C₂²×D₃	—	6	16	no	—
307	C₂²×D₃	—	12	16	no	—
308	C₃×Q₈	—	18	2	no	—
309	C₃×D₄	—	2	8	no	—
310	C₃×D₄	—	2	8	no	—
311	C₃×D₄	—	2	2	no	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	4	8	no	—
314	C₃×D₄	—	4	8	no	—
315	C₃×D₄	—	4	16	no	—
316	C₃×D₄	—	4	4	no	—
317	C₃×D₄	—	4	32	no	—
318	C₃×D₄	—	18	4	no	—
319	C₃×D₄	—	18	4	no	—
320	C₃×D₄	—	18	2	no	—
321	C₃×D₄	—	36	4	no	—
322	C₂×C₃×C₄	—	2	8	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	9	1	no	—
325	C₂×C₃×C₄	—	9	4	no	—
326	C₂×C₃×C₄	—	9	2	no	—
327	C₂×C₃×C₄	—	9	2	no	—
328	C₂×C₃×C₄	—	18	4	no	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
331	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
332	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
333	#67	—	6	16	no	—
334	#67	—	6	16	no	—
335	#67	—	12	16	no	—
336	C₂×Dic₃	—	3	4	no	—
337	C₂×Dic₃	—	3	8	no	—
338	C₂×Dic₃	—	3	8	no	—
339	C₂×Dic₃	—	6	16	no	—
340	D₁₂	—	6	8	no	—
341	C₄×D₃	—	3	16	no	—
342	Dic₆	—	6	8	no	—
343	C₂×C₃²	—	2	4	no	—
344	C₂×C₃²	—	2	8	no	—
345	C₂×C₃²	—	4	2	no	—
346	C₂×C₃²	—	4	2	no	—
347	C₂×C₃²	—	4	8	no	—
348	C₂×C₃²	—	4	8	no	—
349	C₂×C₃²	—	8	8	no	—
350	C₂×C₃²	—	8	8	no	—
351	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
352	C₂×C₃²	#1004	1	8	yes	—
353	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
355	C₃⋊D₃	—	2	2	no	—
356	C₃⋊D₃	—	4	2	no	—
357	C₃×D₃	—	6	8	no	—
358	C₃×D₃	—	12	8	no	—
359	C₂⁴	—	9	2	no	—
360	#41	—	18	4	no	—
361	C₂×Q₈	—	9	1	no	—
362	C₂×D₄	—	9	2	no	—
363	C₂×D₄	—	9	2	no	—
364	C₂×D₄	—	9	4	no	—
365	C₂×D₄	—	9	1	no	—
366	C₂×D₄	—	18	4	no	—
367	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
368	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
369	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
370	C₂²×C₄	—	9	1	no	—
371	C₂²×C₄	—	9	2	no	—
372	C₄⋊C₄	—	9	2	no	—
373	C₂²⋊C₄	—	9	4	no	—
374	C₂²⋊C₄	—	9	2	no	—
375	C₂²⋊C₄	—	9	4	no	—
376	C₄²	—	9	1	no	—
377	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
378	C₂²×C₃	—	2	8	no	—
379	C₂²×C₃	—	2	8	no	—
380	C₂²×C₃	—	2	16	no	—
381	C₂²×C₃	—	2	16	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	2	4	no	—
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	—	4	8	no	—
388	C₂²×C₃	—	4	8	no	—
389	C₂²×C₃	—	4	16	no	—
390	C₂²×C₃	—	4	16	no	—
391	C₂²×C₃	—	9	2	no	—
392	C₂²×C₃	—	18	2	no	—
393	C₂²×C₃	—	18	2	no	—
394	C₂²×C₃	—	18	4	no	—
395	C₂²×C₃	—	36	8	no	—
396	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
397	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
398	C₂×D₃	—	3	8	no	—
399	C₂×D₃	—	6	8	no	—
400	C₂×D₃	—	6	8	no	—
401	C₂×D₃	—	6	16	no	—
402	C₂×D₃	—	12	32	no	—
403	C₃×C₄	—	2	16	no	—
404	C₃×C₄	—	2	8	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	8	no	—
407	C₃×C₄	—	9	2	no	—
408	C₃×C₄	—	18	2	no	—
409	C₃×C₄	—	18	2	no	—
410	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
411	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
412	Dic₃	—	3	8	no	—
413	Dic₃	—	6	8	no	—
414	Dic₃	—	6	8	no	—
415	C₃²	—	2	4	no	—
416	C₃²	#5715	1	4	yes	complemented
417	C₃²	C₃×#535	1	1	yes	characteristic, complemented
418	C₂³	—	9	1	no	—
419	C₂³	—	9	2	no	—
420	C₂³	—	18	4	no	—
421	C₂³	—	36	4	no	—
422	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
423	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
424	Q₈	—	18	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	18	4	no	—
429	D₄	—	18	4	no	—
430	D₄	—	18	2	no	—
431	D₄	—	36	4	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	4	no	—
434	C₂×C₄	—	9	2	no	—
435	C₂×C₄	—	9	2	no	—
436	C₂×C₄	—	18	4	no	—
437	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
438	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
439	C₂×C₃	—	2	4	no	—
440	C₂×C₃	—	2	8	no	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	—	4	8	no	—
444	C₂×C₃	—	4	8	no	—
445	C₂×C₃	—	8	8	no	—
446	C₂×C₃	—	8	8	no	—
447	C₂×C₃	—	18	2	no	—
448	C₂×C₃	—	36	2	no	—
449	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
450	C₂×C₃	C₃×#1004	1	8	yes	—
451	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
452	C₂×C₃	#64361	1	2	yes	—
453	D₃	—	6	8	no	—
454	D₃	—	12	8	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	9	2	no	—
460	C₂²	—	18	2	no	—
461	C₂²	—	18	2	no	—
462	C₂²	—	18	4	no	—
463	C₂²	—	36	8	no	—
464	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	9	2	no	—
467	C₄	—	18	2	no	—
468	C₄	—	18	2	no	—
469	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
470	C₃	—	2	4	no	—
471	C₃	C₃×#5715	1	4	yes	complemented
472	C₃	#10596186	1	1	yes	characteristic, direct product factor
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	18	2	no	—
476	C₂	—	36	2	no	—
477	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
478	C₂	C₃×#64361	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#127	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×#127	C₃⋊D₃
hypocenter	C₃²	C₃×#535
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3830	C₂	semidirect
2. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
3. C₃³×#127	C₂	semidirect
4. C₃×#64149	C₂	semidirect
5. C₃×#64148	C₂	semidirect
6. C₃×#64146	C₂	semidirect
7. C₃×#64145	C₂	semidirect
8. C₃×#64084	C₂	semidirect
9. C₃×#64081	C₂	semidirect
10. #10596186	C₃	direct (N × H)
14. C₂×C₃³×D₄	C₂²	semidirect
15. C₂×C₃³×D₄	C₂²	semidirect
18. C₂×C₃×#638	C₂²	semidirect
19. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
24. C₂×C₃×#634	C₂²	semidirect
25. C₃³×C₄²	C₂²	semidirect
26. C₃×#3757	C₂²	semidirect
28. C₃×#3752	C₂²	semidirect
29. C₃×#3750	C₂²	semidirect
30. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
31. C₂×#3830	C₂×C₃	semidirect
32. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
36. C₃²×#127	D₃	semidirect
37. C₃²×#127	C₂×C₃	semidirect
38. #64149	C₂×C₃	semidirect
39. #64148	C₂×C₃	semidirect
40. #64146	C₂×C₃	semidirect
41. #64145	C₂×C₃	semidirect
42. #64084	C₂×C₃	semidirect
43. #64081	C₂×C₃	semidirect
69. C₃×C₄×C₃⋊D₃	D₄	semidirect
79. C₂×C₃²×D₄	C₂×D₃	semidirect
80. C₂×C₃²×D₄	C₂×D₃	semidirect
82. C₂×C₃²×D₄	C₂²×C₃	semidirect
83. C₂×C₃²×D₄	C₂²×C₃	semidirect
86. C₂×#638	C₂²×C₃	semidirect
87. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
92. C₂×#634	C₂²×C₃	semidirect
103. C₃²×C₄²	C₂×D₃	semidirect
104. C₃²×C₄²	C₂²×C₃	semidirect
105. #3757	C₂²×C₃	semidirect
107. #3752	C₂²×C₃	semidirect
108. #3750	C₂²×C₃	semidirect
109. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
136. C₃×#127	C₃×D₃	semidirect
137. C₃×#127	C₃⋊D₃	semidirect
186. C₄×C₃⋊D₃	C₃×D₄	semidirect
218. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
219. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
221. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
222. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
240. C₃×C₄²	C₂×C₃×D₃	semidirect
241. C₃×C₄²	C₂×C₃⋊D₃	semidirect
287. #127	C₃×C₃⋊D₃	semidirect
293. C₃³	#535	semidirect
368. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
369. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
377. C₄²	C₂×C₃×C₃⋊D₃	semidirect
416. C₃²	#5715	semidirect
417. C₃²	C₃×#535	semidirect
471. C₃	C₃×#5715	semidirect
472. C₃	#10596186	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3830	2
C₂×C₃×D₄×C₃⋊D₃	2
C₃³×#127	2
C₃×#64149	2
C₃×#64148	2
C₃×#64146	2
C₃×#64145	2
C₃×#64084	2
C₃×#64081	2
#10596186	3
C₃×#5715	3

Subgroups — C3×#10596186 #13179467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596186 #13179467